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 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 RATIOS

The discussion which follows concerns Ratios, not Quotients.

TABLE 12
Intelligence Quotients and Subject Ratios for All Periods Grouped by Child. The Order of Entries is Just as in Table 1

Grade III

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

TABLE 13

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.

SUMMARY

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]