AN ANALYSIS OF SOME FACTORS INFLUENCING ALPHA

SCORES BY STATES

HOWARD H. LONG

Knoxville College.

The results from the psychological examining in the army during the World War have provoked many very interesting discussions and given remarkable impetus to the measurement movement in both psychology and education. Of those discussions none have been more interesting, perhaps, than those bearing upon racial "differences" revealed by the alpha and beta results. These seem to show a genuine superiority of the native-born whites of native parentage over immigrants of the last few decades. This information came to light when to be a foreigner was of no particular advantage to one in America. Dynamiting manufacturing plants, sabotage, incendiary crimes, and other deeds calculated to impede the progress of the nation in its energetic prosecution of the war had been rather freely and popularly laid at the door of foreigners. Perhaps this situation in part accounts for the bulk of the literature on immigration which so roundly disparages them.1

There are those who doubt that many of these sweeping statements are justified in fact. Is it true that the mental test scores justify us in believing that our recent foreign population is very much inferior natively to the native-born white American stock? The whole matter reduces practically to two considerations. (1) Do the tests measure native mental capacity within reasonable experimental error? (2) Were there other factors influencing the different racial groups which resulted in a difference in scores a difference which has been popularly attributed to hereditary and racial inequalities.

There is now much more conservatism among those who have adequate knowledge of intelligence tests to give worth while opinion upon them than there was in 1918-19. It seems generally accepted that mental tests at best measure native ability reliably for purposes of comparison when and only when the subjects have had similar opportunity and similar incentives to learn. It is implicit in the above statement that mental test results may be influenced by other factors

1 For instance, American Intelligence, by Carl Brigham, 1923; and Analysis of America's Modern Melting Pot. Hearings before the Committee on Immigration, H. R. Sixty-seventh Congress. Serial 7-C. Washington, 1923.

2 Colvin, S. S. Twenty-first Year Book of the National Society for the Study of Education, 1922, pp. 11-44.

than native ability. No one denies this. What factors may have influenced the results then that have probably confused the issue with reference to racial differences? There are several very obvious possibilities: educational efficiency, percentage of urban population, temperature, etc. Alexander found that median alpha scores by states correlated (rank method) with educational efficiency with a coefficient of +.72, with the percentage of native white stock -.61, and with per centage of urban population .62.3 Alexander says:

* Whatever one's inclination may be, one fact stands out clearly, that where density of population, favorable economic conditions, and educational opportunities exist in conjunction, there will be found the better intelligence. The substantiation of this statement is as follows: When the average position for each of the forty-one states is found from the rankings for per cent. of urban population, ownership of farms, average wage for farm labor, literacy and Ayres school systems, and the correlation of this combined rank-order is made with Alpha, the resulting coefficient is +.89 ±.02.

"Our conclusion is that in so far as it applies to such large social groups as the American states, Army Alpha appears as a test of what has been learned rather than what can be learned." 4 Lippman presents evidence to show that the alpha scores and the per centage of native white population correlate negatively.5

Whole or zero correlations can not decide for us what part these several factors play in determining the alpha scores. The realm of concomitance is too complex. We may assume that the number of causes operating to produce any effect is infinite. We can not be assured that we have isolated any one of these causes unless we know that the particular one does not correlate with any of the rest-an obviously impossible task. Fortunately in most practical situations, there are just a few prepotent causes which may be selected a priori. If these can be isolated so that they do not correlate among themselves at all or such aspects as do correlate are eliminated from or held constant in the comparison, then we can study causes in the scientific sense. It is obviously impossible for us to disentangle concretely and

3 Alexander, Herbert B. A Comparison of Ranks of American States in Army Alpha and in Social-Economic Status, School and Society, Vol. XVI, No. 45, pp. 388-392.

4 Op. cit., p. 392.

5 Lippman, Walter. A Defense of Education, The Century Magazine, May, 1923, pp. 95-103. 6 The term "cause" used here is to be taken in its scientific sense. This explantation seems necessary on occasion to relieve the stress of tender metaphysical consciences.

directly the intertwining factors which influence alpha scores. Educational efficiency can not be separated from density of population for the two are found coexistent side by side. One does not know where the one begins and the other ends when it comes to measuring them directly. The northern, eastern, and western states made higher median scores than the southern states; the former have greater school efficiency, but also they have a higher percentage of urban population. Are the higher scores due to superior school efficiency or to greater density of population? We have no direct way of knowing. But there is an indirect way of determining the relative influences of these factors. It is the method of partial correlation. By this method alpha scores may be correlated with the residuals of educational efficiency after the latter's correlation with, say, urban population has been eliminated. The correlation of alpha scores with educational efficiency is thus independent of the influence of urban population. In other words, we can measure the correlation between alpha and educational efficiency in so far as educational efficiency is not correlated with the percentage of urban population. This is truly a mathematical isolation of these. factors and hence enables us, when extended to several variables, to study causes in a complex realm of concomitance. If we designate alpha as variable 1, educational efficiency as variable 2, and percentage of urban population as variable 3, the formula becomes:

This formula is capable of extension theoretically to include as many variables as one wishes to investigate, but practically the calculation becomes laborious when the variables exceed four, and becomes disproportionately more laborious with each added variable. In this investigation, because of the crudeness of the data, it seemed unwise to include more than four variables in the partial procedure. I have taken the ranks in respect of alpha and percentage of native-born whites from Alexander's paper.8

From ranked data one can secure directly r's only by one of the several rank methods. Two difficulties arise at once: first, the r's are not as accurate as the r's obtained by Pearson's product-moment method and, second, if we wish to utilize the partial regression equation in our analysis we find that we cannot do so unless we have the measures of variability in a's. Recently Hull has devised a convenient method for

7 Yule, Udny. An Introduction to the Theory of Statistics, 1919, p. 236. 8 Op. cit., pp. 389-390.

transmuting ranked data into normal distributions on an arbitrary linear scale with a range of ten.9

In the use of this procedure it is necessary, for clear thinking, to keep in mind that this transmutation does not guarantee an increase of accuracy beyond that inhering in the original data; and, moreover, since it assumes that the function transmuted distributes according to the normal law, further inaccuracy may be introduced, though the latter is likely to be negligible. The transmuted variables have the same means and standard deviations. This fact decreases the calculations considerably in finding both the zero co-efficients and in setting up the regression equation.

The four variables used are: 1. alpha scores, the criterion; 2. school efficiency, determined by Ayres;10 3. percentage of urban population, and 4. percentage of native-born white persons of native percentage. These variables will be designated hereafter by these numerals used as subscripts to coefficients or otherwise. The analysis employs three methods: (a) the partial correlation, (b) multiple correlations, and (c) the regression equation.

9 Hull, Clark L. The Computation of Pearson's r from Ranked Data. Jour

nal of Applied Psychology, Vol. VI, pp. 385-390.

10 Ayres, Leonard P.: An Index Number for State School Systems, Sage Foundations, 1920.

It is clear from Table I that variable 4 (percentage of native-born whites) exerts less influence upon the correlation between 1 and 2 than does variable 3 since the elimination of variable 3 lowers the correlation from .67 to .421 whereas the elimniation of variable 4 lowers it to only .494. Similarly variable 4 has less influence upon the correlation between 1 and 3 than does variable 2. The latter lowers the correlation from .58 to .099, whereas the former lowers it only to .419. Coefficient 14.2 shows that when school efficiency is eliminated there is no correlation between alpha scores and percentage of native-born white stock. The same is true when variables 2 and 3 are eliminated. It follows then from this that the native white stock, as such, did not exert the influence upon the scores that has been urged from time to time.

Turning to Table II we find this conclusion confirmed. The correlation between variable 1 and the other three variables is .674. We can investigate the influence of these variables upon this correlation by successively eliminating each, one at a time. When variable 4 is eliminated, R1 (23), the value is not altered.

4

2

The partial regression equation exhibits the same state of affairs. In the prediction of X,, X, has a weight of +.562, X, of +.123, and X, of .01. Thus school efficiency contributes more than four times as much as the percentage of urban population, and native white stock contributes nothing when the probable error is taken into account.

Conclusions

1. We may conclude from the above after making all reasonable allowances for crudeness of data that native-born whiteness has been unwarrantably "played up" by propagandists who have utilized alpha scores for their purpose.

2. These results have an obvious bearing upon the question, How far may we depend upon the alpha scores as indicators of native ability? 3. Once more comes to light the insecurity of drawing any but very limited conclusions from zero coefficients of correlation.