The accomplishment ratio

PART II STATISTICAL TREATMENT OF THE EXPERIMENT — THE QUOTIENTS — TABLE 1⁠ [10] Intelligence Quotients for All Periods Grouped by Children — TABLE 2⁠ [11] Group Taking All Tests at All Periods Arranged in Order of Magnitude of Intelligence Quotients — TABLE 3 Intercorrelation of All Quotients for All Periods of the 48 Children Who Took All Tests — TABLE 4 Reliability Coefficients — TABLE 5 Intercorrelation of All Quotients in June, 1920. All Children Exclusive of Grade 3 are Here Represented — TABLE 6 Partial Correlations of Quotients Irrespective of Intelligence Quotients — TABLE 7 All Correlations, Means, and Standard Deviations by Grade, Showing Progress from November, 1918 to June, 1919 — TABLE 8 All Correlations, Means, and Standard Deviations of Quotients by Grade, Showing Progress from November, 1919 to June, 1920 — TABLE 9 Summary of Progress in Arithmetic by Increase in r , Decrease in M IQ -M AQ and Decrease in Difference of Standard Deviations Irrespective of Direction — TABLE 10 Summary of Progress in Reading, November, 1918 to June, 1919, by Increase in r , Decrease in M IQ -M RQ , and Decrease in Difference of Standard Deviations Irrespective of Sign — TABLE 11 Summary of Progress in Reading, November, 1919 to June, 1920, by Increase in r , Decrease in M IQ -M RQ , and Decrease in Difference of Standard Deviations Irrespective of Sign — THE RATIOS — TABLE 12 Intelligence Quotients and Subject Ratios for All Periods Grouped by Child. The Order of Entries is Just as in Table 1 — TABLE 13 — SUMMARY

In the discussion and tables which follow:

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.

AQ means Woody-McCall Arithmetic Age divided by Chronological Age, and AR means this AA divided by Mental Age.

VQ means Thorndike Vocabulary Age divided by Chronological Age, and VR means this VA divided by Mental Age.

RQ means Alpha 2 Reading Age divided by Chronological Age, and RR means this RA divided by Mental Age.

CQ means Kelley-Trabue Completion Age divided by Chronological Age, and CR means this CA divided by Mental Age.

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.

EQ means the average of all Subject Quotients and AccR, the Accomplishment Ratio, means the average of all Subject Ratios.

All r’s are product-moment correlation coefficients, uncorrected. As the reliabilities (Table 4) are almost what the other coefficients are in June, 1920 (Table 5), it is apparent that the corrected coefficients, when Grade III is excluded, would all be very near unity at that time.

In Table 1 are presented all the quotients for all periods of testing, grouped by children. The table, a sample of which is included here,⁠[9] 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 Table 2. 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.

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; a is November, 1918, b is June, 1919, c is November, 1919 and d is June, 1920. * = Zero Score

Grade 3

The intercorrelations of the quotients of these 48 cases for all periods may be seen in Table 3 (page 21). 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 r can go as high as the ∜(r₁₁⋅r₂₂) since an r 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.

The reliabilities and limits defining a limit as the fourth root of the multiplied reliability coefficients are in Table 4.

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 r, the corrected r is over 1.00 and hence absurd.⁠[12]

Therefore we use here instead, a comparison to the maximum possibility in a true sense. Since a test correlates with the “true ability” √(r₁₁), ∜(r₁₁⋅r₂₂) is the limit of an r, 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.

Limits of the r’s = ∜(r₁₁ × r₂₂)

The limits of the June, 1920 r’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.

The correlations in 1920 of another group—the whole school except Grade III—are reproduced in Table 5. Grade III was excluded since here there had as yet been little chance to push the r’s. Partials were obtained with these data (Table 6). Little faith may be placed in the relative sizes of these partials, much because the r_VQ.RQ is here only .73 and, in the data presented in Table 3, it is .87. This is due to the fact that the data in Table 3 cover all periods (2 years) while those in Table 5 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 r 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.

The P.E.’s are all less than .05

N = 81

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 r’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 of the IQ’s of the same data; small intercorrelation of SR’s and negative correlation of AccR with IQ.

The general lowness of the partials (Table 6) 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.

N = 81

What happened by grade in 1918-1919 is summarized in Table 7. What happened by grade in 1919-1920 is summarized in Table 8. Since there were many changes in personnel from 1918-1919 to 1919-1920, we need expect no continuity from Table 7 to Table 8. For the continuous influence of the two years, see Table 3, which includes 48 children taking all tests at all periods.

• I stands for Intelligence Quotient
• V stands for Vocabulary Quotient
• R stands for Reading Quotient
• C stands for Completion Quotient

• I stands for Intelligence Quotient
• V stands for Vocabulary Quotient
• R stands for Reading Quotient
• C stands for Completion Quotient
• A stands for Arithmetic Quotient

Note—Totals without Grade III are much higher than these (Table 5). 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.

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 pushed correlations. If the association of IQ and the SQ’s is what we are attempting to establish, it is necessary to show:

1. That the r comes near unity;

2. That the central tendencies come near coincidence;

3. That the S.D.’s come near coincidence.

The value of the r is obvious; the value of coincidence of means becomes clearer if we think of Σ(IQ-EQ)/n, 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 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 x must equal its corresponding y. Then b₁₂ = b₂₁ = 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 r.

It will be observed that both Tables 7 and 8 give evidence of each of these tendencies in all grades. In Table 8 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.

It is noticeable that when r’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 higher than that of a group all mentally ten, since many of the mentally advanced have not been pushed in product. The group used here to establish norms gives more nearly pushed norms than the others would.

The tendency of the low IQ’s to go over unity in their SR’s is apparent in Table 1 and in Table 12 and also in the negative correlation between AccR and IQ.

In both years some second grade children were advanced to Grade III during the year. This accounts for the low r’s in June, 1919, but in 1919-1920 the Grade III correlations are raised and the means raised toward the M_IQ, even though some second grade children were put in this group during the year.

The changes in rates of progress are expressed in summaries by subject matter in Tables 9, 10, and 11. Approach of Arithmetic Quotient to Intelligence Quotient is measured in Table 9 by:

1. Comparison of r in June with r in November.

2. Comparison of M_IQ-M_AQ in June and M_IQ-M_AQ in November.

3. Comparison of S.D.’s of Arithmetic and Intelligence Quotients in June and November.

The P.E.’s of each of these differences were obtained by

P.E._diff² = P.E.₁² + P.E.₂² - 2 r₁₂ P.E.₁ P.E.₂

The only M_IQ-M_SQ in Table 9 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._IQ-S.D._SQ is due to the same cause.

Tables 10 and 11 present the summary of facts with regard to Thorndike Reading Quotients, the first and second years respectively.

The discussion which follows concerns Ratios, not Quotients.

Grade III

The remainder of this table is filed in Teachers College Library, Columbia University.

In Table 12 are presented the Subject Ratios in the same order as the Quotients appear in Table 1.⁠[15] 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_{AccR₁₉₁₈} is 11.17; the S.D._{AccR₁₉₂₀} is 9.09; the S.D._IQ 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 = X, AccR₁₉₁₈ = Y and AccR₁₉₂₀ = S and when AccR = average of Vocabulary, Reading and Completion Ratios, are:⁠[16]

The remaining disparity is then due to something which is in negative correlation with intelligence.

The number of cases here is only 48.

The P.E.’s are then as follows:

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.E._diff = √P.E._X² + P.E._Y² - 2 r_XY P.E._X P.E._Y

P.E._{M₂₀-M₁₈} = 0.94

P.E._{S.D.₁₈-S.D.₂₀} = 0.47

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.

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 Table 13 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.

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.

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 it not for the fact that this same influence stands in negative association to intelligence. 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.

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 2, 3, 5, 7, 8, 9, 10 and 11.)

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 6 and 13.)

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.

Therefore intelligence is far and away the most important determinant of individual differences in product.

As part of the relation between tests, irrespective of intelligence, is due to common elements in the tests, this reasoning becomes still more probable.

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.

McCall has correlations varying continually in size from -.63 to +.98 between various measurements of a group of 6B children.⁠[17] 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 are, not the way they might be by heritage; still others, such as handwriting and cancellation (unless bright children do badly in cancellation tests because they are more bored 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.

It is well to know about music tests and such tests as Stenquist’s mechanical ability test when the correlation with intelligence is pushed, before we decide whether the quality measured is a manifestation of specific talent or general intelligence.

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 r’s. I will present his conclusions with regard to a general factor which are in substantial though not complete agreement with those advanced here.

“Evidence of a Single Common Factor.

“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?

“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 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.

“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.

“Nature of the Common Factor.

“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.

“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 provisionally that this capacity more or less determines prowess in all school subjects.

“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.”⁠[18]

PART III THE PSYCHOLOGICAL CONCLUSIONS OF THE EXPERIMENT — THE NEGLECT OF GENIUS — IS GENIUS SPECIALIZED? — CURRENT PSYCHOLOGICAL OPINION — INDICATIONS OF THE GARDEN CITY DATA — CONCLUSIONS

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.

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 them rather than to let others develop better.

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 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.

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.

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?

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.

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, 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.

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.

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.

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. 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.

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.

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.

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.

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.”⁠[19]

I believe that the amount of influence which inheritance has upon the kind of thing a man does in life has been overestimated; that the inherited factors influence more the way 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, how much 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.

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 of possible 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.

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.

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.

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 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 The Intelligence of School Children.⁠[20] Also, though very infrequent, we account for the genius who could not have done other things as well as those he did.

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.

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 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.”⁠[21]

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?

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 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.

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.

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, Educational Psychology, III, pp. 242.)

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. But in the field of human psychology too little is known of the genesis of character, of the distinction between nature and acquired behaviour to provide a very firm foundation for the work of the geneticist.” (Watson, Behaviour, p. 156. Italics are mine.)

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.

“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, Educational Psychology, III, p. 257.)

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, Hereditary Genius, pp. 103, 104.)

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.”

This cautious and sagacious commentary is in marked contrast to the following:

5. “But no training and no external influence can entirely supersede the inborn tendencies. They are the product of inheritance. 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: Psychology, General and Applied, p. 230.)

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, Psychology, General and Applied, p. 237.)

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:

“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.” (Educational Psychology, III, p. 262.)

Hollingworth and Poffenberger, commenting on the data of Galton and Ellis mentioned in the quotation above, say:

“Francis Galton has made a statistical study of the inheritance of specified 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.

“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 complicating influence of environment.” (Applied Psychology, p. 43.)

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.

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.

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: The Distribution and Relation of Educational Abilities, p. 83.)

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:

“The influence of inheritance upon a very specific 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 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: Applied Psychology, p. 44.)

The data presented in this thesis indicate that that correlation could have been pushed as high as the r 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.

Table 3 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 7 and 8, that there is little association between traits which is not a result of differences in intelligence. Table 3 shows the same 48 children throughout. The r’s are not corrected for attenuation. Though the r’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 r = 1.00 S.D._x = S.D._y and M_x = M_y. We have seen that the r increases, M-M decreases and S.D.-S.D. regardless of sign decreases. (Tables 9, 10 and 11.)

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, and Completion Subject Ratios is -.61 in November, 1918, and -.49 in June, 1920.

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)/n registered in Tables 9, 10, and 11 give evidence of this as does also the increase in the AccR, an average of the Arithmetic, Reading, Vocabulary and Completion Ratios. (Table 13.)

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 Table 13. The partial correlations of quotients when intelligence is rendered constant will be found in Table 6. These intercorrelations, and the partials as well, give an indication of some general factor other than intelligence since the r’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.

These correlations all being positive and the r’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 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.

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.

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.

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 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.

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.

1. IQ can be used as a limit of school achievement expressed as SQ.

a Progress in Σ(IQ-SQ)/n may be used as a measure of school efficiency.

b SQ/IQ may be used as a measure of individual efficiency.

2. Correlations between intelligence and achievement are very different before and after the abilities are pushed.

a Many r’s are reported where conclusions are drawn as though they had been pushed. These conclusions should be restated.

b Intelligence and achievement are far more closely associated than has been assumed to date.

3. Disparity of school product can be reduced to individual differences in intelligence.

a Little specific inheritance of school abilities.

b Little unremovable difference in industry, conscientiousness and concentration.

c Intelligence is the only inherited general factor.

4. Negative association between AccR and IQ.

a To-day’s educational procedure involves a handicap to intelligence.

b The genius has been neglected.

FOOTNOTES