416 



MEMOIRS NATIONAL ACADEMY OF SCIENCES. 



[Vol. XV, 



The following correlations sum up the results so far as they can be indicated in the total 



scores for single time and for double time: 



Correlation of single-time total score with officers' rating, 0.490. 

 Correlation of double-time total score with officers' rating, 0.530. 

 Correlation of single-time total score with double-time total score, 0.965. 

 Correlation ratio of single-time total score with double-time total score, 0.980. 



It will be seen from the above that doubling the time does not greatly alter the character of 

 alpha. The coefficient of correlation between single time and double time is 0.965 and is based 

 on approximately linear data, since the correlation ratio is but slightly greater. The close agree- 

 ment between the two coefficients of correlation of officers' ratings with time substantiates this 

 conclusion. The slight difference of 4 per cent is scarcely significant (especially since the data 

 are for the same group), and can not be taken to mean that double time would give a better 

 measure of the quantity which officers rate as intelligence. 



In general, then, we have no reason to assume that an extension of time limits would have 

 improved the test or have given an opportunity to many individuals materially to alter their 

 ratings. We can, of course, gain considerable information concerning the characteristics of 

 alpha by a further study of the data. 



Table 74 shows the amount of gam made by persons of different levels of intelligence (as 

 indicated by score, "single time") and the percentage of gain. The column for percentage indicates 

 that, in general, individuals scoring low gain more than individuals scoring high — a fact that is 

 undoubtedly due in part to the limited possibility for gain at the upper end of the scale. A sub- 

 ject can not do more than all the items. The column for totals in Table 75 gives these facts in 

 summary. The increase in score was, on the average, from 62 to 80.5 — a mean gain of 18.5. 



Table 74. — The mean gain, the ■percentage of gain, a?id the frequency for men making various scores, single time. 



The agreement of the distributions for single time and double time on any one test is a meas- 

 ure of the effect of double time on that test and is indicated roughly by the means and standard 

 deviations in Table 75. It appears that test 2 is affected least and test 3 most by the extension 

 of time. An arrangement in order from the least to the most affected gives 2, 4, 6, 7, 8, 5, 3. 

 But in the order of the mean gain arranged from least to most, we have 2, 6, 4, 5, 3, 7, 8. These 

 means, however, are not exactly comparable because there is more chance for gain in tests 

 4, 7, and 8, since there are 40 items in each. Moreover, the items are not equal in different 

 tests; a gain of one item in one test is not the same as a gain of one item in another test. The 

 order derived directly from the distributions is, therefore, more nearly the truth. 



Table 75. — Means and standard deviations of double time, single time, andgain on each alpha test. 



