| A | B | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Cases | Class 1 | Cases | Class 2 | Cases | No tendency | Cases | Class 1 | Cases | Class 2 | Cases | No tendency | |
| Angier | 4 | 19.1 | 2 | 6.3 | 3 | 2.9 | ||||||
| Davison | 3 | 23.1 | ||||||||||
| Dunlap | 2 | 13.7 | 1 | 2.2 | ||||||||
| Holt | 3 | 15.5 | 1 | 25 | 2 | 4.5 | 1 | 22 | 1 | 21.6 | 2 | 3.1 |
| Hylan | 1 | 11.4 | 2 | 14 | 3 | 6.7 | 2 | 50.8 | 1 | 11.4 | 1 | 8.4 |
| Johnston | 5 | 30.4 | ||||||||||
| Meakin | 3 | 34.9 | ||||||||||
| Meriam | 1 | 16 | 2 | 6.8 | ||||||||
| Miller | 5 | 32.1 | ||||||||||
| Moore | 1 | 39.8 | 2 | 5.7 | ||||||||
| Olmsted | 1 | 27.2 | ||||||||||
| Peterson | 3 | 42.1 | ||||||||||
| Rogers | 1 | 11.4 | 2 | 5.7 | ||||||||
| Rouse | 2 | 14.2 | ||||||||||
| Shaw | 6 | 29.1 | 2 | 26 | 1 | 0 | ||||||
| Windate | 3 | 30 | ||||||||||
| Yerkes | 3 | 17.8 | ||||||||||
Here as elsewhere the per cents recorded indicate the average per cent of difference in favor of a given class.
Here are the facts, first of A: (1) The only lapses from consistency are confined to two observers; and in both these cases there is but a single break in a uniform trend. (2) With three exceptions all agree in the trend of their difference-values. Of these three—Holt, Hylan, and Moore—the last furnishes but one significant value, and so must be left out of the reckoning on this point. (3) Of the 64 cases, 50 rise above 10%, some far beyond, showing the importance for the judgment of relative number of this factor of distribution. (4) Of the 50 cases, 45 agree in tendency. (5) That with this surprising agreement we have still a few exceptions, adds another item to the growing array of evidence on behalf of the importance of some subjective factor for the number-judgment. As to the nature of this factor we are yet in the dark. (6) To these facts B of this same table adds the further information that the observers inconsistent in the old are not consistent in the new, while the consistent still maintain their record.
a. Analysis of the Experimental Conditions of Distribution. At once we are interested to enquire for the factors underlying these results. To put ourselves upon the right track we must first consider what factors are involved in any such arrangement of objects as we have used in the material for these studies, and then, more precisely, we may ask in what way such arrangements could differ significantly. Finally, by an experimental trial-and-error process, we may solve our problem.
The groups of objects in our material were arranged in an area marked out in each corner by a circle. Within this area the circles were set irregularly, with the result that the group, as a mass of objects distinguished from a homogeneous background, had a more or less irregular outline whose irregularity varied with different internal arrangements. Within its outlines this area presented a mixed pattern of bright and dark. While the total enclosure marked off by the corner circles was always the same and theoretically the relative amounts of brightness and darkness in equal groups was likewise the same, yet practically differences, more or less slight, might enter through the changing character of the rude outlines whose ideal completeness could scarcely be brought out of a black background by the uninitiated. The amount of this difference is sometimes surprising to one whose chief thought of the group has been as vignetted in process of construction. As the objects are pushed toward the edges the central spaces open out; as they are withdrawn toward the interior gaps appear in the margin.
It is not a very easy task to fill an area with objects in irregular arrangement in such a way that no sections of vacancy or filling stand out by contrast against the remainder of the same element. To succeed in this is to fill the area homogeneously. But the chances are good that some vacant patch will get slightly the better of its neighbors or some section of circles will gather a little more closely than the surrounding circles; or perhaps a gap in the outline will be unexpectedly intrusive. Now in a given area the circles of one part cannot become more thickly massed without a corresponding enlargement of the vacancies of the other parts, and of course the converse is as true; but this theoretical situation may be quite out of ken at the moment when the group is seen. Either member of this pair of complements may stand out vividly in the field and its fellow quite escape perception. The very nicety with which in practical affairs we have to make a reliable comparison of this sort shows what suspicion of accuracy the off-hand judgment has bred. And further, the widening of a gap or thickening of the filling in one small part of a group may give a complementary loss to the rest of the group small enough to be unperceived when distributed throughout the larger section.
Two factors must therefore be considered as possibly significant in moving the judgment,—vacancies and filling; and with the former must be reckoned indrawing of the outline. Psychologically, increase in the prominence of either of these factors would be all one with their objective increase. With respect to the direction of their influence upon the judgment of number the increase of vacancies must signify the waning, and the increase of filling the waxing, of the objective number in the group.
It is in advance altogether probable that the results gathered into Table XVI were brought about by these two factors, at least in large part. And we have also in these factors the possibility of two types; for as we saw above, increased vacancies in one part involves increase of filling in another, and conversely. So the interesting question turns upon the altogether disproportional representation of types. Which is the type of the majority?
b. Experimental Test of Hypotheses. The question was put to the test of experiment. This was done by using groups in which now vacancies and now filling were objectively emphasized in contrast with the usual homogeneous group. First the vacancies. A set of cards was prepared after the method previously used to eliminate the distribution-error without duplication of groups on any one card. (See Section II.) In the present case, however, the two sets of arrangements were definitely differentiated as already indicated. One set had a homogeneously filled area, the other a prominent vacancy within or gap in the edge. The size of these variations was kept pretty close to the limit of noticeableness, that the increase in compactness of the other portions might be as slight as possible. It was experimentally necessary to free the material as far as might be from ambiguity, and practically important to avoid rousing the suspicions of the observers and the resulting reflections. It seemed very likely that the strength of the tendency shown by the distribution-error was due to its appearance in situations where the observers knew that other factors were being tested.
The general method already described was used in preparing the groups that gave objective prominence to compacted parts of the filling. To fulfil the conditions outlined above was here even more difficult than in the first set; and the cause will appear in the sequel. The small-difference cards were omitted and the One-Group Apparatus used.