| ρ = 1 − | 6Σd2 | = 1 − | 6 × 1411.5 | = 1 − | 8469. | = 1 − .386 = .614, |
| n(n2 − 1) | 28 × 783 | 21924. |
it appears that the tests more closely correspond with the average of the scholarship marks given by the teacher than with the teacher’s estimate of intelligence. This is partly to be explained by the fact that the tests given were measurements of ability in school subjects rather than tests of intelligence, and still more by the fact that the teacher gave scholarship marks on the basis of relatively objective examinations while her estimates of intelligence are always wholly subjective.
The eighth and ninth columns on page [8] give the differences between the ranks in the teacher’s estimates of intelligence and the ranks in the scholarship marks given during a half year. The coefficient of coördination worked out from these differences is
| .833 | ( | ρ = 1 − | 6 × 611 | = 1 − | 3666 | = 1 − .167 = .833 | ) |
| 28 × 783 | 21924 |
which would seem to indicate that the teacher drew very heavily on her knowledge of the relative scholarship of her pupils in making her estimates of their intellectual capacities.
The three coefficients worked out above for 28 pupils in a sixth grade are typical of the mathematical relationships the reader will wish to work out between known degrees of ability in a certain type of work and the results of the Mentimeter tests. The coefficients of coördination for the sixth-grade pupils studied above are, between
| Educational Measurements and Estimated Intelligence | = .51 |
| Educational Measurements and Scholarship Averages | = .61 |
| Estimated Intelligence and Scholarship Averages | = .83 |
No method of forecasting degree of success in one line of work from quality of performance in another task (or in a test) will give a perfect coefficient of coordination of 1.00, but the nearer the coefficient approaches 1.00 the more reliance one may put in the test which furnishes such a ranking of the individuals.
APPENDIX D
Correct Answers for Mentimeter Tests
The advantages of a carefully standardized test over an ordinary examination which any one might prepare for his own use are chiefly the characteristics implied in the word “standard.” A standard test is one which has been carefully prepared after extensive experience with similar tests; one which is made exact and objective by the most minute specifications as to how it shall be applied, marked, scored, and interpreted; and one on which many persons of varying degrees of proved ability have been tested and reported, for comparison with the results to be obtained later from testing other persons of undetermined degrees of ability. The purpose of this section of the appendix is to make definite and unmistakable the answers to the questions asked in the Mentimeter tests, in order that each reader may mark and interpret the results of these tests in exactly the same way, that is, in the “standard” way.