Page:Popular Science Monthly Volume 81.djvu/459

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year of college or professional school in my hundred individuals this figure is, on the average 9, three fifths of the individuals showing sums of from 6 to 12 for column 2 of Table 3. This average result of 9 may be expressed as a coefficient of correlation or correspondence, such as is in customary use to measure resemblances of various sorts. It is equivalent to a correlation of over.60. This means that a person's interests in the late elementary-school period resemble, in their order and relative strength, the constitution of interests which he will have eight years later to the extent of six tenths of perfect resemblance. For the coefficient of correlation is a magnitude running from 1.0, which would be the coefficient if the sum of differences was 24, through 0, which would correspond to a sum of differences of 16, to 1.0, which would correspond to a sum of differences of 0. A sum of differences of 8 means a resemblance greater than half of perfect resemblance, as the reader expert in the mathematics of probability will realize. The sums 12, 10, 8 and 6, in fact, mean coefficients of resemblance or correlation of +.38, +.55 +.71, and +.83, respectively.

The effect which the errors to which the original reports are subject would have in making this obtained degree of permanence too high or too low may now be considered. The chance errors—the mere failures of memory or carelessness in report or inability to distinguish slight differences in the interest of nearly equally interesting subjects—would make the obtained estimate too low. Their action would be to change the true sum of differences, whatever it was, toward 16, or the true coefficient of correlation toward zero. The effect of errors of prejudice, on the other hand, might have been toward so distorting memory and observation as to make the order given for interests in the two later periods more like the order given for the elementary-school period than was in truth the case. This would, of course, unduly raise the obtained estimate of permanence (that is, lower the sum of the differences). I do not believe that such tendencies to read present interests into the past and to leave the order reported for one period unchanged so far as possible, are very strong, there being a contrary tendency to remember and look for differences. On the whole, I should expect the effect of the large chance errors in lowering the estimate of permanence to nearly or quite counteract whatever balance of prejudice there may be in favor of similarity of interests or projection of present conditions into the past.

A correlation of .6 or .7 seems then to be approximately the true degree of resemblance between the relative degree of an interest in a child of from ten to fourteen and in the same person at twenty-one.

Consider now the difference between a subject's rank for interest and its rank for ability at the same period. Using the same sample record (Table 2) and assuming it to be a true record of the order of interests