We may now apply to the results of our efficiency-of-training tables the method of measuring efficiency which was mentioned at the end of the preceding chapter as the index of modifiability (that number of tests after which no errors occur for at least thirty tests). By taking the average number of tests for the several individuals in each of the Tables 42, 43, 44, and 45 we obtain the following expressions of efficiency:—
METHOD INDEX OF MODIFIABILITY (EFFICIENCY)
Two-five-test 81.7 ± 2.7
Ten-test 88.0 ± 4.1
Twenty-test 91.0 ± 5.3
Continuous-test 170.0 ± 4.8
Since the difference between the indices for the ten-test and the twenty- test methods lies within the limits of their probable errors (±4.1 and ±5.3) it is evident that it is not significant. Except for this, I think these indices may be accepted as indications of real differences in the value of the several methods of training.
A somewhat different interpretation of our results is suggested by the grouping of individuals according to sex. In Table 47 appear the general averages for the males and the females which were tested by the several methods. The most striking fact exhibited by this table is that of the high efficiency of the twenty-test method for the females. Apparently they profited much more quickly by this method than by the ten-test method, whereas just the reverse is true of the males. I present the data of this table merely to show that general averages may hide important facts.
TABLE 47
EFFICIENCY OF TRAINING
CONDITION MALES FEMALES INDEX OF MODIFIABILITY INDEX OF MODIFIABILITY 2 or 5 tests per day 85.0 80.0 10 tests per day 72.0 104.0 20 tests per day 94.0 88.0 100 or more tests per day 160.0 180.0
From all considerations that have been mentioned thus far the reader would be justified in concluding that I made a mistake in selecting the ten-test method for my study of the modifiability of the behavior of the dancer. That this conclusion is not correct is due to the time factor in the experiments. If the dancer could acquire a perfect habit as a result of twelve days' training, no matter whether two, five, ten, or twenty tests were given daily, it would, of course, be economical of time for the experimenter to employ the two-test method. But if, on the contrary, the two-test method required twice as many days' training as the five-test method, it would be economical for him to use the five-test method despite the fact that he would have to give a larger number of tests than the two- test method would have demanded. In a word, the time which the work requires depends upon the number of series which have to be given, as well as upon the number of tests in each series. As it happens, the ten-test method demands less of the experimenter's time than do methods with fewer tests per day. The twenty-test method is even more economical of time, but it has a fatal defect. It is at times too tiresome for both mouse and man. These facts indicate that a balance should be struck between number of tests and number of series. The fewer the tests per day, within the limits of two and one hundred, the higher the efficiency of the method of training, as measured in terms of the total number of tests necessary for the establishment of a perfect habit, and the lower its efficiency as measured in terms of the number of series given. The greater the number of tests per day, on the other hand, the higher the efficiency of the method in terms of the number of series, and the lower its efficiency in terms of the total number of tests. By taking into account these facts, together with the fact of fatigue, we are led to the conclusion that ten tests per day is the most satisfactory number.
If my time and attention had not been fully occupied with other problems, I should have determined the efficiency of various methods of training in terms of the duration of habit, as well as in terms of the rapidity of its formation. As these two measures of efficiency might give contradictory results, it is obvious that a training method cannot be fairly evaluated without consideration of both the rapidity of habit formation and the permanency of the habit. A priori it seems not improbable that slowness of learning should be directly correlated with a high degree of permanency. By the further application of the method which I have used in this study of the efficiency of training we may hope to get a definite answer to this and many other questions concerning the nature of the educative process and the conditions which influence it.