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diff --git a/76891-h/76891-h.htm b/76891-h/76891-h.htm new file mode 100644 index 0000000..e5410da --- /dev/null +++ b/76891-h/76891-h.htm @@ -0,0 +1,6171 @@ +<!DOCTYPE html> +<html lang="en"> +<head> + <meta charset="UTF-8"> + <title> + The accomplishment ratio | Project Gutenberg + </title> + <link rel="icon" href="images/cover.jpg" type="image/x-cover"> + <style> + +a { + text-decoration: none; +} + +body { + margin-left: 10%; + margin-right: 10%; +} + +h1,h2,h3,h4 { + text-align: center; + clear: both; +} + +h2.nobreak { + page-break-before: avoid; +} + +hr.chap { + margin-top: 2em; + margin-bottom: 2em; + clear: both; + width: 65%; + margin-left: 17.5%; + margin-right: 17.5%; +} + +img.w100 { + width: 100%; +} + +div.chapter { + page-break-before: always; +} + +ul { + list-style-type: none; +} + +li { + margin-top: .5em; + padding-left: 2em; + text-indent: -2em; +} + +p { + margin-top: 0.5em; + text-align: justify; + margin-bottom: 0.5em; + text-indent: 1em; +} + +table { + margin: 1em auto 1em auto; + max-width: 40em; + border-collapse: collapse; +} + +th { + padding: 0.25em; + font-weight: normal; + font-size: 90%; +} + +td { + padding-left: 0.25em; + padding-right: 0.25em; +} + +table.borders { + border-top: double black; + border-bottom: thin solid black; +} + +.borders th { + border-right: thin solid black; + border-bottom: thin solid black; +} + +.borders td { + border-right: thin solid black; +} + +.group td { + padding-top: 1em; +} + +.borders th:last-child, .borders td:last-child { + border-right: none; +} + +.bb, .borders .bb { + border-bottom: thin solid black; +} + +.tdc { + text-align: center; +} + +.tdr { + text-align: right; +} + +.contents td { + padding-left: 2.25em; + padding-right: 0.25em; + vertical-align: top; + text-indent: -2em; +} + +.contents .sub { + padding-left: 4.25em; +} + +.contents .tdpg { + vertical-align: bottom; + text-align: right; +} + +.contents .tdr { + text-align: right; +} + +blockquote { + margin: 1.5em 10%; +} + +.center { + text-align: center; + text-indent: 0; +} + +.figcenter { + margin: auto; + text-align: center; +} + +.footnotes { + margin-top: 1em; + border: dashed 1px; +} + +.footnote { + margin-left: 10%; + margin-right: 10%; + font-size: 0.9em; +} + +.footnote .label { + position: absolute; + right: 84%; + text-align: right; +} + +.fnanchor { + vertical-align: super; + font-size: .8em; + text-decoration: none; +} + +.gothic { + font-family: 'Old English Text MT', 'Old English', serif; +} + +.hanging { + padding-left: 2em; + text-indent: -2em; +} + +.in { + padding-left: 2em; +} + +.note { + font-size: 90%; + margin-bottom: 1em; +} + +.nw { + white-space: nowrap; +} + +.pagenum { + position: absolute; + right: 4%; + font-size: smaller; + text-align: right; + font-style: normal; +} + +.right { + text-align: right; +} + +.smaller { + font-size: 80%; +} + +.smcap { + font-variant: small-caps; + font-style: normal; +} + +.titlepage { + text-align: center; + margin-top: 3em; + text-indent: 0; +} + +.u { + text-decoration: underline; +} + +.x-ebookmaker img { + max-width: 100%; + width: auto; + height: auto; +} + +.x-ebookmaker blockquote { + margin: 1.5em 5%; +} + +/* Illustration classes */ +.illowp100 {width: 100%;} +.illowp75 {width: 75%;} +.x-ebookmaker .illowp75 {width: 100%;} + </style> + </head> +<body> +<div style='text-align:center'>*** START OF THE PROJECT GUTENBERG EBOOK 76891 ***</div> + +<h1>THE ACCOMPLISHMENT RATIO</h1> + +<p class="titlepage">A Treatment of the Inherited Determinants<br> +of Disparity in School Product</p> + +<p class="titlepage"><i>By</i><br> +RAYMOND FRANZEN<br> +<span class="smaller">A.B. (Harvard), M.A. (Columbia)<br> +Ph.D. (Columbia)</span></p> + +<p class="titlepage">Teachers College, Columbia University<br> +Contributions to Education, No. 125</p> + +<p class="titlepage">Published by<br> +<span class="gothic">Teachers College, Columbia University</span><br> +<span class="smaller">New York City<br> +1922</span></p> + +<p class="titlepage smaller"><span class="u"><i>Copyright, 1922, by <span class="smcap">Raymond Franzen</span></i></span></p> + +<hr class="chap x-ebookmaker-drop"> + +<div class="chapter"> + +<h2 class="nobreak" id="PREFACE">PREFACE</h2> + +</div> + +<p>The results of the experiment reported here have become so +much a portion of my process of reasoning that duplication of +material presented elsewhere is unavoidable. I wish in particular +to recognize my indebtedness to the <span class="smcap">Teachers College Record</span> +for permission to reprint here revised portions of an article which +appeared in the November, 1920, number of that journal. I will +warn here any reader to whom the intricacies of a full statistical +account are irksome that the logic and conclusions presented in +this study are incorporated in a more palatable and abbreviated +form in Chapter IV of <i>Intelligence Tests and School Reorganization</i> +(World Book Company).</p> + +<p>The work presented here has been made possible by the cooperation +and interest of the two principals of the Garden City +public school during the period of my work there, Miss Gladys +Locke and Mrs. Edna Maule. I also owe any success that this +experiment may have had to the teachers who did the real work +of “pushing” abilities to their limit. My indebtedness to Gladys +Locke Franzen for help in expression and correction is surpassed +only by what I credit to her encouragement and cooperation at its +inception.</p> + +<p>During the period in which this experiment was planned and +executed it grew into a real problem through the advice of two of +my teachers to whom I owe all such inspiration and knowledge as +I possess—Edward L. Thorndike and Truman L. Kelley.</p> + +<p class="right"><span class="smcap">Raymond H. Franzen</span></p> + +<p><i>Des Moines, Iowa, 1922.</i></p> + +<hr class="chap x-ebookmaker-drop"> + +<div class="chapter"> + +<h2 class="nobreak" id="CONTENTS">CONTENTS</h2> + +</div> + +<table class="contents"> + <tr> + <td class="tdr">I.</td> + <td><span class="smcap">An Outline of the Experiment</span></td> + <td class="tdpg"><a href="#PART_I">1</a></td> + </tr> + <tr> + <td class="tdr"></td> + <td class="sub">The Use of Quotients and Ratios</td> + <td class="tdpg"></td> + </tr> + <tr> + <td class="tdr"></td> + <td class="sub">The Derivation of Age Norms</td> + <td class="tdpg"></td> + </tr> + <tr> + <td class="tdr"></td> + <td class="sub">A Method of Survey of Reading, Language and Arithmetic</td> + <td class="tdpg"></td> + </tr> + <tr> + <td class="tdr">II.</td> + <td><span class="smcap">Statistical Treatment of the Experiment</span></td> + <td class="tdpg"><a href="#PART_II">17</a></td> + </tr> + <tr> + <td class="tdr"></td> + <td class="sub">The Quotients</td> + <td class="tdpg"></td> + </tr> + <tr> + <td class="tdr"></td> + <td class="sub">The Ratios</td> + <td class="tdpg"></td> + </tr> + <tr> + <td class="tdr"></td> + <td class="sub">Summary</td> + <td class="tdpg"></td> + </tr> + <tr> + <td class="tdr">III.</td> + <td><span class="smcap">The Psychological Conclusions of the Experiment</span></td> + <td class="tdpg"><a href="#PART_III">43</a></td> + </tr> + <tr> + <td class="tdr"></td> + <td class="sub">The Neglect of Genius</td> + <td class="tdpg"></td> + </tr> + <tr> + <td class="tdr"></td> + <td class="sub">Is Genius Specialized?</td> + <td class="tdpg"></td> + </tr> + <tr> + <td class="tdr"></td> + <td class="sub">Current Psychological Opinion</td> + <td class="tdpg"></td> + </tr> + <tr> + <td class="tdr"></td> + <td class="sub">Conclusions</td> + <td class="tdpg"></td> + </tr> +</table> + +<hr class="chap x-ebookmaker-drop"> + +<div class="chapter"> + +<p><span class="pagenum" id="Page_1">[1]</span></p> + +<h2 class="nobreak" id="PART_I">PART I⁠<a id="FNanchor_1" href="#Footnote_1" class="fnanchor">[1]</a><br> +AN OUTLINE OF THE EXPERIMENT</h2> + +</div> + +<h3>THE USE OF QUOTIENTS AND RATIOS</h3> + +<p>Standardized measurement of educational product has won its +way to a recognized place in the school life of this country. Many +of our larger cities have research bureaus of tests and measurements, +and advanced private schools have departments of measurement. +The logic of the use of statistically derived evaluations +versus the use of opinion, swayed as it is by the haphazard captions +of emotion and condition, has become widely recognized. The case +of scientific measurement in education has been argued and won. +The objections to older forms of measurement have become the +criteria of the value of the new.</p> + +<p>Still administrators, although they have been convinced theoretically +of its importance, find it hard to see just what measurement +does for their schools. They often object that measurements +are made, the tests are carried away by the examiner, and some +time later they are presented with a neat series of distributions +and are told where their school stands in relation to certain other +schools or to schools in general. This is undoubtedly a very important +piece of information; since a determination of the extent +to which a goal has been attained forms the basis of the commendation +or condemnation of the methods, curricula, and text-books +employed in the process. But administrators want to know +which of the various elements of school procedure are to be praised +and which are to be blamed.</p> + +<p>We cannot condemn or support a whole school system on the basis +of composite results (unless all possible educational objectives have +been measured, and show one common drift; or unless it is necessary +that the system fall or stand as a whole) since then we should +be throwing good and bad into a common discard. We must +measure each thing separately. We must build our ideal system of +education synthetically, taking the best methods from each of the +<span class="pagenum" id="Page_2">[2]</span>prevalent groups of theories. There has been too much absolutism +in education, too little of a realism that sees the good and bad in +all and diminishes the bad and augments the good. If we adopt +this point of view we become really empirical in our method, +living through each educational experiment to incorporate it into a +growing treasury of tested theory, not deducing success or failure +from metaphysical or doctrinaire prejudice. In this administrators +have been more scientific than those who measure. They have +always objected that they wanted differential diagnoses. Here +the answer to their needs must come through experimentation +and it is only through nation-wide study and careful comparison +and integration of results that methods of teaching can be scientifically +established.</p> + +<p>Three uses of measurement commonly stressed are: (1) Diagnosis +of degree of attainment of goal; (2) selection of method of +attainment of goal; (3) definitive outline of goals. We have seen +that the first two are of little immediate value to the administrator. +The first only gives him an accurate notion of where he stands in +any one subject without pretending to tell him why; the second +is a promissory note. Some day we shall be able to tell him the +best methods for the attainment of his goal. The third has slightly +more immediate value. Measurement splits up the goals of education, +gives them concrete formulation, allows teachers to see an +advance in the class in one function as separate from the rest; +allows them, for instance, to distinguish more clearly than they +otherwise would between oral reading and silent reading, or between +addition and division. But this, too, is rather too general +to appeal to administrative economy. One would find it very +difficult to sell one’s services as a measurer to a school board or +a superintendent on the basis of these three values. They answer +that universities and scientific research give them as much as they +want of these values. What an expert on measurement could add +in interpretation of results would seem of small additional value +to them.</p> + +<p>Still there is a very marked function that such an expert can +perform; but he must serve a fourth and fifth use of measurement +while he serves a particular school. When he serves the first three +he is serving the science of education and, unfortunately, no one +school will pay him to do that. The uses of measurement that +directly benefit any one school are: (4) Classification by information +<span class="pagenum" id="Page_3">[3]</span>and intelligence and (5) diagnosis of individual disability. For +the proper prosecution of these aims individual measurements and +age norms are essential. Only with such equipment can we make +the prognoses of future school behavior which the administrator +so urgently needs.</p> + +<p>Grade norms cannot be used to make individual diagnoses. +Though we can see by them which children are below and which +above the level that in their grade they should attain, we cannot +see just what administrators most need to know; namely, whether +the retardation and acceleration are justified or not—how many +children are working at maximum. More than that, computations +based on grade norms are very inaccurate in individual cases +because the variability within any grade is so great. As it becomes +necessary to use new norms for such purposes it is important to +have them in terms that are directly comparable to intelligence +mensuration.⁠<a id="FNanchor_2" href="#Footnote_2" class="fnanchor">[2]</a></p> + +<p>First in importance is an interpretation of the meaning of an +Intelligence Quotient. Too often it is stated as a number and +left as a number with the belief that somehow or other that is a +tag which carries its own divine implication. Its importance lies +in its diagnosis of power of adaptation, and it has a high correlation +with the maximum possible rate of school progress. Just as a pure +information test diagnoses the neural bonds that have been formed +in any one field, so an intelligence test diagnoses the ability to form +bonds, to meet a new situation and form satisfactory habits—power +to learn. It may be thought of as a diagnosis of the neural +chemistry of the individual. As such it is not concerned with the +connections or quantity, but rather with the quality of the neural +tissue.</p> + +<p><span class="pagenum" id="Page_4">[4]</span></p> + +<p>As an intelligence quotient is actual mental age divided by +chronological age—which is the normal mental level of the child’s +age-group—so it is the rate at which the child has progressed to +mental maturity. It is his potential rate of progress. It is a division +of what is by what normally would be. Then, when we use IQ +we express the various degrees of power of adaptation due to +various degrees of fitness of neural equipment to form bonds, by +means of a diagnosis of the rate of formation of bonds which +everyone forms sooner or later in an environment such as ours. +It is conceivable that we might test this same power without +testing the presence of such bonds at all. Such a test would detect +directly the quality of the neural equipment irrespective of quantity +or conformation.</p> + +<p>A ten-year-old child whose mental age is ten has progressed +at the rate which is normal, and his IQ is 1.00. A very exceptional +ten-year-old child whose mental age is fifteen has progressed just +one and one half times as fast as the former, and his IQ is 1.50. +Another exceptional ten-year-old child whose mental age is five +has progressed at just one-half the rate of the first, and his IQ is +.50. What we mean, then, by an Intelligence Quotient is the +rate at which a child grows to the mental maturity of human +beings in the world as it is.</p> + +<p>For purposes of presentation of a problem one can here assume +(an hypothesis the value of which will here be determined) that +each child can attain this rate of progress in each of the elementary +school subjects. The degree to which this is true is the degree +to which the IQ is a valid index of power to deal with school subjects. +This assumes that inherited special disabilities in the school subjects +are uncommon, that school progress is determined by the interplay +of intelligence and environment, and that so-called interest characteristics +which aid in development are the result of an earlier +interplay of intelligence and environment. The degree to which +educational product of children can be made to approach this +intelligence will allow us to judge how far these factors are inherited, +since differences that are removable must be learned, +not innate.</p> + +<p>We can the more readily see the significance of viewing a child’s +equipment in terms of educational and mental age, when we +conceive of a Subject Quotient. This is a quotient resulting from +the division of the age level reached in the test in question by the +<span class="pagenum" id="Page_5">[5]</span>chronological age of the pupil. It is a measure of the rate of progress +of the child in the school subject under consideration. Thus a +ten-year-old child with ten-year-old ability in Thorndike Reading +Scale Alpha 2 would have as his reading age divided by chronological +age, 1.00. This may be called his Subject Quotient in +Reading or his Reading Quotient. The division of what is by what +would be if the child were normal gives the percentage of normality, +the actual rate of progress. Since the IQ is the potential +rate of progress and the SQ the actual rate of progress, the ratio +of SQ to IQ gives the percentage of what that child could do, that +he has actually done. Thus a child with an IQ of 1.32 whose reading +quotient (his RQ) is 1.10, though he is doing work which is +above normal, is not doing work which is above normal for him. +His RQ/IQ is 1.10/1.32, whereas if he were progressing at his optimum +rate it would equal 1.32/1.32. This RQ/IQ is the same quantity as RA/MA. +We may call this a Subject Ratio and the average of Subject Ratios +an Accomplishment Ratio. We could, if the absolute association +between reading age and mental age were perfect, measure the +approximation to ideal educational performance of any one child +in any one elementary school subject through the approximation +of this Subject Ratio to 1.00. As we will see later, Subject Quotients +approach the Intelligence Quotients when special treatment +is given; that is, the correlation of SQ and IQ becomes nearer 1.00 +and the difference between the average IQ and the average +SQ approaches zero. It is safe then to expect these Subject Ratios +to be at least 1.00 before we pronounce satisfaction with the school +product.</p> + +<p>There is certainly a significant relation between IQ and SQ, +and the more perfect the educational procedure has been, the more +it has called forth all that the child is capable of, the higher it +will be. To determine whether the quotient in any school subject +can be greater than the Intelligence Quotient in any significant +amount, it will only be necessary after we have perfect age norms +by months to get that quotient amongst enough pupils whom +we know to be working at maximum. What is significant here is +that the more nearly any such quotient reaches or exceeds the Intelligence +Quotient the more nearly has the child been brought up to +<span class="pagenum" id="Page_6">[6]</span>what he is able to do under the best conditions. The Accomplishment +Ratio is the degree to which his actual progress has attained to +his potential progress by the best possible measures of both.</p> + +<p>This would be a mark of the child’s effort, a mark of the concentration +and interest that the child has in the school work, and as +far as no inherited traits or capacities other than intelligence affect +school work it is a measure of the efficiency of a child’s education +thus far. If there are such other innate bases, it is also a measure +of those inherited traits and capacities or their predisposition, such +as concentration, effort, written expression, etc. At any rate it is a +measure of the child’s accomplishment, and so of the effort and +concentration as they really are at present working under those +school conditions. It is an index of achievement irrespective of +intelligence.</p> + +<p>A very convenient graph representing the same facts and easily +interpreted by the teacher may be constructed thus:</p> + +<figure class="figcenter illowp100" id="graph" style="max-width: 37.5em;"> + <img class="w100" src="images/graph.jpg" alt=""> +</figure> + +<p>Here it can be easily shown that Spelling Age, Reading Age, +Arithmetic Age, etc., are in some definite relation to both Chronological +Age and Mental Age. Using the Mental Age line as a goal, +these records may be kept constantly up to date. Another use of +the Accomplishment Ratio is as the medium in which the children +may keep records of their own work. As it is a mark in terms of +intelligence, dull and brilliant children may compete on a parity +to bring their Accomplishment Ratios as high as possible.</p> + +<p>Mainly we have advanced formal education. We have in many +ways promoted the abilities to read, write, spell and figure. But +our philosophy of education has advanced far beyond that. We +have other aims in education, and consequently other methods and +modes, which also must be measured and judged. We wish to +promote such qualities as stability, self-reliance, concentration, +and ambition. It does not necessarily follow that we must measure +these things directly, although every one vitally interested in +<span class="pagenum" id="Page_7">[7]</span>measurement cherishes the hope that we may some day measure +their behavioristic correlates,—“For the quality of anything exists +in some quantity, and that quantity can be measured.”</p> + +<p>“Some of us might be entirely willing to rest the case after asking +whether in practical school life anyone ever saw a teacher thoroughly +confident of teaching ideals but neglectful of reading and +arithmetic. The fact is that the conscientious teacher always gives +attention to both and the successful teacher is able, without omitting +one, to cultivate the other. The theoretical possibility of thinking +of the two results separately has little significance in dealing with +real teachers and real schools. Good reading is a school virtue; +and when one has measured good reading he has measured more +than the trivial or formal side of education.”⁠<a id="FNanchor_3" href="#Footnote_3" class="fnanchor">[3]</a></p> + +<p>This I believe to be true, but I also believe that through measurement +we can actually promote those other more ethical ideals in +education. Through classification by information and by intelligence +we gain a marked increase of attention, concentration, ambition, +and other objectives, measured in part by Accomplishment +Ratios. More discussion due to a greater homogeneity promotes +powers of inference and insight; being only with equals promotes +self-confidence and honor, and in many cases prevents a regrettable +conceit among supernormals; having work to do which is hard +enough prevents habits of indolence and carelessness so commonly +found among intelligent children.⁠<a id="FNanchor_4" href="#Footnote_4" class="fnanchor">[4]</a></p> + +<p>It is a well-known fact that much work must be done in classification +to get homogeneity or real conditions of teaching. As it is, +most teachers are talking to the middle of their classes. When +they do they mystify the lower quarter and bore the upper quarter; +they talk to the upper quarter and mystify the lower three quarters; +<span class="pagenum" id="Page_8">[8]</span>or they talk to the lower quarter and bore the upper three quarters. +When a child is bored or mystified his Subject Quotients become less +while his Intelligence Quotient remains constant. Then his Accomplishment +Ratios become less as long as he remains in a position +where he is being mistreated educationally. This, then, is the +proper measure to see whether a child is classified properly or not. +At the Garden City public school I changed as far as I was able +the conditions of education of each child in that subject wherein +his Accomplishment Ratio was markedly below 1.00. The concentration +and effort of the child were obviously low and my +attempt was to change conditions and to promote habits of consistent +work. When the Accomplishment Ratio increased I knew +that the child was profiting, that he was working. Our objective +was to increase Ratios of all children, not to attain any set +standard.</p> + +<p>This Accomplishment Ratio would, to my mind, be an ideal +school mark. Besides the inaccuracy of marks to-day, which are +accurate marks only of the teacher’s opinion, biased as it is by the +personal equation of her character with that of the pupil, there is +another fault of prevalent school marking. It is based on average +work. The mark is the link between education in the school and +education in the home. It gives the parents an index of the child’s +work and allows them to encourage or discourage the child’s attitudes. +Such indices have no real significance when they are based +upon average development, as the parent is generally mistaken +about the ability of the child.</p> + +<p>Marks given by a teacher are satisfactory only for a normal +child with normal age for the grade. Brilliant children are over-praised +for work which, though over the ability for the group, is +under their own ability. Marks given to stupid children are +misinterpreted by parents so as greatly to prejudice the effort +of the child. Though his work may be such as to merit encouragement +his mark may be very low. Teachers’ marks are, aside from +their inaccuracy, just, only in a group that is perfectly classified; +just, only when the children are all of the same ability and all +possess the same initial information. So far as they are unjust +they are subversive of our aims, as they then transmit a faulty +<span class="pagenum" id="Page_9">[9]</span>message to the home and disrupt the continuity of school and +home education.⁠<a id="FNanchor_5" href="#Footnote_5" class="fnanchor">[5]</a></p> + +<p>Such marks as are here advocated would correct this feature +of our present system, as well as the inaccuracy of our present +marks. It is a mark which evaluates the accomplishment of the +child in terms of his own ability. A brilliant child would no longer +be praised for work which in terms of his own effort is 70 per cent +perfect, in terms of the maximum of the group 90 per cent. The +teacher gives him a mark of 90 while we mark him 70. A stupid +child who does work which is marked 70 in terms of the maximum +of the class but 90 in terms of his own, a limited ability, is no longer +discouraged. His effort is evaluated, and the praise which he +receives from home is merited and consequently economical, since +the resultant satisfaction cements the bonds of concentration and +attention. Such a mark is an actual index of the effort that child +is making and consequently forms the proper link between the +school and the home.</p> + +<p>Parents would need no great instruction in the interpretation of +these marks, since they have always acted as though the other +marks were these, and since these also are in percentage form. +The only kind of mark they can understand is an Accomplishment +Ratio. I found that the parents of the children at Garden City +were more attentive to such marks than to others, and acted upon +them more readily. Of course the parents of the very intelligent +children, who are used to marks above 90, are surprised at first +when you tell them that your mark of the child is 80; but upon +explanation, which should in all cases precede the first report to +the parents, they immediately see the value of such grading. It +is fortunate in this connection that the greatest amount of explanation +is necessary about intelligent children, as one usually +deals then with intelligent parents.</p> + +<h3>THE DERIVATION OF AGE NORMS</h3> + +<p>In this study age norms were derived empirically, both regression +lines being taken into consideration. From the point of view of +<span class="pagenum" id="Page_10">[10]</span>statistics it becomes imperative, in order to use the technique +here advised, to have the average age of a score—since we are +going to predict age from score—to translate crude scores into +indices of maturity in each subject under consideration. We are +in error in the use of grade norms, if we find the average score of a +grade and then, when we obtain that score in practice, say that the +work is of that grade. To be able to say this we must know the +average grade of a score. This takes in an entirely different cross-section +of data. If we get the average score of all children in grade +6, then we can predict what a 6th grade child is likely to get, but +we can say nothing about a child who is not in grade 6. In order to +decide that a 4th grade child has 6th grade ability, we must know +that he has such ability that all children who share this score +make an average grade of 6.⁠<a id="FNanchor_6" href="#Footnote_6" class="fnanchor">[6]</a> It would be wise then to get the +regression of score on age as well as the regression of age on score, +since they are not identical, the correlation between score and +age being less than unity.</p> + +<p>We will note in passing that the data to establish these norms, +except those of reading, are not as complete as may be desired, +inasmuch as it was difficult to get test scores where the age in +months also was available. However, the general data behind the +grade norms could be used to keep the results from any crude +error; and the averages were obtained for every month from 8 +years to 14 years, with a corresponding refinement in intervals of +score, which made still more improbable an error in the general +tendency of the regression lines. Then all the distributions, when +grouped by years, were corrected for truncation; that is, the +tendency for the brighter children of the older group to be in high +school (the data were from elementary schools only) and the +duller children of the younger group to be in the lower grades +where they could not be reached was recognized and corrected by +finding the average, standard deviation, and number of cases which +would have existed if these forces of truncation were not operating. +This was done by the use of the other one half of the figures comprising +Table XI of Pearson’s <i>Tables for Statisticians and Biometricians</i>. +Dr. Truman L. Kelley pointed the way to its derivation.</p> + +<p>These norms differ somewhat from those derived from the grade +<span class="pagenum" id="Page_11">[11]</span>norms by translation of grade into average age for the grade. This +is because the norm for a grade is the average score for a grade. +Hence the norm of age 10 obtained in this way is the average score +obtained by a grade whose average age is 10. Then the data used +to obtain this average are made up of diverse ages, all of one grade, +instead of all of one age and diverse grades. Even then, we would +have only an average score of an age which approximates what +we want, but is not as reliable to use as average age for a score.</p> + +<h3>A METHOD OF SURVEY OF READING, LANGUAGE, AND ARITHMETIC</h3> + +<p>The following procedure was employed in the experiment. The +experiment was carried out in the public school at Garden City. +Two hundred children were given the tests. The instructions, shown +below, were followed in November, 1919, and in November, 1918; +in June, 1919, and in June, 1920, with the exception that no +arithmetic test was used in November, 1918, and June, 1919. The +Binet tests were given by the author; all of the others were given +either by the author or the principal who was careful not to deviate +from the directions in any way. In June of both years the author +gave instructions for a test in one room, and then left the teacher +in charge and went on to the next. This could be done in June of +each year as the teachers were then fully acquainted with the +experiment and their coöperation was assured.</p> + +<blockquote> + +<p class="center"><span class="smcap">Directions</span></p> + +<p class="hanging">I. Administer and score the following tests according to standard instructions. +Give all tests to grades 3 and above.</p> + +<ul> + <li>Woody-McCall Mixed Fundamentals in Arithmetic</li> + <li>Thorndike Reading Scale Alpha 2</li> + <li>Thorndike Visual Vocabulary Scale, A2</li> + <li>Kelley-Trabue Completion Exercises in Language</li> + <li>Stanford-Binet Tests (given by the author)</li> +</ul> + +<p class="hanging">II. Translate the scores into year-month indices of maturity by means +of the following table. (Use Mental Age for the Binet.) Assume rectilinear +development, that is, that the amount of score which equals +the development of one month is the same as the amount of score which +equals the development of any other month. Then interpolation and +extension are allowable. Use the table in this way: Find in the table +the score made by a child (for instance in the Woody-McCall); find the +age to which it corresponds, then call this age the Arithmetic Age of +<span class="pagenum" id="Page_12">[12]</span>the child. For instance, if the score in Woody-McCall is 20, his Arithmetic +Age is about halfway between 10 and 11 or 10 years 6 months.</p> + +<table class="borders"> + <tr> + <th>Age</th> + <th>Woody-McCall</th> + <th>Alpha 2</th> + <th>Visual Vocab.</th> + <th>Kelley-Trabue</th> + </tr> + <tr> + <td class="tdc"> 8—0</td> + <td class="tdc">12.00 </td> + <td class="tdc">4.50</td> + <td class="tdc">3.60</td> + <td class="tdc">4.30</td> + </tr> + <tr> + <td class="tdc"> 9—0</td> + <td class="tdc">15.16⅔</td> + <td class="tdc">4.98</td> + <td class="tdc">4.32</td> + <td class="tdc">5.00</td> + </tr> + <tr> + <td class="tdc">10—0</td> + <td class="tdc">18.33⅓</td> + <td class="tdc">5.46</td> + <td class="tdc">5.04</td> + <td class="tdc">5.65</td> + </tr> + <tr> + <td class="tdc">11—0</td> + <td class="tdc">21.50 </td> + <td class="tdc">5.94</td> + <td class="tdc">5.76</td> + <td class="tdc">6.35</td> + </tr> + <tr> + <td class="tdc">12—0</td> + <td class="tdc">24.66⅔</td> + <td class="tdc">6.42</td> + <td class="tdc">6.48</td> + <td class="tdc">7.05</td> + </tr> + <tr> + <td class="tdc">13—0</td> + <td class="tdc">27.83⅓</td> + <td class="tdc">6.90</td> + <td class="tdc">7.20</td> + <td class="tdc">7.70</td> + </tr> +</table> + +<p class="hanging">III. Arrange these Arithmetic Ages of all the children of your school in +order from high to low with the names opposite the scores in the +extreme left-hand column of the paper. At the right have parallel +columns of the grades. Check the grade of each child in these columns. +You will then have a sheet like this:</p> + +<table class="borders" style="border-bottom: none;"> + <tr> + <th rowspan="3">Name</th> + <th rowspan="3">Arith. Age</th> + <th colspan="10">Grade</th> + </tr> + <tr> + <th colspan="2">4</th> + <th colspan="2">5</th> + <th colspan="2">6</th> + <th colspan="2">7</th> + <th colspan="2">8</th> + </tr> + <tr> + <th>B</th> + <th>A</th> + <th>B</th> + <th>A</th> + <th>B</th> + <th>A</th> + <th>B</th> + <th>A</th> + <th>B</th> + <th>A</th> + </tr> + <tr> + <td>Gertrude Smith</td> + <td class="tdc">180</td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="tdc bb">#</td> + <td class="bb"></td> + </tr> + <tr> + <td>Saul Sampson</td> + <td class="tdc">176</td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="tdc bb">#</td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + </tr> + <tr> + <td>Ed Jones</td> + <td class="tdc">176</td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="tdc bb">#</td> + <td class="bb"></td> + </tr> + <tr> + <td>George Calut</td> + <td class="tdc">172</td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="tdc bb">#</td> + </tr> + <tr> + <td>Ida Henry</td> + <td class="tdc">172</td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="tdc bb">#</td> + </tr> + <tr> + <td>Raymond Teller</td> + <td class="tdc">172</td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="bb"></td> + <td class="tdc bb">#</td> + </tr> + <tr> + <td>Ed Hoard</td> + <td class="tdc">172</td> + <td></td> + <td></td> + <td></td> + <td></td> + <td></td> + <td></td> + <td class="tdc">#</td> + <td></td> + <td></td> + <td></td> + </tr> + <tr> + <td colspan="12"><i>Etc.</i></td> + </tr> +</table> + +<p class="in">Do the same with each of the tests. It is clear that, independent of +the unreliability of the test, if your school were perfectly classified all +the 8th grade children would come first on each relation sheet and then +<span class="pagenum" id="Page_13">[13]</span>the 7th grade children, etc. You have now a picture of the overlapping +of your grades. Regrade in reading and arithmetic. Draw horizontal lines +across these relation sheets at the points of delineation. Divide your +total number of children by the number of teachers available and then +make a class division by the number of pupils, that is, call the upper +one-sixth of the total number of pupils grade 8 in this subject, the next +one-sixth, grade 7, etc. Teach all grades of arithmetic at the same time +and all grades of reading at the same time. You can now send each +pupil to the grade in which he belongs in each subject.</p> + +<p class="hanging">IV. Call each derived age a Subject Age (SA). Divide each subject age by +the chronological age of the child. This will yield what may be called +a Subject Quotient (SQ), previously called an Educational Quotient +(EQ).⁠<a id="FNanchor_7" href="#Footnote_7" class="fnanchor">[7]</a> Dividing the Reading Age by the Chronological Age, you arrive +at a Reading Quotient. This RQ is the rate at which the child has +progressed in reading. We have the same kind of quotient for intelligence +(Stanford-Binet IQ). This IQ is the potential rate of progress +of the child.</p> + +<p class="hanging">V. The ratio of any Subject Age to Mental Age⁠<a id="FNanchor_8" href="#Footnote_8" class="fnanchor">[8]</a> may be called a Subject +Ratio (SR), previously called an Accomplishment Quotient (AccQ).⁠<a href="#Footnote_7" class="fnanchor">[7]</a> +This Subject Ratio gives the proportion that the child has done in that +subject of what he actually could have done, and is a mark of the +efficiency of the education of the child in that subject to date. The goal +is to bring up these Subject Ratios as high as possible. When they are +above .90, the child may be considered as receiving satisfactory treatment, +providing norms for subject ages are reasonably accurate. (This +figure, .90, applies to a Subject Ratio obtained by using a Stanford-Binet +Mental Age.) An Arithmetic Ratio based on one arithmetic test +and one intelligence test only is not as good as one based on three +arithmetic tests and three intelligence tests. If Subject Ratios go far +over 1.00 the chances are that the Mental Age diagnosis is too low. +The average of the Subject Ratios of a child may be called his Accomplishment +Ratio.</p> + +<p>In the application of the above instructions, whenever opportunity offers +for classification of both subject matter and intelligence (which means many +teachers or a large school), use a Relation Sheet (for instance for Arithmetic) +and then have additional columns at the extreme right for intelligence +headed <i>A</i>, <i>B</i>, <i>C</i>, and <i>D</i>. If a child’s IQ is in the upper quarter of the IQ’s +of your school, check in the column A opposite his name; if it is in the upper +<span class="pagenum" id="Page_14">[14]</span>half but not in the upper quarter check in <i>B</i>, and so on with <i>C</i> and <i>D</i>. +Then you will be able to split each group; for instance, the one which is +defined as 8th grade in arithmetic ability, into four sections, each of which +progresses at a rate differing from the others. The <i>A</i> section will progress +most rapidly, <i>B</i> next, <i>C</i> more slowly, and <i>D</i> most slowly.</p> + +</blockquote> + +<p>As Garden City was a small school, adjustment of procedure to +individual differences in intelligence, besides the grouping for +subject matter, was done mostly by pushing children. Children +were advanced whole years (the grade they “belonged to” was the +one in which geography and history were taught; this was their +home grade) besides the readjustment made by the special regrading +in reading and arithmetic. A special treatment class was formed +where pronounced negative deviates were given special attention. +Regrading was also instituted for spelling. Children were promoted +whenever it was considered advisable; teachers were switched from +subject to subject whenever that was considered advisable by the +principal and the author. The Thorndike <i>Arithmetics</i> and other +new texts were introduced to some extent. <i>Any change possible was +made in order to bring EQ/IQ as high as possible.</i> That was the goal. +The purpose was not to prove that any certain educational procedure +would tend to promote abilities more rapidly than others, +but that abilities could be promoted to the level of intelligence—that +intelligence is substantially the exclusive inherited determinant +of variety of product among school children. (It is to be understood +that intelligence may be, and probably is, the summation of +thousands of inherited factors,—neutral elements, here merged +in the broader behavioristic concept of intelligence.)</p> + +<h3>SCIENTIFIC QUESTIONS INVOLVED IN CLASSIFICATION</h3> + +<p>If we were able to negate other influences upon disparity of +product, we could conclude that these were not inherited. Hence +it would be our burden as educators so to manipulate education as +to prevent their operation. We will attempt to analyze the determinants +of individual differences in product in these children, +to see which influences besides intelligence are part of the inborn +equipment which is not the province of education, but of eugenics, +to correct. No absolute validity is held for any of the conclusions +stated here. The subject is, at best, vague and complicated; but +<span class="pagenum" id="Page_15">[15]</span>our conclusions can be used as the basis for a good guess in school +procedure. We can judge general tendencies from the educational +experiences of the two hundred children whose abilities for two years +are here charted.</p> + +<p>The importance to educators of the subject in hand is excuse +enough for its treatment. All educational procedure points a prophetic +finger toward the classification of pupils and a reduction of +the individual differences of product to the inherited bases of these +differences.</p> + +<p>Classification, however, needs some more accurate psychological +foundation than the mere awareness of individual variance. We +must know:</p> + +<p>1. What tests to use.</p> + +<p>2. How to use them.</p> + +<p>3. Whether abilities in reading, spelling, and arithmetic or +their predispositions exist as special abilities, or whether children +differ in these simply because of their innate differences of intelligence.</p> + +<p>4. Whether individual differences in ambition, interest, and +industry, in so far as they influence accomplishment, are due to +special tendencies, or whether they are learned manifestations of a +more general heritage.</p> + +<p>5. How these proclivities, specific or general, are related to +intelligence.</p> + +<p>Points 1 and 2 are problems of procedure which must be evolved +from our existent knowledge of measurements and statistics. Points +3, 4, and 5 are problems which must be solved from the evidence +resulting from an experiment in classification using these methods. +Points 4 and 5 introduce the vexed question of whether there is a +“general factor” or some general inherited cause of disparity in +school product other than intelligence. Should reading ability +prove to be the result of certain inherited abilities, or predisposition +to abilities, we could not use a measure of mental ability alone as +the guide to what a child could attain in reading. If intelligence, +however, were the only inherited prognostic factor of school achievement, +we could mark the education which had functioned in the +child’s life by the percentage which the actual accomplishment of +the child was of the maximum accomplishment of which he was +capable at that stage of his mental development. So, too, if interest +in particular subjects and ambition are not mainly the result of +<span class="pagenum" id="Page_16">[16]</span>rewards and punishments of early life, but are themselves significantly +rooted in the nature of the child, we could not condemn or +commend curricula and methods upon a basis of the ratio of resultant +accomplishment to mental ability, but must include a measure of +this potentiality. The practical queries whether or not a child +can do reading as well as he does arithmetic, whether his ambition +and his honesty have their origin in the same strength or weakness, +can be answered only when these problems are fully solved. The +immediate consequences of knowing that a child can usually be +taught to read if he does other tasks well is of obvious import. It +would be of great service, too, to know whether lack of application +can be corrected so as to bring concentration to the level of the +other traits. If a child is normal in other ways and not in his +tendency to respond to the approval of others by satisfaction, can +this “drive” be increased or reduced to the average, or are individual +differences in specific original tendencies basic to development +of character, and if they are, how much influence do these differences +exert upon school accomplishment? In order to classify children +and comprehendingly watch and control their progress we +must know the relation of achievement to the inherited bases upon +which it depends. We must be able to state a child’s progress in +any one school subject in terms of the potential capacity of the +child to progress. We must know the inherited determinants of +disparity in school product.</p> + +<hr class="chap x-ebookmaker-drop"> + +<div class="chapter"> + +<p><span class="pagenum" id="Page_17">[17]</span></p> + +<h2 class="nobreak" id="PART_II">PART II<br> +STATISTICAL TREATMENT OF THE EXPERIMENT</h2> + +</div> + +<p>In the discussion and tables which follow:</p> + +<p>Q stands for Quotient, which will mean a Subject Age divided +by a Chronological Age. R stands for Ratio, which will mean a +Subject Age divided by a Mental Age.</p> + +<p>AQ means Woody-McCall Arithmetic Age divided by Chronological +Age, and AR means this AA divided by Mental Age.</p> + +<p>VQ means Thorndike Vocabulary Age divided by Chronological +Age, and VR means this VA divided by Mental Age.</p> + +<p>RQ means Alpha 2 Reading Age divided by Chronological Age, +and RR means this RA divided by Mental Age.</p> + +<p>CQ means Kelley-Trabue Completion Age divided by Chronological +Age, and CR means this CA divided by Mental Age.</p> + +<p>SQ means any Subject Quotient, that is, any Subject Age divided +by Chronological Age, and SR means any Subject Ratio, +that is, any SA divided by Mental Age.</p> + +<p>EQ means the average of all Subject Quotients and AccR, the +Accomplishment Ratio, means the average of all Subject Ratios.</p> + +<p>All <i>r</i>’s are product-moment correlation coefficients, uncorrected. +As the reliabilities (<a href="#table4">Table 4</a>) are almost what the other coefficients +are in June, 1920 (<a href="#table5">Table 5</a>), it is apparent that the corrected +coefficients, when Grade III is excluded, would all be very near +unity at that time.</p> + +<h3>THE QUOTIENTS</h3> + +<p>In <a href="#table1">Table 1</a> are presented all the quotients for all periods of +testing, grouped by children. The table, a sample of which is +included here,⁠<a id="FNanchor_9" href="#Footnote_9" class="fnanchor">[9]</a> shows clearly how all SQ’s approach IQ as special +treatment continues. The grades indicated in this grouping are +as of June, 1920. Inasmuch as many double and triple promotions +were made in an effort to get maximum product for intelligence +invested, no conclusion can here be formed of the grade to which +these children belonged at any time except June, 1920. The correspondence +between IQ and the SQ’s in June, 1920 is further +shown in <a href="#table2">Table 2</a>. In this table the 48 children who took all tests +at all periods are ranked from high to low IQ and their SQ’s are +listed opposite. The high correspondence is readily apparent.</p> + +<p><span class="pagenum" id="Page_18">[18]</span></p> + +<h4 id="table1">TABLE 1⁠<a id="FNanchor_10" href="#Footnote_10" class="fnanchor">[10]</a><br> +<span class="smcap">Intelligence Quotients for All Periods Grouped by Children</span></h4> + +<p>The children are arranged by grade as they were in June, 1920, and alphabetically +within the grade. The periods of testing are lettered in their chronological +sequence; <i>a</i> is November, 1918, <i>b</i> is June, 1919, <i>c</i> is November, 1919 and <i>d</i> is +June, 1920. * = Zero Score</p> + +<p class="center"><span class="smcap">Grade 3</span></p> + +<table class="borders"> + <tr> + <th>Intelligence Quotient</th> + <th>Test Period</th> + <th>Arithmetic Quotient</th> + <th>Vocabulary Quotient</th> + <th>Reading Quotient</th> + <th>Completion Quotient</th> + </tr> + <tr class="group"> + <td rowspan="4" class="tdr">101</td> + <td class="tdc"><i>a</i></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td class="tdc"><i>b</i></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td class="tdc"><i>c</i></td> + <td class="tdr">64</td> + <td class="tdr">58</td> + <td class="tdr"></td> + <td class="tdr">43</td> + </tr> + <tr> + <td class="tdc"><i>d</i></td> + <td class="tdr">106</td> + <td class="tdr">88</td> + <td class="tdr"></td> + <td class="tdr">93</td> + </tr> + <tr class="group"> + <td rowspan="4" class="tdr">128</td> + <td class="tdc"><i>a</i></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td class="tdc"><i>b</i></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td class="tdc"><i>c</i></td> + <td class="tdr">80</td> + <td class="tdr">102</td> + <td class="tdr"></td> + <td class="tdr">81</td> + </tr> + <tr> + <td class="tdc"><i>d</i></td> + <td class="tdr"></td> + <td class="tdr">152</td> + <td class="tdr">124</td> + <td class="tdr">153</td> + </tr> + <tr class="group"> + <td rowspan="4" class="tdr">116</td> + <td class="tdc"><i>a</i></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td class="tdc"><i>b</i></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td class="tdc"><i>c</i></td> + <td class="tdr">56</td> + <td class="tdr">90</td> + <td class="tdr">*</td> + <td class="tdr">49</td> + </tr> + <tr> + <td class="tdc"><i>d</i></td> + <td class="tdr">94</td> + <td class="tdr">95</td> + <td class="tdr">77</td> + <td class="tdr">89</td> + </tr> + <tr class="group"> + <td rowspan="4" class="tdr">87</td> + <td class="tdc"><i>a</i></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td class="tdc"><i>b</i></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td class="tdc"><i>c</i></td> + <td class="tdr">90</td> + <td class="tdr">40</td> + <td class="tdr">35</td> + <td class="tdr">54</td> + </tr> + <tr> + <td class="tdc"><i>d</i></td> + <td class="tdr">72</td> + <td class="tdr">74</td> + <td class="tdr">61</td> + <td class="tdr">52</td> + </tr> + <tr class="group"> + <td rowspan="4" class="tdr">112</td> + <td class="tdc"><i>a</i></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td class="tdc"><i>b</i></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td class="tdc"><i>c</i></td> + <td class="tdr">90</td> + <td class="tdr">137</td> + <td class="tdr">133</td> + <td class="tdr">112</td> + </tr> + <tr> + <td class="tdc"><i>d</i></td> + <td class="tdr">112</td> + <td class="tdr">113</td> + <td class="tdr">121</td> + <td class="tdr">131</td> + </tr> +</table> + +<p><span class="pagenum" id="Page_19">[19]</span></p> + +<h4 id="table2">TABLE 2⁠<a id="FNanchor_11" href="#Footnote_11" class="fnanchor">[11]</a><br> +<span class="smcap">Group Taking All Tests at All Periods Arranged in Order of +Magnitude of Intelligence Quotients</span></h4> + +<table class="borders"> + <tr> + <th>Intelligence Quotients</th> + <th>Arithmetic Quotients</th> + <th>Vocabulary Quotients</th> + <th>Reading Quotients</th> + <th>Completion Quotients</th> + </tr> + <tr> + <td class="tdr">146</td> + <td class="tdr">111</td> + <td class="tdr">154</td> + <td class="tdr">164</td> + <td class="tdr">150</td> + </tr> + <tr> + <td class="tdr">142</td> + <td class="tdr">129</td> + <td class="tdr">135</td> + <td class="tdr">137</td> + <td class="tdr">136</td> + </tr> + <tr> + <td class="tdr">141</td> + <td class="tdr">109</td> + <td class="tdr">118</td> + <td class="tdr">107</td> + <td class="tdr">121</td> + </tr> + <tr> + <td class="tdr">139</td> + <td class="tdr">124</td> + <td class="tdr">141</td> + <td class="tdr">124</td> + <td class="tdr">134</td> + </tr> + <tr> + <td class="tdr">138</td> + <td class="tdr">101</td> + <td class="tdr">112</td> + <td class="tdr">105</td> + <td class="tdr">106</td> + </tr> + <tr class="group"> + <td class="tdr">138</td> + <td class="tdr">121</td> + <td class="tdr">130</td> + <td class="tdr">110</td> + <td class="tdr">109</td> + </tr> + <tr> + <td class="tdr">130</td> + <td class="tdr">107</td> + <td class="tdr">139</td> + <td class="tdr">135</td> + <td class="tdr">136</td> + </tr> + <tr> + <td class="tdr">122</td> + <td class="tdr">127</td> + <td class="tdr">130</td> + <td class="tdr">124</td> + <td class="tdr">121</td> + </tr> + <tr> + <td class="tdr">122</td> + <td class="tdr">113</td> + <td class="tdr">121</td> + <td class="tdr">117</td> + <td class="tdr">124</td> + </tr> + <tr> + <td class="tdr">122</td> + <td class="tdr">112</td> + <td class="tdr">102</td> + <td class="tdr">114</td> + <td class="tdr">129</td> + </tr> + <tr class="group"> + <td class="tdr">121</td> + <td class="tdr">128</td> + <td class="tdr">125</td> + <td class="tdr">128</td> + <td class="tdr">128</td> + </tr> + <tr> + <td class="tdr">120</td> + <td class="tdr">100</td> + <td class="tdr">116</td> + <td class="tdr">102</td> + <td class="tdr">119</td> + </tr> + <tr> + <td class="tdr">118</td> + <td class="tdr">117</td> + <td class="tdr">123</td> + <td class="tdr">114</td> + <td class="tdr">125</td> + </tr> + <tr> + <td class="tdr">117</td> + <td class="tdr">131</td> + <td class="tdr">111</td> + <td class="tdr">118</td> + <td class="tdr">124</td> + </tr> + <tr> + <td class="tdr">117</td> + <td class="tdr">106</td> + <td class="tdr">122</td> + <td class="tdr">112</td> + <td class="tdr">111</td> + </tr> + <tr class="group"> + <td class="tdr">114</td> + <td class="tdr">105</td> + <td class="tdr">126</td> + <td class="tdr">110</td> + <td class="tdr">114</td> + </tr> + <tr> + <td class="tdr">109</td> + <td class="tdr">83</td> + <td class="tdr">113</td> + <td class="tdr">117</td> + <td class="tdr">103</td> + </tr> + <tr> + <td class="tdr">107</td> + <td class="tdr">103</td> + <td class="tdr">112</td> + <td class="tdr">95</td> + <td class="tdr">103</td> + </tr> + <tr> + <td class="tdr">107</td> + <td class="tdr">94</td> + <td class="tdr">126</td> + <td class="tdr">94</td> + <td class="tdr">123</td> + </tr> + <tr> + <td class="tdr">104</td> + <td class="tdr">99</td> + <td class="tdr">117</td> + <td class="tdr">96</td> + <td class="tdr">104</td> + </tr> + <tr class="group"> + <td class="tdr">104</td> + <td class="tdr">103</td> + <td class="tdr">110</td> + <td class="tdr">94</td> + <td class="tdr">116</td> + </tr> + <tr> + <td class="tdr">103</td> + <td class="tdr">108</td> + <td class="tdr">113</td> + <td class="tdr">112</td> + <td class="tdr">106</td> + </tr> + <tr> + <td class="tdr">101</td> + <td class="tdr">100</td> + <td class="tdr">114</td> + <td class="tdr">109</td> + <td class="tdr">106</td> + </tr> + <tr> + <td class="tdr">100</td> + <td class="tdr">90</td> + <td class="tdr">103</td> + <td class="tdr">92</td> + <td class="tdr">92</td> + </tr> + <tr> + <td class="tdr">100</td> + <td class="tdr">109</td> + <td class="tdr">118</td> + <td class="tdr">108</td> + <td class="tdr">113</td> + </tr> + <tr class="group"> + <td class="tdr">99</td> + <td class="tdr">114</td> + <td class="tdr">104</td> + <td class="tdr">106</td> + <td class="tdr">110</td> + </tr> + <tr> + <td class="tdr">99</td> + <td class="tdr">114</td> + <td class="tdr">119</td> + <td class="tdr">117</td> + <td class="tdr">115</td> + </tr> + <tr> + <td class="tdr">98</td> + <td class="tdr">102</td> + <td class="tdr">101</td> + <td class="tdr">108</td> + <td class="tdr">104</td> + </tr> + <tr> + <td class="tdr">98</td> + <td class="tdr">99</td> + <td class="tdr">106</td> + <td class="tdr">107</td> + <td class="tdr">106</td> + </tr> + <tr> + <td class="tdr">97</td> + <td class="tdr">95</td> + <td class="tdr">109</td> + <td class="tdr">107</td> + <td class="tdr">105</td> + </tr> + <tr class="group"> + <td class="tdr">97</td> + <td class="tdr">108</td> + <td class="tdr">101</td> + <td class="tdr">102</td> + <td class="tdr">105<span class="pagenum" id="Page_20">[20]</span></td> + </tr> + <tr> + <td class="tdr">97</td> + <td class="tdr">95</td> + <td class="tdr">104</td> + <td class="tdr">89</td> + <td class="tdr">110</td> + </tr> + <tr> + <td class="tdr">96</td> + <td class="tdr">90</td> + <td class="tdr">104</td> + <td class="tdr">91</td> + <td class="tdr">91</td> + </tr> + <tr> + <td class="tdr">95</td> + <td class="tdr">84</td> + <td class="tdr">99</td> + <td class="tdr">93</td> + <td class="tdr">100</td> + </tr> + <tr> + <td class="tdr">95</td> + <td class="tdr">90</td> + <td class="tdr">107</td> + <td class="tdr">99</td> + <td class="tdr">105</td> + </tr> + <tr class="group"> + <td class="tdr">95</td> + <td class="tdr">85</td> + <td class="tdr">117</td> + <td class="tdr">114</td> + <td class="tdr">103</td> + </tr> + <tr> + <td class="tdr">94</td> + <td class="tdr">106</td> + <td class="tdr">57</td> + <td class="tdr">89</td> + <td class="tdr">108</td> + </tr> + <tr> + <td class="tdr">94</td> + <td class="tdr">103</td> + <td class="tdr">103</td> + <td class="tdr">106</td> + <td class="tdr">104</td> + </tr> + <tr> + <td class="tdr">92</td> + <td class="tdr">96</td> + <td class="tdr">86</td> + <td class="tdr">94</td> + <td class="tdr">85</td> + </tr> + <tr> + <td class="tdr">87</td> + <td class="tdr">83</td> + <td class="tdr">88</td> + <td class="tdr">92</td> + <td class="tdr">87</td> + </tr> + <tr class="group"> + <td class="tdr">87</td> + <td class="tdr">95</td> + <td class="tdr">96</td> + <td class="tdr">94</td> + <td class="tdr">102</td> + </tr> + <tr> + <td class="tdr">84</td> + <td class="tdr">85</td> + <td class="tdr">87</td> + <td class="tdr">93</td> + <td class="tdr">87</td> + </tr> + <tr> + <td class="tdr">83</td> + <td class="tdr">106</td> + <td class="tdr">91</td> + <td class="tdr">87</td> + <td class="tdr">104</td> + </tr> + <tr> + <td class="tdr">80</td> + <td class="tdr">77</td> + <td class="tdr">91</td> + <td class="tdr">80</td> + <td class="tdr">84</td> + </tr> + <tr> + <td class="tdr">80</td> + <td class="tdr">84</td> + <td class="tdr">75</td> + <td class="tdr">79</td> + <td class="tdr">84</td> + </tr> + <tr class="group"> + <td class="tdr">80</td> + <td class="tdr">89</td> + <td class="tdr">107</td> + <td class="tdr">88</td> + <td class="tdr">86</td> + </tr> + <tr> + <td class="tdr">78</td> + <td class="tdr">87</td> + <td class="tdr">90</td> + <td class="tdr">93</td> + <td class="tdr">85</td> + </tr> + <tr> + <td class="tdr">60</td> + <td class="tdr">69</td> + <td class="tdr">56</td> + <td class="tdr">71</td> + <td class="tdr">77</td> + </tr> +</table> + +<p>The intercorrelations of the quotients of these 48 cases for +all periods may be seen in <a href="#table3">Table 3</a> (<a href="#Page_21">page 21</a>). The correlations with +IQ and the intercorrelations of the SQ’s have increased toward +positive unity or rather toward the limits of a correlation with +tools of measurement such as we have used. This limit is a function +of the reliability of the tests employed. It is customary to use a +formula to correct for attenuation in order to find the percentage +which the correlation is of the geometric mean of the two reliability +coefficients. This is tantamount to saying that any correlation +can go no higher than the geometric mean of the reliability +coefficients of the tests used. It is better to assume that an <i>r</i> +<span class="pagenum" id="Page_21">[21]</span>can go as high as the ∜(<i>r</i>₁₁⋅<i>r</i>₂₂) since an <i>r</i> can go as high as the +square root of its reliability coefficient. Dr. Truman L. Kelley +has shown that the correlation of a test with an infinite number of +forms of the same test would be as the square root of its correlation +with any one other form.</p> + +<p>The reliabilities and limits defining a limit as the fourth root of +the multiplied reliability coefficients are in <a href="#table4">Table 4</a>.</p> + +<p>Correction for attenuation is often ridiculously high because +the reliability coefficient of one of the measures used is so low. If +an element is included in the two tests which are correlated, but +not in the other forms of each test used to get reliability, the +“corrected coefficient” is corrected for an element which is not +chance. Whenever the geometric mean of the reliabilities is less +than the obtained <i>r</i>, the corrected <i>r</i> is over 1.00 and hence absurd.⁠<a id="FNanchor_12" href="#Footnote_12" class="fnanchor">[12]</a></p> + +<p>Therefore we use here instead, a comparison to the maximum +possibility in a true sense. Since a test correlates with the +“true ability” √(<i>r</i>₁₁), ∜(<i>r</i>₁₁⋅<i>r</i>₂₂) is the limit of an <i>r</i>, its optimum +with those tools. Although these limits apply, strictly speaking, +only to the total correlations, since the reliability correlations are +with all the data; we may assume that the same facts hold with +regard to the correlations of each of the grades, that is, the reliability +is a function of the test not of the data selected.</p> + +<h4 id="table3">TABLE 3<br> +<span class="smcap">Intercorrelation of All Quotients for All Periods of the 48 Children +Who Took All Tests</span></h4> + +<table> + <tr> + <th colspan="7"><span class="smcap">November, 1918</span></th> + </tr> + <tr> + <th></th> + <th>IQ</th> + <th></th> + <th>VQ</th> + <th>RQ</th> + <th>S.D.</th> + <th>M</th> + </tr> + <tr> + <td>IQ</td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr">19.12</td> + <td class="tdr">105.15</td> + </tr> + <tr> + <td></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr">±1.32</td> + <td class="tdr">±1.86</td> + </tr> + <tr> + <td>VQ</td> + <td class="tdr">.72</td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr">20.54</td> + <td class="tdr">102.52</td> + </tr> + <tr> + <td></td> + <td class="tdr">±.05</td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr">±1.41</td> + <td class="tdr">±2.00</td> + </tr> + <tr> + <td>RQ</td> + <td class="tdr">.64</td> + <td class="tdr"></td> + <td class="tdr">.64</td> + <td class="tdr"></td> + <td class="tdr">19.09</td> + <td class="tdr">95.90</td> + </tr> + <tr> + <td></td> + <td class="tdr">±.06</td> + <td class="tdr"></td> + <td class="tdr">±.06</td> + <td class="tdr"></td> + <td class="tdr">±1.31</td> + <td class="tdr">±1.86</td> + </tr> + <tr> + <td>CQ</td> + <td class="tdr">.63</td> + <td class="tdr"></td> + <td class="tdr">.71</td> + <td class="tdr">.77</td> + <td class="tdr">19.34</td> + <td class="tdr">99.44</td> + </tr> + <tr> + <td></td> + <td class="tdr">±.06</td> + <td class="tdr"></td> + <td class="tdr">±.05</td> + <td class="tdr">±.04</td> + <td class="tdr">±1.33</td> + <td class="tdr">±1.88<span class="pagenum" id="Page_22">[22]</span></td> + </tr> + <tr> + <th colspan="7"><span class="smcap">June, 1919</span></th> + </tr> + <tr> + <th></th> + <th>IQ</th> + <th></th> + <th>VQ</th> + <th>RQ</th> + <th>S.D.</th> + <th>M</th> + </tr> + <tr> + <td>IQ</td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr">19.12</td> + <td class="tdr">105.15</td> + </tr> + <tr> + <td></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr">±1.32</td> + <td class="tdr">±1.86</td> + </tr> + <tr> + <td>VQ</td> + <td class="tdr">.73</td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr">20.80</td> + <td class="tdr">113.54</td> + </tr> + <tr> + <td></td> + <td class="tdr">±.05</td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr">±1.43</td> + <td class="tdr">±2.02</td> + </tr> + <tr> + <td>RQ</td> + <td class="tdr">.65</td> + <td class="tdr"></td> + <td class="tdr">.58</td> + <td class="tdr"></td> + <td class="tdr">14.73</td> + <td class="tdr">101.31</td> + </tr> + <tr> + <td></td> + <td class="tdr">±.06</td> + <td class="tdr"></td> + <td class="tdr">±.06</td> + <td class="tdr"></td> + <td class="tdr">±1.01</td> + <td class="tdr">±1.43</td> + </tr> + <tr> + <td>CQ</td> + <td class="tdr">.62</td> + <td class="tdr"></td> + <td class="tdr">.68</td> + <td class="tdr">.77</td> + <td class="tdr">19.76</td> + <td class="tdr">101.04</td> + </tr> + <tr> + <td></td> + <td class="tdr">±.06</td> + <td class="tdr"></td> + <td class="tdr">±.05</td> + <td class="tdr">+.04</td> + <td class="tdr">±1.36</td> + <td class="tdr">±1.92</td> + </tr> + <tr> + <th colspan="7"><span class="smcap">November, 1919</span></th> + </tr> + <tr> + <th></th> + <th>IQ</th> + <th>AQ</th> + <th>VQ</th> + <th>RQ</th> + <th>S.D.</th> + <th>M</th> + </tr> + <tr> + <td>IQ</td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr">19.12</td> + <td class="tdr">105.15</td> + </tr> + <tr> + <td></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr">±1.32</td> + <td class="tdr">±1.86</td> + </tr> + <tr> + <td>AQ</td> + <td class="tdr">.46</td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr">14.08</td> + <td class="tdr">102.90</td> + </tr> + <tr> + <td></td> + <td class="tdr">±.08</td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr">±0.97</td> + <td class="tdr">±1.37</td> + </tr> + <tr> + <td>VQ</td> + <td class="tdr">.86</td> + <td class="tdr">.23</td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr">17.07</td> + <td class="tdr">109.17</td> + </tr> + <tr> + <td></td> + <td class="tdr">±.03</td> + <td class="tdr">±.09</td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr">±1.18</td> + <td class="tdr">±1.66</td> + </tr> + <tr> + <td>RQ</td> + <td class="tdr">.65</td> + <td class="tdr">.56</td> + <td class="tdr">.71</td> + <td class="tdr"></td> + <td class="tdr">13.91</td> + <td class="tdr">101.42</td> + </tr> + <tr> + <td></td> + <td class="tdr">±.06</td> + <td class="tdr">±.07</td> + <td class="tdr">±.05</td> + <td class="tdr"></td> + <td class="tdr">±0.96</td> + <td class="tdr">±1.35</td> + </tr> + <tr> + <td>CQ</td> + <td class="tdr">.79</td> + <td class="tdr">.47</td> + <td class="tdr">.83</td> + <td class="tdr">.82</td> + <td class="tdr">17.53</td> + <td class="tdr">105.21</td> + </tr> + <tr> + <td></td> + <td class="tdr">±.04</td> + <td class="tdr">±.08</td> + <td class="tdr">±.03</td> + <td class="tdr">±.03</td> + <td class="tdr">±1.21</td> + <td class="tdr">±1.71</td> + </tr> + <tr> + <th colspan="7"><span class="smcap">June, 1920</span></th> + </tr> + <tr> + <th></th> + <th>IQ</th> + <th>AQ</th> + <th>VQ</th> + <th>RQ</th> + <th>S.D.</th> + <th>M</th> + </tr> + <tr> + <td>IQ</td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr">19.12</td> + <td class="tdr">105.15</td> + </tr> + <tr> + <td></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr">±1.32</td> + <td class="tdr">±1.86</td> + </tr> + <tr> + <td>AQ</td> + <td class="tdr">.73</td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr">14.10</td> + <td class="tdr">101.79</td> + </tr> + <tr> + <td></td> + <td class="tdr">±.05</td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr">±0.97</td> + <td class="tdr">±1.37</td> + </tr> + <tr> + <td>VQ</td> + <td class="tdr">.81</td> + <td class="tdr">.60</td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr">18.89</td> + <td class="tdr">108.94</td> + </tr> + <tr> + <td></td> + <td class="tdr">±.03</td> + <td class="tdr">±.06</td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr">±1.30</td> + <td class="tdr">±1.84</td> + </tr> + <tr> + <td>RQ</td> + <td class="tdr">.79</td> + <td class="tdr">.68</td> + <td class="tdr">.87</td> + <td class="tdr"></td> + <td class="tdr">16.43</td> + <td class="tdr">104.94</td> + </tr> + <tr> + <td></td> + <td class="tdr">±.04</td> + <td class="tdr">±.05</td> + <td class="tdr">±.02</td> + <td class="tdr"></td> + <td class="tdr">±1.13</td> + <td class="tdr">±1.60</td> + </tr> + <tr> + <td>CQ</td> + <td class="tdr">.84</td> + <td class="tdr">.77</td> + <td class="tdr">.78</td> + <td class="tdr">.84</td> + <td class="tdr">15.87</td> + <td class="tdr">108.08</td> + </tr> + <tr> + <td></td> + <td class="tdr">±.03</td> + <td class="tdr">±.04</td> + <td class="tdr">±.04</td> + <td class="tdr">±.03</td> + <td class="tdr">±1.09</td> + <td class="tdr">±1.54</td> + </tr> +</table> + +<p><span class="pagenum" id="Page_23">[23]</span></p> + +<h4 id="table4">TABLE 4<br> +<span class="smcap">Reliability Coefficients</span></h4> + +<table> + <tr> + <th></th> + <th>One Form of Each Test</th> + <th>Two Forms of Each Test (by Brown’s Formula)</th> + <th>One Form with an Infinite Number of Forms</th> + <th>Two Forms with an Infinite Number of Forms</th> + </tr> + <tr> + <th></th> + <th><i>r</i>₁₁</th> + <th><i>r</i>₁₁</th> + <th>√<i>r</i>₁₁</th> + <th>√<i>r</i>₁₁</th> + </tr> + <tr> + <td class="nw">Intelligence Quotient</td> + <td class="tdr">.888</td> + <td class="tdr"></td> + <td class="tdr">.942</td> + <td class="tdr"></td> + </tr> + <tr> + <td></td> + <td colspan="4">(by Brown’s Formula)⁠<a id="FNanchor_13" href="#Footnote_13" class="fnanchor">[13]</a></td> + </tr> + <tr> + <td class="nw">Arithmetic Quotient</td> + <td class="tdr">.824</td> + <td class="tdr">.904</td> + <td class="tdr">.908</td> + <td class="tdr">.951</td> + </tr> + <tr> + <td class="nw">Vocabulary Quotient</td> + <td class="tdr">.820</td> + <td class="tdr">.901</td> + <td class="tdr">.906</td> + <td class="tdr">.949</td> + </tr> + <tr> + <td class="nw">Reading Quotient</td> + <td class="tdr">.866</td> + <td class="tdr">.928</td> + <td class="tdr">.931</td> + <td class="tdr">.963</td> + </tr> + <tr> + <td class="nw">Completion Quotient</td> + <td class="tdr">.883</td> + <td class="tdr">.938</td> + <td class="tdr">.940</td> + <td class="tdr">.968</td> + </tr> +</table> + +<p class="center">Limits of the <i>r</i>’s = ∜(<i>r</i>₁₁ × <i>r</i>₂₂)</p> + +<table> + <tr> + <th></th> + <th>Nov. 1918,<br>June and<br>Nov. 1919</th> + <th>June 1920</th> + </tr> + <tr> + <td>IQ and AQ</td> + <td class="tdr">.925</td> + <td class="tdr">.946</td> + </tr> + <tr> + <td>IQ and VQ</td> + <td class="tdr">.924</td> + <td class="tdr">.946</td> + </tr> + <tr> + <td>IQ and RQ</td> + <td class="tdr">.936</td> + <td class="tdr">.953</td> + </tr> + <tr> + <td>IQ and CQ</td> + <td class="tdr">.941</td> + <td class="tdr">.955</td> + </tr> +</table> + +<p class="note">The limits of the June, 1920 <i>r</i>’s are naturally somewhat larger than +the others since two forms of tests (except the Binet) were used; the +unreliability of the quantitative indices is therefore lower and hence +the correlation with IQ may be larger.</p> + +<p>The correlations in 1920 of another group—the whole school +except Grade III—are reproduced in <a href="#table5">Table 5</a>. Grade III was +excluded since here there had as yet been little chance to push the +<i>r</i>’s. Partials were obtained with these data (<a href="#table6">Table 6</a>). Little +faith may be placed in the relative sizes of these partials, much +because the <i>r</i><sub>VQ.RQ</sub> is here only .73 and, in the data presented +in <a href="#table3">Table 3</a>, it is .87. This is due to the fact that the data in +<a href="#table3">Table 3</a> cover all periods (2 years) while those in <a href="#table5">Table 5</a> cover +only one. This difference has comparatively slight influence on +our general conclusions; but it makes a huge difference in the correlation +of RQ and VQ when IQ is rendered constant, whether +the one or the other set of data is used. Moreover, the whole +logic of arguing for general factors by reduction of partial correlations +from the original <i>r</i> has been called gravely into question +in Godfrey H. Thomson’s recent work on this subject: “The Proof +or Disproof of the Existence of General Ability.” Thomson shows +that partial correlation gives one possible interpretation of the +facts, but not an inevitable one. Thus we cannot say that because +RQ and IQ and RQ and AQ are highly correlated, correlation +of IQ and AQ is dependent upon RQ. We can say, however, +that it is likely to be. IQ and AQ may be correlated by reason of +inclusion of some element not included at all in RQ. The higher +the correlations which we deal with the less we need worry about +this, and of course correlations of unity exclude any such consideration.</p> + +<p><span class="pagenum" id="Page_24">[24]</span></p> + +<h4 id="table5">TABLE 5<br> +<span class="smcap">Intercorrelation of All Quotients in June, 1920. All Children +Exclusive of Grade 3 are Here Represented</span></h4> + +<p class="center">The P.E.’s are all less than .05</p> + +<p class="center"><i>N</i> = 81</p> + +<table> + <tr> + <th></th> + <th>IQ</th> + <th>Arithmetic<br>Quotient</th> + <th>Vocabulary<br>Quotient</th> + <th>Reading<br>Quotient</th> + </tr> + <tr> + <td class="nw">Arithmetic Quotient</td> + <td class="tdr">.733</td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td class="nw">Vocabulary Quotient</td> + <td class="tdr">.837</td> + <td class="tdr">.628</td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td class="nw">Reading Quotient</td> + <td class="tdr">.758</td> + <td class="tdr">.694</td> + <td class="tdr">.734</td> + <td class="tdr"></td> + </tr> + <tr> + <td class="nw">Completion Quotient</td> + <td class="tdr">.821</td> + <td class="tdr">.770</td> + <td class="tdr">.825</td> + <td class="tdr">.801</td> + </tr> +</table> + +<p>I therefore draw no conclusions from the comparative size of +these partials, nor do I get partials with any of the other data, +and rest the case mainly on the high <i>r</i>’s between IQ and SQ’s in +1920; increase in correspondence of the central tendencies and +range of the SQ’s by grade with the central tendency and range +<span class="pagenum" id="Page_25">[25]</span>of the IQ’s of the same data; small intercorrelation of SR’s and +negative correlation of AccR with IQ.</p> + +<p>The general lowness of the partials (<a href="#table6">Table 6</a>) does, however, +indicate the great causative relation between IQ and disparity +of product. The elements still in here are common elements in +the tests and the mistreatment of intelligence.</p> + +<h4 id="table6">TABLE 6<br> +<span class="smcap">Partial Correlations of Quotients Irrespective of Intelligence +Quotients</span></h4> + +<p class="center"><i>N</i> = 81</p> + +<table> + <tr> + <th></th> + <th>Arithmetic<br>Quotient</th> + <th>Vocabulary<br>Quotient</th> + <th>Reading<br>Quotient</th> + </tr> + <tr> + <td class="nw" rowspan="2">Vocabulary Quotient</td> + <td class="tdr">.04</td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td class="tdr">±.07</td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td class="nw" rowspan="2">Reading Quotient</td> + <td class="tdr">.31</td> + <td class="tdr">.28</td> + <td class="tdr"></td> + </tr> + <tr> + <td class="tdr">±.07</td> + <td class="tdr">±.07</td> + <td class="tdr"></td> + </tr> + <tr> + <td class="nw" rowspan="2">Completion Quotient</td> + <td class="tdr">.43</td> + <td class="tdr">.44</td> + <td class="tdr">.47</td> + </tr> + <tr> + <td class="tdr">±.08</td> + <td class="tdr">±.06</td> + <td class="tdr">±.06</td> + </tr> +</table> + +<p>What happened by grade in 1918-1919 is summarized in <a href="#table7">Table +7</a>. What happened by grade in 1919-1920 is summarized in <a href="#table8">Table +8</a>. Since there were many changes in personnel from 1918-1919 +to 1919-1920, we need expect no continuity from <a href="#table7">Table 7</a> to <a href="#table8">Table +8</a>. For the continuous influence of the two years, see <a href="#table3">Table 3</a>, +which includes 48 children taking all tests at all periods.</p> + +<h4 id="table7">TABLE 7<br> +<span class="smcap">All Correlations, Means, and Standard Deviations by Grade, Showing +Progress from November, 1918 to June, 1919</span></h4> + +<ul> + <li>I stands for Intelligence Quotient</li> + <li>V stands for Vocabulary Quotient</li> + <li>R stands for Reading Quotient</li> + <li>C stands for Completion Quotient</li> +</ul> + +<table> + <tr> + <th rowspan="2">GRADE</th> + <th rowspan="2"></th> + <th colspan="2"><i>r</i></th> + <th></th> + <th colspan="2">M</th> + <th></th> + <th colspan="2">S.D.</th> + </tr> + <tr> + <th>Nov.</th> + <th>June</th> + <th></th> + <th>Nov.</th> + <th>June</th> + <th></th> + <th>Nov.</th> + <th>June</th> + </tr> + <tr> + <td>III</td> + <td class="tdc">I V</td> + <td class="tdr">.467</td> + <td class="tdr">.633</td> + <td class="tdc">I</td> + <td class="tdr">109.89</td> + <td class="tdr">113.20</td> + <td class="tdc">I</td> + <td class="tdr">12.83</td> + <td class="tdr">15.49</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.12</td> + <td class="tdr">±.07</td> + <td class="tdc"></td> + <td class="tdr">±1.98</td> + <td class="tdr">±1.91</td> + <td class="tdc"></td> + <td class="tdr">±1.40</td> + <td class="tdr">±1.35</td> + </tr> + <tr> + <td></td> + <td class="tdc">I R</td> + <td class="tdr">.541</td> + <td class="tdr">.492</td> + <td class="tdc">V</td> + <td class="tdr">96.11</td> + <td class="tdr">109.90</td> + <td class="tdc">V</td> + <td class="tdr">21.21</td> + <td class="tdr">18.69</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.11</td> + <td class="tdr">±.09</td> + <td class="tdc"></td> + <td class="tdr">±3.28</td> + <td class="tdr">±2.30</td> + <td class="tdc"></td> + <td class="tdr">±2.32</td> + <td class="tdr">±1.63</td> + </tr> + <tr> + <td></td> + <td class="tdc">I C</td> + <td class="tdr">.641</td> + <td class="tdr">.386</td> + <td class="tdc">R</td> + <td class="tdr">82.26</td> + <td class="tdr">101.40</td> + <td class="tdc">R</td> + <td class="tdr">22.58</td> + <td class="tdr">15.85</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.09</td> + <td class="tdr">±.11</td> + <td class="tdc"></td> + <td class="tdr">±3.49</td> + <td class="tdr">±1.95</td> + <td class="tdc"></td> + <td class="tdr">±2.47</td> + <td class="tdr">±1.38</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc">C</td> + <td class="tdr">86.89</td> + <td class="tdr">108.40</td> + <td class="tdc">C</td> + <td class="tdr">22.76</td> + <td class="tdr">15.79</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc"></td> + <td class="tdr">±3.52</td> + <td class="tdr">±1.94</td> + <td class="tdc"></td> + <td class="tdr">±2.49</td> + <td class="tdr">±1.37</td> + </tr> + <tr class="bb"> + <td class="tdr"><i>N</i> =</td> + <td class="tdc"></td> + <td class="tdr">19</td> + <td class="tdr">30</td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"><span class="pagenum" id="Page_26">[26]</span></td> + </tr> + <tr> + <td>IV</td> + <td class="tdc">I V</td> + <td class="tdr">.724</td> + <td class="tdr">.819</td> + <td class="tdc">I</td> + <td class="tdr">105.90</td> + <td class="tdr">104.82</td> + <td class="tdc">I</td> + <td class="tdr">18.08</td> + <td class="tdr">18.21</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.07</td> + <td class="tdr">±.05</td> + <td class="tdc"></td> + <td class="tdr">±2.73</td> + <td class="tdr">±2.98</td> + <td class="tdc"></td> + <td class="tdr">±1.93</td> + <td class="tdr">±2.11</td> + </tr> + <tr> + <td></td> + <td class="tdc">I R</td> + <td class="tdr">.665</td> + <td class="tdr">.845</td> + <td class="tdc">V</td> + <td class="tdr">97.20</td> + <td class="tdr">108.53</td> + <td class="tdc">V</td> + <td class="tdr">17.26</td> + <td class="tdr">24.92</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.08</td> + <td class="tdr">±.05</td> + <td class="tdc"></td> + <td class="tdr">±2.60</td> + <td class="tdr">±4.08</td> + <td class="tdc"></td> + <td class="tdr">±1.84</td> + <td class="tdr">±2.88</td> + </tr> + <tr> + <td></td> + <td class="tdc">I C</td> + <td class="tdr">.596</td> + <td class="tdr">.717</td> + <td class="tdc">R</td> + <td class="tdr">91.06</td> + <td class="tdr">107.82</td> + <td class="tdc">R</td> + <td class="tdr">27.85</td> + <td class="tdr">10.35</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.10</td> + <td class="tdr">±.08</td> + <td class="tdc"></td> + <td class="tdr">±4.20</td> + <td class="tdr">±1.69</td> + <td class="tdc"></td> + <td class="tdr">±2.97</td> + <td class="tdr">±1.20</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc">C</td> + <td class="tdr">101.45</td> + <td class="tdr">108.12</td> + <td class="tdc">C</td> + <td class="tdr">21.53</td> + <td class="tdr">17.75</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc"></td> + <td class="tdr">±3.25</td> + <td class="tdr">±2.90</td> + <td class="tdc"></td> + <td class="tdr">±2.30</td> + <td class="tdr">±2.05</td> + </tr> + <tr class="bb"> + <td class="tdr"><i>N</i> =</td> + <td class="tdc"></td> + <td class="tdr">20</td> + <td class="tdr">17</td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td>V</td> + <td class="tdc">I V</td> + <td class="tdr">.887</td> + <td class="tdr">.822</td> + <td class="tdc">I</td> + <td class="tdr">101.64</td> + <td class="tdr">99.42</td> + <td class="tdc">I</td> + <td class="tdr">24.76</td> + <td class="tdr">17.63</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.04</td> + <td class="tdr">±.05</td> + <td class="tdc"></td> + <td class="tdr">±3.56</td> + <td class="tdr">±2.73</td> + <td class="tdc"></td> + <td class="tdr">±2.52</td> + <td class="tdr">±1.93</td> + </tr> + <tr> + <td></td> + <td class="tdc">I R</td> + <td class="tdr">.799</td> + <td class="tdr">.832</td> + <td class="tdc">V</td> + <td class="tdr">100.59</td> + <td class="tdr">111.58</td> + <td class="tdc">V</td> + <td class="tdr">26.71</td> + <td class="tdr">19.78</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.05</td> + <td class="tdr">±.05</td> + <td class="tdc"></td> + <td class="tdr">±3.84</td> + <td class="tdr">±3.06</td> + <td class="tdc"></td> + <td class="tdr">±2.72</td> + <td class="tdr">±2.16</td> + </tr> + <tr> + <td></td> + <td class="tdc">I C</td> + <td class="tdr">.818</td> + <td class="tdr">.890</td> + <td class="tdc">R</td> + <td class="tdr">94.59</td> + <td class="tdr">101.42</td> + <td class="tdc">R</td> + <td class="tdr">22.10</td> + <td class="tdr">12.56</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.05</td> + <td class="tdr">±.03</td> + <td class="tdc"></td> + <td class="tdr">±3.18</td> + <td class="tdr">±1.94</td> + <td class="tdc"></td> + <td class="tdr">±2.25</td> + <td class="tdr">±1.37</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc">C</td> + <td class="tdr">97.00</td> + <td class="tdr">102.68</td> + <td class="tdc">C</td> + <td class="tdr">22.52</td> + <td class="tdr">17.71</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc"></td> + <td class="tdr">±3.24</td> + <td class="tdr">±2.74</td> + <td class="tdc"></td> + <td class="tdr">±2.29</td> + <td class="tdr">±1.94</td> + </tr> + <tr class="bb"> + <td class="tdr"><i>N</i> =</td> + <td class="tdc"></td> + <td class="tdr">22</td> + <td class="tdr">19</td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td>VI</td> + <td class="tdc">I V</td> + <td class="tdr">.793</td> + <td class="tdr">.772</td> + <td class="tdc">I</td> + <td class="tdr">109.90</td> + <td class="tdr">115.90</td> + <td class="tdc">I</td> + <td class="tdr">23.45</td> + <td class="tdr">24.38</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.08</td> + <td class="tdr">±.09</td> + <td class="tdc"></td> + <td class="tdr">±5.00</td> + <td class="tdr">±5.20</td> + <td class="tdc"></td> + <td class="tdr">±3.54</td> + <td class="tdr">±3.68</td> + </tr> + <tr> + <td></td> + <td class="tdc">I R</td> + <td class="tdr">.497</td> + <td class="tdr">.726</td> + <td class="tdc">V</td> + <td class="tdr">108.00</td> + <td class="tdr">126.80</td> + <td class="tdc">V</td> + <td class="tdr">30.20</td> + <td class="tdr">25.25</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.16</td> + <td class="tdr">±.10</td> + <td class="tdc"></td> + <td class="tdr">±6.44</td> + <td class="tdr">±5.39</td> + <td class="tdc"></td> + <td class="tdr">±4.55</td> + <td class="tdr">±3.81</td> + </tr> + <tr> + <td></td> + <td class="tdc">I C</td> + <td class="tdr">.798</td> + <td class="tdr">.891</td> + <td class="tdc">R</td> + <td class="tdr">103.10</td> + <td class="tdr">107.20</td> + <td class="tdc">R</td> + <td class="tdr">13.77</td> + <td class="tdr">20.62</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.08</td> + <td class="tdr">±.04</td> + <td class="tdc"></td> + <td class="tdr">±2.94</td> + <td class="tdr">±4.40</td> + <td class="tdc"></td> + <td class="tdr">±2.08</td> + <td class="tdr">±3.11</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc">C</td> + <td class="tdr">108.90</td> + <td class="tdr">117.10</td> + <td class="tdc">C</td> + <td class="tdr">15.23</td> + <td class="tdr">18.81</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc"></td> + <td class="tdr">±3.25</td> + <td class="tdr">±4.01</td> + <td class="tdc"></td> + <td class="tdr">±2.30</td> + <td class="tdr">±2.84</td> + </tr> + <tr class="bb"> + <td class="tdr"><i>N</i> =</td> + <td class="tdc"></td> + <td class="tdr">10</td> + <td class="tdr">10</td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td>VII and VIII</td> + <td class="tdc">I V</td> + <td class="tdr">.625</td> + <td class="tdr">.504</td> + <td class="tdc">I</td> + <td class="tdr">99.29</td> + <td class="tdr">98.92</td> + <td class="tdc">I</td> + <td class="tdr">11.11</td> + <td class="tdr">11.45</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.11</td> + <td class="tdr">±.14</td> + <td class="tdc"></td> + <td class="tdr">±2.00</td> + <td class="tdr">±2.14</td> + <td class="tdc"></td> + <td class="tdr">±1.42</td> + <td class="tdr">±1.51</td> + </tr> + <tr> + <td></td> + <td class="tdc">I R</td> + <td class="tdr">.622</td> + <td class="tdr">.709</td> + <td class="tdc">V</td> + <td class="tdr">109.43</td> + <td class="tdr">115.23</td> + <td class="tdc">V</td> + <td class="tdr">14.07</td> + <td class="tdr">17.43</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.11</td> + <td class="tdr">±.09</td> + <td class="tdc"></td> + <td class="tdr">±2.54</td> + <td class="tdr">±2.95</td> + <td class="tdc"></td> + <td class="tdr">±1.79</td> + <td class="tdr">±2.31<span class="pagenum" id="Page_27">[27]</span></td> + </tr> + <tr> + <td></td> + <td class="tdc">I C</td> + <td class="tdr">.782</td> + <td class="tdr">.730</td> + <td class="tdc">R</td> + <td class="tdr">97.00</td> + <td class="tdr">98.85</td> + <td class="tdc">R</td> + <td class="tdr">12.59</td> + <td class="tdr">15.77</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.07</td> + <td class="tdr">±.09</td> + <td class="tdc"></td> + <td class="tdr">±2.27</td> + <td class="tdr">±3.26</td> + <td class="tdc"></td> + <td class="tdr">±1.61</td> + <td class="tdr">±2.09</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc">C</td> + <td class="tdr">102.43</td> + <td class="tdr">95.85</td> + <td class="tdc">C</td> + <td class="tdr">13.49</td> + <td class="tdr">17.72</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc"></td> + <td class="tdr">±2.43</td> + <td class="tdr">±3.31</td> + <td class="tdc"></td> + <td class="tdr">±1.72</td> + <td class="tdr">±2.34</td> + </tr> + <tr class="bb"> + <td class="tdr"><i>N</i> =</td> + <td class="tdc"></td> + <td class="tdr">14</td> + <td class="tdr">13</td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td><span class="smcap">Total</span></td> + <td class="tdc">I V</td> + <td class="tdr">.685</td> + <td class="tdr">.680</td> + <td class="tdc">I</td> + <td class="tdr">105.07</td> + <td class="tdr">106.88</td> + <td class="tdc">I</td> + <td class="tdr">19.34</td> + <td class="tdr">18.45</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.04</td> + <td class="tdr">±.04</td> + <td class="tdc"></td> + <td class="tdr">±1.41</td> + <td class="tdr">±1.32</td> + <td class="tdc"></td> + <td class="tdr">±1.00</td> + <td class="tdr">±0.93</td> + </tr> + <tr> + <td></td> + <td class="tdc">I R</td> + <td class="tdr">.568</td> + <td class="tdr">.626</td> + <td class="tdc">V</td> + <td class="tdr">101.12</td> + <td class="tdr">112.67</td> + <td class="tdc">V</td> + <td class="tdr">22.83</td> + <td class="tdr">21.58</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.05</td> + <td class="tdr">±.04</td> + <td class="tdc"></td> + <td class="tdr">±1.67</td> + <td class="tdr">±1.54</td> + <td class="tdc"></td> + <td class="tdr">±1.18</td> + <td class="tdr">±1.09</td> + </tr> + <tr> + <td></td> + <td class="tdc">I C</td> + <td class="tdr">.639</td> + <td class="tdr">.702</td> + <td class="tdc">R</td> + <td class="tdr">92.40</td> + <td class="tdr">102.91</td> + <td class="tdc">R</td> + <td class="tdr">22.65</td> + <td class="tdr">15.27</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.04</td> + <td class="tdr">±.04</td> + <td class="tdc"></td> + <td class="tdr">±1.66</td> + <td class="tdr">±1.09</td> + <td class="tdc"></td> + <td class="tdr">±1.17</td> + <td class="tdr">±0.77</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc">C</td> + <td class="tdr">98.08</td> + <td class="tdr">106.27</td> + <td class="tdc">C</td> + <td class="tdr">21.48</td> + <td class="tdr">18.19</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc"></td> + <td class="tdr">±1.57</td> + <td class="tdr">±1.30</td> + <td class="tdc"></td> + <td class="tdr">±1.11</td> + <td class="tdr">±0.92</td> + </tr> + <tr class="bb"> + <td class="tdr"><i>N</i> =</td> + <td class="tdc"></td> + <td class="tdr">85</td> + <td class="tdr">89</td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> +</table> + +<h4 id="table8">TABLE 8<br> +<span class="smcap">All Correlations, Means, and Standard Deviations of Quotients by +Grade, Showing Progress from November, 1919 to June, 1920</span></h4> + +<ul> + <li>I stands for Intelligence Quotient</li> + <li>V stands for Vocabulary Quotient</li> + <li>R stands for Reading Quotient</li> + <li>C stands for Completion Quotient</li> + <li>A stands for Arithmetic Quotient</li> +</ul> + +<table> + <tr> + <th rowspan="2"></th> + <th></th> + <th colspan="2"><i>r</i></th> + <th></th> + <th colspan="2">M</th> + <th></th> + <th colspan="2">S.D.</th> + </tr> + <tr> + <th></th> + <th>Nov.</th> + <th>June</th> + <th></th> + <th>Nov.</th> + <th>June</th> + <th></th> + <th>Nov.</th> + <th>June</th> + </tr> + <tr> + <td>III</td> + <td class="tdc">I A</td> + <td class="tdr">.413</td> + <td class="tdr">.709</td> + <td class="tdc">I</td> + <td class="tdr">102.00</td> + <td class="tdr">105.53</td> + <td class="tdc">I</td> + <td class="tdr">9.60</td> + <td class="tdr">10.89</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.16</td> + <td class="tdr">±.08</td> + <td class="tdc"></td> + <td class="tdr">±1.87</td> + <td class="tdr">±1.68</td> + <td class="tdc"></td> + <td class="tdr">±1.32</td> + <td class="tdr">±1.19</td> + </tr> + <tr> + <td></td> + <td class="tdc">I V</td> + <td class="tdr">.649</td> + <td class="tdr">.667</td> + <td class="tdc">A</td> + <td class="tdr">82.75</td> + <td class="tdr">97.84</td> + <td class="tdc">A</td> + <td class="tdr">15.88</td> + <td class="tdr">18.62</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.11</td> + <td class="tdr">±.09</td> + <td class="tdc"></td> + <td class="tdr">±3.09</td> + <td class="tdr">±2.88</td> + <td class="tdc"></td> + <td class="tdr">±2.19</td> + <td class="tdr">±2.04</td> + </tr> + <tr> + <td></td> + <td class="tdc">I R</td> + <td class="tdr">.651</td> + <td class="tdr">.609</td> + <td class="tdc">V</td> + <td class="tdr">94.00</td> + <td class="tdr">103.47</td> + <td class="tdc">V</td> + <td class="tdr">33.44</td> + <td class="tdr">27.66</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.11</td> + <td class="tdr">±.10</td> + <td class="tdc"></td> + <td class="tdr">±6.51</td> + <td class="tdr">±4.28</td> + <td class="tdc"></td> + <td class="tdr">±4.60</td> + <td class="tdr">±3.03<span class="pagenum" id="Page_28">[28]</span></td> + </tr> + <tr> + <td></td> + <td class="tdc">I C</td> + <td class="tdr">.612</td> + <td class="tdr">.719</td> + <td class="tdc">R</td> + <td class="tdr">87.59</td> + <td class="tdr">93.88</td> + <td class="tdc">R</td> + <td class="tdr">32.06</td> + <td class="tdr">19.02</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.12</td> + <td class="tdr">±.07</td> + <td class="tdc"></td> + <td class="tdr">±6.24</td> + <td class="tdr">±3.21</td> + <td class="tdc"></td> + <td class="tdr">±4.41</td> + <td class="tdr">±2.27</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc">C</td> + <td class="tdr">90.17</td> + <td class="tdr">96.84</td> + <td class="tdc">C</td> + <td class="tdr">28.82</td> + <td class="tdr">25.59</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc"></td> + <td class="tdr">±5.58</td> + <td class="tdr">±3.96</td> + <td class="tdc"></td> + <td class="tdr">±3.95</td> + <td class="tdr">±2.80</td> + </tr> + <tr class="bb"> + <td class="tdr"><i>N</i> =</td> + <td class="tdc"></td> + <td class="tdr">12</td> + <td class="tdr">19</td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td>IV</td> + <td class="tdc">I A</td> + <td class="tdr">.426</td> + <td class="tdr">.725</td> + <td class="tdc">I</td> + <td class="tdr">111.48</td> + <td class="tdr">113.00</td> + <td class="tdc">I</td> + <td class="tdr">14.73</td> + <td class="tdr">15.04</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.10</td> + <td class="tdr">±.06</td> + <td class="tdc"></td> + <td class="tdr">±1.85</td> + <td class="tdr">±1.93</td> + <td class="tdc"></td> + <td class="tdr">±1.30</td> + <td class="tdr">±1.36</td> + </tr> + <tr> + <td></td> + <td class="tdc">I V</td> + <td class="tdr">.635</td> + <td class="tdr">.772</td> + <td class="tdc">A</td> + <td class="tdr">94.07</td> + <td class="tdr">111.08</td> + <td class="tdc">A</td> + <td class="tdr">12.34</td> + <td class="tdr">15.02</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.075</td> + <td class="tdr">±.05</td> + <td class="tdc"></td> + <td class="tdr">±1.55</td> + <td class="tdr">±1.99</td> + <td class="tdc"></td> + <td class="tdr">±1.09</td> + <td class="tdr">±1.40</td> + </tr> + <tr> + <td></td> + <td class="tdc">I R</td> + <td class="tdr">.316</td> + <td class="tdr">.569</td> + <td class="tdc">V</td> + <td class="tdr">109.79</td> + <td class="tdr">115.61</td> + <td class="tdc">V</td> + <td class="tdr">16.97</td> + <td class="tdr">18.39</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.11</td> + <td class="tdr">±.09</td> + <td class="tdc"></td> + <td class="tdr">±2.13</td> + <td class="tdr">±2.34</td> + <td class="tdc"></td> + <td class="tdr">±1.50</td> + <td class="tdr">±1.66</td> + </tr> + <tr> + <td></td> + <td class="tdc">I C</td> + <td class="tdr">.594</td> + <td class="tdr">.837</td> + <td class="tdc">R</td> + <td class="tdr">99.31</td> + <td class="tdr">110.11</td> + <td class="tdc">R</td> + <td class="tdr">17.89</td> + <td class="tdr">14.67</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.08</td> + <td class="tdr">±.04</td> + <td class="tdc"></td> + <td class="tdr">±3.24</td> + <td class="tdr">±1.67</td> + <td class="tdc"></td> + <td class="tdr">±1.58</td> + <td class="tdr">±1.32</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc">C</td> + <td class="tdr">108.14</td> + <td class="tdr">118.14</td> + <td class="tdc">C</td> + <td class="tdr">15.51</td> + <td class="tdr">12.70</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc"></td> + <td class="tdr">±1.94</td> + <td class="tdr">±1.62</td> + <td class="tdc"></td> + <td class="tdr">±1.37</td> + <td class="tdr">±1.15</td> + </tr> + <tr class="bb"> + <td class="tdr"><i>N</i> =</td> + <td class="tdc"></td> + <td class="tdr">29</td> + <td class="tdr">28</td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td>V</td> + <td class="tdc">I A</td> + <td class="tdr">.698</td> + <td class="tdr">.713</td> + <td class="tdc">I</td> + <td class="tdr">103.72</td> + <td class="tdr">98.83</td> + <td class="tdc">I</td> + <td class="tdr">19.57</td> + <td class="tdr">18.84</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.07</td> + <td class="tdr">±.07</td> + <td class="tdc"></td> + <td class="tdr">±2.69</td> + <td class="tdr">±2.65</td> + <td class="tdc"></td> + <td class="tdr">±1.91</td> + <td class="tdr">±1.87</td> + </tr> + <tr> + <td></td> + <td class="tdc">I V</td> + <td class="tdr">.881</td> + <td class="tdr">.908</td> + <td class="tdc">A</td> + <td class="tdr">87.58</td> + <td class="tdr">99.71</td> + <td class="tdc">A</td> + <td class="tdr">12.43</td> + <td class="tdr">16.47</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.03</td> + <td class="tdr">±.02</td> + <td class="tdc"></td> + <td class="tdr">±1.71</td> + <td class="tdr">±2.27</td> + <td class="tdc"></td> + <td class="tdr">±1.21</td> + <td class="tdr">±1.60</td> + </tr> + <tr> + <td></td> + <td class="tdc">I R</td> + <td class="tdr">.773</td> + <td class="tdr">.891</td> + <td class="tdc">V</td> + <td class="tdr">109.00</td> + <td class="tdr">105.17</td> + <td class="tdc">V</td> + <td class="tdr">15.58</td> + <td class="tdr">19.97</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.06</td> + <td class="tdr">±.03</td> + <td class="tdc"></td> + <td class="tdr">±2.14</td> + <td class="tdr">±2.81</td> + <td class="tdc"></td> + <td class="tdr">±1.52</td> + <td class="tdr">±1.99</td> + </tr> + <tr> + <td></td> + <td class="tdc">I C</td> + <td class="tdr">.786</td> + <td class="tdr">.923</td> + <td class="tdc">R</td> + <td class="tdr">104.46</td> + <td class="tdr">103.00</td> + <td class="tdc">R</td> + <td class="tdr">16.99</td> + <td class="tdr">17.07</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.05</td> + <td class="tdr">±.02</td> + <td class="tdc"></td> + <td class="tdr">±2.34</td> + <td class="tdr">±2.40</td> + <td class="tdc"></td> + <td class="tdr">±1.65</td> + <td class="tdr">±1.70</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc">C</td> + <td class="tdr">107.00</td> + <td class="tdr">103.48</td> + <td class="tdc">C</td> + <td class="tdr">16.12</td> + <td class="tdr">14.51</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc"></td> + <td class="tdr">±2.22</td> + <td class="tdr">±2.04</td> + <td class="tdc"></td> + <td class="tdr">±1.57</td> + <td class="tdr">±1.44</td> + </tr> + <tr class="bb"> + <td class="tdr"><i>N</i> =</td> + <td class="tdc"></td> + <td class="tdr">24</td> + <td class="tdr">23</td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td>VI</td> + <td class="tdc">I A</td> + <td class="tdr">.533</td> + <td class="tdr">.805</td> + <td class="tdc">I</td> + <td class="tdr">102.43</td> + <td class="tdr">105.39</td> + <td class="tdc">I</td> + <td class="tdr">11.61</td> + <td class="tdr">13.56</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.13</td> + <td class="tdr">±.06</td> + <td class="tdc"></td> + <td class="tdr">±2.09</td> + <td class="tdr">±2.16</td> + <td class="tdc"></td> + <td class="tdr">±1.48</td> + <td class="tdr">±1.52</td> + </tr> + <tr> + <td></td> + <td class="tdc">I V</td> + <td class="tdr">.774</td> + <td class="tdr">.858</td> + <td class="tdc">A</td> + <td class="tdr">91.43</td> + <td class="tdr">104.53</td> + <td class="tdc">A</td> + <td class="tdr">11.43</td> + <td class="tdr">11.31</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.07</td> + <td class="tdr">±.04</td> + <td class="tdc"></td> + <td class="tdr">±2.06</td> + <td class="tdr">±1.75</td> + <td class="tdc"></td> + <td class="tdr">±1.46</td> + <td class="tdr">±1.24<span class="pagenum" id="Page_29">[29]</span></td> + </tr> + <tr> + <td></td> + <td class="tdc">I R</td> + <td class="tdr">.420</td> + <td class="tdr">.661</td> + <td class="tdc">V</td> + <td class="tdr">106.07</td> + <td class="tdr">112.94</td> + <td class="tdc">V</td> + <td class="tdr">11.93</td> + <td class="tdr">10.94</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.15</td> + <td class="tdr">±.09</td> + <td class="tdc"></td> + <td class="tdr">±2.15</td> + <td class="tdr">±1.74</td> + <td class="tdc"></td> + <td class="tdr">±1.52</td> + <td class="tdr">±1.23</td> + </tr> + <tr> + <td></td> + <td class="tdc">I C</td> + <td class="tdr">.739</td> + <td class="tdr">.620</td> + <td class="tdc">R</td> + <td class="tdr">96.64</td> + <td class="tdr">106.20</td> + <td class="tdc">R</td> + <td class="tdr">12.38</td> + <td class="tdr">11.88</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.08</td> + <td class="tdr">±.10</td> + <td class="tdc"></td> + <td class="tdr">±2.23</td> + <td class="tdr">±1.79</td> + <td class="tdc"></td> + <td class="tdr">±1.58</td> + <td class="tdr">±1.27</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc">C</td> + <td class="tdr">100.36</td> + <td class="tdr">107.61</td> + <td class="tdc">C</td> + <td class="tdr">13.95</td> + <td class="tdr">10.55</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc"></td> + <td class="tdr">±2.51</td> + <td class="tdr">±1.68</td> + <td class="tdc"></td> + <td class="tdr">±1.78</td> + <td class="tdr">±1.19</td> + </tr> + <tr class="bb"> + <td class="tdr"><i>N</i> =</td> + <td class="tdc"></td> + <td class="tdr">14</td> + <td class="tdr">18</td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td>VII</td> + <td class="tdc">I A</td> + <td class="tdr">.740</td> + <td class="tdr">.795</td> + <td class="tdc">I</td> + <td class="tdr">107.27</td> + <td class="tdr">100.58</td> + <td class="tdc">I</td> + <td class="tdr">23.29</td> + <td class="tdr">19.78</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.09</td> + <td class="tdr">±.07</td> + <td class="tdc"></td> + <td class="tdr">±4.74</td> + <td class="tdr">±2.85</td> + <td class="tdc"></td> + <td class="tdr">±3.35</td> + <td class="tdr">±2.72</td> + </tr> + <tr> + <td></td> + <td class="tdc">I V</td> + <td class="tdr">.867</td> + <td class="tdr">.718</td> + <td class="tdc">A</td> + <td class="tdr">100.00</td> + <td class="tdr">99.31</td> + <td class="tdc">A</td> + <td class="tdr">9.26</td> + <td class="tdr">11.00</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.05</td> + <td class="tdr">±.09</td> + <td class="tdc"></td> + <td class="tdr">±1.86</td> + <td class="tdr">±2.06</td> + <td class="tdc"></td> + <td class="tdr">±1.33</td> + <td class="tdr">±1.45</td> + </tr> + <tr> + <td></td> + <td class="tdc">I R</td> + <td class="tdr">.862</td> + <td class="tdr">.799</td> + <td class="tdc">V</td> + <td class="tdr">114.36</td> + <td class="tdr">108.75</td> + <td class="tdc">V</td> + <td class="tdr">19.15</td> + <td class="tdr">14.42</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.05</td> + <td class="tdr">±.07</td> + <td class="tdc"></td> + <td class="tdr">±3.89</td> + <td class="tdr">±2.81</td> + <td class="tdc"></td> + <td class="tdr">±2.75</td> + <td class="tdr">±1.98</td> + </tr> + <tr> + <td></td> + <td class="tdc">I C</td> + <td class="tdr">.833</td> + <td class="tdr">.677</td> + <td class="tdc">R</td> + <td class="tdr">101.73</td> + <td class="tdr">98.58</td> + <td class="tdc">R</td> + <td class="tdr">12.28</td> + <td class="tdr">11.56</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.06</td> + <td class="tdr">±.11</td> + <td class="tdc"></td> + <td class="tdr">±2.50</td> + <td class="tdr">±2.25</td> + <td class="tdc"></td> + <td class="tdr">±1.77</td> + <td class="tdr">±1.59</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc">C</td> + <td class="tdr">105.82</td> + <td class="tdr">101.42</td> + <td class="tdc">C</td> + <td class="tdr">17.41</td> + <td class="tdr">16.02</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc"></td> + <td class="tdr">±3.54</td> + <td class="tdr">±3.12</td> + <td class="tdc"></td> + <td class="tdr">±2.50</td> + <td class="tdr">±2.21</td> + </tr> + <tr class="bb"> + <td class="tdr"><i>N</i> =</td> + <td class="tdc"></td> + <td class="tdr">11</td> + <td class="tdr">12</td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td>VIII</td> + <td class="tdc">I A</td> + <td class="tdr">.663</td> + <td class="tdr">.796</td> + <td class="tdc">I</td> + <td class="tdr">104.83</td> + <td class="tdr">108.79</td> + <td class="tdc">I</td> + <td class="tdr">15.46</td> + <td class="tdr">18.25</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.11</td> + <td class="tdr">±.07</td> + <td class="tdc"></td> + <td class="tdr">±3.01</td> + <td class="tdr">±3.29</td> + <td class="tdc"></td> + <td class="tdr">±2.13</td> + <td class="tdr">±2.33</td> + </tr> + <tr> + <td></td> + <td class="tdc">I V</td> + <td class="tdr">.828</td> + <td class="tdr">.750</td> + <td class="tdc">A</td> + <td class="tdr">92.92</td> + <td class="tdr">93.86</td> + <td class="tdc">A</td> + <td class="tdr">10.20</td> + <td class="tdr">9.74</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.06</td> + <td class="tdr">±.08</td> + <td class="tdc"></td> + <td class="tdr">±1.99</td> + <td class="tdr">±1.76</td> + <td class="tdc"></td> + <td class="tdr">±1.40</td> + <td class="tdr">±1.24</td> + </tr> + <tr> + <td></td> + <td class="tdc">I R</td> + <td class="tdr">.775</td> + <td class="tdr">.722</td> + <td class="tdc">V</td> + <td class="tdr">111.67</td> + <td class="tdr">117.21</td> + <td class="tdc">V</td> + <td class="tdr">16.44</td> + <td class="tdr">14.02</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.08</td> + <td class="tdr">±.08</td> + <td class="tdc"></td> + <td class="tdr">±3.20</td> + <td class="tdr">±2.53</td> + <td class="tdc"></td> + <td class="tdr">±2.26</td> + <td class="tdr">±1.79</td> + </tr> + <tr> + <td></td> + <td class="tdc">I C</td> + <td class="tdr">.838</td> + <td class="tdr">.868</td> + <td class="tdc">R</td> + <td class="tdr">100.83</td> + <td class="tdr">104.38</td> + <td class="tdc">R</td> + <td class="tdr">11.52</td> + <td class="tdr">20.62</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.06</td> + <td class="tdr">±.04</td> + <td class="tdc"></td> + <td class="tdr">±2.24</td> + <td class="tdr">±3.72</td> + <td class="tdc"></td> + <td class="tdr">±1.59</td> + <td class="tdr">±2.63</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc">C</td> + <td class="tdr">104.92</td> + <td class="tdr">109.64</td> + <td class="tdc">C</td> + <td class="tdr">18.11</td> + <td class="tdr">17.41</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc"></td> + <td class="tdr">±3.53</td> + <td class="tdr">±3.14</td> + <td class="tdc"></td> + <td class="tdr">±2.49</td> + <td class="tdr">±2.22</td> + </tr> + <tr class="bb"> + <td class="tdr"><i>N</i> =</td> + <td class="tdc"></td> + <td class="tdr">12</td> + <td class="tdr">14</td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"><span class="pagenum" id="Page_30">[30]</span></td> + </tr> + <tr> + <td><span class="smcap">Total</span></td> + <td class="tdc">I A</td> + <td class="tdr">.576</td> + <td class="tdr">.686</td> + <td class="tdc">I</td> + <td class="tdr">106.02</td> + <td class="tdr">105.87</td> + <td class="tdc">I</td> + <td class="tdr">16.73</td> + <td class="tdr">16.87</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.05</td> + <td class="tdr">±.03</td> + <td class="tdc"></td> + <td class="tdr">±1.12</td> + <td class="tdr">±1.07</td> + <td class="tdc"></td> + <td class="tdr">±0.79</td> + <td class="tdr">±0.75</td> + </tr> + <tr> + <td></td> + <td class="tdc">I V</td> + <td class="tdr">.679</td> + <td class="tdr">.727</td> + <td class="tdc">A</td> + <td class="tdr">91.35</td> + <td class="tdr">102.01</td> + <td class="tdc">A</td> + <td class="tdr">13.22</td> + <td class="tdr">15.61</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.04</td> + <td class="tdr">±.03</td> + <td class="tdc"></td> + <td class="tdr">±0.88</td> + <td class="tdr">±0.98</td> + <td class="tdc"></td> + <td class="tdr">±0.62</td> + <td class="tdr">±0.69</td> + </tr> + <tr> + <td></td> + <td class="tdc">I R</td> + <td class="tdr">.529</td> + <td class="tdr">.609</td> + <td class="tdc">V</td> + <td class="tdr">107.95</td> + <td class="tdr">110.54</td> + <td class="tdc">V</td> + <td class="tdr">19.76</td> + <td class="tdr">19.57</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.05</td> + <td class="tdr">±.04</td> + <td class="tdc"></td> + <td class="tdr">±1.32</td> + <td class="tdr">±1.24</td> + <td class="tdc"></td> + <td class="tdr">±0.93</td> + <td class="tdr">±0.87</td> + </tr> + <tr> + <td></td> + <td class="tdc">I C</td> + <td class="tdr">.678</td> + <td class="tdr">.731</td> + <td class="tdc">R</td> + <td class="tdr">99.22</td> + <td class="tdr">103.65</td> + <td class="tdc">R</td> + <td class="tdr">18.85</td> + <td class="tdr">17.12</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr">±.04</td> + <td class="tdr">±.03</td> + <td class="tdc"></td> + <td class="tdr">±1.26</td> + <td class="tdr">±1.08</td> + <td class="tdc"></td> + <td class="tdr">±0.89</td> + <td class="tdr">±0.76</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc">C</td> + <td class="tdr">104.06</td> + <td class="tdr">108.00</td> + <td class="tdc">C</td> + <td class="tdr">18.87</td> + <td class="tdr">18.11</td> + </tr> + <tr> + <td></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc"></td> + <td class="tdr">±1.26</td> + <td class="tdr">±1.14</td> + <td class="tdc"></td> + <td class="tdr">±0.89</td> + <td class="tdr">±0.81</td> + </tr> + <tr class="bb"> + <td class="tdr"><i>N</i> =</td> + <td class="tdc"></td> + <td class="tdr">102</td> + <td class="tdr">114</td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdc"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> +</table> + +<p class="note"><span class="smcap">Note</span>—Totals without Grade III are much higher than these (<a href="#table5">Table 5</a>). +Grade III has many children in it who have not been long enough in an +academic situation to allow their SQ’s to go as high as they may.</p> + +<p>It is proper to note here that not much can be expected from +Grades III and VIII and from totals including Grade III, since +children in Grade III have not been there long enough to be pushed, +and children in Grade VIII have been pushed beyond the limits +which the tests used will register. Our logic is one of <i>pushed</i> correlations. +If the association of IQ and the SQ’s is what we are +attempting to establish, it is necessary to show:</p> + +<p>1. That the <i>r</i> comes near unity;</p> + +<p>2. That the central tendencies come near coincidence;</p> + +<p>3. That the S.D.’s come near coincidence.</p> + +<p>The value of the <i>r</i> is obvious; the value of coincidence of means +becomes clearer if we think of Σ(IQ-EQ)/<i>n</i>, the average difference +of potential rate of progress and actual rate of progress. This +average of differences is the same as the difference of the averages, +which is more readily calculated. Obviously, if we wish to use +an AccR, it is necessary to show more than correspondence when +<span class="pagenum" id="Page_31">[31]</span>differences in average and spread are equated as they are by the +correlation coefficient. Besides, coincidence of M’s, correspondence +of S.D.’s is also necessary since a correlation might be positive +unity, the M’s might be equal, and still the spread of one measure +might be more than the spread of the other. If the spreads are the +same and the M’s are the same, and the correlation is positive +unity, each <i>x</i> must equal its corresponding <i>y</i>. Then <i>b</i>₁₂ = <i>b</i>₂₁ = 1.00; +and the M’s being equal, the deviations are from the same point. +Therefore, we will attempt to measure similarity of M’s and +S.D.’s as well as <i>r</i>.</p> + +<p>It will be observed that both Tables <a href="#table7">7</a> and <a href="#table8">8</a> give evidence of +each of these tendencies in all grades. In <a href="#table8">Table 8</a> marked progress +in arithmetic is apparent. This is due to re-classification in terms +of the Woody-McCall test, which was not done in 1918-1919. +In 1918-1919 no arithmetic test was given and all re-classification +was in terms of reading, being done on the basis of both reading +tests. Spelling re-classification was done each year, but the data +were not treated in this manner. It can be said that wherever +re-classification in terms of intelligence and pedagogical need was +undertaken the desired result of pushing the SQ’s up to IQ was +hastened. Of all the remedial procedure, such as changing teachers +and time allotment and books and method, all of which were +employed to some extent, it is my opinion that the re-classification +was more important than everything else combined.</p> + +<p>It is noticeable that when <i>r</i>’s approach the limit which the +unreliability of the test allows them, they drop down again. This +is probably due to continued increase of SQ’s over IQ. Of course, +for some SQ’s to be greater than IQ out of proportion to the +general amount lowers the correlation as much as for some to lag +behind. When the SQ’s of the children of lower intelligence +reach their IQ they continue above. This, of course, is due to +errors in establishment of the age norms. The norms are not +limits of pushing, though an attempt was made by correction for +truncation to get them as nearly so as possible. It is to be noted, +however, that these norms are up the growth curve, that is, reading +age of 10 means a score such that the average age of those getting +it is 10, not the average score of children whose mental age is 10. +The average reading achievement of children all ten years old +chronologically is <i>higher</i> than that of a group all mentally ten, +since many of the mentally advanced have not been pushed in +<span class="pagenum" id="Page_32">[32]</span>product. The group used here to establish norms gives more nearly +pushed norms than the others would.</p> + +<p>The tendency of the low IQ’s to go over unity in their SR’s is +apparent in <a href="#table1">Table 1</a> and in <a href="#table12">Table 12</a> and also in the negative correlation +between AccR and IQ.</p> + +<p>In both years some second grade children were advanced to +Grade III during the year. This accounts for the low <i>r</i>’s in June, +1919, but in 1919-1920 the Grade III correlations are raised and +the means raised toward the M<sub>IQ</sub>, even though some second grade +children were put in this group during the year.</p> + +<h4 id="table9">TABLE 9<br> +<span class="smcap">Summary of Progress in Arithmetic by Increase in</span> <i>r</i>, <span class="smcap">Decrease in M<sub>IQ</sub>-M<sub>AQ</sub> +and Decrease in Difference of Standard Deviations +Irrespective of Direction</span></h4> + +<table> + <tr> + <th>GRADE</th> + <th colspan="2"><i>r</i></th> + <th colspan="2">Average Intelligence<br>Quotient Minus<br>Average Arithmetic<br>Quotient</th> + <th colspan="2">Difference of<br>Standard Deviations<br>Irrespective of<br>Sign (of IQ and Arith. Q)</th> + </tr> + <tr> + <th></th> + <th>Nov.</th> + <th>June</th> + <th>Nov.</th> + <th>June</th> + <th>Nov.</th> + <th>June</th> + </tr> + <tr> + <td>III</td> + <td class="tdr">.413</td> + <td class="tdr">.709</td> + <td class="tdr">19.25</td> + <td class="tdr">8.16</td> + <td class="tdr">6.27</td> + <td class="tdr">6.63</td> + </tr> + <tr> + <td></td> + <td>±.16</td> + <td class="tdr">±.08</td> + <td class="tdr">±2.87</td> + <td class="tdr">±2.05</td> + <td class="tdr">±2.04</td> + <td class="tdr">±1.45</td> + </tr> + <tr> + <td>IV</td> + <td class="tdr">.426</td> + <td class="tdr">.725</td> + <td class="tdr">7.41</td> + <td class="tdr">0.46</td> + <td class="tdr">2.39</td> + <td class="tdr">0.47</td> + </tr> + <tr> + <td></td> + <td>±.10</td> + <td class="tdr">±.06</td> + <td class="tdr">±1.84</td> + <td class="tdr">±1.50</td> + <td class="tdr">±1.29</td> + <td class="tdr">±1.02</td> + </tr> + <tr> + <td>V</td> + <td class="tdr">.698</td> + <td class="tdr">.713</td> + <td class="tdr">16.14</td> + <td class="tdr">0.54</td> + <td class="tdr">7.14</td> + <td class="tdr">2.06</td> + </tr> + <tr> + <td></td> + <td>±.07</td> + <td class="tdr">±.07</td> + <td class="tdr">±1.93</td> + <td class="tdr">±1.84</td> + <td class="tdr">±1.37</td> + <td class="tdr">±1.30</td> + </tr> + <tr> + <td>VI</td> + <td class="tdr">5.33</td> + <td class="tdr">.805</td> + <td class="tdr">11.00</td> + <td class="tdr">3.00</td> + <td class="tdr">0.19</td> + <td class="tdr">1.63</td> + </tr> + <tr> + <td></td> + <td>±.13</td> + <td class="tdr">±.06</td> + <td class="tdr">±2.01</td> + <td class="tdr">±1.19</td> + <td class="tdr">±1.42</td> + <td class="tdr">±0.85</td> + </tr> + <tr> + <td>VII</td> + <td class="tdr">.740</td> + <td class="tdr">.795</td> + <td class="tdr">7.27</td> + <td class="tdr">0.62</td> + <td class="tdr">14.03</td> + <td class="tdr">8.15</td> + </tr> + <tr> + <td></td> + <td>±.09</td> + <td class="tdr">±.07</td> + <td class="tdr">±3.58</td> + <td class="tdr">±2.33</td> + <td class="tdr">±2.53</td> + <td class="tdr">±1.63</td> + </tr> + <tr> + <td>VIII</td> + <td class="tdr">.663</td> + <td class="tdr">.796</td> + <td class="tdr">11.92</td> + <td class="tdr"><a id="FNanchor_14" href="#Footnote_14" class="fnanchor">[14]</a>⁠14.93</td> + <td class="tdr">5.26</td> + <td class="tdr"><a href="#Footnote_14" class="fnanchor">[14]</a>⁠8.53</td> + </tr> + <tr> + <td></td> + <td>±.11</td> + <td class="tdr">±.07</td> + <td class="tdr">±2.25</td> + <td class="tdr">±2.69</td> + <td class="tdr">±1.59</td> + <td class="tdr">±1.54</td> + </tr> + <tr> + <td>Total</td> + <td class="tdr">.576</td> + <td class="tdr">.686</td> + <td class="tdr">14.67</td> + <td class="tdr">3.72</td> + <td class="tdr">3.51</td> + <td class="tdr">1.16</td> + </tr> + <tr> + <td></td> + <td>±.05</td> + <td class="tdr">±.03</td> + <td class="tdr">±0.94</td> + <td class="tdr">±0.81</td> + <td class="tdr">±0.67</td> + <td class="tdr">±0.57</td> + </tr> +</table> + +<p><span class="pagenum" id="Page_33">[33]</span></p> + +<h4 id="table10">TABLE 10<br> +<span class="smcap">Summary of Progress in Reading, November, 1918 to June, 1919, by Increase +in</span> <i>r</i>, <span class="smcap">Decrease in M<sub>IQ</sub>-M<sub>RQ</sub>, and Decrease in Difference +of Standard Deviations Irrespective of Sign</span></h4> + +<table> + <tr> + <th>GRADE</th> + <th colspan="2"><i>r</i></th> + <th colspan="2">Average Intelligence<br>Quotient Minus<br>Average Reading<br>Quotient</th> + <th colspan="2">Difference of<br>Standard Deviations<br>Irrespective of<br>Sign (of IQ and RQ)</th> + </tr> + <tr> + <th></th> + <th>Nov.</th> + <th>June</th> + <th>Nov.</th> + <th>June</th> + <th>Nov.</th> + <th>June</th> + </tr> + <tr> + <td>III</td> + <td class="tdr">.541</td> + <td class="tdr">.492</td> + <td class="tdr">27.63</td> + <td class="tdr">11.80</td> + <td class="tdr">9.75</td> + <td class="tdr">0.36</td> + </tr> + <tr> + <td></td> + <td>±.11</td> + <td class="tdr">±.09</td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td>IV</td> + <td class="tdr">.665</td> + <td class="tdr">.845</td> + <td class="tdr">14.84</td> + <td class="tdr">-3.00</td> + <td class="tdr">9.77</td> + <td class="tdr">7.86</td> + </tr> + <tr> + <td></td> + <td>±.08</td> + <td class="tdr">±.05</td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td>V</td> + <td class="tdr">.799</td> + <td class="tdr">.832</td> + <td class="tdr">7.05</td> + <td class="tdr">-2.00</td> + <td class="tdr">2.66</td> + <td class="tdr">5.07</td> + </tr> + <tr> + <td></td> + <td>±.05</td> + <td class="tdr">±.05</td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td>VI</td> + <td class="tdr">.497</td> + <td class="tdr">.726</td> + <td class="tdr">6.80</td> + <td class="tdr">8.70</td> + <td class="tdr">9.68</td> + <td class="tdr">3.76</td> + </tr> + <tr> + <td></td> + <td>±.16</td> + <td class="tdr">±.10</td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td>VII</td> + <td class="tdr">.622</td> + <td class="tdr">.709</td> + <td class="tdr">2.28</td> + <td class="tdr">0.07</td> + <td class="tdr">1.48</td> + <td class="tdr">5.98</td> + </tr> + <tr> + <td class="nw">3 of VIII</td> + <td class="tdr">±.11</td> + <td class="tdr">±.09</td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td>Total</td> + <td class="tdr">.568</td> + <td class="tdr">.626</td> + <td class="tdr">12.67</td> + <td class="tdr">3.97</td> + <td class="tdr">3.31</td> + <td class="tdr">3.18</td> + </tr> + <tr> + <td></td> + <td>±.05</td> + <td class="tdr">±.04</td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> +</table> + +<h4 id="table11">TABLE 11<br> +<span class="smcap">Summary of Progress in Reading, November, 1919 to June, 1920, by Increase +in</span> <i>r</i>, <span class="smcap">Decrease in M<sub>IQ</sub>-M<sub>RQ</sub>, and Decrease in Difference +of Standard Deviations Irrespective of Sign</span></h4> + +<table> + <tr> + <th>GRADE</th> + <th colspan="2"><i>r</i></th> + <th colspan="2">Average Intelligence<br>Quotient Minus<br>Average Reading<br>Quotient</th> + <th colspan="2">Difference of<br>Standard Deviations<br>Irrespective of<br>Sign (of IQ and RQ)</th> + </tr> + <tr> + <th></th> + <th>Nov.</th> + <th>June</th> + <th>Nov.</th> + <th>June</th> + <th>Nov.</th> + <th>June</th> + </tr> + <tr> + <td>III</td> + <td class="tdr">.651</td> + <td class="tdr">.609</td> + <td class="tdr">14.41</td> + <td class="tdr">11.57</td> + <td class="tdr">22.46</td> + <td class="tdr">8.62</td> + </tr> + <tr> + <td></td> + <td>±.11</td> + <td class="tdr">±.10</td> + <td class="tdr">±5.22</td> + <td class="tdr">±2.55</td> + <td class="tdr">±3.69</td> + <td class="tdr">±1.81</td> + </tr> + <tr> + <td>IV</td> + <td class="tdr">.316</td> + <td class="tdr">.569</td> + <td class="tdr">12.17</td> + <td class="tdr">2.43</td> + <td class="tdr">3.16</td> + <td class="tdr">0.76</td> + </tr> + <tr> + <td></td> + <td>±.11</td> + <td class="tdr">±.09</td> + <td class="tdr">±2.41</td> + <td class="tdr">±1.78</td> + <td class="tdr">±1.70</td> + <td class="tdr">±1.26</td> + </tr> + <tr> + <td>V</td> + <td class="tdr">.773</td> + <td class="tdr">.891</td> + <td class="tdr">-0.74</td> + <td class="tdr">-4.17</td> + <td class="tdr">2.58</td> + <td class="tdr">1.77</td> + </tr> + <tr> + <td></td> + <td>±.06</td> + <td class="tdr">±.03</td> + <td class="tdr">±1.72</td> + <td class="tdr">±1.20</td> + <td class="tdr">±1.22</td> + <td class="tdr">±0.85</td> + </tr> + <tr> + <td>VI</td> + <td class="tdr">.420</td> + <td class="tdr">.661</td> + <td class="tdr">5.79</td> + <td class="tdr">0.90</td> + <td class="tdr">0.77</td> + <td class="tdr">0.87</td> + </tr> + <tr> + <td></td> + <td>±.15</td> + <td class="tdr">±.09</td> + <td class="tdr">±2.33</td> + <td class="tdr">±1.53</td> + <td class="tdr">±1.65</td> + <td class="tdr">±1.09</td> + </tr> + <tr> + <td>VII</td> + <td class="tdr">.862</td> + <td class="tdr">.799</td> + <td class="tdr">5.54</td> + <td class="tdr">0.92</td> + <td class="tdr">11.00</td> + <td class="tdr">8.31</td> + </tr> + <tr> + <td></td> + <td>±.05</td> + <td class="tdr">±.07</td> + <td class="tdr">±2.88</td> + <td class="tdr">±2.54</td> + <td class="tdr">±2.03</td> + <td class="tdr">±1.80</td> + </tr> + <tr> + <td>VIII</td> + <td class="tdr">.775</td> + <td class="tdr">.722</td> + <td class="tdr">4.00</td> + <td class="tdr">4.43</td> + <td class="tdr">3.94</td> + <td class="tdr">2.41</td> + </tr> + <tr> + <td></td> + <td>±.08</td> + <td class="tdr">±.09</td> + <td class="tdr">±1.90</td> + <td class="tdr">±2.64</td> + <td class="tdr">±1.92</td> + <td class="tdr">±1.87</td> + </tr> + <tr> + <td>Total</td> + <td class="tdr">.529</td> + <td class="tdr">.609</td> + <td class="tdr">6.80</td> + <td class="tdr">2.86</td> + <td class="tdr">2.12</td> + <td class="tdr">0.06</td> + </tr> + <tr> + <td></td> + <td>±.05</td> + <td class="tdr">±.04</td> + <td class="tdr">±1.16</td> + <td class="tdr">±0.30</td> + <td class="tdr">±0.82</td> + <td class="tdr">±0.67</td> + </tr> +</table> + +<p><span class="pagenum" id="Page_34">[34]</span></p> + +<p>The changes in rates of progress are expressed in summaries +by subject matter in Tables <a href="#table9">9</a>, <a href="#table10">10</a>, and <a href="#table11">11</a>. Approach of Arithmetic +Quotient to Intelligence Quotient is measured in <a href="#table9">Table 9</a> by:</p> + +<p>1. Comparison of <i>r</i> in June with <i>r</i> in November.</p> + +<p>2. Comparison of M<sub>IQ</sub>-M<sub>AQ</sub> in June and M<sub>IQ</sub>-M<sub>AQ</sub> in +November.</p> + +<p>3. Comparison of S.D.’s of Arithmetic and Intelligence Quotients +in June and November.</p> + +<p>The P.E.’s of each of these differences were obtained by</p> + +<p class="center">P.E.<sub>diff</sub>² = P.E.₁² + P.E.₂² - 2 <i>r</i>₁₂ P.E.₁ P.E.₂</p> + +<figure class="figcenter illowp100" id="formula1" style="max-width: 34.375em;"> + <img class="w100" src="images/formula1.jpg" alt=""> +</figure> + +<p>The only M<sub>IQ</sub>-M<sub>SQ</sub> in <a href="#table9">Table 9</a> which does not show a decrease +at least two times as large as the P.E. of either of the elements +involved, is the 8th grade; and this is due to the limits of the test +used. As mentioned before, the 8th grade did not register its true +abilities in June since a perfect, or nearly perfect, score in the test +was too easy to obtain. The small arithmetic S.D.’s in Grade 8 +and consequent great S.D.<sub>IQ</sub>-S.D.<sub>SQ</sub> is due to the same cause.</p> + +<p>Tables <a href="#table10">10</a> and <a href="#table11">11</a> present the summary of facts with regard +to Thorndike Reading Quotients, the first and second years respectively.</p> + +<h3>THE RATIOS</h3> + +<p>The discussion which follows concerns <i>Ratios</i>, not <i>Quotients</i>.</p> + +<p><span class="pagenum" id="Page_35">[35]</span></p> + +<h4 id="table12">TABLE 12<br> +<span class="smcap">Intelligence Quotients and Subject Ratios for All Periods Grouped +by Child. The Order of Entries is Just as in <a href="#table1">Table 1</a></span></h4> + +<p class="center"><span class="smcap">Grade III</span></p> + +<table> + <tr> + <th>Intelligence Quotient</th> + <th></th> + <th>Arithmetic Ratio</th> + <th>Vocabulary Ratio</th> + <th>Reading Ratio</th> + <th>Completion Ratio</th> + </tr> + <tr> + <td rowspan="4">101</td> + <td><i>a</i></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td><i>b</i></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td><i>c</i></td> + <td class="tdr">63</td> + <td class="tdr">57</td> + <td class="tdr"></td> + <td class="tdr">43</td> + </tr> + <tr> + <td><i>d</i></td> + <td class="tdr">105</td> + <td class="tdr">87</td> + <td class="tdr"></td> + <td class="tdr">92</td> + </tr> + <tr class="group"> + <td rowspan="4">128</td> + <td><i>a</i></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td><i>b</i></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td><i>c</i></td> + <td class="tdr">62</td> + <td class="tdr">80</td> + <td class="tdr"></td> + <td class="tdr">63</td> + </tr> + <tr> + <td><i>d</i></td> + <td class="tdr"></td> + <td class="tdr">119</td> + <td class="tdr">97</td> + <td class="tdr">120</td> + </tr> + <tr class="group"> + <td rowspan="4">116</td> + <td><i>a</i></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td><i>b</i></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td><i>c</i></td> + <td class="tdr">48</td> + <td class="tdr">78</td> + <td class="tdr">*</td> + <td class="tdr">42</td> + </tr> + <tr> + <td><i>d</i></td> + <td class="tdr">81</td> + <td class="tdr">82</td> + <td class="tdr">66</td> + <td class="tdr">77</td> + </tr> + <tr class="group"> + <td rowspan="4">87</td> + <td><i>a</i></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td><i>b</i></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td><i>c</i></td> + <td class="tdr">103</td> + <td class="tdr">46</td> + <td class="tdr">40</td> + <td class="tdr">62</td> + </tr> + <tr> + <td><i>d</i></td> + <td class="tdr">83</td> + <td class="tdr">85</td> + <td class="tdr">70</td> + <td class="tdr">60</td> + </tr> + <tr class="group"> + <td rowspan="4">112</td> + <td><i>a</i></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td><i>b</i></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td><i>c</i></td> + <td class="tdr">80</td> + <td class="tdr">122</td> + <td class="tdr">119</td> + <td class="tdr">100</td> + </tr> + <tr> + <td><i>d</i></td> + <td class="tdr">100</td> + <td class="tdr">101</td> + <td class="tdr">108</td> + <td class="tdr">117</td> + </tr> + <tr class="group"> + <td rowspan="4">101</td> + <td><i>a</i></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td><i>b</i></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td><i>c</i></td> + <td class="tdr">84</td> + <td class="tdr">93</td> + <td class="tdr">37</td> + <td class="tdr">55</td> + </tr> + <tr> + <td><i>d</i></td> + <td class="tdr">90</td> + <td class="tdr">110</td> + <td class="tdr">98</td> + <td class="tdr">92</td> + </tr> + <tr class="group"> + <td rowspan="4">90</td> + <td><i>a</i></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td><i>b</i></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td><i>c</i></td> + <td class="tdr">76</td> + <td class="tdr">58</td> + <td class="tdr">72</td> + <td class="tdr">89</td> + </tr> + <tr> + <td><i>d</i></td> + <td class="tdr">68</td> + <td class="tdr">121</td> + <td class="tdr">77</td> + <td class="tdr">102</td> + </tr> + <tr class="group"> + <td rowspan="4">105</td> + <td><i>a</i></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td><i>b</i></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr"></td> + </tr> + <tr> + <td><i>c</i></td> + <td class="tdr">60</td> + <td class="tdr">43</td> + <td class="tdr">*</td> + <td class="tdr">57</td> + </tr> + <tr> + <td><i>d</i></td> + <td class="tdr">104</td> + <td class="tdr">95</td> + <td class="tdr">83</td> + <td class="tdr">66</td> + </tr> +</table> + +<p class="note">The remainder of this table is filed in Teachers College Library, Columbia University.</p> + +<p><span class="pagenum" id="Page_36">[36]</span></p> + +<h4 id="table13">TABLE 13</h4> + +<table> + <tr> + <th></th> + <th>Nov., 1918</th> + <th>June, 1919</th> + <th>Nov., 1919</th> + <th>June, 1920</th> + </tr> + <tr> + <th colspan="5"><span class="smcap">Means</span></th> + </tr> + <tr> + <td>Arithmetic Ratio</td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr">89.02</td> + <td class="tdr">97.16</td> + </tr> + <tr> + <td></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr">±1.05</td> + <td class="tdr">±1.07</td> + </tr> + <tr> + <td>Vocabulary Ratio</td> + <td class="tdr">98.96</td> + <td class="tdr">111.44</td> + <td class="tdr">106.20</td> + <td class="tdr">107.61</td> + </tr> + <tr> + <td></td> + <td class="tdr">±1.48</td> + <td class="tdr">±1.61</td> + <td class="tdr">±0.90</td> + <td class="tdr">±0.93</td> + </tr> + <tr> + <td>Reading Ratio</td> + <td class="tdr">96.47</td> + <td class="tdr">101.96</td> + <td class="tdr">98.98</td> + <td class="tdr">100.60</td> + </tr> + <tr> + <td></td> + <td class="tdr">±1.19</td> + <td class="tdr">±1.18</td> + <td class="tdr">±1.03</td> + <td class="tdr">±0.97</td> + </tr> + <tr> + <td>Completion Ratio</td> + <td class="tdr">99.76</td> + <td class="tdr">101.83</td> + <td class="tdr">101.67</td> + <td class="tdr">103.10</td> + </tr> + <tr> + <td></td> + <td class="tdr">±1.11</td> + <td class="tdr">±1.23</td> + <td class="tdr">±0.93</td> + <td class="tdr">±0.85</td> + </tr> + <tr> + <th colspan="5"><span class="smcap">Standard Deviations</span></th> + </tr> + <tr> + <td>Arithmetic Ratio</td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr">12.03</td> + <td class="tdr">12.53</td> + </tr> + <tr> + <td></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr">±0.74</td> + <td class="tdr">±0.76</td> + </tr> + <tr> + <td>Vocabulary Ratio</td> + <td class="tdr">15.71</td> + <td class="tdr">16.58</td> + <td class="tdr">10.34</td> + <td class="tdr">10.84</td> + </tr> + <tr> + <td></td> + <td class="tdr">±1.05</td> + <td class="tdr">±1.14</td> + <td class="tdr">±0.64</td> + <td class="tdr">±0.66</td> + </tr> + <tr> + <td>Reading Ratio</td> + <td class="tdr">12.63</td> + <td class="tdr">12.14</td> + <td class="tdr">11.82</td> + <td class="tdr">11.36</td> + </tr> + <tr> + <td></td> + <td class="tdr">±0.84</td> + <td class="tdr">±0.84</td> + <td class="tdr">±0.73</td> + <td class="tdr">±0.69</td> + </tr> + <tr> + <td>Completion Ratio</td> + <td class="tdr">12.34</td> + <td class="tdr">12.63</td> + <td class="tdr">10.85</td> + <td class="tdr">9.90</td> + </tr> + <tr> + <td></td> + <td class="tdr">±0.82</td> + <td class="tdr">±0.87</td> + <td class="tdr">±0.67</td> + <td class="tdr">±0.60</td> + </tr> + <tr> + <th colspan="5"><span class="smcap">Correlations of Ratios</span></th> + </tr> + <tr> + <td>Arithmetic and Vocabulary</td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr">.60</td> + <td class="tdr">.30</td> + </tr> + <tr> + <td></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr">±.06</td> + <td class="tdr">±.08</td> + </tr> + <tr> + <td>Arithmetic and Reading</td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr">.70</td> + <td class="tdr">.64</td> + </tr> + <tr> + <td></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr">±.04</td> + <td class="tdr">±.05</td> + </tr> + <tr> + <td>Arithmetic and Completion</td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr">.48</td> + <td class="tdr">.61</td> + </tr> + <tr> + <td></td> + <td class="tdr"></td> + <td class="tdr"></td> + <td class="tdr">±.07</td> + <td class="tdr">±.05</td> + </tr> + <tr> + <td>Vocabulary and Reading</td> + <td class="tdr">.34</td> + <td class="tdr">.32</td> + <td class="tdr">.57</td> + <td class="tdr">.47</td> + </tr> + <tr> + <td></td> + <td class="tdr">±.08</td> + <td class="tdr">±.09</td> + <td class="tdr">±.06</td> + <td class="tdr">±.07</td> + </tr> + <tr> + <td>Vocabulary and Completion</td> + <td class="tdr">.45</td> + <td class="tdr">.36</td> + <td class="tdr">.53</td> + <td class="tdr">.54</td> + </tr> + <tr> + <td></td> + <td class="tdr">±.07</td> + <td class="tdr">±.08</td> + <td class="tdr">±.06</td> + <td class="tdr">±.06</td> + </tr> + <tr> + <td>Reading and Completion</td> + <td class="tdr">.61</td> + <td class="tdr">.65</td> + <td class="tdr">.67</td> + <td class="tdr">.67</td> + </tr> + <tr> + <td></td> + <td class="tdr">±.06</td> + <td class="tdr">±.06</td> + <td class="tdr">±.05</td> + <td class="tdr">±.05</td> + </tr> +</table> + +<p><span class="pagenum" id="Page_37">[37]</span></p> + +<p>In <a href="#table12">Table 12</a> are presented the Subject Ratios in the same order +as the Quotients appear in <a href="#table1">Table 1</a>.⁠<a id="FNanchor_15" href="#Footnote_15" class="fnanchor">[15]</a> There plainly is a rapid +rise of SQ/IQ from period to period, excluding all pupils who did +not take all tests and excluding Grade III; which includes all +children taking all tests who were in school in June, 1920, and were +Grade IV and above in November, 1918. The average AccR is +98.24 in November, 1918, and 102.78 in June, 1920. The average +IQ for these children is 105.22. The S.D<sub>AccR₁₉₁₈</sub> is 11.17; +the S.D.<sub>AccR₁₉₂₀</sub> is 9.09; the S.D.<sub>IQ</sub> is 19.24. It is obvious that +the average amount of product per intelligence has increased, +that the range of AccR’s has decreased (which means that factors +causing disparities, other than intelligence, have been removed), +and that the S.D. of the AccR’s is about one half the S.D. of the +IQ’s. M’s are about equal so it is not necessary to use coefficients +of variability. The variability of children, intelligence aside, is +only one half what the variability is otherwise. The correlations +when IQ = <i>X</i>, AccR₁₉₁₈ = <i>Y</i> and AccR₁₉₂₀ = <i>S</i> and when AccR = +average of Vocabulary, Reading and Completion Ratios, are:⁠<a id="FNanchor_16" href="#Footnote_16" class="fnanchor">[16]</a></p> + +<table> + <tr> + <td><i>r</i><sub>X.Y.</sub></td> + <td>=</td> + <td class="tdr">-.602</td> + </tr> + <tr> + <td><i>r</i><sub>X.S.</sub></td> + <td>=</td> + <td class="tdr">-.493</td> + </tr> + <tr> + <td><i>r</i><sub>Y.S.</sub></td> + <td>=</td> + <td class="tdr">+.549</td> + </tr> +</table> + +<p>The remaining disparity is then due to something which is in +negative correlation with intelligence.</p> + +<p>The number of cases here is only 48.</p> + +<p>The P.E.’s are then as follows:</p> + +<table> + <tr> + <td></td> + <td>P.E.<sub>M</sub></td> + <td>P.E.<sub>S.D.</sub></td> + </tr> + <tr> + <td><i>X</i></td> + <td>1.91</td> + <td>1.35</td> + </tr> + <tr> + <td><i>Y</i></td> + <td>1.11</td> + <td>0.79</td> + </tr> + <tr> + <td><i>S</i></td> + <td>0.90</td> + <td>0.64</td> + </tr> + <tr> + <td></td> + <td>P.E.<i>r</i><sub>X.Y.</sub></td> + <td>= .06</td> + </tr> + <tr> + <td></td> + <td>P.E.<i>r</i><sub>X.S.</sub></td> + <td>= .08</td> + </tr> + <tr> + <td></td> + <td>P.E.<i>r</i><sub>Y.S.</sub></td> + <td>= .07</td> + </tr> +</table> + +<p>The differences between the M’s and between the S.D.’s of our +1918 and our 1920 AccQ’s; namely, 102.78 - 98.24 = 4.54 and +11.17 - 9.09 = 2.08, have formed a step in the argument. We must +have the P.E.’s of these amounts in order to establish the reliability +of the quantitative indices we employ:</p> + +<p class="center">P.E.<sub>diff</sub> = √P.E.<sub>X</sub>² + P.E.<sub>Y</sub>² - 2 <i>r</i><sub>XY</sub> P.E.<sub>X</sub> P.E.<sub>Y</sub></p> + +<p class="center">P.E.<sub>M₂₀-M₁₈</sub> = 0.94</p> + +<p class="center">P.E.<sub>S.D.₁₈-S.D.₂₀</sub> = 0.47</p> + +<figure class="figcenter illowp100" id="formula2" style="max-width: 37.5em;"> + <img class="w100" src="images/formula2.jpg" alt=""> +</figure> + +<p><span class="pagenum" id="Page_38">[38]</span></p> + +<p>These differences are then reliable. If the same data were +accumulated again in the same way with only 48 cases, the chances +are even that the 4.54 would be between 3.50 and 5.48 and the 2.08 +between 1.61 and 2.55. That there would be positive differences +is practically certain, since the difference between the means is +over four times as large as its P.E., and the difference between +the S.D.’s over four times as large as its P.E.</p> + +<p>To make still more certain this observation of positive amount +in M of second testing minus M of first testing and in S.D. of +first testing minus S.D. of second testing (AccR), which means +an increase in central tendency of AccR’s and a decrease in spread +of AccR’s under special treatment, we have listed in <a href="#table13">Table 13</a> +the means and standard deviations of Subject Ratios of each +test for each period and the intercorrelations of these Subject +Ratios. These do not include exactly the same children in each +period but are inclusive of all grades for all periods. They are a +measurement of increased efficiency of the school as a whole, +rather than of any one group of children; though, of course, the +bulk of the children have representation in each of these indices. +Too much continuity is not to be expected from June, 1919, to +November, 1919, as the children are different. Comparison should +always be from November to June.</p> + +<p>These tables bear out the fact presented by AccR. It is clear +that there is a marked development in the S.R.’s, both by increase +of M. and decrease of S.D. The decrease of correlation between +S.R.’s is not so marked, but neither is the negative correlation +between AccR and IQ much less in June, 1920, than in November, +1918. The association of achievements in terms of intelligence is +very probably due to mistreatment, since it is in negative correlation +with IQ, as a general inherited ethical factor could not be.</p> + +<p>We will note that the Arithmetic Ratios are in as high positive +association with the Reading Ratios as the Vocabulary Ratios are +with the Reading Ratios. This makes it highly improbable that +the intercorrelation of these remnants is due, to any large extent, +to common elements in the test or to specific abilities. The common +interassociation of all Ratios seems to point to the operation +of some common factor other than intelligence as a determinant +of disparity in school progress. It would be easy to identify this +as the part of Burt’s “General Educational Factor” which is not +intelligence—that is, industry, general perseverance and initiative—were +<span class="pagenum" id="Page_39">[39]</span>it not for the fact that this same influence <i>stands in +negative association to intelligence</i>. It is our belief that it is the +influence of a maladjusted system of curricula and methods which +accounts for these rather high interassociations of achievements, +irrespective of intelligence.</p> + +<h3>SUMMARY</h3> + +<p>The association of abilities in arithmetic, reading, and completion +with intelligence is markedly raised by special treatment. +Disparities of educational product are therefore to a great extent +due to intelligence. (Tables <a href="#table2">2</a>, <a href="#table3">3</a>, +<a href="#table5">5</a>, <a href="#table7">7</a>, <a href="#table8">8</a>, +<a href="#table9">9</a>, <a href="#table10">10</a> and <a href="#table11">11</a>.)</p> + +<p>The remnants (intelligence being rendered constant by division +of each SQ by IQ) intercorrelate about .5. If there were specialized +inherited abilities, these intercorrelations would not all be +positive nor would they be as uniform. (Tables <a href="#table6">6</a> and <a href="#table13">13</a>.)</p> + +<p>The averages of these remnants, for reading, vocabulary, and +completion, correlate -.61 in 1918 and -.49 in 1920 with IQ. +These remnants are in negative association to intelligence. If +the intercorrelations of these remnants were due to a “General +Factor,” this correlation would not be negative.</p> + +<p>Therefore intelligence is far and away the most important +determinant of individual differences in product.</p> + +<p>As part of the relation between tests, irrespective of intelligence, +is due to common elements in the tests, this reasoning becomes +still more probable.</p> + +<p>General factor in education, as distinct from intelligence, has +not been separated here from inherited bases of ambition, concentration, +and industry. It seems out of our province to conjure +up some inherited complex of abilities other than intelligence, +specialized inherited abilities, or proclivities and interests tending +to thorough prosecution of school work. I have therefore meant +this last by the general factor.</p> + +<p>McCall has correlations varying continually in size from -.63 +to +.98 between various measurements of a group of 6B children.⁠<a id="FNanchor_17" href="#Footnote_17" class="fnanchor">[17]</a> +The abilities involved were not pushed as are those considered here. +Some of the low correlations are no doubt indications of low association +because of the way children <i>are</i>, not the way they <i>might be</i> +<span class="pagenum" id="Page_40">[40]</span>by heritage; still others, such as handwriting and cancellation +(unless bright children do badly in cancellation tests because they +are <i>more bored</i> than the others), are correlated low or negatively +with intelligence when the correlation is at its maximum. Such +results as those of McCall serve as a guide not to argue about +other tests by analogy. It is necessary to find which traits and +abilities can be pushed to unity in their relation to intelligence and +which, like handwriting, are practically unrelated to general mental +power.</p> + +<p>It is well to know about music tests and such tests as Stenquist’s +mechanical ability test <i>when the correlation with intelligence +is pushed</i>, before we decide whether the quality measured is a +manifestation of specific talent or general intelligence.</p> + +<p>Cyril Burt obtained data much like that presented here except +that instead of getting rid of the influence of intelligence and finding +determinants for the remnants of disparity, he built up a hierarchy +of coefficients as they would be if they were due entirely to a common +factor and compared these with his obtained <i>r</i>’s. I will present his +conclusions with regard to a general factor which are in substantial +though not complete agreement with those advanced here.</p> + +<blockquote> + +<p class="center">“Evidence of a Single Common Factor.</p> + +<p>“The correlations thus established between the several school +subjects may legitimately be attributed to the presence of common +factors. Thus, the fact that the test of Arithmetic (Problems) +correlates highly with the test of Arithmetic (Rules) is most naturally +explained by assuming that the same ability is common to +both subjects; similarly, the correlation of Composition with Arithmetic +(Problems) may be regarded as evidence of a common factor +underlying this second pair; and so with each of the seventy-eight +pairs. But is the common factor one and the same in each case? +Or have we to recognise a multiplicity of common factors, each +limited to small groups of school subjects?</p> + +<p>“To answer this question a simple criterion may be devised. It is +a matter of simple arithmetic to reconstruct a table of seventy-eight +coefficients so calculated that all the correlations are due to one +factor and one only, common to all subjects, but shared by each in +different degrees. Such a theoretical construction is given in +Table XIX. In this table theoretical values have been calculated +so as to give the best possible fit to the values actually obtained in +<span class="pagenum" id="Page_41">[41]</span>the investigation, and printed in Table XVIII. It will be seen +that the theoretical coefficients exhibit a very characteristic arrangement. +The values diminish progressively from above downwards +and from right to left. Such an arrangement is termed a ‘hierarchy.’ +Its presence forms a rough and useful criterion of the presence of a +single general factor.</p> + +<p>“On turning to the values originally obtained (Table XVIII.) it +will be seen that they do, to some extent, conform to this criterion. +In certain cases, however, the correlations are far too high—for +instance, those between Arithmetic (Rules) and Arithmetic (Problems), +and again Drawing and both Handwork and Writing +(Quality). Now these instances are precisely those where we might +anticipate special factors—general arithmetical ability, general +manual dexterity—operating over and above the universal factor +common to all subjects. These apparent exceptions, therefore, are +not inconsistent with the general rule. Since, then, the chief +deviations from the hierarchical arrangement occur precisely where, +on other grounds, we should expect them to occur, we may accordingly +conclude that performances in all the subjects tested appear +to be determined in varying degrees by a single common factor.</p> + +<p class="center">“Nature of the Common Factor.</p> + +<p>“What, then, is this common factor? The most obvious suggestions +are that it is either (1) General Educational Ability or (2) +General Intelligence. For both these qualities, marks have been +allotted by teachers, quite independently of the results of the tests. +The correlations of these marks with performances in the tests are +given in the last two lines of Table XVIII.</p> + +<p>“Upon certain assumptions, the correlation of each test with the +Hypothetical Common Factor can readily be deduced from the +coefficients originally observed. These estimates are given in the +last line but two of the table. They agree more closely with the +observed correlations for General Educational Ability, especially +if the latter are first corrected for unreliability. (Correlations: +Hypothetical General Factor coefficients and General Educational +Ability coefficients .86; after correction .84. Hypothetical General +Factor coefficients and General Intelligence coefficients .84; after +correction .77.) We may, therefore, identify this hypothetical +general factor with General Educational Ability, and conclude +<span class="pagenum" id="Page_42">[42]</span>provisionally that this capacity more or less determines prowess in +all school subjects.</p> + +<p>“The high agreement of the estimated coefficients with the intelligence +correlations suggest that General Intelligence is an important, +though not the only factor in General Educational Ability. Other +important factors are probably long-distance memory, interest and +industry. It is doubtless not a pure intellectual capacity; and, +though single, is not simple, but complex.”⁠<a id="FNanchor_18" href="#Footnote_18" class="fnanchor">[18]</a></p> + +</blockquote> + +<hr class="chap x-ebookmaker-drop"> + +<div class="chapter"> + +<p><span class="pagenum" id="Page_43">[43]</span></p> + +<h2 class="nobreak" id="PART_III">PART III<br> +THE PSYCHOLOGICAL CONCLUSIONS OF THE EXPERIMENT</h2> + +</div> + +<h3>THE NEGLECT OF GENIUS</h3> + +<p>Schools of to-day are organized and administered so as to yield +less chance to a child to obtain as much information as is possible +for him to have in direct proportion to his mental ability. The +correlation between accomplishment and intelligence (using AccR, +the average of Reading, Vocabulary, and Completion Ratios with +IQ) was -.61 in November, 1918, and -.49 in June, 1920, in the +Garden City public school. The regrading and special promotion +work from November, 1918, to June, 1920, reduced the handicap +of brightness, but could not obliterate the sparsity of returns per +increment of capacity in the upper reaches of the intelligence. +Further, work along this same line done by A. J. Hamilton in the +Washington School, Berkeley, California, indicates that this was +not a peculiarity of the school at Garden City.</p> + +<p>The wide range of abilities which we know exists in pupils of any +one age makes it impossible to adjust our formal education to the +extremes. Much adjustment has been made in favor of the lower +extreme, but little has been done for our genius. Of course the work +with extreme subnormals is conceived and prosecuted more in the +sense of clearing them away for the good of those remaining than +of fitting education to their own needs. We are neglecting, however, +our duty to those whom nature has endowed with the essentials of +leadership. They do not interfere quite as much with ordinary +classroom procedure, but they are greater social assets and need +special treatment to develop <i>them</i> rather than to let others develop +better.</p> + +<p>Neither of the extreme groups is certain of getting the normal +stamina necessary for good citizenship. Neither group forms good +habits of study nor accumulates such information as it might. +Being aware of this discrepancy between the gift and the recipient, +we have made our lessons easier and we have segregated the lower +percentile. There is much more to be done. We must adapt +<span class="pagenum" id="Page_44">[44]</span>education to at least five varying classes in order to reduce the +spread within each to a commodious span. But the genius is the +most important and should have the greatest claim to our immediate +attention.</p> + +<p>First, our social needs demand special attention for the genius +in order that we may better exploit our best nervous resources. +Second, our educational needs demand it since the very bright as +well as the very stupid disrupt calm and cogent classroom procedure. +Third, they themselves demand it in order that they may, even +when they do function as leaders, be happier in that function, since +now they often lose much in social contact by peculiarities which +prevent an integration of their “drives” into a harmonious economy +of tendency. These peculiarities come from their continuous maladjustment, +since when they are with children of their own mental +maturity they are physically and physiologically handicapped; +when they are with children of their own size and muscular equipment +they are so far mentally superior that they are unhappily +adjusted. Only classification on a large scale will allow sufficient +numbers of them to congregate to correct this.</p> + +<p>I am reminded of a boy ten years old whose IQ on the Terman +test was 172. He defined a nerve as the “conduction center of +sensation” and, when asked to explain, did so in terms of sensation +of heat and motive to withdraw. He explained the difference +between misery and poverty thus: “Misery is a lack of the things +we want; poverty is a lack of the things we need.” How can we +expect a boy like this to grow into a normal citizen if we do not +provide the companionship of peers in mentality and in physique?</p> + +<p>Fourth, our eugenic needs demand it, since we are not conserving +this, our chiefest asset, genius. Unless we conserve better these +rare products, the standard deviation of the intelligence of humanity +will keep shrinking as we select against imbeciles and against genius +as well. The waste of a genius who becomes an intellectual dilettante, +as many now in fact do, is double. We lose what he might +do for society; he does not marry and we lose the potentiality of +his highly endowed germ-plasm.</p> + +<p>And they do become dilettantes when special treatment is not +given. I know of a young man who was first of his high-school class, +who got all A’s his first year in College (at Wisconsin), and all +A’s his second year (at Harvard); and then he began to read all +manner of literature with no schema of expression, no vocation, +<span class="pagenum" id="Page_45">[45]</span>because, as he said, all college courses are so stupidly easy. He +attended no lectures and read none of the books in one course, and +then two days before the examination he was taunted with not +being able to pass this course. He spent two nights and two days +studying, and he received B in the course. But now he is a failure +because he has no organized, purposive schema of expression; +he was always in classes with people less fortunately endowed than +he, and so he never had a chance.</p> + +<p>On these four counts then we must segregate our genius: (1) +Social exploitation of our resources. (2) Educational procedure for +the sake of other children as well as for them. (3) Happiness for +them, organization of their trends, and formation of social habits. +(4) Biologic conservation of great positive deviation from average +human intelligence.</p> + +<h3>IS GENIUS SPECIALIZED?</h3> + +<p>This genius is of various kinds, political and business leaders, +scientists and artists. Have they then the same inherited nervous +structure with regard to abilities and capacities as distinct from +interests? We know that they must have something in common, +something that we call intelligence, power of adaptation. Calling +this the nervous chemistry, the way the nervous system acts its +quality, we must still know whether we have also an inherited +nervous physics to deal with, or a further inherited nervous chemistry +which predisposes to specific ability. Are there inherited +capacities or predispositions to ability? We are in a position to +answer this question with regard to the elementary school subjects, +and are tempted here into a more general discussion of the matter +in hand.</p> + +<p>The need to clarify our view on what is inherited and what is due +to environment can be clearly envisaged in terms of our teachers. +Whatever psychologists may mean by “predisposition to ability” +it is quite certain that teachers make no distinction between this +and the inheritance of a capacity. They feel that some children +figure better than they read, and others read better than they +figure, “by nature,” and there their obligation ends. If it is a +grave matter that we shoulder the burden of bringing a child to his +optimum achievement, then it is an immediate duty that we find +how much of the failure to produce product of one kind or another +is due to unremovable factors, and how much is due to our inadequacy. +<span class="pagenum" id="Page_46">[46]</span>So, too, we have much loose discussion about finding +out what children can do and want to do in the way of vocational +diagnosis,—loose because it assumes that children are born with +definite vocational capacities. Certainly we can do much more in +the way of development and much more in the way of preparation +for social needs if we know just how much “predisposition to ability” +means. The teacher interprets it to mean about what was meant +by the turtle that held up Atlas who held up the world. She makes +no real distinction between predisposition to ability and specific +ability, just as there was no real causal distinction between the +turtle and Atlas. She then gets at her conception of intelligence +additively,—a summation of school abilities.</p> + +<p>The correlation of teachers’ judgment of “power of adaptation,” +carefully explained, and marks given six months previously by the +same teachers was .82. The correlation of this same average +judgment with the average of thirteen intelligence tests was only .58. +These teachers obviously reached their conclusions of the intelligence +of a child in the same way as they reached their conclusions of +what marks he earned in their subjects.</p> + +<p>The unit characteristics which make up what we describe in +terms of gross behavior as intelligence must of course be many. +No one denies that if we knew just what these units were we could +describe two possible manifestations of what we now call intelligence, +of which one person could do one only and another person could +do the other only because of the particular combinations of the +units inherited. This would constitute inheritance of predisposition +to special capacities. But it is not the same to assume that the +vocations and aptitudes desirable in a world such as ours have +specialized inherited bases. It is far more probable that substantially +the same inherited characteristics are necessary to success in +all the gross cross-sections of behavior which we call vocations and +abilities.</p> + +<p>As the unit characteristics are certainly not so closely allied to +our social needs as “mechanical intelligence” and “social intelligence” +or even “rote memory for numbers,” we may not even +distinguish presence of any five hundred elements from presence of +any other five hundred elements in terms of what we now measure +as intelligence. It is just as likely that all the elements of intelligence +are necessary for every vocation and that all contribute to success +of any one kind as it is likely that some are necessary for one vocation +and others for another.</p> + +<p><span class="pagenum" id="Page_47">[47]</span></p> + +<p>This is a question of more or less. I believe that the amount to +which a person’s specific talents, his vocation as distinct from his +general power, are shaped by the combinations of elements which +make up his inheritance, is much less than believed by Francis +Galton, who says: “There cannot then remain a doubt but that +the peculiar type of ability that is necessary to a judge is often +transmitted by descent.” And again: “In other words, the combination +of high intellectual gifts, tact in dealing with men, power +of expression in debate, and ability to endure exceedingly hard work, +is hereditary.”⁠<a id="FNanchor_19" href="#Footnote_19" class="fnanchor">[19]</a></p> + +<p>I believe that the amount of influence which inheritance has upon +the <i>kind</i> of thing a man does in life has been overestimated; that +the inherited factors influence more the <i>way</i> in which he shall do +whatever the environment influences him to do. This leaves plenty +of play for the close correlation between parents and children in +both intelligence and vocation. The former is the result of inheritance, +the latter is the result of environment. All competent +psychologists would agree to-day to less specific inheritance than a +basis, for instance, for the distinction in vocation of minister and +orator; and more specific inheritance than for such a statement +as “We inherit how well we will do, we learn what we will do.” +There would be substantial agreement to the statement that the +inherited nervous bases of a very intelligent plumber are more like +those of a very intelligent statesman than like those of a stupid +plumber. This question is, <i>how much</i> inheritance we can conceive +of as being made up of neuro-chemical elements determining us to +do one kind of a thing rather than another.</p> + +<p>Interpretation statistically of one thousand possible elements, +simply viewed as present or absent, and again simply viewed only +as combinations and not permutations, would mean that the less +the intelligence the more specific the inheritance. The most intelligent +man alive could, by what he is born with, do anything since +he has all of the one thousand factors, all of which help him in the +prosecution of any venture. But the fewer elements he has the +less well he does most things, and when lacking certain elements +he has lost the capacity to do some things more completely than +others. (I have neglected physiological characteristics necessary to +an ability. A deaf man certainly is handicapped in music. I speak +<span class="pagenum" id="Page_48">[48]</span>of <i>possible</i> mental capacities.) Such a view leaves scope for some +degree of special abilities. It accounts for the idiot-savants, it +accounts for the cases where genius is diverse as well as where it is +not though it would demand that specialized genius be very rare +and that inherited specialization be much rarer in the upper than +in the lower reaches of intelligence. It allows for such cases as +Galileo, whose father was a composer, as well as the cases cited by +Galton. Heredity need not imply the same kind of genius though +it does suggest it, whereas the environment backs up this inherited +implication. We further can here absolutely resent an inheritance +of such things as ability in the common school subjects without +being involved in a view to deny the inheritance of a predisposition +to mechanical rather than musical successes.</p> + +<p>Observation of brilliant children would corroborate this view. +They can do anything. Observation of the mentally deficient is +equally encouraging to this view. It has always been puzzling that +they seem to do a few things much better than others. According +to this conception there would be a negative correlation between +intelligence and specialized inheritance.</p> + +<p>We will then consider each inherited element, not as music or as +science, but rather as an element of intelligence which will help in +all lines of work, but which may be a little more necessary for +some than others. This is a predisposition in a true sense. If a +man had only one element out of one thousand, he could do only +a few things. If he had all thousand he could do everything. +Inheritance of ability is not in terms of units valuable to us socially, +but only in terms of undefined nervous elements; and we may conceive +of specialization, and still hold that there be less, the more +intelligent a man is.</p> + +<p>To make the matter still more concrete, imagine two men each +of whom have 900 of the hypothetical 1000 elements, this being a +value of +3 S.D. from the mean intelligence of the human race. +One is a composer, the other financier. According to this view the +greatest number of their inherited bases on which they could +differ would be 100 of the 900 elements. The other 800 must be +alike. Assuming that all of the elements contribute to all of the +activities, but that some of them are more essential to some activities +than to others, we could in this case say that the 100 which are +different decided in some measure the vocation of each man. But +it is much more probable that they overlap in 850 and that each +<span class="pagenum" id="Page_49">[49]</span>has only 50 distinct elements, and further that the 50 which are +distinct in each would not all be such as to influence one kind of +ability rather than another. Then these two men, had they interchanged +environments, would probably have interchanged vocations +in that transaction. For the purposes of this discussion we treat +physiological inherited features (such as hearing), as environment, +as we are considering the mental capacity of composer as distinct +from the necessary conditions to its development. According to +this view, then, we account easily for the versatility of genius, which +is so apparent in such accounts as Terman’s <i>The Intelligence of +School Children</i>.⁠<a id="FNanchor_20" href="#Footnote_20" class="fnanchor">[20]</a> Also, though very infrequent, we account for +the genius who could not have done other things as well as those he +did.</p> + +<p>Let us consider the case of negative deviates, say 3 S.D. from +the mean intelligence of the human race. Two men each have 100 +of the 1000 hypothetical elements. It is much more probable here +than not, that an appreciable amount of the 100 elements would +be distinct in each person, though it is improbable that they would +often be such as to form the basis of an “ability.” This then would +account for specific abilities amongst morons and also for the +presence but rarety of idiot-savants. Also since there are a limited +number of such combinations possible and since many overlap for +all practical purposes, we would account for the common likenesses +as well as the relatively more uncommon extreme differences. This +view is consistent with an examination of the data of this thesis +which are contrary to the common belief in special abilities or to +a view of inheritance of units which are actually the goals of +education and the uses of a civilization too recent to leave its +imprint on inheritance. We found no unremovable predispositions +to one school subject more than to the others in any of the children. +We would thus argue that such predispositions as to mathematics +or to oratory are extremely rare and cannot be used as rules by +which to interpret human nature.</p> + +<p>Woodworth says in a criticism of McDougall’s view of instincts: +“What he here overlooks is the fact of native capacities or rather, +the fact that each native capacity is at the same time a drive towards +the sort of activity in question. The native capacity for mathematics +<span class="pagenum" id="Page_50">[50]</span>is, at the same time, an interest in things mathematical and +in dealing with such things. This is clearly true in individuals +gifted with a great capacity for mathematics.”⁠<a id="FNanchor_21" href="#Footnote_21" class="fnanchor">[21]</a></p> + +<p>I do not wish to become involved here in a discussion of the +original nature of man on the instinctive side. I wish merely to +rebel at the assumption of specific inheritance of abilities that are +really sociological units. Mathematics is an ability which is useful +to us, which we have come to encourage in education. But it is a +man-made unit. There is no reason to believe that the inherited +components of mentality are in any direct way related to such +talents as mathematics or music. The units may vaguely predispose, +but the units are not mathematics and music. We may say +that the inherited physical and chemical units of the nervous +system may be so distributed as to predispose one man to mathematics, +and another to music, but we must not argue for inherited +interests as correlates. The evidence is all that the inherited +nervous chemistry of the individual is what on the side of behavior, +we define as intelligence—power of adaptation. We may logically +fall back on the inheritance of predisposition to ability, meaning +thereby the inheritance of such nervous qualities as will better +fit the individual to cope with mathematical than with musical +situations; but if we adopt this cautious ground in disputation we +cannot argue in another matter for an inherited interest in mathematics, +innate because of the inborn mathematical talent. If the +inherited qualities merely predispose they merely delimit; just as +a man born without arms would probably not become a great baseball +player, nor a deaf man a great musician, nor a man with poor +motor control a skilled mechanic—so we are predisposed nervously +for capacities. Hence can we argue that the inborn root of the +interest is the capacity? Is it not safer to assume that interests in +success, approval of fellowmen and general mental activity led to +the development of the capacity by virtue of a favorable environment, +and led by the same environment to interests centered about +its activity?</p> + +<p>It is far from my intention to say that inheritance is not as +specific nervously as it is in matters of blood pressure and texture +of skin. As we, in our limited knowledge, still define abilities in +terms of behaviour and not by nervous elements, my contention is +<span class="pagenum" id="Page_51">[51]</span>that intelligence should be regarded as the sum total of this inheritance, +much as general strength is, in terms of the body. We +have still to find the component units of this intelligence. We can +then define predisposition to ability. To split intelligence into +inherited units of mathematics, reading, composition, mechanics, +etc., is as unjustifiable as to split inherited vigor of body into baseball +capacity, running capacity, climbing capacity, etc. Mathematics +and music are what we do with intelligence, not what intelligence +is made of. Of course everyone agrees to this. The lack of +emphasis upon the chance that the inherited units are general in +their application, that the same inherited elements are involved in +many of the behavior complexes which we call traits and abilities, +is what confuses the situation.</p> + +<h3>CURRENT PSYCHOLOGICAL OPINION</h3> + +<p>We must know what these elements are, and how many contribute +to which capacities. Then we can decide the question of specialized +inheritance. In all crude behavior data it is impossible to separate +the influence of nature and nurture. A theory of specialized inheritance +will inevitably infringe upon common sense in its claims. +Of the following statements, it would be easier for most of us to +endorse 1 and 2 than 3 and 4, whereas few would agree with 5 +and 6.</p> + +<p>1. “Unless one is a blind devotee to the irrepressibility and +unmodifiability of original nature, one cannot be contented with +the hypothesis that a boy’s conscientiousness or self-consciousness +is absolutely uninfluenced by the family training given to him. Of +intelligence in the sense of ability to get knowledge rather than +amount of knowledge got, this might be maintained. But to prove +that conscientiousness is irrespective of training is to prove too +much.” (Thorndike, <i>Educational Psychology</i>, III, pp. 242.)</p> + +<p>2. “Some attempts have been made to apply these laws to +behavior complexes, but as yet psychology has provided little +foundation for such studies. The most thorough-going attempts +have been made with human mental traits and some evidence has +been collected here in favor of the view that differences in the +instinctive behavior of individuals are inherited according to Mendelian +ratios. <i>But in the field of human psychology too little is known +of the genesis of character, of the distinction between nature and +<span class="pagenum" id="Page_52">[52]</span>acquired behaviour to provide a very firm foundation for the work of +the geneticist.</i>” (Watson, <i>Behaviour</i>, p. 156. Italics are mine.)</p> + +<p>3. “Even, however, when we omit the trades as well as the cases +in which the fathers were artists, we find a very notable predominance +of craftsmen in the parentage of painters, to such an extent +indeed that while craftsmen only constitute 9.2 per cent among +the fathers of our eminent persons generally, they constitute nearly +35 per cent among the fathers of the painters and sculptors. It is +difficult to avoid the conclusion that there is a real connection +between the father’s aptitude for craftsmanship and the son’s +aptitude for art.</p> + +<p>“To suppose that environment adequately accounts for this +relationship is an inadmissible theory. The association between +the craft of builder, carpenter, tanner, jeweller, watchmaker, wood-carver, +rope-maker, etc., and the painter’s art is small at the best +and in the most cases non-existent.” (Ellis, quoted in Thorndike, +<i>Educational Psychology</i>, III, p. 257.)</p> + +<p>4. “—the statesman’s type of ability is largely transmitted or +inherited. It would be tedious to count the instances in favor. +Those to the contrary are Disraeli, Sir P. Francis (who was hardly +a statesman, but rather bitter a controversialist) and Horner. +In all the other 35 or 36 cases in my Appendix, one or more statesmen +will be found among their eminent relations. In other words, +the combination of high intellectual gifts, tact in dealing with men, +power of expression in debate and ability to endure exceedingly +hard work, is hereditary.” (Galton, <i>Hereditary Genius</i>, pp. 103, +104.)</p> + +<p>Thorndike comments on this last quotation: “Of course there +is, in the case of all of Galton’s facts the possibility that home surroundings +decided the special direction which genius took, that +really original nature is organized only along broad lines. Moreover, +it is difficult to see just what in the nervous system could +correspond to a specialized original capacity, say, to be a judge. +Still the latter matter is a question of fact, and of the former issue +Galton’s studies make him the best judge. We should note also +that it is precisely in the traits the least amenable to environmental +influence such as musical ability, that the specialization of family +resemblance is most marked.”</p> + +<p>This cautious and sagacious commentary is in marked contrast +to the following:</p> + +<p><span class="pagenum" id="Page_53">[53]</span></p> + +<p>5. “But no training and no external influence can entirely supersede +the inborn tendencies. They are the product of <i>inheritance</i>. +Not only unusual talents like musical or mathematical or linguistic +powers can be traced through family histories, but the subtlest +shades of temperament, character and intelligence can often be +recognized as an ancestral gift.” (Munsterberg: <i>Psychology, +General and Applied</i>, p. 230.)</p> + +<p>6. “Statistical studies which covered many characteristic +opposites like industrious and lazy, emotional and cool, resolute +and undecided, gay and depressed, fickle and constant, cautious +and reckless, brilliant and stupid, independent and imitative, +loquacious and silent, greedy and lavish, egoistic and altruistic +and so on, have indicated clearly the influence of inheritance on +every such mental trait.” (Munsterberg, <i>Psychology, General and +Applied</i>, p. 237.)</p> + +<p>Undoubtedly Munsterberg here refers to the data accumulated +by Heymans and Wiersma since they used such opposites as these, +and also used what might be called statistical methods. Speaking +of the same data Thorndike says:</p> + +<p>“In view of the insecurity of their original data it seems best +not to enter upon an explanation of their somewhat awkward +method of measuring the force of heredity, and not to repeat +the figures which are got by this method. Also they do not attempt +to estimate an allowance for the influence of similarity in home +training, though they state that some such allowance must be +made.” (<i>Educational Psychology</i>, III, p. 262.)</p> + +<p>Hollingworth and Poffenberger, commenting on the data of +Galton and Ellis mentioned in the quotation above, say:</p> + +<p>“Francis Galton has made a statistical study of the inheritance +of <i>specified</i> mental abilities and found that the abilities required +for success as a judge, statesman, minister, commander, poet, +artist, and scientific man, are inherited. But the nature of his +data makes him unable to make exact allowances for influences +of training and environmental influences. Consequently, his +figures might really show general intelligence to be inherited and +the form of its expression to be dependent upon environment.</p> + +<p>“Other investigators, among them F. A. Woods and Havelock +Ellis, have made similar statistical studies and conclude that +there is inheritance of even such qualities as temper, common +sense, and the like, but these reports are also subject to the same +<span class="pagenum" id="Page_54">[54]</span>complicating influence of environment.” (<i>Applied Psychology</i>, +p. 43.)</p> + +<p>It can readily be seen, from these quotations, that there is fundamental +disagreement among psychologists with regard to the +inheritance of specific ability,—fundamental disagreement in +three ways: (1) Interpretation of Galton’s and Ellis’s data. (2) +Opinion on the matter. (3) Degree of precision possible in giving +judgment.</p> + +<p>We have noted that it is very difficult to understand what the +neural bases for such special abilities as Galton speaks of could +be; that they are social, not neural or psychological units. A +view of a large number of inherited elements all of which contribute +to what we call general intelligence and each of which is slightly +more necessary to some vocation than others, would account for +all the observed facts, is neurally imaginable, and does not need +to view ability to be a “judge” or “artistic talents” as biological +entities. It further explains the differences in their limited abilities +of mentally deficient children.</p> + +<p>Burt says in this connection: “Among children of special (M.D.) +schools, the evidence for a general factor underlying educational +abilities and disabilities of every kind is not so clear. In administrative +practice, ‘mental deficiency’ implies among different +children deficiencies in very different capacities, both general and +specific.” (Cyril Burt: <i>The Distribution and Relation of Educational +Abilities</i>, p. 83.)</p> + +<p>For these reasons it is justifiable to attempt to present evidence +of the inheritance of school abilities with a view to showing that +school abilities are not dependent upon special inherited aptitudes, +as teachers so often assume, but that general intelligence is the +only inherited cause of disparity in product. Investigations where +the correlation between educational product and intelligence, +irrespective of chronological age, was less than around .75, used +data where many removable causes were not removed, and consequently +measured results of the environment as well as heredity. +A case such as this follows:</p> + +<p>“The influence of inheritance upon a <i>very specific</i> mental quality, +namely, spelling ability, has been tested experimentally, although +here there is some difficulty in separating the influence of heredity +from that of environment. Earle studied the spelling ability of +180 pairs of brothers and sisters who had uniform school training +<span class="pagenum" id="Page_55">[55]</span>and found a correlation of .50. This means that if one child deviated +by a certain amount from the average child in spelling ability, +his brother or sister would deviate from the average child just +half as much; that is, he would resemble his brother or sister to +that extent.” (Hollingworth and Poffenberger: <i>Applied Psychology</i>, +p. 44.)</p> + +<p>The data presented in this thesis indicate that that correlation +could have been pushed as high as the <i>r</i> between the intelligence +of the pairs of brothers. In other words, a child could be made +to resemble his brother as nearly in spelling ability as he did in +intelligence. All disparity could be reduced to that of general +intelligence. Then intelligence alone is inherited as far as the +data here presented have any bearing on the matter in hand. +The influence of environment is in this case a matter of no consequence, +since the subjects all had the same schooling, and home +influence does not as a rule teach children to spell; but the data +are not irrespective of the influence of intelligence.</p> + +<h3>INDICATIONS OF THE GARDEN CITY DATA</h3> + +<p><a href="#table3">Table 3</a> presents intercorrelations between IQ and quotients in +the various subjects. The correlations are in each instance irrespective +of chronological age since all quantitative indices are +expressed as quotients. We have seen that they go up from September, +1918, to June, 1920. Every possible means was used to +push these correlations to their limit, to remove all removable +factors. We have seen that the data show here, as in Tables <a href="#table7">7</a> and +<a href="#table8">8</a>, that there is little association between traits which is not a result +of differences in intelligence. <a href="#table3">Table 3</a> shows the same 48 children +throughout. The <i>r</i>’s are not corrected for attenuation. Though +the <i>r</i>’s are high throughout and go higher under special treatment, +the association can still be more accurately registered by some +attention to relation of the means and the S.D.’s. Two traits +to be identical must have <i>r</i> = 1.00 S.D.<sub><i>x</i></sub> = S.D.<sub><i>y</i></sub> and M<sub><i>x</i></sub> = M<sub><i>y</i></sub>. +We have seen that the <i>r</i> increases, M-M decreases and S.D.-S.D. +regardless of sign decreases. (Tables <a href="#table9">9</a>, <a href="#table10">10</a> and <a href="#table11">11</a>.)</p> + +<p>But as the S.D.’s of the Subject Quotients (though they do +approach S.D. of IQ) sometimes go below the S.D. of IQ, we +must know why. It is because the low IQ’s do better per their +intelligence than the high IQ’s. We have seen above that the +correlation between IQ and average of the Vocabulary, Reading, +<span class="pagenum" id="Page_56">[56]</span>and Completion Subject Ratios is -.61 in November, 1918, and +-.49 in June, 1920.</p> + +<p>Then the ratio of achievement to intelligence is in definite +relation to intelligence—a negative relation. It is this same +tendency to adapt our education to a low level which has prevented +a perfect association between intelligence and the various subjects. +The relation of one subject to another, irrespective of intelligence, +would be zero if there were no other factors except intelligence +responsible for the product. After two years of such attempts as +an ordinary public school will allow, we have removed many of the +causes of disparity and increased the association between potential +progress and progress in arithmetic, reading and language. The +correlations, correspondence of S.D.’s, and Σ(IQ-EQ)/<i>n</i> registered +in Tables <a href="#table9">9</a>, <a href="#table10">10</a>, and <a href="#table11">11</a> give evidence of this as does also the increase +in the AccR, an average of the Arithmetic, Reading, Vocabulary +and Completion Ratios. (<a href="#table13">Table 13.</a>)</p> + +<p>Are the unremoved causes other than intelligence unremovable? +These causes might be, besides the unreliability of tests and the +common elements in the tests, the specialized inheritance we have +considered, ethical qualities of endurance, ambition, initiative and +industry or a general factor. The correlations between Arithmetic +Ratios and Reading Ratios and the other intercorrelations +of Subject Ratios will yield us an index of how much of this remaining +disparity is due to specialized inheritance. These intercorrelations +for all years are embodied in <a href="#table13">Table 13</a>. The partial +correlations of quotients when intelligence is rendered constant +will be found in <a href="#table6">Table 6</a>. These intercorrelations, and the partials +as well, give an indication of some general factor other than intelligence +since the <i>r</i>’s irrespective of intelligence are uniform and +all are positive. Only the correlation of arithmetic with vocabulary, +intelligence being rendered constant, goes to zero. Though +this might be due in part to common elements in the tests, it is +more likely that there is another factor in operation. Inheritance +of specific abilities could not have this uniform effect on the correlations.</p> + +<p>These correlations all being positive and the <i>r</i>’s being very +uniform, both correlation of ratios and the partials, makes the +interpretation of specialized inheritance of ability extremely +unlikely. The correlation of Arithmetic Ratios with Reading +<span class="pagenum" id="Page_57">[57]</span>Ratios is higher in 1920 than that of Vocabulary Ratios with +Reading Ratios. It leaves the possibility that the unremoved +factors are inherited ethical differences or that they are a “general +educational factor.” The negative correlation of AccR with +intelligence, however, being as high as these positive remnants of +interrelation, would tend to make more probable an interpretation +of this as a remnant of disparity, intelligence accounted for, which +is entirely due to the organization of our schools.</p> + +<p>All disparity not due to intelligence was worked on as far as it +was possible. Thereupon the association of intelligence and educational +product increased markedly and the negative association +of intelligence with achievement in terms of intelligence decreased +somewhat. However, some association of abilities not due to +intelligence remains. Exactly as much negative association of +achievement in terms of intelligence, with intelligence, remains. +So, when some of the disparities due to the environment have +been removed and therefore the correlation of Arithmetic Ratio +with Vocabulary Ratio and Reading Ratio has been decreased, +the causes which contributed to a correlation such as lack of +interest having been removed, there still remains some relation +of school qualities. But there also still remains a negative association +between this accomplishment and intelligence which means +that we still have a remnant of such removable influence as is due +to badly adjusted curricula.</p> + +<p>This enables us to interpret our partials. The partials are not +nearer zero because although we have partialed out the effect +of intelligence, we have not partialed out the factor which controls +the negative relation to intelligence of these very partial resultants, +since that is the effect of the methods and curricula. Though we +did advance bright pupils and give them more chance, we have +not given them a chance proportionate to the stupid children. +And that is true since we often wanted to advance pupils and were +not allowed to; whereas we were never allowed to demote pupils +except in particular subject matter. The stupid children were +always at the frontier of their intelligence at the educational cost +of the others.</p> + +<p>It is this remnant which has usually been interpreted as “general +factor” or as inherited factors basic to initiative, ambition, and +industry. The fact of importance is that these remnants, these +marks of children independent of their intelligence, are associated +<span class="pagenum" id="Page_58">[58]</span>negatively with intelligence to the same degree that they are +associated positively to each other. Unless we wish to assume +that the “general factor” or the inherited bases of initiative and +industry are associated negatively with intelligence we must account +for the remnant in some other way. It seems far more reasonable +to attribute this remaining association to the educational handicaps +of intelligence which we were unable to remove.</p> + +<p>The original tendencies of man, as distinct from his original +equipment, have not been considered in this study. If the quantitative +differences in endowment of this kind were added to the +denominator of our accomplishment ratio formula, we would +have a better measure and better results. We share in this investigation +a general limitation of educational psychology—the requisite +technique to measure individual differences of instincts and the +ethical traits of which they are the predisposition. Industry, +ambition, and initiative are not inherited units. They are, however, +the rules of an economy of expression and as such are dependent +upon individual differences in strength of instinct.</p> + +<h3>CONCLUSIONS</h3> + +<p>1. IQ can be used as a limit of school achievement expressed +as SQ.</p> + +<blockquote> + +<p class="hanging"><i>a</i> Progress in Σ(IQ-SQ)/<i>n</i> may be used as a measure of +school efficiency.</p> + +<p class="hanging"><i>b</i> SQ/IQ may be used as a measure of individual efficiency.</p> + +</blockquote> + +<p>2. Correlations between intelligence and achievement are very +different before and after the abilities are pushed.</p> + +<blockquote> + +<p class="hanging"><i>a</i> Many <i>r</i>’s are reported where conclusions are drawn as +though they had been pushed. These conclusions should +be restated.</p> + +<p class="hanging"><i>b</i> Intelligence and achievement are far more closely associated +than has been assumed to date.</p> + +</blockquote> + +<p>3. Disparity of school product can be reduced to individual +differences in intelligence.</p> + +<blockquote> + +<p class="hanging"><i>a</i> Little specific inheritance of school abilities.</p> + +<p><span class="pagenum" id="Page_59">[59]</span></p> + +<p class="hanging"><i>b</i> Little unremovable difference in industry, conscientiousness +and concentration.</p> + +<p class="hanging"><i>c</i> Intelligence is the only inherited general factor.</p> + +</blockquote> + +<p>4. Negative association between AccR and IQ.</p> + +<blockquote> + +<p class="hanging"><i>a</i> To-day’s educational procedure involves a handicap to +intelligence.</p> + +<p class="hanging"><i>b</i> The genius has been neglected.</p> + +</blockquote> + +<figure class="figcenter illowp75" id="columbia" style="max-width: 15.625em;"> + <img class="w100" src="images/columbia.jpg" alt=""> +</figure> + +<hr class="chap x-ebookmaker-drop"> + +<div class="footnotes"> + +<div class="chapter"> + +<h2 class="nobreak" id="FOOTNOTES">FOOTNOTES</h2> + +</div> + +<div class="footnote"><p><a id="Footnote_1" href="#FNanchor_1" class="label">[1]</a> Part of this section is reprinted with revisions from <span class="smcap">Teachers College Record</span>, +Vol. XXI, No. 5 (November, 1920).</p></div> + +<div class="footnote"><p><a id="Footnote_2" href="#FNanchor_2" class="label">[2]</a> For scientific purposes we want year-month means and standard deviations, that +we may say that Charlie Jones is 2.1 S.D. above the mean for his age level, while +Harold Smith is .1 S.D. below that mean. It is in terms such as these that we may +be able to compare accomplishment in one function with accomplishment in another, +progress in one with progress in another. For many of our problems we need a common +denominator of measurement so that we may compare progress between tests and +age-groups. The best common denominator is, I believe, S.D. in an age-group. +Thus we may locate a child in any age-group in any test and compare that location +with the position of any other child in any other test in his age-group.</p> + +<p>For practical purposes, however, it is for many reasons more convenient to use +quotients in elementary schools. Principals would rather deal with quotients since it +is easier to explain them in terms of attainment and capacity. It is the use of such +quotients that this thesis discusses.</p></div> + +<div class="footnote"><p><a id="Footnote_3" href="#FNanchor_3" class="label">[3]</a> Judd, C. H., “A Look Forward,” in <i>Seventeenth Yearbook</i>, Pt. II, of the N.S.S.E., +1918.</p></div> + +<div class="footnote"><p><a id="Footnote_4" href="#FNanchor_4" class="label">[4]</a> When the disadvantages of “pushing” children are discussed, the disadvantages +of keeping children at their chronological age levels should be considered as well. +Although it is true that a supernormal child placed in that grade for which he is mentally +equipped loses much in social contact, it is also true that he loses a great deal by +remaining in the grade where he physiologically belongs. There he develops habits +of conceit, indolence, and carelessness. It is in all cases much better to group intelligent +children and enrich the curriculum than to “push” them; but pushing may be +better than leaving them where they belong by age. It is a possibility worth considering +that the explanation of the “peculiarities” of genius lies in the fact that he has +never associated with equals. When his fellows are mentally his equals they are +physically far older and when they are physically his equals they are mentally inferior.</p></div> + +<div class="footnote"><p><a id="Footnote_5" href="#FNanchor_5" class="label">[5]</a> Whether only the Accomplishment Ratio as a percentage should be given the +parents, or whether they should know both the IQ and all the SQ’s, is a question on +which I am not prepared to give an opinion. I incline to believe that the parents +should know only the final marks and am sure that I advise telling the children these +only.</p></div> + +<div class="footnote"><p><a id="Footnote_6" href="#FNanchor_6" class="label">[6]</a> There will be reported elsewhere a fuller consideration of this aspect of +the technique of derivation of norms, together with a complete presentation of the +data used to obtain the age norms herein used.</p></div> + +<div class="footnote"><p><a id="Footnote_7" href="#FNanchor_7" class="label">[7]</a> “The Accomplishment Quotient,” <i>Teachers College Record</i>, November, 1920.</p></div> + +<div class="footnote"><p><a id="Footnote_8" href="#FNanchor_8" class="label">[8]</a> Or the ratio of the Subject Quotient to the Intelligence Quotient, which is the +same as the ratio of the Subject Age to the Mental Age.</p></div> + +<div class="footnote"><p><a id="Footnote_9" href="#FNanchor_9" class="label">[9]</a> This table is too bulky for complete publication but may be found on file in +Teachers College Library, Columbia University.</p></div> + +<div class="footnote"><p><a id="Footnote_10" href="#FNanchor_10" class="label">[10]</a> The remainder of this table is filed in Teachers College Library, Columbia University. +Decimals are dropped in this table.</p></div> + +<div class="footnote"><p><a id="Footnote_11" href="#FNanchor_11" class="label">[11]</a> Decimals are dropped in this table.</p></div> + +<div class="footnote"><p><a id="Footnote_12" href="#FNanchor_12" class="label">[12]</a> Truman L. Kelley: <i>Statistics</i>, The Macmillan Co.</p></div> + +<div class="footnote"><p><a id="Footnote_13" href="#FNanchor_13" class="label">[13]</a> This correlation was obtained by correlating one half of the Binet against the other +one half and then using Brown’s Formula to determine the correlation of a whole +Binet against another whole Binet.</p></div> + +<div class="footnote"><p><a id="Footnote_14" href="#FNanchor_14" class="label">[14]</a> These quantities do not decrease because a perfect score on the arithmetic test was +too easy to obtain at this time. The children had reached the limits of this test.</p></div> + +<div class="footnote"><p><a id="Footnote_15" href="#FNanchor_15" class="label">[15]</a> Table 12 is too bulky for complete publication. The first page is reproduced here +and the complete table is filed at the library, Teachers College, Columbia University.</p></div> + +<div class="footnote"><p><a id="Footnote_16" href="#FNanchor_16" class="label">[16]</a> No arithmetic was given in 1918, therefore arithmetic was not used in these +averages.</p></div> + +<div class="footnote"><p><a id="Footnote_17" href="#FNanchor_17" class="label">[17]</a> William Anderson McCall: <i>Correlations of Some Psychological and Educational +Measurements</i>, Teachers College Contributions to Education, No. 79.</p></div> + +<div class="footnote"><p><a id="Footnote_18" href="#FNanchor_18" class="label">[18]</a> Cyril Burt: <i>The Distribution and Relations of Educational Abilities</i>, pp. 53-56.</p></div> + +<div class="footnote"><p><a id="Footnote_19" href="#FNanchor_19" class="label">[19]</a> Quotations from Galton: <i>Hereditary Genius</i>, ’92, pp. 61-62 and pp. 103-104.</p></div> + +<div class="footnote"><p><a id="Footnote_20" href="#FNanchor_20" class="label">[20]</a> Terman, Lewis: <i>The Intelligence of School Children</i>. Boston: Houghton Mifflin, +1919.</p></div> + +<div class="footnote"><p><a id="Footnote_21" href="#FNanchor_21" class="label">[21]</a> Woodworth, R. S.: <i>Dynamic Psychology</i>, p. 200. New York: Columbia University +Press, 1918.</p></div> + +</div> + +<div style='text-align:center'>*** END OF THE PROJECT GUTENBERG EBOOK 76891 ***</div> +</body> +</html> + diff --git a/76891-h/images/columbia.jpg b/76891-h/images/columbia.jpg Binary files differnew file mode 100644 index 0000000..1daaed5 --- /dev/null +++ b/76891-h/images/columbia.jpg diff --git a/76891-h/images/cover.jpg b/76891-h/images/cover.jpg Binary files differnew file mode 100644 index 0000000..505e99b --- /dev/null +++ b/76891-h/images/cover.jpg diff --git a/76891-h/images/formula1.jpg b/76891-h/images/formula1.jpg Binary files differnew file mode 100644 index 0000000..18f8956 --- /dev/null +++ b/76891-h/images/formula1.jpg diff --git a/76891-h/images/formula2.jpg b/76891-h/images/formula2.jpg Binary files differnew file mode 100644 index 0000000..7d08520 --- /dev/null +++ b/76891-h/images/formula2.jpg diff --git a/76891-h/images/graph.jpg b/76891-h/images/graph.jpg Binary files differnew file mode 100644 index 0000000..fb2ae33 --- /dev/null +++ b/76891-h/images/graph.jpg |
