The method consisted in the employment of active effort upon a fist dynamometer or a wooden handle during the appearance of one of the groups. The handle was preferable because noiseless. The effort was made with the left hand because the right was used in recording. The amount of it was left to the observer's regulation, with the one instruction that its presence be made decidedly evident but without too great fatigue. The cards of Section IV 1 and 2 were used in the One-Group Apparatus. Similarly again the experiments were repeated with the duplicate-group cards. I present no table here because the figures show practically no influence of the effort. On one subject 176 experiments were made; on a second 132; on a third 88.
It is interesting to note here certain results obtained from one observer when he was in what he described as an active attitude toward the groups, in which he seemed to rouse himself to an unusual pitch of concentration upon the visual situation. This was evidently a condition of increased effort to abstract. Without abstraction he gave 26 to 6 in favor of the effort while with abstraction this tendency had fallen off to 30 to 17. The strength of the tendency is thus strongly indicated. Another observer felt a kind of motor difference between the groups; he expected the effort-group to look larger and felt additionally excited, a scattered activity, while he was passive toward the other group. Perhaps this account puts a little meaning into his small per cent. That his power of abstraction was effective here is hinted by his remark that he felt a difference in the groups even when he judged them equal. The third observer found no subjective evidence that effort modified his judgment.
V. THE "ERRORS" OF EXPERIMENTATION
Throughout the foregoing experiments has been involved the possibility of some one of the three "errors" of experimentation, those of time, space, and distribution, and sometimes all three. Their effect on the results, if it existed, was, to be sure, eliminated in the well-known way, but their existence, if actual, would raise an interesting problem. It was possible, in the case of every group of experiments, to rearrange the tables in such a way as to bring out the evidence for any tendency to overestimate, for instance, the first group as against the second, the right as against the left, or one kind of irregular distribution as against another.
The distribution-error must have a word of explanation. It refers to a tendency to give more wrong judgments in favor of one kind of irregular distribution than of the other kind with which, in a given card, it is mated. In the construction of a set of cards several forms of irregular internal arrangement were used, in order that the judgment might not be one merely of form, and of course on any given card the forms were not the same. Elimination of the effect of these form-differences from the results involved the appearance of any given one as many times in connection with one of the two contrasting factors studied in a given experiment as with the other. Thus two sets of forms were carried through an experimental series—a source of error indeed, but avoidable only by such means as were used to escape the effects of the space-error. Analysis would show which, if either, of the two sets received more judgments in its favor, resulting in further evidence as to the extent to which the judgment of relative number is a function of distribution, and as to the fineness of discrimination for such differences.
Now the tables, when thus rearranged, show that these errors exist to a surprisingly large extent. In many cases their causes, whatever they are, seem to be the controlling factors in the judgment of relative number.
Barring the experiments of Section III, in which the space-error has largely been accounted for, I now propose to gather in one survey all the results of those analyses that have given us the information of the existence of these errors, and all the material of later tables that bears on this point, and to test them by further experimentation. I will begin with the space-error.
TABLE X
| Av. % of difference in favor of | Av. % of difference in favor of | Av. % of difference in favor of | ||||
| Cases | Right | Cases | Left | Cases | No tendency | |
| Angier | 1 | 25 | 6 | 17.9 | 9 | 5.7 |
| Davison | 5 | 26.4 | 1 | 10.8 | 6 | 6.2 |
| Dunlap | 7 | 18.3 | 4 | 4.4 | ||
| Holt | 2 | 13.6 | 7 | 17.6 | 4 | 3.2 |
| Hylan | 8 | 23.6 | 7 | 6.7 | ||
| Meakin | 2 | 19.2 | 1 | 29.6 | 8 | 5.5 |
| Meriam | 2 | 16.5 | 2 | 12.9 | 7 | 6.8 |
| Moore | 2 | 11 | 3 | 16.6 | 7 | 3.1 |
| Peterson | 1 | 13.6 | 1 | 12.2 | 9 | 4.3 |
| Rogers | 4 | 21.9 | 2 | 15.9 | 6 | 4.5 |
| Rouse | 3 | 15.5 | 8 | 5.1 | ||
| Shaw | 3 | 20.9 | 5 | 18 | 7 | 6.1 |
| Windate | 1 | 22.8 | 4 | 19.5 | 7 | 4.5 |
| Yerkes | 6 | 26.6 | 8 | 5.2 | ||
| Henry | 1 | 10 | 2 | 16.6 | 3 | 8.1 |
| Woods | 3 | 19.3 | 3 | 4.8 |