CHAPTER XV. The Efficiency of Training Methods

THE EFFICIENCY OF TRAINING METHODS

The nature of the modifications which are wrought in the behavior of an organism varies with the method of training. This fact is recognized by human educators, as well as by students of animal behavior (makers of the science of comparative pedagogy), but unfortunately accurate measurements of the efficiency of our educational methods are rare.

Whatever the subject of investigation, there are two preeminently important aspects of the educative process which may be taken as indications of the value of the method of training by which it was initiated and stimulated. I refer to the rapidity of the learning process and its degree of permanency, or, in terms of habit formation, to the rapidity with which a habit is acquired, and to its duration. Of these two easily measurable aspects of the modifications in which training results, I have chosen the first as a means to the special study of the efficiency of the training to which the dancing mouse has been subjected in my experiments.

The reader who has followed my account of the behavior of the dancer up to this point will recall that in practically all of the discrimination experiments the number of tests in a series was ten. Some readers doubtless have wondered why ten rather than five or twenty tests was selected as the number in each continuous series. I shall now attempt to answer the question. It was simply because the efficiency of that number of tests, given daily, when taken in connection with the amount of time which the conduct of the experiments required, rendered it the most satisfactory number. But this statement demands elaboration and explanation.

Very early in my study of the dancer, I learned that a single experience in a given experiment day after day had so little effect upon the animal that a perfect habit could not be established short of several weeks or months. Similarly, experiments in which two tests per day were given proved that even a simple discrimination habit cannot be acquired by the animal under this condition of training with sufficient rapidity to enable the experimenter to study the formation of the habit advantageously. Next, ten tests in succession each day were given. The results proved satisfactory, consequently I proceeded to carry out my investigation on the basis of a ten-test series. After this method had been thoroughly tried, I decided to investigate the efficiency of other methods for the purpose of instituting comparisons of efficiency and discovering the number of tests per day whose efficiency, as measured by the rapidity of the formation of a white-black discrimination habit, is highest.

For this purpose I carefully selected five pairs of dancers of the same age, descent, and previous experience, and gave them white-black tests in series of two tests per day (after the twentieth day the number was increased to five) until they had acquired a perfect habit of discriminating. Similarly other dancers were trained by means of series of ten tests, twenty tests, or one hundred tests per day. Since it was my aim to make the results of these various tests strictly comparable, I spared no pains in selecting the individuals, and in maintaining constancy of experimental conditions. The order of the changes in the position of the cardboards which was adhered to in these efficiency tests was that given in Table 12.

At the beginning of the two-test training I thought it possible that the animals might acquire a perfect habit with only a few more days' training than is required by the ten-test method. This did not prove to be the case, for at the end of the twentieth day (after forty tests in all) the average number of mistakes, as Table 42 shows, was 3.2 for the males and 3.0 for the females. Up to this time there had been clear evidence of the formation of a habit of discriminating white from black, but, on the other hand, the method had proved very unsatisfactory because the first test each day usually appeared to be of very different value from the second. On account of the imminent danger of the interruption of the experiment by the rapid spread of an epidemic among my mice, I decided to increase the number of tests in each series to five in order to complete the experiment if possible before the disease could destroy the animals. On the twenty- first day and thereafter, five-test series were given instead of two-test. Unfortunately I was able to complete the experiment up to the point of thirty successive correct tests with only six of the ten individuals whose numbers appear at the top of Table 42. That the results of this table are reliable, despite the fact that some of the individuals had to be taken out of the experiment on account of bad condition, is indicated by the fact that all the mice continued to do their best to discriminate so long as they were used. Possibly the habit would have been acquired a little more quickly by some of the individuals had they been stronger and more active.

It should be explained at this point that the results in all the efficiency-of-training tables of this chapter are arranged, as in the previous white-black discrimination tables, in tens, that is, each figure in the tables indicates the number of errors in a series of ten tests. In all cases A and B mark preliminary series of tests which were given at the rate of ten tests per series. The numbers in the first column of these tables designate groups of ten tests each, and not necessarily daily series. In Table 42, for example, 1 includes the results of the first five days of training, 2, of the next five days, and so on. The table shows that No. 80 made seven wrong choices in the first five series of two tests each. This method of grouping results serves to make the data for the different methods directly comparable, and at the same time it saves space at the sacrifice of very little valuable information concerning the nature of the daily results. It is to be noted, with emphasis, that the two-five tests per day training established a perfect habit after four weeks of training. This method is therefore costly of the experimenter's time.

TABLE 42

EFFICIENCY OF TRAINING. WHITE-BLACK TESTS AT THE RATE OF 2 OR 5 PER DAY

MALES FEMALES SETS 80 82 84 86 88 AV. 73 79 83 85 89 AV. OF 10

A 5 5 4 8 5 5.4 5 6 7 7 6 6.2 B 5 3 6 5 6 5.0 7 5 7 6 7 6.4

1 7 7 6 6 6 6.4 7 6 9 4 6 6.4 2 2 1 0 6 6 3.0 6 5 6 5 5 5.4 3 4 5 5 1 2 3.2 6 5 2 4 1 3.6 4 3 4 7 2 0 3.2 4 3 1 4 3 3.0 5 2 3 3 2 4 2.8 - 3 4 3 1 2.7 6 2 2 - 2 2 2.0 - 0 2 2 0 1.0 7 - 1 - 0 1 0.7 - 1 0 2 1 1.0 8 - - - 1 1 1.0 - 1 1 0 0 0.5 9 - - - 0 1 0.5 0 1 1 0 0 0.5 10 - - - 0 0 0 - 0 0 0 0 0 11 - - - 0 0 0 - 0 0 0 12 - - - 0 0 - 0 0 0

TABLE 43

EFFICIENCY OF TRAINING. WHITE-BLACK TESTS AT THE RATE OF 10 PER DAY

MALES FEMALES SETS 210 220 230 410 420 AV. 215 225 235 415 425 AV. OF 10

A 6 5 6 6 6 5.8 8 4 4 8 5 5.8 B 6 8 8 5 1 5.6 8 7 6 6 2 5.8

1 6 7 6 2 4 5.0 7 6 5 6 4 5.6 2 4 3 1 2 3 2.6 5 6 4 2 5 4.4 3 3 1 4 3 4 3.0 3 3 4 2 5 4.4 4 5 0 3 3 2 3.2 2 1 3 3 3 2.4 5 3 0 4 1 4 2.4 1 3 3 3 3 2.6 6 2 1 4 0 1 1.6 2 1 1 1 0 1.0 7 1 0 3 1 0 1.0 1 1 2 3 3 2.0 8 0 0 1 0 0 0.2 0 0 2 2 3 2.0 9 0 0 0 1 0 0.2 1 0 0 1 1 0.6 10 0 0 0 0 0 2 1 0 2 1.0 11 0 0 0 0 3 0 1 0 0.8 12 0 0 0 0 0 2 0 0.4 13 0 0 0 0 0 14 0 0 0 15 0 0

TABLE 44

EFFICIENCY OF TRAINING. WHITE-BLACK TESTS AT THE RATE OF 20 PER DAY

MALES FEMALES SETS 72 74 208 240 402 AV. 217 230 245 403 407 AV. OF 10

A 4 6 7 7 6 6.0 5 4 7 7 6 5.8 B 6 4 6 8 7 6.2 7 3 5 8 5 5.6

1 3 5 7 5 5 5.0 3 6 4 4 6 4.6 2 4 3 7 5 4 4.6 7 3 5 4 6 5.0 3 3 3 3 5 3 3.4 4 3 3 2 5 3.4 4 6 3 1 4 5 3.8 5 0 1 2 3 2.2 5 4 1 0 2 3 2.0 6 0 0 1 2 1.8 6 3 1 0 2 2 1.6 4 1 1 0 6 2.2 7 3 2 0 1 1 1.4 1 0 0 0 1 0.4 8 2 0 1 1 0.6 0 3 3 0 2 1.6 9 2 1 1 1 1.0 1 0 0 3 0.8 10 1 2 1 0 0.8 0 1 1 2 0.8 11 3 1 0 0 0.8 0 0 0 0 0 12 1 2 0 0 0.6 0 0 0 0 0 13 0 0 0 0 0 0 0 0 14 0 0 0 15 0 0 0

The results of the ten-test training as they appear in Table 43 need no special comment, for quite similar data have already been examined in other connections. In the case of this table it is to be remembered that each figure represents the number of errors for a single day as well as for a series of ten successive tests. The results of Table 44, on the other hand, appear as subdivided series, since each daily series was constituted by two series of ten tests, or in all twenty tests.

Finally, in Table 45 I have arranged the results of what may fairly be called the continuous training method. In connection with several of the labyrinth experiments of Chapter XIII continuous training proved very satisfactory. It therefore seemed worth while to ascertain whether the same method would not be more efficient than any other for the establishment of a white-black discrimination habit. That this method was not applied to ten individuals as were the two-five-test, the ten-test, and the twenty-test methods is due to the fact that it proved practically inadvisable to continue the tests long enough to complete the experiment. I have usually designated the method as one hundred or more tests daily. I applied this training method first to individuals Nos. 51 and 60. At the end of one hundred and twenty tests with each of these individuals I was forced to discontinue the experiment for the day because of the approach of darkness. In the table the end of a series for the day is indicated by a heavy line. The following day Nos. 51 and 60 succeeded in acquiring a perfect habit after a few more tests.

TABLE 45

EFFICIENCY OF TRAINING. WHITE-BLACK TESTS AT THE RATE OF 100 OR MORE PER DAY

SETS 51 60 87 Av. OF 10

A 5 5 6 5.3 B 5 3 7 5.0

1 6 6 5 5.7 2 3 2 5 3.3 3 5 4 7 5.3 4 7 4 5 5.3 5 6 2 3 3.7 6 1 1 3 1.7 7 4 2 3 3.0 8 3 3 0 2.0 9 2 2 3 2.3 10 5 0 2 2.3 11 1 2 2 1.7 12 2 1 1 1.3

13 4 1 2 2.3 14 1 2 1 1.3 15 3 1 5 3.0 16 3 3 2 2.7 17 1 0 1 0.7 18 2 0 1 1.0 19 0 0 2 0.7 20 0 0 0 21 0 1 0.3 22 - 23 - 24 -

The results of the continuous training method for these two mice were so strikingly different from those yielded by the other methods that I at once suspected the influence of some factor other than that of the number of tests per day. The ages of Nos. 51 and 60 at the time of their tests were twenty-two and seventeen weeks, respectively, whereas all the individuals used in connection with the other efficiency tests were four weeks of age. It seemed possible that the slow habit formation exhibited in the continuous training experiments might be due to the greater age of the mice. I therefore selected a healthy active female which was only eight weeks old, and tried to train her by the continuous training method. With this individual, No. 87, the results were even more discouraging than those previously obtained, for she was still imperfect in her discrimination at the end of two hundred and ten tests. At that point the experiment was interrupted, and it seemed scarcely worth while to continue it further at a later date. The evidence of the extremely low efficiency of the continuous method in comparison with the other methods which we have been considering is so conclusive that further comment seems superfluous.

We are now in a position to compare the results of the several methods of training which have been applied to the dancer, and to attempt to get satisfactory quantitative expressions of the efficiency of each method. I have arranged in Table 46 the general averages yielded by the four methods. Although these general results hide certain important facts which will be exhibited later, they clearly indicate that an increase in the number of tests per day does not necessarily result in an increase in the rapidity of habit formation. Should we attempt, on superficial examination, to interpret the figures of this table, we would doubtless say that in efficiency the two-five-test method stands first, the continuous-test method last, while the ten-test and twenty-test methods occupy intermediate positions.

TABLE 46

EFFICIENCY OF TRAINING

Number of Errors in White-Black Series for Different Methods of Training

SETS OF 10 2 OR 5 TESTS 10 TESTS 20 TESTS 100 OR MORE PER DAY PER DAY PER DAY TESTS PER DAY

A 5.8 5.8 5.9 5.3 B 5.7 5.7 5.9 5.0

1 6.4 5.3 4.8 5.7 2 4.2 3.5 4.8 3.3 3 3.4 3.2 3.4 5.3 4 3.1 2.5 3.0 5.3 5 2.7 2.5 1.9 3.7 6 1.5 1.3 1.9 1.7 7 0.9 1.5 0.9 3.0 8 0.7 0.8 1.1 2.0 9 0.5 0.4 0.9 2.3 10 0 0.5 0.8 2.3 11 0 0.4 0.4 1.7 12 0 0.2 0.3 1.3 13 0 0 2.3 14 0 0 1.3 15 0 0 3.0 16 2.7 17 0.7 18 1.0 19 0.7 20 0

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.