The preference series, _A_ and _B_, reveal a constant tendency to choose the black box, whose strength as compared with the tendency to choose the white box is as 5.8 is to 4.2. In other words, the dancer on the average chooses the black box almost six times in ten. The first series of training tests reduced this preference for black to zero, and succeeding series brought about a rapid and fairly regular decrease in the number of errors, until, in the thirteenth series, the white was chosen every time.

Since I arbitrarily define a perfect habit of discrimination as the ability to choose the right box in three successive series of ten tests each, the tests ended with the fifteenth series.

The discrimination curve, Figure 29, is a graphic representation of the general averages of Table 41.--It is an error curve, therefore. Starting at 5.85 for the first preliminary series, it descends to 5.8 for the second series, and thence abruptly to 5.05 for the first training series.

This series of ten tests therefore served to reduce the black preference very considerably. The curve continues to descend constantly until the tenth series, for which the number of errors was the same as for the preceding series, .65. This irregularity in the curve, indicative, as it would appear, of a sudden cessation in the learning process, demands an explanation. My first thought was that an error in computation on my part might account for the shape of the curve. The error did not exist, but in my search for it I discovered what I now believe to be the cause of the interruption in the fall of the error curve. In all of the training series up to the tenth the white cardboard had been on the right and the left alternately or on one side two or three times in succession, whereas in the tenth series, as may be seen by referring to Table 12 (p.111), it was on the left for the first four tests, then on the right four times, and, finally, on the left for the ninth test and on the right for the tenth.

This series was therefore a decidedly more severe test of the animal's ability to discriminate white from black and to choose the white box without error than were any that had preceded it. If my interpretation of the results is correct, it was so much more severe than the ninth series that the process of habit formation was obscured. It would not be fair to say that the mouse temporarily ceased to profit by its experience; instead it profited even more than usually, in all probability, but the unavoidably abrupt increase in the difficultness of the tests was just sufficient to hide the improvement.

As I have suggested, the plan of experimentation may be criticised adversely in the light of this irregularity in the error curve. Had the conditions been perfectly satisfactory the curve would not have taken this form. I admit this, but at the same time I am glad that I chose that series of shifts in the position of the cardboards which, as it happens, served to exhibit an important aspect of quant.i.tative measures of the modifiability of behavior that otherwise would not have been revealed. Our mistakes in method often teach us more than our successes. I have taken pains, therefore, to describe the unsatisfactory as well as the satisfactory steps in my study of the dancer.

[Ill.u.s.tration: FIGURE 30.--Error curve plotted from the data given by thirty dancers, of different ages and under different conditions of training, in white-black discrimination tests.]

The form of the white-black discrimination curve of Figure 29 is more surprising than disappointing to me, for I had antic.i.p.ated many more irregularities than appear. What I had expected, as the result of training five or even ten pairs of mice, was the kind of curve which is presented, for contrast with the one already discussed, in Figure 30. This also is an error curve, but, unlike the previous one, it is based upon results which were got from individuals of different ages which were trained according to the following different methods. Ten of these individuals were given two or five tests daily, ten were given ten tests daily, and ten were given twenty tests daily. The form of the curve serves to call attention to the importance of uniform conditions of training, in case the results are to be used as accurate measures of the rapidity of learning.

Examination of the detailed results of the white-black discrimination tests as they appear in the tables of Chapter VII will reveal the fact that some individuals succeeded in choosing correctly in a series of ten tests after not more than five series, whereas others required at least twice as many tests as the basis of a perfect series. In very few instances, however, was a perfect habit of discrimination established by fewer than one hundred tests. As the averages just presented in Table 41 indicate, fifteen series, or one hundred and fifty tests, were required for the completion of the experiment. One might search a long time, possibly, for another mammal whose curve of error in a simple discrimination test would fall as gradually as that of the dancer. It is fair to say that this animal learns very slowly as compared with most mammals which have been carefully studied. It is to be remembered, however, that quant.i.tative results such as are here presented for the dancer are available for few if any other animals except the white rat.

Neither in the form of the curve of learning nor in the behavior of the animal as it makes its choice of an electric-box is there evidence of anything which might be described as a sudden understanding of the situation. The dancer apparently learns by rote. It exhibits neither intelligent insight into an experimental situation nor ability to profit by the experience of its companions. That the selection of the white box occurs in various ways in different individuals, and even in the same individual at different periods in the training process, is the only indication of anything suggestive of implicit reasoning. Naturally enough comparison of the two boxes is the first method of selection. It takes the dancers a surprisingly long time to reach the point of making this comparison as soon as they are confronted by the entrances to the two electric-boxes. The habit of running from entrance to entrance repeatedly before either is entered, once having been acquired, is retained often throughout the training experiments. But in other cases, an individual finally comes to the point of choosing by what appears to be the immediate recognition of the right or the wrong box. In the former case the mouse enters the white box immediately; in the latter, it rushes from the black box into the white one without hesitation. So much evidence the discrimination tests furnish of forms of behavior which in our fellow-men we should interpret as rational.

[Ill.u.s.tration: FIGURE 31.--Curve of habit formation, plotted from the data of labyrinth-D tests with ten males and ten females.]

Comparison of the error curves for the labyrinth tests (Figures 26 and 31) with those for the discrimination tests (Figures 29 and 30) reveals several interesting points of difference. The former fall very abruptly at first, then with decreasing rapidity, to the base line; the latter, on the contrary, fall gradually throughout their course. Evidently the labyrinth habit is more readily acquired by the dancer than is the visual discrimination habit. Certain motor tendencies can be established quickly, it would seem, whereas others, and especially those which depend for their guidance upon visual stimuli, are acquired with extreme slowness. From this it might be inferred that the labyrinth method is naturally far better suited to the nature of the dancer than is any form of the discrimination method. I believe that this inference is correct, but at the same time I am of the opinion that the discrimination method is of even greater value than the labyrinth method as a means of discovering the capacity of the animal for modification of behavior.

Inasmuch as my first purpose in the repet.i.tion of white-black discrimination tests with a number of individuals was to obtain quant.i.tative results which should accurately indicate individual, age, and s.e.x differences in the rapidity of learning, it is important to consider the reliability of the averages with which we have been dealing. Possibly two groups of five male dancers each, chosen at random, would yield very different results in discrimination tests. This would almost certainly be true if the animals were selected from different lots, or were kept before and during the tests under different environmental conditions. But from my experiments it has become apparent that the average of the results given by five individuals of the same s.e.x, age, and condition of health, when kept in the same environment and subjected to the same experimental tests, is sufficiently constant from group to group to warrant its use as an index of modifiability for the race. This expression, index of modifiability, is a convenient mode of designating the average number of tests necessary for the establishment of a perfect habit of white-black discrimination. Hereafter I shall use it instead of a more lengthy descriptive phrase.

As an indication of the degree of accuracy of measurements of the rapidity of learning which are obtained by the use of 5 individuals I may offer the following figures. For one of two directly comparable groups of 5 male dancers which were chosen from 16 individuals which had been trained, the number of tests which resulted in a perfect habit of white-black discrimination was 92; for the other group it was 96. These indices for strictly comparable groups of 5 individuals each differ from one another by less than 5 per cent. Similarly, in the case of two groups of females, the indices of modifiability were 94 and 104. These figures designate the number of tests up to the point at which errors ceased for at least three successive series (30 tests).

The determination of the probable error of the index of modifiability further aids us in judging of the reliability of the measure of the rapidity of learning which is obtained by averaging the results for 5 individuals. For a group of 5 males (Table 43, p. 243) the index was 72 3.5; and for a group of 5 females of the same age as the males and strictly comparable with respect to conditions of white-black training, it was 104 2.9. A probable error of 3.5 indicates the reliability of the first of these indices of modifiability; one of 2.9, that of the second.

I do not doubt that 10 individuals would furnish a more reliable average than 5, but I do doubt whether the purposes of my experiments would have justified the great increase in work which the use of averages based upon so large a group would have necessitated.

Further discussion of the index of modifiability may be postponed until the several indices which serve as measures of the efficiency of different methods of training have been presented in the next chapter.

From the data which const.i.tute the materials of the present chapter it is apparent that the results of the discrimination method are amenable to much more accurate quant.i.tative treatment than are those of the problem method or the labyrinth method. But I have done little more as yet than describe the method by which it is possible to measure certain dimensions of the intelligence of the dancer, and to state some general results of its application. In the remaining chapters it will be our task to discover the value of this method and of the results which it has yielded.

CHAPTER XV

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 inst.i.tuting 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 s.p.a.ce 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 const.i.tuted by two series of ten tests, or in all twenty tests.