It is of interest in this connection to note that the length of a second is usually underestimated by females, overestimated by males. The average number of seconds counted in half a minute by twenty men and twenty women was as follows:
Men. M. 30.4, M.V. 8.7, R.V. 34.94. Women. M. 38.9, M.V. 10.6, R.V. 36.70
These figures would seem to indicate that the overestimation of the intervals of these experiments by the females is due to the use of a time-unit which is shorter than that of the males (although presumably of the same length).
We cannot with certainty say whether inaccuracy of judgment stands in the relation of condition or consequence of the occurrence of simple fractions of a minute, but it would appear that the female tendency to overestimate is responsible for the sex-differences already noted. For whatever be the facts concerning longer intervals the second as judged by the female is considerably shorter than that of the male.
Since a complicated periodicity of frequency in the distribution of the judgments is exhibited in the results of Tables 3-6 it is obvious that the distribution-curve will have a tertiary mode for each number ending in 0 or 5, a secondary mode for 15, 30, 60, and their multiples, and a primary mode which may or may not coincide with one of the secondary or tertiary modes. Extreme irregularity is characteristic of the distribution-curve. Different groups of judgments, as, for example, those for the two sexes, those for the different intervals, etc., give somewhat different forms of distribution, for the frequency of occurrence of 0 and 5, as well as of the multiples of 15, is variable.
These facts are important in connection with the selection of an interval for the construction of the distribution-curves, in that they indicate how large the interval or class of the distribution-curves and tables should be.
It is clear from the results of Tables 3 and 4 that the smallest interval which can be of value is 10 seconds, for a smaller interval would necessarily exhibit irregularities due to the greater frequency of 0 than of 5. The question is whether the interval can be so enlarged, without the loss of all details of the nature of the distribution, that every class will represent the influence of the same conditions. For this purpose only three intervals are possible: 10, 30, and 60 seconds. Of these 30 and 60 are undesirable because the interval 60 gives classes which are so large that all details of the distribution are lost, while 30 exhibits only a few details without doing away with the periodicity due to the preference for multiples of 60.
The further question remains, with which digit should the interval end, in order that uniformity of conditions for the various classes may be gained? Theoretically there are ten possibilities, but of these all except two, 0 and 5, are excluded by reason of the unequal frequency of the various digits already discussed. In favor of 0 is the fact that all the classes thus formed are of equal size, i. e. 1-10, 11-20, etc., whereas for 5 the first class would differ from the others in being only half as large, 1-5. This, however, is only a slight disadvantage, for there are very few judgments which fall in this class. On the other hand, since 0 is the final digit of most frequent occurrence, classes ending in 5 have the advantage of placing the value of greatest weight in the middle. On the whole it seemed desirable to arrange the judgments in 10 second classes, beginning with the class 1-10. But for purposes of comparison the male judgments have been distributed in classes of 10 seconds, which end in 5, 1-5, 6-15, 16-25, etc.[129]