A further attempt was made to head off reflection by a subterfuge. It had been found that, among the factors whose influence on the judgment had been studied, hearing had been as little effective as any. So the small stopped pipe used for those experiments was again brought into service and the error resulting eliminated in the usual way. Incidentally our new tables will thus give us further information about the effect of this factor, though of course under conditions that are theoretically highly unfavorable, since we are forcing upon the attention of the observers other factors that experience has shown them only too ready to seize upon. So if a tendency traceable to the factor of hearing should appear, we ought perhaps to give it somewhat more than its face value.
TABLE XVII
| A. | B. | C. 88 experiments each | |||||||
|---|---|---|---|---|---|---|---|---|---|
| Exposure = 125 sec. | Exposure = 14 sec. | Exposure = 125 sec. | |||||||
| Homogeneous | Vacant | No tendency | Homogeneous | Vacant | No tendency | Homogeneous | Vacant | No tendency | |
| Angier | [1]50 | [2]51.2 | 39.6 | ||||||
| Baldwin | [2]53.4 | [2]55.6 | 35.2 | ||||||
| Bell | [1]52.2 | 3.4 | |||||||
| Holt | [2]44.4 | [1]13.6 | 27.2 | ||||||
| Hylan | [2]51.2 | [1]52.2 | 39.6 | ||||||
| Johnston | [1]56.8 | [2]62.6 | 44.4 | ||||||
| Miller | [2]4.2 | [1]25 | 16 | ||||||
| Shaw | [1]29.6 | [2]14.8 | 2.2 | ||||||
[1] 44 Experiments.
[2] 88 Experiments.The per cents recorded indicate the average per cent of difference in favor of a given factor.
Now we are ready to inspect the results. Table XVII, A is the outcome of the attempt to emphasize vacancies. Its experiments with 125 sec. exposure were repeated with one of 14 sec. as Table XVII, B, shows. In Table XVII, C, the emphasis of compactness is concerned.
For convenience we may again resort to a summary outline in extracting the meaning from these tables. First Table XVII, A. (1) All the observers but one agree in favoring the homogeneous, most of them with very high difference-values. (2) Miller alone gives no tendency, and his notes show a conflict between the increased vacancy and the increased compactness. In other words, his discrimination was too keen for the material. Under the circumstances he constitutes no exception to the conclusion that the vacancy objectively emphasized was the cause for an underestimation of its group.
From Table XVII, B, we learn the following: (1) All the observers save one favor the homogeneous group, in most cases by large values. (2) The difference in the length of exposure seems to have no significance for this tendency, since, while Holt and Shaw decline, Miller rises in the scale.
Table XVII, C, gives us these facts: (1) The difference-values have noticeably fallen off. (2) We have again the customary three classes, but with homogeneous leading as in the earlier tables. (3) By his present favoring of the compact, Miller has now appeared in all three classes, while Holt has developed the preference for the compact that was budding in XVII, B. (4) The presence of four well-marked preferences for the homogeneous shows that the vacancies in the compact group were more significant for the number-judgment than was the increased compactness of the filling, and that in spite of the experimental effort to the contrary. (5) The decrease of this tendency and the growth of the opposing, indicates that the judgment is determined in either case by the more vivid factor.
The conclusions to be drawn from these facts lie close at hand. (a) The results in Table XVI, with their disproportionate division into classes, were evidently due to the tendency of three observers to note the filling and of the rest to be concerned with the vacancies. (b) The judgment of relative number under these conditions is primarily a judgment of vacancies. (c) The subjective factor of vividness determines the direction of error, and may attach to either vacancies or filling, though it usually attaches to the former.
It may not be out of place here to speculate a bit as to the probable cause for so close a dependence of the number-judgment upon what has no number, so to say; upon an object that has no standing in the official conclusion. The situation seems to be fundamentally based upon the conditions that determine contrast. In a homogeneous field no part stands out. Introduce a small object quite different in brightness or complementary in color and the attention is drawn instantly to it, but internal differences in its content are quite lost in the common quality by which it differs from the ground. A case somewhat analogous is furnished by our material, particularly in the One- and Two-Group Apparatus. The small group is so unified by its contrast with the field that internal differences must be made out with relative effort. Now internal differences are necessary to the numerical character demanded of it, and they can be brought out in no way save by attending to the vacancies and so isolating parts in the threatening unity, each in a kind of space-matrix. The most careful observer could not do better on his way to truth; and that is why the error was so much larger when the factor of space-differences was studied.