TABLE XVIII
| A | B | C | |||||||
|---|---|---|---|---|---|---|---|---|---|
| 44 experiments with each of 4 subjects, 88 with each of 3. | 88 experiments with each of 3 subjects, 44 with each of 3. | 88 experiments each | |||||||
| Exposure = 125 sec. | Exposure = 14 sec. | Exposure = 125 sec. | |||||||
| Sound | No Sound | No tendency | Sound | No Sound | No tendency | Sound | No Sound | No tendency | |
| Subjects | 1 | 6 | 6 | 3 | 1 | 3 | |||
| Av. % of difference in favor of | 27.2 | 4.1 | 5.9 | 12.9 | 20.4 | 4.5 | |||
It is a further curious fact, well sustained by these same experiments, that where there is some confusion, each of the factors present has a better chance to determine the judgment. The values for both time-error and sound rise higher for the majority in C than in A or B.
VI. THE INFLUENCE OF FACTORS IN THE SAME SENSE-FIELD UPON THE JUDGMENT OF ABSOLUTE NUMBER
The nature of the enquiry that we have been pursuing through so many pages is such that it may be raised exactly as well in the case of absolute as in that of relative number. There appears to be no reason why in this new field the results should not be exactly comparable with those in the old, to be taken indeed as a kind of test for the interpretation to be put upon the old. Without a single exception, unless it were imposed by a technical difficulty, all the earlier factors could be studied with the new purpose. Our practical interest to go to such lengths would depend pretty largely upon the results of first attempts. If wholly confirmatory, these would probably suffice.
The experimental conditions were of the simplest. The 3-8 in. steel balls of Section III were again pressed into service as objects for the number-judgment. They were thrown loosely into a fixed black frame, 20 cm. square. To avoid suggestive noises, its undersurface was made of a thick piece of felt covered with black cloth; and the whole rested of course on a black-topped table. The exposures were 2 sec. long, timed by watch-ticks. Between experiments the observer held a cardboard screen between him and the objects. When conditions were ready for a new judgment, closing his eyes he lowered the screen, opening his eyes again at the word of command and shutting them at the close of the experiment.
Of course the observers felt that their judgments were for the most part extremely vague. With small numbers they had a greater feeling of confidence. Yet altogether it was surprising with what readiness an absolute number-judgment would spring up in the presence of any given collection whatever within the limits set by the experimental series. Sometimes the observers thought that they made rough calculations on the basis of the filling in a unit of area. So far as this held it would tend to cut off the more astonishing departures from correctness, and it would probably advantage the smaller groups more than the large. Still it was entirely too rough a method to prevent the influence of the factors introduced, as the results will show. There was no time for systematic counting, which, in any case, the observers knew to be forbidden.
The figures in which the observers reported their judgments of absolute number have a value that is chiefly qualitative. The marked inconsistencies and disagreements are our guarantee for this statement. With all the observers there was but the loosest association between group-appearance and number-name. The innumerable variations in internal space-relations were of course responsible. For one observer a particular name probably had a quantitative significance far in excess of its value for another observer in this respect. To one man 100 might have meant about the same as 60, for example, to his neighbor. On the whole they were parsimonious; but Baldwin decidedly not.
A more or less constant influence was exerted on any given judgment by the comparison of the presented group with the traces of the preceding still in mind. The observers felt, however, that the judgment was largely independent of such comparison, and its fluctuations give some credence to this feeling.
The numbers chosen ranged by fives, from 25 to 100. In four cases a number was immediately repeated that rough suggestions as to the definiteness of the judgment and its dependence upon the actual number might be gained. These were indeed but rough suggestions, since, with certain exceptions to be noticed later, the arrangement was disturbed between times; but they made possible a closer watch upon the flickering of the judgment than could be kept by a mere repetition of the series. In the latter case it might be unstable and yet relatively firm in the other. A standard series is here recorded. Its order was determined by drawing the numbers out of a heap, but the repetitions were inserted arbitrarily.
- 1. 95
- 2. 25
- 3. 35
- 4. 65
- 5. No change
- 6. 30
- 7. 90
- 8. 85
- 9. 45
- 10. 100
- 11. 50
- 12. No change
- 13. 60
- 14. 40
- 15. No change
- 16. 70
- 17. 80
- 18. 55
- 19. 75
- 20. No change
1. Absolute Number under Standard Conditions.
An indispensable preliminary for the present study is the establishment of a standard. Unless we know something in advance about the characteristics of the judgment of absolute number in relatively simple conditions, we shall be unable to tell what influence, if any, to attribute to the modifying factor in later experiments. Having then decided as to the general conditions under which we will study the problem we must make these the standard conditions of our work; and having discovered the nature of the judgments given under them, measure up to these results in all that is to follow. These standard conditions have already been set forth in the introduction to this section. The results are recorded in Tables XIX and XX.
TABLE XIX
| Subject = Baldwin | Subject = Miller | ||||||
|---|---|---|---|---|---|---|---|
| Trials with each number | 6 | 3 | 3 | 4 | 2 | 3 | |
| Original Numbers | Standard | Scattered | Compact | Standard | Scattered | Compact | |
The figures recorded Baldwin never under- | 25 | 1 | 0 | -6 | -10 | -6 | -4 |
| 30 | 3 | 5 | -5 | -12 | -7 | -6 | |
| 35 | 10 | 7 | -3 | -14 | -4 | -7 | |
| 40 | 10 | 13 | -8 | -15 | -8 | -11 | |
| 40 | 10 | 8 | -8 | -14 | -10 | -12 | |
| 45 | 10 | 18 | -3 | -21 | -13 | -10 | |
| 50 | 17 | 23 | 2 | -19 | -15 | -17 | |
| 50 | 15 | 22 | 2 | -17 | -15 | -14 | |
| 55 | 27 | 40 | 0 | -18 | -3 | -12 | |
| 60 | 19 | 33 | 5 | -20 | -23 | -17 | |
| 65 | 27 | 53 | 2 | -18 | -3 | -7 | |
| 65 | 24 | 57 | 5 | -13 | -13 | 2 | |
| 70 | 38 | 77 | 0 | -19 | 8 | -8 | |
| 75 | 31 | 73 | 0 | -24 | 10 | -20 | |
| 75 | 28 | 78 | -5 | -24 | 8 | -8 | |
| 80 | 36 | 83 | -5 | -14 | 5 | -18 | |
| 85 | 54 | 85 | 5 | -19 | -8 | 0 | |
| 90 | 54 | 90 | 5 | -13 | 8 | -3 | |
| 95 | 48 | 73 | 5 | -30 | 20 | -15 | |
| 100 | 61 | 87 | 7 | -13 | 10 | -7 | |
Turning to these tables we notice at once, as characteristic of all the observers, the following facts: (1) Wide variation from objective correctness. (2) A far wider discrepancy with the larger numbers than with the smaller. Miller does not wholly agree here. His judgments by series show inconstancy, tending at first to follow the rule, but in the last two series to a maximum error near the middle. Certain remarks of this observer suggest that possibly in the latter case reflection as to the convenience of certain actual numbers for manipulation may have had influence. The three earlier series of Hutchison conform to the rule. The remainder, on the contrary, show no definite progression in tendency. It should be noted here that both Miller and Hutchison were more inclined than the other two observers to rough calculation. The effect of its adoption or of increased practice in it is shown by the disappearance of the characteristics of the earlier series. We have thus in these two cases a doubleness of standard that we must not fail to consider in our later comparisons. (3) There is a pronounced instability of judgment, as shown by the fluctuations for the same number in different series, and especially in successive judgments, of the same in any given series. (4) There is a general tendency to judge in multiples of five. That there should be any splitting of fives, particularly in the large numbers, might be regarded as mere caprice. Not so did it seem to the observers. They were conscious of an apparent absurdity in it where judgments were necessarily so vague; but they insisted that this stood for a kind of qualitative shading in the perception which threw out the choice of the round numbers just above and below. (5) The number is on the whole underestimated, three observers agreeing in this respect; but the fourth shows a very large and consistent tendency in the opposite direction.
In spite of the manifold special inconstancies and disagreements, these general tendencies are decidedly well-featured in the results. We may say that we have found a kind of standard illusion that will serve us for a guide through our later studies.
2. The Influence of Distribution.
TABLE XX
| Subject = Hutchison | Subject = Olmsted | |||||||
| Trials with each number | 3 | 2 | 4 | 6 | 2 | 3 | ||
For the meaning | Original numbers | First Standard Series | Second Standard Series | Mixed Sizes | Small Sizes | Standard | Mixed Sizes | Small Sizes |
| 25 | -5 | -2 | -3 | -1 | -8 | -8 | -12 | |
| 30 | -4 | 0 | -5 | 0 | -11 | -14 | -16 | |
| 35 | -6 | -5 | 10 | 1 | -8 | -5 | -14 | |
| 40 | -11 | -5 | -5 | -13 | -18 | -17 | -20 | |
| 40 | -12 | -9 | -13 | -11 | -13 | -18 | -22 | |
| 45 | -7 | -4 | -15 | -10 | -18 | -20 | -18 | |
| 50 | -14 | -10 | -20 | -12 | -19 | -18 | -23 | |
| 50 | -13 | -8 | -15 | -15 | -22 | -15 | -27 | |
| 55 | -10 | -7 | -20 | -11 | -24 | -28 | -23 | |
| 60 | -19 | -18 | -25 | -20 | -22 | -23 | -27 | |
| 65 | -15 | -7 | -20 | -5 | -28 | -28 | -33 | |
| 65 | -15 | -10 | -10 | -18 | -22 | -28 | -23 | |
| 70 | -14 | -3 | -15 | -20 | -27 | -30 | -28 | |
| 75 | -21 | -17 | -28 | -23 | -32 | -23 | -27 | |
| 75 | -25 | -20 | -20 | -24 | -33 | -25 | -32 | |
| 80 | -24 | -17 | -30 | -19 | -27 | -23 | -33 | |
| 85 | -17 | -13 | -35 | -13 | -27 | -38 | -38 | |
| 90 | -13 | -7 | -25 | -20 | -33 | -40 | -37 | |
| 95 | -25 | -13 | -40 | -23 | -39 | -55 | -40 | |
| 100 | -22 | -13 | -35 | -24 | -36 | -15 | -37 | |
The first of the modifying factors to be considered has to do with the arrangement of the objects. Hitherto they had been thrown loosely into the frame. Now in successive studies they were, first, well scattered over the surface and, second, brought together into several compact nuclei. The last arrangement was adopted in preference to that of a single mass as being less open to comparison with preceding judgments and to judgment on the basis of form and size of group.
The results are shown in Table XIX: (1) The effect of scattering the objects is very markedly to raise the apparent number. Baldwin's preceding overestimations soar still higher; while Miller's former tendency to underestimation is checked to such an extent that 13 overestimations appear. (2) The effect of compacting the objects is just as markedly in the opposite direction. Baldwin gives 31 underestimations, and Miller reverts in a measure to his former type. (3) When similar arrangements were up for study in relative number we found two classes of observers, one favoring the compact, the other the scattered. The present results of Baldwin and Miller put them into the latter class.
3. The Influence of Complexity of Group-Content.
This new factor of complexity in the content of the group was realized experimentally by making up the collection out of steel balls of two sizes, 1/8 in. and 3/8 in. The former looked almost infinitesimal beside the latter. The same objective numbers were still maintained and divided between the two sizes except where in so doing a five must be broken. In such a case the extra five went to the larger balls.
The results are found in Table XX. Olmsted shows no definite influence of the new factor. Hutchison, however, shows a very evident decrease in his estimations, when comparison is made with his second standard series. With the earlier series the new results rather closely correspond. That the latter are not simply a vacillating reversion seems fairly clear from this observer's account of his method. The small balls, he says, did not distinctly come in visually. To his judgment of the large he added an amount based on a very insecure estimate of the small. The number of the latter seemed from time to time pretty constant.
This situation corresponds very fully to that in the investigation of the same factor by use of a group of mixed colors, where relative number was in question. (Section II.) The tendency there discovered was to neglect the other colors in favor of one which thus surpassed the others in vividness. There as here the mixed group seemed smaller.
4. The Influence of Size of Objects.
A study of this factor was made possible by substituting for the usual objects steel balls of a smaller size, 1-4 in. The results are contained in Table XX. They are not so striking as those obtained in our study of distribution. Still the influence of this new factor is evident, in the reduction of the apparent number. Olmsted shows this more generally for the smaller numbers. We find it in Hutchison when we compare the new results with the second standard series. This tendency to underestimation increases in the two final series of the present set. At the beginning of these two he remarked that he thought he had been overestimating the group. This tendency of smaller size to reduce apparent number was found true for the majority of observers in our earlier study of relative number.
5. The Influence of the Length of Exposure.
I found that in relative number the shorter the look the more marked was the influence of certain factors. Reports of the observers making this seem highly probable happened in this way: When working with the One-Group Apparatus in relative number the shutter of the camera would occasionally stick, leaving a group exposed beyond its usual time. The effect of this upon some but not all the observers was to cause a noticeable shrinking in numerousness. Of those questioned, the only one failing to notice this effect is included among the observers in this new study.
To test this possibility resort was had to the One-Group Apparatus as affording a more satisfactory means for getting different lengths of exposure of small absolute magnitude. Cards were prepared containing a single group of larger area (67 × 82 mm.) than had been used for relative number. The objects were the usual white circles. Each corner was marked as usual; and, by reason of the number involved, the outline of the area was more regular than had been true in the earlier work. The number of circles on each card varied by steps of two from 16 to 30, giving eight cards in all. The series was arranged irregularly as before, and two of the cards repeated immediately upon their first presentation, making ten experiments in one set. The order of the series follows:
- 1. 24
- 2. 22
- 3. 26
- 4. No change
- 5. 18
- 6. 28
- 7. 16
- 8. 20
- 9. 30
- 10. No change
Two time-magnitudes were used for comparison,—1-25 sec. and 1 sec. The latter was managed with bulb exposure. All the experiments with the shorter time were made before those with the longer had been begun. The results are given in Table XXI. So far as the material is comparable, we may include in our comparison the standard experiments of Tables XIX and XX with 2 sec. exposure.
TABLE XXI
| Baldwin | Miller | Hutchison | Olmsted | ||||||
| Actual Numbers | 125 sec. | 1 sec. | 125 sec. | 1 sec. | 125 sec. | 1 sec. | 125 sec. | 1 sec. | |
| Number of trials with each number | |||||||||
| 5 | 6 | 5 | 5 | 5 | 4 | 4 | 4 | ||
| 16 | 6 | 9 | -2 | -3 | 11 | -1 | 2 | -5 | |
| 18 | 8 | 10 | -4 | -1 | 12 | -1 | -3 | -5 | |
| 20 | 34 | 19 | 1 | 3 | 19 | 1 | 1 | 1 | |
| 22 | 37 | 17 | 6 | 6 | 14 | 6 | 4 | -2 | |
| 24 | 49 | 26 | 12 | 5 | 14 | 10 | 5 | 0 | |
| 26 | 70 | 33 | 15 | 8 | 12 | 9 | 5 | 4 | |
| 26 | 79 | 37 | 21 | 9 | 14 | 4 | 9 | 4 | |
| 28 | 93 | 42 | 29 | 11 | 18 | 7 | 8 | 7 | |
| 30 | 106 | 52 | 38 | 12 | 18 | 5 | 19 | 10 | |
| 30 | 103 | 50 | 45 | 11 | 20 | 4 | 19 | 4 | |
For the meaning of these figures see note under Table XIX.
The outcome may be thus summarized: (1) The apparent number is inversely proportional to the length of exposure. The tables show a perfectly clear progression from 2 sec. to 1-25 sec. All those that formerly underestimated are brought into the opposite class. (2) The results of the earlier experiments are confirmed on the whole with respect to the occurrence of greater errors with the larger numbers. (3) Baldwin's overestimation reaches astonishing heights. (4) These new facts for absolute number are quite in accord with Table XII, where, under the conditions of interpretation laid down, the tendencies were wholly in favor of the shorter look.
The issue of these tentative experiments in absolute number confirms the teaching of our studies in the related field. Absolute number, like relative, has been found largely subject to a modifying influence of certain factors. In the new field, too, distribution has asserted its supremacy among these, and similar effects of shortening exposure have been observed. There has been variation among the observers and some shifting of tendency, both of which point as before to the coöperation of some subjective factor in our results. Indeed the whole situation, as opened by these preliminary studies, indicates a theoretical interpretation that for both fields is at bottom one. So to an attempt to reach such an interpretation the next section will be devoted.
VII. THEORETICAL DISCUSSION
1. The Fact of Modification.
That such an influence upon the judgment of number should have been exercised by the factors considered seems in many cases to receive an adequate account on the principle of association. Our practical experience in the simultaneous variability of number and certain other characteristics of a group of objects has been such as to lead us into illusions when the two no longer vary together. In such a case, when we have no time to count, we are actually led to see a group as smaller or larger in accordance with the variations perceived in the associated factor. This interpretation is supported by the fact that on the whole the space-factors were more markedly influential in creating illusions than were any others. For those cases, however, in which the modification was effected by a factor unconnected with number, as color, or the simultaneous stimulation of other senses by irrelevant objects, it appears that the mere occurrence of greater total stimulation during the appearance of one group is sufficient to create illusion, either through failure of the observer to discriminate between the relevant and the irrelevant, or because he is led through fear of disturbance to overemphasize the other group.
2. The Direction of Modification.
The foregoing account of the general fact throws no light upon the direction of the influence. Why should a given factor make a group seem more numerous and not less? Why should it affect one man in one way and his neighbor in another? Why should it vary with the same man at different times? Appearances no less contradictory than these are what we must face in carrying a theoretical account to completion. The following propositions with appended commentary are offered in satisfaction of these requirements.
a. Differences in vividness among the factors determine differences in number.
Our study of the factor of distribution in Table XVII, where it was possible in a measure to control the vividness, furnishes evidence for this proposition. Introspective reports in other cases confirm this view by showing that the direction of the attention, the popular way of stating our proposition, was the determining feature. This will receive further support in our discussion of the following proposition.
b. If the vivid factor or complex be positive, i. e., associated in experience with the numerous, or if it be neutral, its group will seem the more numerous. If negative, i. e., associated in experience with the few, its group will seem the less numerous.
The experiments upon the effect of distribution support this proposition, especially as set out in Table XVII. When the vacancies in a given group were made vivid, the other group seemed more numerous; when its filling surpassed in vividness, the judgment was given for it. We have other confirmation in the fact that lengthening the time of exposure reduced the absolute number. Take also this note of one observer on the material in Table II, C:
"I noticed that I had set the open spaces in the outlined group over against the lack of them in the homogeneous, without paying much attention to the nearness together of the spots in the lines of the outlined. Then for a time my attitude was quite vacillating. I found my attention drawn to the nearness together of the spots in part of the outlined group so strongly that if I did not turn it voluntarily to the fact that the other was filled without any large open spaces, I was led to call almost any outlined group the larger. Toward the end of the experiment I got back into my original attitude, in which the outlined group seemed to have its spots hardly more thickly arranged in any part than the homogeneous, and to have also the bare spots and so to be the fewer."
That the vividness of a neutral factor or complex increases the apparent number was suggested by comments of the observers. One observer reported of the material in Table IV: "The greater brightness of red gave it more importance. The natural thing seemed to be to give the red the judgment. The gray fought more for recognition." And again: "The red seems a vitalized space and the dots more omnipresent, also the red lasts longer in memory and is there more vivid, so that often in cases of doubt, where the decisive comparison was made in memory, the red may have been given the vote. Often there was an immediate unanalyzed feeling that if the groups had been both of the same color, the judgment would have been for the gray." In both cases his results showed this tendency. Another observer, whose results agree with the former, found that his eye was directed involuntarily toward the red.
This fact was put to a special test. In the material of Table II, B, a card, in which the pattern group had an appearance strikingly different from the normal, was introduced, the two groups being objectively equal. With three observers the effect was overestimation of this group, and with a fourth, the suppression to equality of a previous overestimation of the opposite group. This fact, together with the observers' comments, seems to justify the conclusion that the vividness of a neutral factor or complex was the determining condition of the judgment. That the observers did not all show positive results in this experiment may be set down to the difficulty in controlling the subjective conditions of vividness. Of course the space-relations within the new pattern were different from those in the old. The only justification for taking no account of these is the character of the introspections themselves.
It should be said of the red group that beside its vividness it had characters mentioned by other observers that might independently have made its number seem greater. It was called "dazzling," "blurred," and its area seemed increased. In this respect the effect of the color should be discussed as a special case of distribution or object-size.
The vividness tested in this special way seems due to contrast, in the one case with surroundings, in the other case with the expected. Such a judgment is very far removed from the normal bases, rather more so, it would seem, than even those where a group had sound or touch accompaniment; for in the latter case there could be no question about the "moreness"; the only doubt could be about its legitimacy. Of the precise extent to which this cause of vividness has operated throughout our studies, even where spatial differences have been concerned, we cannot be sure. The patterns of the materials in B and C of Table II seem to offer that possibility. That it should enter anywhere opens, indeed, the entire field.
c. The observers fall into the following classes on the basis of the character of the association:
(1) Relatively fixed association,
(a) involving correct adjustment to objects (vividness of relevant factors);
(b) involving incorrect adjustment to objects (vividness of irrelevant factors).
(2) Relatively unstable association.
It will be remembered that in the case of nearly every factor studied under Relative Number, we found three classes of observers,—those favoring one group, those favoring the other group, and a so-called "no-tendency" class. The bases of classification were, first, the relative constancy in the character of the error, and, secondly, its direction. In this third or "no-tendency" class were really lumped off two kinds of observers, not separated at the time because our special interest did not demand it. Along with those that gave large errors in both directions was a much smaller class that gave a relatively large proportion of correct judgments; but could never claim any one observer all the time. In the new classification of Proposition c this mixed composition is recognized by dividing it between (1) (a) and (2). The prime condition of correct judgment is asserted to be one in principle with that of the illusion,—namely, vividness, but in this case vividness of relevant factors. Our original "tendency" classes both fall under (1) (b).
Proposition c is merely an attempt to apply the principles of association and vividness to an organization of our results. The types in question have no hard-and-fast connection with any particular observer; they rather represent a kind of ideal fixation of opposite tendencies playing through all.
3. The Time-Error.
So far the time-error has been left without interpretation. The chief facts to be considered were: (a) Divergence of error and general trend in favor of last. (b) Individual inconsistencies. (c) Occasional absence.
We are in a position now to invoke at once the principle of vividness to account for the existence of the error and the vividness of recency to account for the predominant tendency to favor the last of the two groups exposed. In this respect this error may be classed with the effect of red. That is to say, a factor or complex, directly through its vividness and not indirectly through its association with the numerous or the few, draws the judgment after it. Here the content of the group is the effective thing, not the character of the vacancies.
But the observers do not all agree in the direction of the time-error nor are they always consistent. Here we shall get help from a proposition offered in the discussion of the distribution-error in which it is asserted that the group seems the more numerous in which the vacancies are less developed under observation. We have already noted a decided tendency to depend in judging upon the vacancies. Let us suppose that the two groups presented in succession differ with respect to the success of the observer in developing these vacancies. If this be true, that difference may well depend upon the occurrence of maximal attention during the exposure of but one of the groups. The tendency of the majority to overestimate the second group suggests that the attention is likely to be at a maximum when the experiment begins. If, on the other hand, it ripen later, or if the observer seek to rescue the second group from relative unclearness, then we should have the first group overestimated. The time-error would disappear for those that could attend alike to both. Clearly enough this account is decidedly hypothetical.
4. The Space-Error.
Our attempt to reduce this error to one of time in some form was proven a failure. The facts brought out indicate that at the bottom is some subjective factor thus far not isolated. This factor is not a preference going directly with right- or left-handedness because on the surface at least it runs in the observers independent of such asymmetry. A single bit of available introspection would seem, however, to point to some relation of that sort; for one observer, who favored the left, felt that a group on that side gained an importance that was somehow due to the greater absolute value of a weight in the left than in the right hand. Even if this be decisive for him it will still be inapplicable to errors in the opposite direction unless we assume that with variations in bodily energy the emphasis is cast now in one, now in the other, direction, after the analogy of those two types of man to be found in our social experience, for whom respectively mountains are molehills and molehills mountains. Such successive differences in type in a single individual would then find an intelligible account in the shifting tides of that bodily energy. It is to be noted that the observer just quoted once, but only once, made a decisive reversal of his error from left to right.
It may occur to some one that the use of two observers sitting side by side may have given them a preference for one position of the groups. In the first place care was taken that both groups should be as readily seen from one point of view as from the other. Secondly and chiefly, there is no regularity among the observers in this respect.
It is not unlikely that a chance aspect of a particular group develops an emphasis that gives the mechanism of subjective adjustment a particular bent that for a time is relatively independent of the objective situation. Still the fact that there are some cases of persistence in type is rather damaging to this assumption and speaks rather for the earlier one. That one, if true, seems indeed adequate to account for the situation. As an hypothesis it accords with analogous physiological facts; but its weakness lies in imposing the burden of a strong tendency upon asymmetrical differences that may be in comparison relatively slight. Finally, these studies furnish no proof that the bodily condition of an observer of a particular type corresponds to the demands of the hypothesis.
Summary: 1. The estimation of relative number in the visual field is modified by group-area, internal distribution, order, and complexity in group-composition; by the size, form, color, brightness, and complexity of the individual members; and by the character of the environment. It is further modified by factors contributed by the objects through other senses, as in active pressure, special differences in pressure character, active weight, and that complex of muscular and spatial factors arising when a group is observed under the condition of eye-muscle strain. The judgment is also influenced by factors outside the group in the field of touch, but not in that of kinæsthetic impressions.
2. On the whole the most influential factors were those lying in the space-characters of the groups; while those of least moment were contributed by other objects in other fields of sensation. Hearing was very nearly ineffectual.
3. In very many cases the observers fell into three groups, one of no-tendency, and a second and third showing opposite tendencies with respect to the factor investigated.
4. With a majority of observers there is a tendency to underestimation in the judgment of absolute number, though with a single observer the tendency is directly the reverse. Scattering the objects increases, and compacting diminishes, the apparent number. The smaller the size of the objects the fewer, under conditions, do they appear; while heterogeneity in group-composition lessens the number for one observer and has no apparent effect upon the other.
5. The apparent absolute number of objects is inversely proportional to the length of exposure of a group; and in relative number the influence of a factor was on the whole greater for shorter exposures.
6. The marked tendency to a space-error was found to be independent of differences between the groups in the length of look, and of the order in which they were viewed.
7. The distribution-error is grounded in a fundamental tendency to base the judgment of relative number upon the character of the vacancies in a group; though a secondary tendency to depend upon the filling was shown to exist. The subjective factor of vividness, attaching now to one and now to the other of the foregoing factors, determines which shall be operative, though it usually is joined to the first. The ground for the primary tendency may very well be the necessities imposed upon discrimination by the material. The contrast effect between the large black background and the brighter objects tends to unify the latter, which, to be discriminated as a number, must be split up by an emphasis of the vacancies.
8. The time-error is possibly due to differences in power to dismember the groups exposed in succession in one experiment, while its variations in direction seem adequately accounted for by differences in the time at which attention becomes maximal during the progress of a single test.
9. The ground for these facts of modification is found in the strength of the association between these several factors and the elements that signify number.
10. The basis for the different tendencies found among the observers is the differing vividness among several factors. If the vivid factor is associated with the idea of numerousness, or is in this respect neutral, its group will seem more numerous. If it has been associated with the idea of fewness, its group will seem less numerous. The difference between the two classes of "tendency" and "no-tendency" lies in the fact that for the latter either only correct clues are vivid, or else there is so frequent an alternation in vividness of opposing incorrect clues that through any given series no tendency appears, while for the "tendency" class misleading clues are without shifting in the ascendant.
At the time when these experiments were completed, no work precisely upon this problem had been published. Since then, however, Dr. J. F. Messenger has issued a monograph entitled The Perception of Number (Psych. Rev., Mono. Supp., vol. 5, no. 5), of which certain parts fall within the scope of the present studies. He was concerned with the estimation of absolute number and was primarily interested to discover the nature of the number-judgment. The reader of both articles will find agreement between the results and interpretations here recorded and such part of Messenger's work as has been a common object of study,—viz., the factors of distribution and size.
TIME-ESTIMATION IN ITS RELATIONS TO SEX, AGE, AND PHYSIOLOGICAL RHYTHMS
BY ROBERT M. YERKES AND F. M. URBAN
The desirability of a statistical study of time-estimation was suggested to us by a note concerning "sex-differences in the sense of time" which was published in Science recently by Prof. Robert MacDougall.[125] By comparing the time-estimates of groups of men and women consisting of fifteen individuals each, MacDougall discovered that for intervals of from one quarter of a minute to a minute and a half, the women exhibited a far stronger tendency to overestimate than did the men, and were at the same time markedly less accurate. The nature and extent of the overestimation discovered by MacDougall are indicated by the results presented in the accompanying table from Science. The numerals, 1, 2, 3, and 4 refer to different fillings of the intervals (listening to reading, marking letters, etc.), the signs + and - to over- and under-estimation respectively.
| Period, One Minute. | ||||
| Sex | 1 | 2 | 3 | 4 |
| Men | +29" | + 1.3" | +22" | - 3.5" |
| Women | +66 | +22.0 | +80 | +24.0 |
These apparent sex-differences in time-estimation demand further attention, first, because the number of individuals studied by MacDougall, as he recognized, is too small to establish the fact of the existence of such differences, and, second, because if the differences really do exist they should be studied in their relations to age and the fundamental physiological rhythms.[126]
It seemed probable that further investigation of this subject might reveal some important facts concerning the development of the ability to estimate time in the individual, the significance of various conditions for time-estimation, the psychology of sex, and the relations of rhythms to personal affinities, antipathies, and motor capacities.
In this report the results of a statistical study of the sex-differences in time-estimation are discussed, and in later papers we shall present the results of investigations of the relations of time-estimation to age and to individual and sex rhythms, and attempt to work out a convenient and serviceable rhythm-formula. The need of such a formula for expressing individual rhythms is obvious, as is also the need of comparative studies of individual and sex rhythms.