It will be noted from these tables that the punished individuals average 2.29 per cent. more correct responses and 15.73 per cent. greater accuracy than the unpunished individuals. Punishment, then, had the effect of increasing performance. But it will be also noted that the values of R dif. are small. Ordinarily, these values are treated as measures of reliability. But they primarily indicate the relative effect of a controlled variable and of one or more uncontrolled variables. If the values are high (3 or more), they show that the controlled factor has been the dominant factor in determining the results and if low that the uncontrolled factors have played a large part in the results. The more uncontrolled factors enter into the results, the greater is the chance that the difference in results with and without the presence of the controlled variable may be due to the uncontrolled rather than to the controlled factor. Hence the numerical values of this measure may be said in a secondary way to indicate reliability. A low value, however, does not necessarily indicate unreliability. It merely leaves the burden of showing reliability to other considerations. In the present case the controlled variable was the electric shock and the uncontrolled variable the individual differences. Since the values of R dif. are low, it is safe to

say that punishment does not affect performance nearly so much as individual difference. Also, since the values of R dif. are low, it is necessary to show by other means that the difference between the two groups can reliably be said to be due to the punishment.

In this connection it will be noted from Table 1-A that on the first two trials the two groups were practically equal in number of correct responses and in accuracy, but that on later trials the difference between the two groups, particularly in accuracy, becomes progressively greater. Table 2-A shows also this progressively increased difference from the first half-minute to the end of the trials. These facts tend to show that the natural or initial ability of the two groups was equal, but that, during the experiment itself, some factor entered to cause a divergence in performance. If the procedure and technique of the experiment were sound, then this factor must have been the punishment.

Another group of facts pointing to reliability of the obtained differences does now show in the tables. As soon as records were secured from ten individuals in each group, the results were tabulated. The first ten with punishment made 1.31 per cent. more correct responses and were 8.14 per cent. more accurate than the first ten without punishment; the second ten with punishment made 0.39 per cent. more correct responses and were 25.13 per cent. more accurate than the second ten without, and the third ten with punishment made 5.25 per cent. more correct responses and were 15.56 per cent. more accurate than the third ten without. In addition a group of ten with punishment made in a preliminary study 2.71 per cent. more correct responses and were 18.62 per cent. more accurate than a group of ten without punishment. It is hardly probable that the results would have been so consistent by chance. In fact, another set of compared groups would have to differ from the average of these four groups by 1.5 sigma if the group with punishment would not show more correct responses than the group without and by 2.7 sigma if the punished group would not show more accuracy than the unpunished group. The

probability that this would happen is lessened by the fact that the groups used give a normal distribution in their scatter, i.e., a random sampling was taken. As an example of the distribution obtained, the following facts might be given. The thirty unpunished individuals, when grouped on the basis of the number of correct responses made on the first trial-20 to 29, 30 to 39, etc., scattered as follows; 2, 4, 5, 7, 5, 4, 2, I. Not all distributions approximated the normal as nearly as this, but all showed the tendency toward normal distribution.

It might be pointed out in this connection that taking more subjects would not have affected to any marked extent the values of R dif. This value would be changed only if the difference between the two groups increased markedly or if the individuals in the two groups decreased markedly in their amount of scatter. The facts presented in the above paragraph tend to show that neither of these changes would have been likely to result.

Another significant fact is that the amount of scatter in the punished group (as shown by the sigmas) becomes progressively less in respect to the amount shown by the unpunished group. This means that the better end-achievement of the punished group is largely due to a very rapid improvement of the individuals who start in poorly. This is to be expected, since the poorer individuals receive more shock and since shock would most affect incentive and comprehension of the task in those individuals in whom these factors are low.

In view of the above considerations, it seems safe to conclude that the differences between the two groups were due to punishment and to say that punishment given under the conditions of part A increases the number of correct responses by 2.29 per cent. and the accuracy by 15.73 per cent. on the average.

The results for part B are shown in Table 1-B and Fig. 1-B. In the figure the data from all subjects have been combined. These average results may be considered first.

The significant fact shown in Fig. 1-B is that even with large sigmas the lines for the two conditions do not cross. This confirms in a fairly positive manner what was said in discussing the results of part A. Although the difference due to punishment is slight, it is, nevertheless, so constant that

one can scarcely doubt that it is a real and significant difference in spite of the fact that the value for the reliability measure is only 0.11.

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

FIG. 1-C

The average decrease of 2.34 per cent. in number of correct responses is seen from Table 1-B to be due to slight decreases by every subject. If it be considered that a subject must either increase or decrease in number of responses with punishment, then the chance that all eight individuals would show a decrease is only I in 264 (to the eighth power).