TABLE II

Alpha 5: Test I

Alpha 5: Test 2

Alpha 5: Test 3

Alpha 5: Test 5

Alpha 6: Test 5

38767

28745

34746

98004

16637

39 34

3559

TABLE III

realize that accuracy is not perfectly constant, since the subjective assurance of the subjects must have varied in different items; nevertheless the bare behavioral test of correctness of response does have some meaning. It is reasonable to hope that variability in the time taken to achieve subjective assurance cancels out for a single subject, whereas any constant individual difference in the degree of assurance required before passing on to a subsequent item becomes simply a factor of individual difference in speed to be analyzed out later, either by an appeal to introspection or by an investigation of simpler reaction times (vide supra).

Of course we are dealing here, even though within the single item, with processes that still are, when psychologically considered, very complex. Not only may the time vary by reason of the fact that the subject now pauses for verification of his response or to allow subjective assurance to accrue in some other way, and then again passes more immediately to the succeeding item; but also the entire process may be different for different subjects with the same item (cf. especially Alpha, test 2, arithmetical problems). We should not, therefore, expect that in every line of Tables II. and III. the rank order of subjects would be A, B, C, D, E. Nevertheless. we think that even mere inspection of these tables will convince the reader that we are here dealing with significant individual differences in the rate of the intelligent reaction, where A or B is the fastest, E is the slowest, and the order is A and B, C, D, E.

Since inspection is dangerous, however, we may resort to statistics. We have tabulated for both Alpha and the Otis Test the relative ranking of every pair of subjects. This table takes the following form:

This table must be read: "B is faster than A, in the 265 items of Alpha, 121 times;" "B is equal to A 41 times;" "B is faster than C 142 times;" etc. It will be noted that the frequencies of the table resemble in form the frequencies of the psychometric functions for a differential limen, and that the foregoing table leaves no doubt of the existence of a superiority of B over A in speed of reaction in Examination Alpha, although the difference between A and B in Alpha is the least significant of any individual difference with which we have to deal. Similarly we can show that C occupies a mid-position in Alpha:

Unfortunately limits of space prevent us from presenting the complete table. It can easily be constructed from Tables II. and III., and it shows that the rank order is B, A, C, D, E for Alpha and A, B, C, D, E for the Otis Tests. The disparity of frequency becomes greater the more remote the subjects are in these series, as anyone accustomed to deal with psychometric functions will understand.

We can also resort to the more usual statistical procedure for the demonstration of the significance of differences. The times for each subject can be averaged, their variability determined, and the difference between averages considered in relation to their variabilities. The direct averaging of Tables II. and III., however, weights the different items unequally since some items require a longer time than others. While direct averages would be meaningful, this procedure would not give us the mean variations that we desire, since, until we press analysis further, our interest must still center in the item as a whole and we can not allow the variation of one large item to offset the contrary variation of several small items. Accordingly we have re-expressed the times of Tables II. and