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
KEY: A = 1/25 sec.
B = 1 sec.
_Baldwin_ _Miller_ _Hutchison_ _Olmsted_
_Actual_
_Numbers_ A B A B A B A B
_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.
FOOTNOTES:
[Footnote 123: 44 experiments.]
[Footnote 124: 88 experiments.]
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.
TIME ESTIMATION
Name Place
Age Date
ORDER OF TESTS TIME IN SECONDS
_Time of_ _Male_ _Female_
_Intervals._ (_17 years_) (_17 years_)
No. 1 No. 9
1. Idleness _108̋_ _70̋_ _120̋_
2. Reading _36_ _30_ _118_
3. Writing _72_ _36_ _60_
4. Estimating _18_ _15_ _30_
5. Reading _108_ _90_ _68_
6. Idleness _36_ _35_ _60_
7. Writing _18_ _10_ _10_
8. Estimating _108_ _100_ _125_
9. Reading _72_ _100_ _66_
10. Idleness _72_ _75_ _58_
11. Writing _36_ _25_ _22_
12. Estimating _72_ _60_ _60_
13. Reading _18_ _14_ _15_
14. Writing _108_ _130_ _59_
15. Estimating _36_ _30_ _41_
16. Idleness _18_ _10_ _18_
How did you estimate the interval when you were asked to estimate it
as accurately as you could?
n o f e y m i q r s a d r g d e s t k n w e r a x u p x z y o n d f n
o d c a e h p m a l g s r w y t b c k p s o n q a r v q c o m p v r i
c p k t o s n q z r l x m i h u v o q g P p f u t o i c n g s c a r n
o t c d a a o b i a r s a d e r w o a i e r g l c r t h f s o r a e n
s i o c r b x g r z b h o w l t s
Number of letters counted 85 88
Pulse-rate 72 81
The experimental data now to be considered were obtained as follows.
Record-sheets of the form reproduced above were printed, with blanks
for age and name of subject, place, date, for sixteen judgments of
time-intervals (numerals 1 to 16), for a statement of the subject's
method of estimating time, for the number of letters counted in thirty
seconds, and for the pulse-rate. Four intervals were used, 18, 36, 72,
and 108 seconds, and for each of these intervals judgments were taken
under the four conditions designated on the record-sheet as idleness,
reading, writing, and estimating. In the experiments the intervals
were not given in order of regular increase or decrease of the length
of interval, nor were all the judgments for any one interval taken
together, but instead, for the purpose of avoiding the influence of
expectation of a particular interval or filling, they were arranged
irregularly in the order of column two of the record-sheet. This
column, as also columns three and four, which are specimen series of
judgments for a male and a female respectively, of course were not
printed on the record-sheets which were supplied to the subjects.
The experimental procedure was as follows:
(1) Each subject was given a record-sheet.
(2) The experimenter was provided with a record-sheet on which the time
of the intervals numbered from 1 to 16 was given. Care was taken that
the subjects should not know the length of the intervals before the
experiments.
(3) The beginning of each interval was indicated to the subjects by the
word "start" uttered distinctly by the experimenter; the end, by the
word "stop."
(4) Before beginning the sixteen tests the experimenter gave a
thirty-second interval as a standard of judgment. The experiment then
proceeded with only sufficient pause between judgments to allow of the
recording of estimates by the subjects.
(5) During the filling called "idleness" the subject did not pay
special attention to the estimation of the time, but instead permitted
his attention to wander.
(6) During "reading" the experimenter read aloud to the subjects.
(7) During "writing" the subjects wrote from the dictation of the
experimenter.
(8) During "estimating" the subjects judged the interval as accurately
as they could, by whatever method they chose except the use of a
time-piece.
(9) Each subject recorded his judgment of the length of an interval in
seconds at the appropriate place on the record-sheet as soon as the
interval was ended.
(10) The question following judgment number 16 on the sheet was
answered as soon as the sixteen judgments had been recorded.
(11) The number of letters counted in thirty seconds was determined
by the use of the lines of letters at the bottom of the sheet. The
subjects began at the left of each line and counted singly as many
letters as they could between the "start" and "stop" signals of the
experimenter. They then marked the last letter counted and immediately
recorded, in the place provided on the record-sheet, the number of
letters counted.
(12) The pulse was counted by the experimenter immediately after the
experiment when possible and the rate recorded on the sheet.
(13) The experimenter avoided delays, interruptions, or other
irregularities in the course of the series of experiments.
The materials for our discussion of the sex-differences in
time-estimation consist of the judgments of 251 males and 274
females. The majority of the males were students in Harvard College,
the majority of the females, in Radcliffe and Smith Colleges. The
remainder of the records were obtained in Ohio State University, Pomona
College, and West Chester State Normal School. The authors gratefully
acknowledge their indebtedness for assistance in the obtaining of
records to Professors A. H. Pierce, T. H. Haines, W. H. Scott, D. R.
Major, A. M. Smith, H. A. Miller, and B. T. Baldwin. The males ranged
in age from 17 to 23 years, the females from 17 to 20. The total number
of judgments, the distribution of which among the various ages is shown
in Table 1, is 4014 for the males, 4375 for the females.
Despite the fact that our experiments are open to the criticisms of all
work done under variable conditions and by different experimenters, it
cannot be doubted that the results indicate certain sex-differences in
time-estimation which suggest additional problems. For the present we
refrain from interpretations for the most part and state merely the
statistical results of the investigation.
Previous studies of the "time-sense" and the conditions which influence
time-estimation suggested to us the desirability of examining our
data with reference to (1) sex-differences in estimates of intervals,
(2) age-differences, (3) the influence of different fillings, and (4)
differences dependent upon the length of the interval. The results have
been studied, therefore, with reference to the significance of sex,
age, filling, and length of interval, but as no marked age-differences
appeared, the detailed tables which were constructed to exhibit the
results for the subjects of each year of age have not been printed.
In all the tables the results for males and females are presented
separately. The judgments for the sixteen intervals are arranged with
reference to the length of the interval, not in the order in which they
were taken; all the 18̋ intervals, for example, are grouped (Table 2).
The letters I, E, R, W, refer to the fillings of the intervals.
TABLE 1
NUMBER OF SUBJECTS, AGE, SEX, AND NUMBER OF JUDGMENTS
_Males_
_Age_ _No. of subjects_ _No. of judgments_
17 yrs. 16 256
18 27 432
19 40 639
20 67 1071
21 50 800
22 35 560
23 16 256
Totals 251 4014
_Interval_ _No. of judgments_
18" 1004
36" 1003
72" 1003
108" 1004
Total 4014
_Females_
_Age_ _No. of subjects_ _No. of judgments_
17 yrs. 73 1160
18 57 911
19 64 1024
20 80 1280
Totals 274 4375
_Interval_ _No. of judgments_
18" 1092
36" 1094
72" 1096
108" 1093
Total 4375
A general survey of the individual records, all of which for any one
year and sex were tabulated, for convenience of examination, on a
single large sheet of coördinate paper, showed that the judgments vary
within a wide range and are very inexact. Table 2 exhibits the number
of correct judgments for each sex, interval, and filling. Of the
4014 male judgments only 96 (2.39%) were correct; of the 4375 female
judgments only 46 (1.05%) were correct. The number of correct judgments
decreases as the length of the interval increases. For the 18-second
intervals there were 7.37% for the males, 2.48% for the females,
while for the 108-second intervals there were only 0.10% and 0.37%
respectively.
TABLE 2
FREQUENCY OF OCCURRENCE OF CORRECT JUDGMENTS
_Males_
18̋ 36̋ 72̋ 108̋
I E R W I E R W I E R W I E R W Σ %
29 26 11 8 5 6 3 0 3 3 0 1 0 1 0 0 96 2.39
Totals 74 = 7.37% 14 = 1.40% 7 = 0.70% 1 =0.10% 96 2.39
_Females_
7 15 1 4 2 4 1 0 2 5 0 1 2 1 0 1 46 1.05
Totals 27 = 2.48% 7 = 0.62% 8 = 0.73% 4 = 0.37% 46 1.05
_List of abbreviations which occur in the tables._
Σ always designates the sum of the results of the column which it
heads.
I, E, R, W refer respectively to the intervals of idleness,
estimating, reading, and writing.
The % sign refers to the value of the result in question in terms of
the total number of judgments.
C refers to the results of the letter-counting test.
The male judgments for the 108-second intervals range from 11 to 300
seconds. If random guesses be made within these limits the probability
of the occurrence of right guesses (108") would be 1 in 290; therefore
among 1004 guesses (the number of male judgments for 108-second
intervals) 3.5 would be right. In the experiment only one judgment of
the 1004 was correct. For the other intervals, with the exception of
18 seconds, the number of correct judgments is only slightly greater
than random guessing would have given. Both males and females, however,
show considerably more correct judgments for 18-second intervals than
the number of probable right guesses. Within the range of the male
judgments and for their number 16.9 right guesses might be expected,
for the females 10.9. In contrast with these numbers the experiments
furnished 74 and 27 correct judgments respectively.
It is noteworthy that for those intervals which are most frequently
correctly judged, not only is the number of correct judgments greater
for the males than for the females (the ratio of the percentages is
about 3 to 1), but the ratio of the number of correct judgments to the
probable number of right guesses is also greater for the males.
The female judgments vary within a wider range and are less often
correct than the male. For the latter the total number of correct
judgments is more than twice that for the former.
Another interesting fact concerning the judgments of the time-intervals
is that certain numerals occur in the last place of a judgment more
frequently than we should expect if their occurrence depended on random
guessing. Tables 3 and 4 exhibit the results of an analysis of the data
made for the purpose of studying this fact. In Table 3 the frequency
of occurrence of the digits 0, 1, 2, 3, etc., in the last place of the
male judgments is given for each filling under the four intervals. For
example, the digit 0 occurred in the last place of the male judgments
for the interval reading 36 seconds 98 times, as we learn by referring
to the first line and third row of the second column of Table 3.
Examination of Tables 3 and 4 shows at once the marked preference of
the subjects for 0 and 5. The percentage of male judgments which end in
0 is 41.50; of female 58.51. Similarly the percentages of occurrence of
the digit 5 for the males is 24.41, and for the females 23.11. Only two
of the other digits (2 and 8) occur with a frequency of over 5%.
Among the 4014 male judgments 0 occurred as a final digit 1666 times,
5, 980 times. Among the 4375 female judgments 0 occurred 2560 times, 5,
1011 times. In the male judgments 0 occurred about four times as often
as it would in random guessing; in the female, almost six times as
often.
Comparison of Tables 3 and 4 indicates that the occurrence of 0 is
17.10% greater for the females, while that of 5 is 1.30% greater for
the males. The sum of the percentages of occurrence of 0 and 5 for the
males is 65.91, therefore the probability that a male judgment ends in
one of these digits is almost twice that in favor of any other digit.
For the females the sum of the same percentages is 81.62, and the
probability of occurrence of 0 or 5 is therefore more than four times
that of the other eight digits.
Tables 3 and 4 show that even numbers occur more frequently than uneven
as final digits. Of the total number of judgments 2461 (3063)[127] end
with even digits and 1553 (1312) with uneven.
TABLE 3. FREQUENCY OF OCCURRENCE OF THE NUMERALS (0 TO 9) AS FINAL
DIGIT OF THE JUDGMENTS COMBINED RESULTS FOR ALL MALES
18̋ 36̋ 72̋
I E R W I E R W I E R W
0 70 57 72 76 131 77 98 90 124 74 120 125
1 5 11 9 9 10 9 8 7 1 18 5 2
2 20 15 21 18 5 19 16 15 11 20 5 14
3 9 17 14 10 8 11 10 8 6 14 12 4
4 8 12 14 9 3 14 12 3 4 14 8 7
5 67 58 56 63 62 54 60 85 72 59 62 73
6 13 17 12 13 9 14 11 6 10 9 7 7
7 15 22 14 12 6 15 11 10 5 14 13 4
8 36 30 29 31 15 19 16 20 11 17 11 11
9 8 12 10 10 2 18 9 7 7 12 8 3
108̋
I E R W Σ % C
0 151 121 127 153 1666 41.504 21.92
1 4 11 10 2 121 3.014 7.57
2 9 12 9 8 217 5.406 13.15
3 3 12 14 3 155 3.861 7.17
4 6 18 9 3 144 3.587 7.57
5 54 45 52 58 980 24.414 10.36
6 8 7 6 4 153 3.812 8.76
7 4 7 10 8 170 4.235 7.17
8 8 13 5 9 281 7.004 8.76
9 4 5 9 3 127 3.164 7.57
TABLE 4. FREQUENCY OF OCCURRENCE OF THE NUMERALS (0 TO 9) AS FINAL
DIGIT OF THE JUDGMENTS COMBINED RESULTS FOR ALL FEMALES
18̋ 36̋ 72̋
I E R W I E R W I E R W
0 120 117 106 126 169 124 182 151 176 145 175 194
1 4 8 3 2 6 7 1 3 2 3 2 1
2 17 18 12 13 9 22 7 11 7 11 3 4
3 4 9 9 11 5 9 3 7 6 15 10 4
4 2 11 13 10 1 6 4 2 9 14 3 1
5 89 63 91 85 62 61 60 79 56 55 65 63
6 9 12 11 6 5 13 7 5 4 6 3 3
7 5 5 7 7 4 9 5 3 2 7 3 3
8 16 22 17 12 10 13 5 10 10 9 6 1
9 5 9 5 1 3 9 0 2 2 9 4 0
108̋
I E R W Σ % C
0 226 197 196 186 2560 58.515 26.14
1 1 5 2 0 50 1.143 9.09
2 4 11 6 3 158 3.611 5.30
3 3 7 4 7 113 2.583 5.68
4 2 4 2 2 86 1.966 11.36
5 32 44 49 57 1011 23.109 14.39
6 0 9 3 1 97 2.217 6.44
7 0 5 2 5 72 1.646 6.44
8 5 11 8 7 162 3.703 10.61
9 1 10 2 4 66 1.508 4.55
In order that the probability of the occurrence of even and uneven
numbers may be calculated, those judgments which end in 0 and 5 must be
subtracted from the total number of judgments, for the occurrence of
these two digits is apparently due to a constant influence. The problem
may be formulated thus. First, what is the probability that a judgment
is determined by the constant influence in favor of 0 and 5? Second,
what is the probability of even and uneven numbers, when the influence
in favor of 0 and 5 is eliminated? The calculated probability of 0
or 5 is 0.65919 (0.81622) and therefore the probability that a given
judgment is not determined by this influence is 0.34081 (0.18378). The
probable limits of these numbers are 0.00505 (0.00395).
After the subtraction of those judgments which end in 0 or 5, there
remain 1368 (804), of which 795 (503) are even and 573 (301) uneven.
The probability of an even number is 0.58115 (0.62562) and the inverse
probability of an uneven number is 0.41885 (0.37438). The probable
limits of these numbers are 0.00900 (0.01027). There are therefore even
chances that the percentage of occurrence of even numbers is between
the limits 57.215 and 59.015 (61.535 and 63.589), or outside these
limits.[128]
Statistical studies have already proved that in random guessing even
numbers occur somewhat more frequently than uneven. It is therefore
worthy of notice that in these results the frequencies of even numbers
are not uniformly greater than that of uneven; for with the exception
of the digit 6 in the female judgments, the digits next to 0 and 5, _i.
e._, 9 and 1, 4 and 6, occur with least frequency.
In the case of the number of letters counted in a half minute, also, it
appears (see last column (C) of Tables 3 and 4) that 0 and 5 occur more
frequently in the last place than chance would lead us to expect. In
contrast with the results for the time-judgments, in the same tables,
the percentages of occurrence of the various digits in counting present
less marked differences. For the males 3 and 7 occur least frequently,
for the females 2 and 9.
To sum up the results of our examination of the materials with
reference to the occurrence of digits in the final place of the
judgments, the order of decreasing frequency of the various digits is
0, 5, 8, and 2. Of the others 3 and 7 occur more frequently than 4 and
6, with one exception. The statement that even numbers in general occur
more frequently than odd must be modified by the statement that in
these results the digits next to 0 and 5, namely, 9, 1, 4, and 6 occur
with least frequency. These statements hold for both males and females,
but for the latter the frequency of occurrence of 0 is far greater than
for the males.
These results clearly indicate that the judgments are not random
guesses. In seeking further for some explanation of the surprising
frequency of occurrence of judgments which end in 0 or 5, we discovered
that certain numbers occur very frequently, namely, the multiples of
15, 30, and 60. In order to exhibit this tendency quantitatively Tables
5 and 6 have been constructed.
In these tables will be found tabulated the number of times 15 and
multiples of it which are not also multiples of 30 or 60 occur for any
given interval and filling. Likewise are tabulated the frequencies of
occurrence of 30 and multiples of it which are not multiples of 60, and
finally, of 60 and its multiples. The numbers as they occurred in the
three categories run as follows:
15 30 60
45 90 120
75 150 180
105 210 240
135 270 300
165 330 360
195 390 420
Fifteen and its multiples, as given above, are arranged in one division
of the tables, thirty and sixty each in its own separate division.
The line at the bottom of the tables marked Σ gives the frequency of
occurrence of these three groups of numbers for all the subjects and
for each interval and filling.
As is shown by the percentage of frequency columns of the tables, in no
instance do the multiples of 15 constitute less than 19.52% of the male
judgments and 23.81% of the female judgments. The lowest frequency for
any of the four intervals is 20.32% of the total number of judgments.
The maximum frequency for the males (43.03%) and for the females
(56.57%) is for the interval idleness 108 seconds. That the male and
female maxima should fall on the same interval is interesting.
TABLE 5
FREQUENCY OF OCCURRENCE OF 15, 30, 60, AND THEIR MULTIPLES
_Males_
15 30 60 Σ % _Average_
{I 48 5 0 53 21.12
{E 42 9 0 51 20.32
18̋ {R 43 8 0 51 20.32 20.32
{W 45 4 0 49 19.52
{I 29 60 7 96 38.25
{E 17 41 5 63 25.20
36̋ {R 22 41 6 69 27.41 29.57
{W 36 28 5 69 27.41
{I 29 18 46 93 37.05
{E 25 7 34 66 26.29
72̋ {R 28 26 33 87 34.66 34.70
{W 28 42 32 102 40.80
{I 25 31 52 108 43.03
{E 16 23 20 59 23.51
108̋ {R 22 30 39 91 36.25 36.16
{W 25 37 43 105 41.83
Σ 480 410 322 1212
% 11.96 10.21 8.02 30.12
TABLE 6
FREQUENCY OF OCCURRENCE OF 15, 30, 60, AND THEIR MULTIPLES
_Females_
15 30 60 Σ % _Average_
{I 58 30 0 88 32.47
{E 30 35 8 73 26.64
18̋ {R 56 26 3 85 31.02 28.48
{W 41 24 0 65 23.81
{I 31 55 39 125 45.62
{E 21 36 17 74 27.21
36̋ {R 31 63 33 127 46.35 38.86
{W 41 45 13 99 36.26
{I 29 28 60 117 42.70
{E 17 18 52 87 31.75
72̋ {R 26 37 52 115 41.97 41.60
{W 30 51 56 137 50.00
{I 12 45 98 155 56.57
{E 21 27 58 106 38.83
108̋ {R 23 36 84 143 52.19 47.83
{W 24 31 64 119 43.75
Σ 491 587 637 1715
% 11.22 13.42 14.56 39.22
If no influence worked in favor of the multiples of 15 in these
experiments only one judgment in thirty would be 15 (3.33%) and only
one in sixty, 30 or 60 (1.67%). For the probability of the occurrence
of 15, 30, and 60 is 1/60 + 1/60 + 1/30 = 1/15, as is obvious from the
fact that among sixty consecutive numbers (1 to 60) there are four
which are multiples of 15. According to probability we should expect
multiples of 15, 30, and 60 to occur 268 times among the 4014 male
judgments and 292 times among the 4375 female judgments. As a matter of
fact there are 1212 such judgments for the males, 1715 for the females.
The probability that a male judgment is a multiple of 15, 30, or 60 is
0.3012 (probable error 0.0049); for a female judgment the probability
is 0.39199 (probable error 0.0050).
These statistics indicate that the subjects are constantly and strongly
influenced in favor of judgments which are simple fractions of a
minute. Closer inspection of the tables gives some suggestion of the
nature of this influence.
Comparison of the four intervals (Tables 5 and 6) with respect to the
occurrence of simple fractions of a minute shows that the frequency of
such numbers increases rapidly as the length of the interval increases.
The various percentages of frequency for males and females and for the
four intervals are again presented here for convenience of comparison.
18̋ 36̋ 72̋ 108̋
_Males_ 20.32% 29.57% 34.70% 36.16%
_Females_ 28.48 38.86 41.60 47.83
As is obvious from these figures both frequency and rate of increase
are far higher for the females than for the males.
Examination of the percentages (totals) at the bottom of Tables 5 and
6 reveals another remarkable sex-difference; for the frequency of
occurrence of 15 and its multiples regularly decreases for males from
the 15 to the 60 class, whereas for females it regularly increases.
Undoubtedly the time-judgments of these experiments were strongly
influenced by thought of the conventional time-unit, the minute, for
in all quantitative work there are errors in favor of the standard of
measurement and simple fractions thereof. In the present instance this
tendency to favor the unit was strengthened, perhaps, by the giving of
a half-minute interval as a standard for comparison at the beginning of
the tests.
Two explanations of the sex-differences above mentioned are suggested
by our study of the data. One is the fact that the females are less
exact than the males; the other that they generally overestimate the
intervals, whereas the males often underestimate them. One's estimate
of an interval is determined partly by confidence of accuracy. The
longer an interval the less we feel able to estimate it accurately,
and, as a consequence, the more frequently it is judged as the same as
the time-unit or a simple fraction of that unit. The females are less
exact in their estimates than the males, and less exact for long than
for short intervals, and as an accompaniment of their inexactitude we
find the frequent occurrence of multiples of 15, 30, and 60.
But confidence of ability to estimate accurately must be considered in
connection with the fact which suggests our second explanation, namely,
that the female estimates are higher than the male. Tables 7 and 8
show that the females almost invariably overestimate the intervals
rather largely, while the males sometimes underestimate considerably.
The range of the male judgments is from 1 to 300, of the female from
1 to 400. Obviously the chance of occurrence of 15, 30, 60, and their
multiples varies with the range. The greater the range the greater
the probable frequency of 30 and 60 in comparison with 15. In random
guessing the probabilities of the occurrence of 15, 30, and 60 for long
and short intervals is the same, but our results show that this is not
true in the case of these time-estimation judgments. It seems possible,
therefore, that the sex-differences referred to are due to the fact
that the intervals seem longer to the females, and that, therefore,
a feeling of greater inexactitude than would be felt for shorter
intervals leads to the choice of simple fractions of a minute more
frequently than in the male judgments and more frequently for the long
than for the short intervals.
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]
TABLE 7
DISTRIBUTION OF MALE JUDGMENTS IN 10" CLASSES
_Classes_ 18̋ 36̋ 72̋ 108̋ C
I E R W I E R W I E R W I E R W
1 - 10" 31 16 69 136 3 1 4 18 1 1 1 4 0 0 0 0 0
11 - 20 174 179 142 108 40 34 45 97 4 2 5 23 1 2 1 7 0
21 - 30 34 47 35 7 99 106 98 82 15 9 26 65 5 0 6 23 0
31 - 40 7 7 3 56 69 69 28 25 16 34 47 10 2 6 31 1
41 - 50 4 2 2 37 23 22 18 41 43 54 33 20 9 19 28 0
51 - 60 1 9 13 9 6 64 68 53 35 31 17 27 32 7
61 - 70 5 3 0 0 37 42 28 18 27 26 22 19 8
71 - 80 0 1 3 1 23 34 16 9 33 34 35 20 34
81 - 90 1 1 1 15 15 15 8 30 40 43 29 58
91 -100 0 9 8 7 1 23 35 25 17 65
101 -110 0 2 6 3 3 10 26 17 6 33
111 -120 0 8 5 5 2 29 16 17 16 29
121 -130 0 3 1 2 0 5 15 7 8 10
131 -140 0 1 1 1 1 6 9 5 0 4
141 -150 1 0 1 0 5 5 8 4 1
151 -160 1 0 2 3 2 2 1
161 -170 1 0 2 1 0 2
171 -180 1 1 5 4 5 2
181 -190 0 1 2 1
191 -200 3 2 2 2
201 -210 0 1 1 0
211 -220 0 0 0 0
221 -230 1 1 0 0
231 -240 2 0 1 0
241 -250 1 1 1
251 -260 0 0
261 -270 0 0
271 -280 0 0
281 -290 0 0
291 -300 1 1
Totals
251 251 251 251 251 250 251 251 251 251 251 250 251 251 251 251 251
As a result of these groupings of the male judgments it appeared
that the former method gives a far more regular distribution than
the latter. In view of this result and the above considerations,
Tables 7 and 8 were constructed by the use of 10-second classes,
beginning with 1-10. In these tables (column C) the distribution of the
letter-counting results has been included for convenience of comparison
of the two kinds of judgments as to form of distribution.
As instances of the general form of distribution of the judgments the
curves have been plotted for letter-counting, Fig. 1 _A_. (Males ----,
Females, ... ,) for idleness 36 seconds, Fig. 1 _B_, and for idleness
108 seconds, Fig. 2. The distribution of the letter-counting judgments
in classes of 10 is very regular in comparison with that of the several
time-estimation judgments. For idleness 36 seconds there are several
fairly distinct modes, and for idleness 108 seconds the modes are still
more numerous and more marked.
[Illustration: Fig. 1_A_. Distribution of the Results of the
Letter-Counting Test. Males ----, Females ....]
[Illustration: Fig. 1_B_. Distribution of the Time-Estimation Judgments
for the Interval Idleness 36̋. Males ----, Females ....]
[Illustration: Fig. 2. Distribution of the Time-Estimation Judgments
for the Interval Idleness 108̋. Males ----, Females ....]
TABLE 8
DISTRIBUTION OF FEMALE JUDGMENTS IN 10̋ CLASSES
18̋ 36̋ 72̋ 108̋
_Classes_
I E R W I E R W I E R W I E R W C
1 - 10 72 20 88 133 5 6 5 33 2 0 1 6 0 1 0 2 0
11 - 20 114 119 109 94 33 29 40 83 7 5 15 25 2 2 7 10 0
21 - 30 50 87 54 29 70 57 73 74 16 13 25 52 4 1 3 27 0
31 - 40 17 17 10 6 51 87 53 30 24 21 24 30 2 1 11 14 0
41 - 50 10 14 7 4 40 35 39 20 35 18 37 32 14 6 17 34 2
51 - 60 2 10 3 1 43 30 40 14 48 44 47 53 30 18 35 36 5
61 - 70 1 3 0 3 11 7 5 2 28 50 20 21 8 11 23 22 18
71 - 80 3 2 1 2 5 8 2 10 29 32 23 14 14 21 20 14 57
81 - 90 0 0 1 1 9 3 6 2 27 29 28 14 41 35 35 19 67
91 -100 0 2 0 1 4 2 1 16 11 15 5 25 35 17 11 50
101 -110 0 0 0 1 1 1 4 7 6 0 9 24 7 6 25
111 -120 0 0 2 3 6 3 17 20 10 8 52 38 33 16 19
121 -130 2 0 0 1 0 3 4 3 3 4 15 6 8 13
131 -140 0 1 1 0 1 2 1 4 6 9 6 6 5
141 -150 0 1 0 1 5 4 4 2 15 13 16 7 1
151 -160 1 1 0 0 0 4 2 0 3 7 2 2 2
161 -170 0 0 0 1 1 0 0 3 2 0 1
171 -180 1 0 0 7 4 7 4 22 14 16 22
181 -190 0 0 1 0 1 0 2 2 3 0
191 -200 0 0 1 1 3 0 3 5 6 6
201 -210 1 0 0 0 0 0 1 0 1 0
211 -220 0 0 1 0 0 1 2 0 0
221 -230 0 0 1 0 0 1 0 6 2
231 -240 0 2 1 0 1 3 3 2 4
241 -250 0 1 0 0 3 0 0
251 -260 0 0 2 0 0 1
261 -270 0 0 1 0 0 0
271 -280 0 0 0 0 0 0
281 -290 0 0 0 0 0 0
291 -300 1 2 4 2 1 1
301 -310 0 0 0 0
311 -320 1 0 0 0
321 -330 0 0 0 0
331 -340 1 0 0 1
341 -350 0 0
351 -360 1 1
361 -370 0
371 -380 0
381 -390 0
391 -400 2
Totals
271 274 274 273 274 273 274 273 274 274 274 274 274 273 274 272 264
Tables 7 and 8 show that the range of the judgments increases with the
length of the interval judged, and that the modal class is always much
nearer the lower than the upper limit. Asymmetry is characteristic of
the distribution of organic data, and in certain instances, as for
example writing 18 seconds, males, the choice of a 10-second class
interval results in extreme asymmetry, and one is reminded of the
tables which Fechner gave as examples of his logarithmic method in
statistics.[130]
It is not to be expected that a method of grouping should be found
which will give regularity of distribution throughout, but it is
important that there should be regularity about the mode. In the table
of distribution for the males (Table 7) all the intervals from idleness
18 seconds to reading 72 seconds are regular.[131] The remaining
intervals, with the exception of estimating 108 seconds, are irregular.
Trial proves that for these intervals increase of the size of the
class to 30 seconds is sufficient to give regular distributions, as is
obvious from Table 9. Grouping by 30-second classes gives regularity
for most of the female judgments, but for idleness 108 seconds and
writing 108 seconds there are still slight irregularities, as Table 10
indicates.
Tables 7 and 8 show that the distribution is far less regular for
the females than for the males. The fact that it becomes regular
when the class interval is increased to 30 seconds suggests that the
irregularities of distribution which appear in the tables are due to
those influences which favor simple fractions of a minute and not to
the small number of judgments.
Having now noted certain important characteristics of the
time-estimation judgments and the nature of their distribution, we
may examine the arithmetical means and other statistical quantities
which have been determined for our data. Those quantities which have
been determined for the several ages, intervals, and fillings as well
as for the sexes are: (1) The Mean (_M._ in tables), (2) the average
variability (_M. V._), (3) the positive variability (+ _V._), (4)
the number of judgments with positive variation (No. + _V._), (5)
the negative variability (- _V._), (6) the number of judgments with
negative variation (No. - _V._), (7) the relative variability (_R. V._)
= _M_ + _V_/_M_ × 100.
Since the sums of the positive and the negative variations are equal,
it is possible to make certain of the accuracy of the means and
average variabilities by comparison of the + _V._ and - _V._ As this
was done in all cases we feel confident of the reliability of the
statistical quantities presented in the tables.
In Table 11 have been arranged the various quantities as determined for
the males and females for each interval. The values given in this table
are averages of the determinations made for the several ages separately.
TABLE 9
DISTRIBUTION OF CERTAIN MALE JUDGMENTS IN 30̋ CLASSES
_Classes._ W. 72̋ I. 108̋ R. 108̋ W. 108̋
1- 30 92 6 7 30
31- 60 115 61 52 91
61- 90 35 90 100 68
91-120 6 62 59 39
121-150 1 16 20 12
151-180 1 9 7 6
181-210 3 5 3
211-240 3 1 0
241-270 1 1
271-300 1
250 251 251 251
TABLE 10
DISTRIBUTION OF FEMALE JUDGMENTS IN 30̋ CLASSES
18̋ 36̋ 72̋ 108̋
_Classes_ I E R W I E R W I E R W I E R W
1- 30 236 226 251 256 108 92 118 190 25 18 41 83 6 4 10 39
31- 60 29 41 20 11 134 152 132 64 107 83 108 115 46 25 63 84
61- 90 4 5 2 6 25 18 13 14 84 111 71 49 63 67 78 55
91-120 0 2 0 3 8 9 5 37 38 31 13 86 97 57 33
121-150 2 0 2 2 1 9 10 8 9 25 37 28 21
151-180 1 2 0 0 8 9 9 4 28 23 18 25
181-210 1 0 2 1 4 0 6 7 10 6
211-240 0 2 3 0 1 5 5 8 6
241-270 0 1 0 3 3 0 1
271-300 1 2 4 2 1 1
301-330 1 0 0 0
331-360 1 1 1 1
361-390 0
391-420 2
Totals 271 274 274 273 274 273 274 273 274 274 274 274 274 273 274 272
TABLE 11
MEANS, ETC., FOR EACH SEX, INTERVAL AND FILLING
KEY: Ma. = _Males_
Fe. = _Females_
M. M. V. +V. No. +V.
Ma. Fe. Ma. Fe. Ma. Fe. Ma. Fe.
{I 17.7 20.74 5.4 10.35 5.8 15.48 15.9 22.75
18" {E 19.5 25.55 4.9 9.84 6.0 13.98 16.9 23.75
{R 15.5 18.46 4.9 9.14 6.3 13.03 14.6 24.25
{W 11.5 15.58 3.7 8.56 4.6 11.83 14.3 25.75
{I 33.3 42.81 9.1 16.55 12.6 20.63 14.2 28.00
36" {E 33.1 41.54 8.4 15.23 10.7 23.34 14.2 23.00
{R 32.1 41.71 8.4 16.42 9.7 20.78 16.3 27.75
{W 24.7 30.10 9.0 14.71 10.9 22.08 14.4 23.50
{I 63.3 73.00 17.2 27.20 20.9 33.72 15.7 27.75
72" {E 63.1 77.13 16.0 26.56 18.8 37.27 16.9 24.75
{R 57.9 70.78 17.3 30.30 20.9 39.28 15.2 26.75
{W 51.2 54.93 19.8 24.21 23.7 29.47 15.0 38.25
{I 92.7 113.37 29.8 40.13 35.3 44.08 15.2 32.00
108"{E 99.8 114.88 26.3 36.38 29.3 49.26 14.9 26.25
{R 90.1 100.47 28.3 40.18 33.9 47.90 15.3 34.25
{W 75.5 87.45 32.4 45.33 40.8 61.12 14.9 34.25
-V. No. -V. R. V.
Ma. Fe. Ma. Fe. Ma. Fe.
{I 5.7 7.78 20.0 45.00 30 49.83
18" {E 4.4 7.69 19.0 44.75 25 39.10
{R 4.4 7.07 21.2 44.25 31 49.26
{W 3.2 7.14 21.6 42.50 33 54.55
{I 8.1 14.01 21.7 40.50 27 38.32
36" {E 7.2 11.57 21.7 45.25 25 36.66
{R 7.5 13.84 19.6 40.75 26 38.84
{W 8.7 11.24 21.5 44.75 36 48.64
{I 15.5 22.83 20.2 40.75 27 36.87
72" {E 14.7 20.98 19.0 43.75 27 34.43
{R 15.7 24.91 20.7 41.75 30 42.77
{W 16.0 21.26 20.9 36.75 37 43.84
{I 25.9 37.87 20.7 36.50 32 35.34
108"{E 24.4 29.51 19.9 42.00 26 31.57
{R 24.8 34.60 20.6 39.75 31 39.95
{W 27.5 35.86 19.9 42.75 42 51.67
The following facts are revealed by comparison of the results for the
two sexes.[132] Without exception the means for the females are larger
than those for the males. All but one of the sixteen intervals (E 18̋)
are underestimated by the males, whereas all but six are overestimated
by the females. The amount of over- and under-estimation is given in
Table 12. In every instance the females overestimate in comparison with
the males. The mean variability is very much greater for the females,
as is also the relative variability. If variability be taken as a
measure of reliability of judgment the males are far superior to the
females.
As is obvious from Table 12, both under- and over-estimation increase
with increase in the length of the interval. For 18̋ intervals they are
least, for 108" intervals greatest.
The influence of the fillings is marked. The writing intervals without
exception are judged as shortest; reading gives the next shortest
intervals, while sometimes idleness, sometimes estimating, comes third.
In order of increasing length of average estimates of the intervals the
fillings stand: writing, reading, idleness, estimating. As a rule the
averages for the idleness and the estimating intervals are nearly the
same, but it is worthy of note that the females always overestimate
to a greater extent when estimating than when idle. This is another
indication of the discrepancy between the female time-unit and the
objective unit.
About ninety per cent of the subjects estimated by some counting
method. The methods most frequently used were "counting seconds,"
counting "1 and 2 and 3 and 4, etc.," counting the swings of a
pendulum, tapping, and counting imaginary watch-ticks.
The above statements might suggest that the overestimation
characteristic of the female judgments is due to a more rapid counting
rhythm. This, however, is not true, for the letter-counting tests
indicate a slightly more rapid rhythm for the males, 93.42 as opposed
to 91.89.
TABLE 12
AMOUNT OF OVER- AND UNDER-ESTIMATION OF INTERVALS
_Males._ _Females._ _Males._
{I - 0.3 + 2.74 Age 17 18 19 20 21 22 23
{E + 1.5 + 7.55 Over- or under- -8.55
18̋ {R - 2.5 + 0.46 estimation -3.60 -7.50 -13.02 -13.49 -8.71 -13.20
{W - 6.5 - 2.42 No. + 6 2 2 0 2 2 2
{I - 2.7 + 6.81 No. - 10 14 14 16 14 14 14
{E - 2.9 + 5.54
36̋ {R - 3.9 + 5.71
{W -11.3 - 5.90 _Females._
{I - 8.7 + 1.00
{E - 8.9 + 5.13 Age 17 18 19 20
72̋ {R -18.1 - 1.22 Over- or under-
{W -24.8 -17.07 estimation + 2.38 - 4.16 - 2.57 + 2.55
{I -15.3 + 5.37 No. + 11 8 8 12
{E - 8.2 + 6.88 No. - 5 8 8 4
108̋{R -17.9 - 7.53 + = overestimation
{W -32.5 -20.55 - = underestimation
In Table 13 are the means, variabilities, errors, etc., for the
letter-counting tests. In this table we have presented the values of
the various statistical quantities for the several ages of both males
and females, for there are certain interesting differences which
should be noted. Similar age-tables have been prepared for all of the
other results, but in no case have noteworthy differences appeared.
From Table 13 it will be observed that the males on the average
count more letters in thirty seconds than do the females, and at the
same time make more errors. The mean and relative variabilities for
the sex-groups are almost the same. Curiously enough the number of
letters counted as well as the accuracy of counting decrease for the
females with age (17 to 20 years being the age-limits of the group
under consideration). The males within the same age-limits increase in
rapidity of counting, but decrease in accuracy. In the examination of
Table 13 it is to be remembered that the 17 and 23 year groups of males
contain only 16 individuals each, and therefore cannot be compared to
advantage with the other groups. Both mean and relative variabilities
decrease from 17 to 20 years for the females, whereas for the males
there is no constancy in the direction of the change.
TABLE 13
MEANS, ETC., FOR LETTER-COUNTING
_Males._
_Age_ 17 18 19 20 21 22 23 _Average_
M. 92.81 92.48 94.00 95.87 92.66 97.06 89.06 93.42
M. V. 10.29 15.31 16.50 12.90 7.81 13.04 19.20 13.58
+V. 11.76 22.96 16.50 11.70 8.13 16.30 21.94 15.61
No. +V. 7 9 20 37 24 14 7 16.96
-V. 9.15 11.48 16.50 14.40 7.51 10.87 17.09 12.57
No. -V. 9 18 20 30 26 21 9 19.00
R. V. 11.1 16.5 17.6 13.5 8.4 13.4 21.6 14.59
Errors 0.88 1.04 2.10 3.03 1.70 0.89 2.75 1.77
_Females._
_Age_ 17 18 19 20 _Average_
M. 97.74 95.51 89.21 85.09 91.89
M. V. 17.06 14.56 11.30 11.28 13.55
+V 18.67 18.49 12.06 14.56 15.94
No. +V. 32 21 30 31 28.50
-V. 15.71 12.14 11.66 9.21 12.18
No. -V. 38 32 31 49 37.50
R. V. 17.5 15.2 12.7 13.3 14.70
Errors 1.35 1.46 1.49 1.65 1.47
SUMMARY
(1) The length of a second is slightly overestimated by men, greatly
underestimated by women.
(2) Intervals of from 18 to 108 seconds are usually slightly
underestimated by men (ages 17 to 23 years), and greatly overestimated
by women (ages 17 to 20 years).
(3) The time-estimates of women are far more variable than those of
men, and on the whole markedly less accurate.
(4) Both men and women favor estimates which end in 0 or 5, as well as
simple fractions of a minute, but the tendency is stronger in women
than in men. Over one third of the estimates reported in this paper
were 15 seconds or simple multiples thereof.
(5) In letter-counting the groups of subjects studied (251 men and
274 women) exhibited differences just the opposite of those in
time-estimation, for the men counted more rapidly and less accurately
than did the women.
(6) Of the four fillings for the intervals used in the experiments,
"writing" gave the smallest estimates of the intervals, listening to
"reading" next, while "idleness" and "estimating" were conditions in
which the intervals seemed much longer to both men and women.
(7) This preliminary study of sex-differences in time-estimation, by
which it has been learned that women overestimate and are notably
inaccurate in comparison with men, is to be followed and supplemented
by the results of an investigation now in progress concerning
the relations of sex-differences in time-estimation to age and
physiological rhythms.
FOOTNOTES:
[Footnote 125: Science, N.S., vol. 19, pp. 708-709, 1904.]
[Footnote 126: E. Mach (Analyse der Empfindungen, 1900, p. 161) thinks
that his physiological time-unit has become larger with age. And he has
also noted that the time-sense differs in animals of the same species
which differ in size.]
[Footnote 127: The unbracketed number is that for the males, the
bracketed that for the females.]
[Footnote 128: It may be asked in connection with the above statistics,
what is the probability that even and uneven digits have unequal
chances of occurrence? The analytic treatment of this problem
indicates that the probability is ½[1+φ(4.25)] = 0.99999999891 for
the males and ½[1+φ(15.93)] for the females. It is therefore almost
certain, theoretically, that even and uneven numbers have not the same
frequency. See Czuber, Wahrscheinlichkeitsrechnung, 1903, pp. 158-161.
The constants of this problem are in Czuber's denotation, _a_ = 52.308
and _b_ = 222.]
[Footnote 129: The judgments might be grouped in 10 second classes
beginning with the lowest number in the experiments, but this would
have the disadvantage of rendering the distribution tables or curves
for different groups of judgments incomparable.]
[Footnote 130: G. Th. Fechner, Collectivmaasslehre, pp. 338-346, 1897.
Compare the asymmetry of writing 18 seconds for both males and females
with Fechner's Table III, p. 442.]
[Footnote 131: The distribution may be called regular if the
classes increase to a maximum, the mode, and then decrease without
interruption. (See Fechner, Collectivmaasslehre, pp. 121-122.)]
[Footnote 132: The values of the means and variabilities was determined
to the second decimal for the females, but only to the first for the
males; consequently the relative variability could be computed exactly
to the first decimal for the females and to the unit only for the
males.]
ASSOCIATIONS UNDER THE INFLUENCE OF DIFFERENT IDEAS
BY BIRD T. BALDWIN
The purpose of the following investigation was to study the influence
of two or more starting-points on the train of associated ideas. It
was begun in October, 1902, and concluded in January, 1905. Nineteen
graduate students acted as subjects, and the experiments were conducted
with each individually for one hour per week, except in a few instances
where two subjects were present together. Occasionally the experimenter
acted as subject in order to get a clearer insight into introspective
data. There are recorded here thirteen groups of one hundred and eight
sections, including eight hundred and fifty-five separate experiments,
with a sum total of eleven thousand, one hundred and thirty-five named
associations.
So far the field has not been studied experimentally, although
Cordes,[133] while attempting to observe the effect of an unconscious
intermediating factor in 'mediate association,' noticed that the
accompanying factor (particularly with a tone) sometimes combined with
the starting-point in determining the associated series. The fact is
simply mentioned, and Scripture's[134] conclusions from the same are
inadequate when he states, "In general we may say that two simultaneous
ideas have an effect that depends on their relative masses; if one of
the ideas is over-poweringly weighty the next idea will be chiefly
influenced by it, but if the two are nearly balanced the next idea will
be the result of the two." Miss Calkins[135] makes a near approach to
the problem in a study of "Mental Combination," where auditory words
were given as nearly simultaneously as possible and the subject was
required to remain for four seconds in silence and then to write the
train of imagery which passed in six following seconds; the words as
auditory starting-points were finally excluded from the experiments
"because the first word pronounced tends often to establish itself so
firmly that its association-images are proof against the intrusion of
the second word, which has therefore no chance to be grasped with the
first." These results differ from the ones here recorded which were
obtained independently and under different conditions. In her valuable
monograph on Association[136] there is in one instance a suggestion of
the problem, but no results are given.
The two or more starting-points were nonsense syllables, concrete or
abstract words, pronounced by the investigator or shown on cards, or
finally, pictures. The associations continued for a period of fifty
seconds unless otherwise indicated. The same letters denote the same
subjects throughout all the experiments, K. and R. being women. In the
examples given, Roman numbers have been used, in place of the letters,
as it was found impossible to get representative series which were
entirely devoid of personal references.
After the associations had been "jotted down," the subjects in each
case copied them, noting also the suggesting ideas, and giving, in many
cases, a number of introspective notes. It is important to mention that
in all of the work these records of suggesting ideas were made by the
subjects without any questions on the part of the investigator.
GROUP I. TWO NONSENSE SYLLABLES
In order that a standard might be obtained that would serve as a basis
for subsequent experiments, two nonsense syllables were pronounced with
equal emphasis, as starting-points, and the subject was asked merely to
wait until both had entered consciousness and not to favor nor inhibit
either. If the subject stated that associations arose between the
pronunciation of the starting-points the results were discarded.
Turning to the notes we find that K. reported, "The first just hovered
around," and the associations followed the second, or as V. states
it, "Sof was carried subconsciously for a while without influence,"
while By. frequently noticed that "The first may be in the background
on the point of breaking in but be inhibited involuntarily," or in
another, "It was frequently present but exerting no influence." A.
"forgot what the other word was, but felt it trying to get a hand in."
Ro. goes further and states in terms similar to A., "The words which
might have been suggested by 'taf' were wholly inhibited, though I
am sure 'taf' was present to me throughout the series, but was not
efficacious as against the other syllable." It is unnecessary to
multiply instances to show that the wraith, so to speak, of one may
linger for a short time, or occasionally for the entire series, but
that the associations are determined by the other. Or the lingering
wraith of a starting-point may hover ineffectively in consciousness
and exert no determining influence on the series until toward its
close; then, however, although both starting-points still persist,
they exchange places so far as effectiveness is concerned, and the
former wraith becomes the primary factor in effecting the series of
associations. For example, "The two syllables were present all the way
through, but the former exhausted itself as a word-suggester after
a few words." Again Ro. gives examples where "One alone may be in
consciousness and determine the associations when the other may enter
without effect upon the series, or may determine the series, the first
persisting but losing its effect"; and a case of both ideas persisting
and each alternately exerting an influence was noted by M. These last
two conditions are exceptional.
Studying carefully the notes and graphic representations as given in
the tables, it is apparent that one starting-point may be followed
independently and exclusively; we find "'fef' suggesting 'theft,' and
the subsequent associations monopolizing the field of consciousness
and 'tuz' not again appearing." (V.) The results show that in the one
hundred and seven experiments one was followed exclusively only twenty
times. The following would be an example:
III. Naf-Tam
--tambour tam
--experiment tambour
--psychology experiment
--laboratory experiment
--space psychology
--time space
--ego space and time
--Ebbinghaus ego
--discussion psychology
--posted notice psychology
--door posted notice
--gray door
--stairs door
--fishes laboratory
--water fishes
--decay fishes
--animal fishes
--meat fishes
--odor meat
In other cases one starting-point may be followed and then the
other for a few or many associations, each "occupying the mind to
the exclusion of the other for a number of words, when suddenly the
other appears and suggests a new series," which V. calls "a curious
zigzagging in consciousness." This may take place at any point along
the series. As Ro. indicates, "There was rivalry here; 'yud' wholly
inhibited all the 'zid' associations, even 'zid' itself for the time,
then, 'yud' apparently being exhausted, 'zid' entered again into the
focus."
In contrast to the above forms, the tables indicate and the notes
verify that while the associations primarily follow one there can be
traced the modifying effect of the other; "The nature of the words
was influenced by a fringe of consciousness which contains the other
starting-point," M.'s comment runs, while J. adds, "The other helped
in the mental picture but had no special significance." There are no
experiments in the first group where this partial fusion took place
throughout the series, and there are only six examples where it took
place before the sixth word and continued to the end. While there are
no cases here of alternating partial fusion, yet it sometimes happens,
that is, the predominating influence is sometimes transferred from one
to the other. The modifying influence may reach such a degree at any
point in the series that the identity of each point of departure of the
association is lost and there is total fusion, resulting in one idea or
one train of thought. For example, 'rel' and 'mem' gave 'realm' for V.;
for Ht. 'fef' and 'tuz' gave 'fezz'; for M. they gave 'fez'; for Ro.
'fuz.'
Of the twenty-one experiments where one starting-point was followed
exclusively, there were two cases for the first and nineteen for the
second. There were but two cases of alternating groups, a third one
being unique in that after the first three words there was a persistent
alternation between two apparently independent series of inter-related
words and inter-related visual images. There were three cases of
complete fusion throughout the series and nine where total fusion
started before the fifth word and continued.
In a number of cases the initial starting-points were forgotten before
the end of the series and the subjects were sometimes unable to recall
them.
As the subjects were kept ignorant of the characteristic persistence
of either starting-point in forming separate associations, and of the
tendency towards fusion, as well as of the preponderance of influence
of one over the other, it is to the tabulated results that we must
look for quantitative measurement of these. 76.2% of the associations
are due to the independent influence of one or the other of the
starting-points; 23.9% are due to the combined influence; for the first
starting-point we have 18.7%, for the second 57.5%. In 15.3% of all the
associations the combined influence was the result of total fusion; in
4.1%, the result of a union where the first starting-point predominated
in influence; in 4.4%, the second predominated. The following graphic
representation indicates the order of influences for the first pair of
syllables. The table gives the results for the ten pairs.
TABLE I. TWO NONSENSE SYLLABLES SPOKEN
Time--50 seconds.
Characters: | represents the influence of the first, - the second, +
complete fusion, α fusion with the first predominating, β fusion with
the second predominating.
1) Taf--Coz
M. | - - - - | | | | | - - - -
F. - - | | + + + + | | | + + β β β β β β
H. - | | | | | | | | | | | | | | |
R. | - - - - - - - - - - - - - - -
K. - - - - - - -
V. | | - - - - | - - | + + + +
Ro. | | | - - - - - - - - - - - - - - - -
Bl. - - - - - - - - - - - - - - -
By. | - | | | - - - - - - - - - - - - - - - - - - -
Bs. - - - - - - - - - - - - - - -
Ht. - - | | | | | | | | | | | | |
Starting-points:
(1) Taf--Coz.
(2) Cim--Bef.
(3) Yud--Zid.
(4) Sof--Deb.
(5) Naf--Tam.
(6) Fef--Tuz.
(7) Sar--Nef.
(8) Sek--Lub.
(9) Hov--Bes.
(10) Rel--Mem.
| - + α β
M. { 20 69 26 4 3
{ 16.5% 56.6% 21.2% 3.3% 2.4%
F. { 28 22 37 0 39
{ 22.2% 17.5% 29.4% 30.9%
H. { 39 98 0 11 0
{ 26.3% 66.2% 7.5%
R. { 9 102 32 0 0
{ 6.3% 71.4% 22.3%
K. { 47 58 1 14 0
{ 39.1% 48.3% .7% 11.9%
V. { 30 79 54 0 0
{ 18.4% 48.4% 33.2%
Ro. { 32 111 0 5 0
{ 21.4% 75.1% 3.5%
Bl. { 5 131 15 15 0
{ 3.1% 78.9% 9.0% 9.0%
By. { 43 102 23 15 22
{ 16.8% 52.6% 11.7% 7.7% 11.2%
Bs. { 9 72 31 0 6
{ 11.4% 58.5% 25.3% 4.8%
Ht. { 32 58 20 0 0
{ 29.0% 52.8% 18.2%
Totals{294 902 239 64 70
{ 18.7% 57.5% 15.3% 4.1% 4.4%
Number of subjects, 11; number of sections, 10; number of
experiments, 110; number of associations, 1569.
GROUP II
Two concrete nouns with apparently equivalent connotation were
pronounced. In order that the subject get no clue as to the
preponderance of one starting-point over the other, the nine sections
were given at irregular intervals in connection with other experiments.
The tables show few cases of fusion, there being but one case in the
eighty experiments where all the associations were the result of the
combined influence of both starting-points. There was no other instance
where complete fusion took place before the sixth association and
continued throughout, and only six cases where any form of fusion took
place in the eighty experiments within the first five words (7.6%),
while in the one hundred and seven experiments of Group I there were
twenty-five (23.9%).
The tables show a tendency which was noted when two syllables were
used and which is emphatically brought out here, namely, it is the
position or sequence which determines which of the two equivalent
starting-points shall produce the greater influence. When the two
starting-points are given in immediate succession, it is the second
which predominates in influence. This preponderance may be clearly
demonstrated by the tables alone, though there are many notes which
show "the greater influence of one" (the second). A. seems to have
realized this when he wrote, "While the first was uppermost the second
hovered in subconsciousness, resting content, knowing that it would
have its turn soon." In corroboration the tables give--abstracting from
all cases of fusion--268 words (23.2%) for the first, 721 words (62.3%)
for the second. In fifty-five of the eighty experiments the last had
full control at the end of the series. Taking the cases where one
was followed exclusively throughout the series, starting between the
first and the sixth named association, we find eight for the first and
twenty-nine for the second. This greater influence is again to be found
in the cases of partial fusion; the first predominating in 2.6%, and
the second in 4.3%.
The results of both groups show that the starting-points tend in a high
degree toward independent influence, and also that such a method of
presentation is one of sequence rather than simultaneity, as the two
words show unequal influence. The former must in a manner be reproduced
to become a point of departure for associations, while the latter acts
directly. Is it then a condition of mind that when similar impressions
are presented the one in the presence of which consciousness is
reacting directly has a greater influence in arousing associations than
one which is just past? This we are forced to conclude is the case, but
the proof of the conclusion will be supplemented by later results.
TABLE II. TWO WORDS SPOKEN
Time--50 seconds.
Characters--same as Table I.
(1) Library--River
M. | + + β - - - - - - - - - - - -
F. | - - - - - - - - - | | | |
H. - - - - - - - - - - - - - - - -
Ro. | | | | - - - - - - - - -
J. | - | | | | - - - - - - - - - - - - - - -
Bl. | | - - - - | | | | | | | | | - - /
By. - - - - - - - - - - - - - - - - - - - - - -
Bos. | - - - - - - -
Bur. - + - - - - - - - - - - -
(1) Library--River.
(2) Hat--Road.
(3) Newspaper--Medicine.
(4) Bicycle--Drum.
(5) Theatre--Magazine.
(6) Store--Church.
(7) Soldier--House.
(8) Ship--Boy.
(9) Furniture--Tree.
TABLE II.--_continued_
| - + α β
M. {32 66 26 0 13
{23.4% 48.2% 18.9% 9.5%
F. {32 67 13 5 1
{27.2% 56.7% 11.0% 4.3% .8%
H. {59 79 5 0 0
{41.3% 55.2% 3.5%
Ro. {44 85 0 0 0
{34.1% 65.9%
J. {21 121 8 5 0
{13.5% 78. % 5.3% 3.2%
Bl. {22 83 6 0 1
{19.7% 74.1% 5.4% .8%
By. {16 97 18 14 23
{ 9.5% 57.8% 10.7% 8.3% 13.7%
Bs. {26 64 3 7 1
{25.8% 63.5% 2.9% 6.9% .9%
Bur. {16 59 8 0 10
{17.2% 63.4% 8.6% 0 10.8%
Total {268 721 87 31 49
{ 23.2% 62.3% 7.6% 2.6% 4.3%
Number of subjects, 9; number of sections, 19; number of
experiments, 80; number of associations, 1156.
GROUP III
For two syllables and like words the second strongly predominates in
awakening associations; will the same be true when two simple outline
pictures are shown in the same order? The following results show in
attestation of the above conclusion percentages remarkably similar
to those of the words. There are 23.7% for the first and 61% for the
second; 84.7% of the associations show no sign of fusion and only 15.3%
for fusion and the different forms of partial fusion, the second still
holding the ascendency. When the two pictures did fuse, R. tells us,
"All the associations were more elaborate pictures than when mere words
were given."
A comparative study, inadequate though it is, offers a partial
parallelism between the predominating memory type and stimulation. The
subjects who are preëminently of the visual, K., visual motor, M., H.,
V., and visual lingual motor, Ht., find the pictures more suggestive
than the syllables, while those of the pure motor, F. and By., reverse
the order and find that the syllables offer more numerous and "more
vivid" (F.) associations.
Common experience, however, immediately shows the limitations of
reaching conclusions, when considering prolificacy as criteria of
suggestiveness, inasmuch as starting-points which are abundantly rich
in associations tend to produce so many points of departure that they
tend to inhibit one another. Again there is to be considered the kind
of associations, those of the syllables being of a very elementary
character and in serial form.
A few experiments were given in which colored slips of paper were used
as starting-points. These proved very suggestive for the subjects. Also
a few tones were given, but these were soon discontinued, as other
tones, which could not be recorded, were frequently suggested. The
sentence which forms a very satisfactory starting-point where one is
used could not be used to an advantage where several were given. As we
are here interested in the mutual influence of the starting-points,
our remaining study will be confined to a quantitative and qualitative
variation of the forms used in the previous groups.
TABLE III. TWO PICTURES SHOWN
Time--50 seconds.
Characters--same as Table I.
(1) Boy Rolling Hoop--Blacksmith
M. | | | - - - - - - | | | | |
F. | | - - | + +
H. - - - - - - - - - - - -
R. - - - - - - - - - - - - - - - -
K. - - - - - - - - - - - - - - - - -
V. - - | | + + + + + + + + + + + + + +
S. - - - - - - - - - | | | | | | |
By. | - - - - - - - - - - - - - - - - - - - - -
Bs. - - - - - - - - -
Ht. | | - - - - - - - -
(1) Boy Rolling Hoop--Blacksmith.
(2) Old Man With Umbrella--Bird House.
(3) Carpenter--Mower.
(4) Children Playing--Boy with Basket.
(5) Horse--Dog House.
(6) Shoemaker--Fisherman.
(7) Little Girl--A Chicken.
(8) Boy--A Sheep.
| - + α β
M. {41 65 2 0 1
{37.6% 59.7% 1.8% .9%
F. {11 42 21 0 5
{13.9% 53.2% 26.6% 6.3%
H. {37 52 11 26 9
{27.4% 38.5% 8.1% 19.3% 6.7%
R. {41 58 8 0 15
{33.4% 48% 6.5% 12.1%
K. {32 82 0 0 0
{27.1% 72.9%
V. {12 95 21 3 5
{ 8.8% 70% 15.4% 2.1% 3.7%
S. {36 44 0 0 0
{45% 55%
By. { 8 111 12 0 13
{ 5.4% 77.2% 8.3% 9.1%
Bs. {13 40 7 0 0
{21.7% 66.7% 11.6%
Ht. {22 72 7 0 4
{20.9% 68.6% 6.7% 3.8%
Totals {253 661 89 29 52
{ 23.7% 61% 8.2% 2.7% 4.4%
Number of subjects, 10; number of sections, 8; number of experiments,
76; number of associations, 1084.
GROUP IV
The previous experiments suggest the conclusion that that
starting-point in the presence of which consciousness is reacting
exerts a greater influence than one just past. The proof of this
anticipated result is supplemented by subsequent consectary data.
It is necessary to test the outcome when the nature of the impressions
is varied and the starting-points are given simultaneously. An outline
picture and a word may be so given. These experiments verify from a
different standpoint the statement that the picture establishes itself
more permanently and is more influential, there being 47.8% of the
associations produced by the picture alone, 14.8% by the words alone,
25% of a fusion of the two, and 12.4% of a uniting influence with
the first predominating. The subject R. is an exception in that she
favors the word when not favoring a combination of the two, a fact
which I am unable to explain except to add that the subject stated
that the æsthetic pleasure connected with the picture was sufficient
to inhibit the associations. K. has 100% for the pictures, which is
partially explained by the fact that she is a remarkable visualizer who
reproduces all situations in visual terms.
TABLE IV. PICTURE SHOWN AND WORD SPOKEN
Time--50 seconds.
Characters same as Table I.
(1) (a rabbit)--Table
M. | - - | | | | | | | + - - - -
R. + + + + + + + + + + + + + + + + + +
K. | | | | | | | | | | | | | | |
S. | | | | | - | | | | |
J. | - - | | | | | | | | | - - - | | | | | | | | |
Ht. | - | | | | | | | | | | | | - - - -
(1) (a rabbit)--Table.
(2) (horse)--Book.
(3) (boy)--Dish.
(4) (duck)--Iron.
(5) (dog)--Paper.
| - + α β
M. { 38 9 16 6 0
{ 55.0% 13.1% 23.3% 8.6%
R. { 1 20 55 0 0
{ 1.3% 26.3% 72.4%
K. { 65 0 0 0 0
{100.0%
S. { 29 15 3 10 0
{ 50.8% 26.3% 5.3% 17.6%
J. { 75 19 14 9 0
{ 64.2% 16.3% 11.9% 7.6%
Ht. { 17 7 30 33 0
{ 19.5% 8.1% 34.5% 37.9%
Totals {225 70 118 58 0
{ 47.8% 14.8% 25.0% 12.4%
Number of subjects, 6; number of sections, 5; number of experiments,
30; number of associations, 471.
GROUP V
The character of the starting-points determines which shall be followed
in a simultaneous presentation; can the character of two immediately
successive starting-points be so varied as to overcome the factor of
temporal difference? The few experiments in this group show an attempt
to shift and measure this influence, selecting as variants words of
general and specific character, the first being a term of everyday
experience with the subjects, of wide connotation, and therefore
presumably rich in associations, and the second, which had the
advantage of position, one of more limited and specific connotation,
thus in a measure making it possible to test the stability of the
second in establishing itself as a word-suggester. For the words
"Gymnasium--Stamens" the second still strongly predominates. There is a
slight increase in the amount of fusion (24.5% in all), the explanation
of which would probably lie in the fact that the first is more
assertive than before and offers more elements common to the two. There
was one case of total fusion, one case where fusion started before the
sixth word and continued, no cases of alternating fusion, four cases of
partial fusion, five cases where the second was followed throughout, no
case where the first was followed throughout, five cases of alternation
between the first and the second. In 75.5%, the influence was exerted
without fusion. Eight of the nine subjects favor the specific term.
TABLE V. GENERAL AND FAMILIAR WORD--SPECIFIC WORD SPOKEN
Time--50 seconds.
Characters--same as Table I.
(1) Laboratory--Rake
M. | | | | | - - - - - - - - - - - - - - - -
F. | - - - - - - - - -
H. + + + + + + + + + + +
V. | - - - - - - - - - - - - - | | | | |
S. - - - - - - - - - - | | | |
Bl. - - - - - - - - - - - - - - - - -
By. | - - | | | | | | | | |
Bs.
Ht. - - - - - - - -
J. | | β β β β β β β β β β β β | | | | |
(1) Laboratory--Rake.
(2) Experiment--Butterfly.
(3) Gymnasium--Stamens.
TABLE V.--_continued_
{ 22 25 4 6 0
M. { 38.6% 43.9% 7.0% 10.5%
{ 4 19 0 0 0
F. { 17.4% 82.6%
{ 4 25 13 0 0
H. { 9.5% 59.6% 30.9%
{ 7 38 2 0 7
V. { 12.8% 70.7% 3.7% 12.8%
{ 11 34 0 0 0
S. { 24.4% 75.6%
{ 0 36 0 0 0
Bl. { 100.0%
{ 11 16 7 0 9
By. { 25.5% 37.1% 16.5% 20.9%
{ 0 9 12 2
Bs. { 39.1% 52.2% 8.7%
{ 10 11 10
Ht. { 32.3% 35.4% 32.3%
{ 17 8 15 0 13
J. { 32.1% 15.1% 28.3% 24.5%
{ 86 221 63 8 29
Totals { 21.2% 54.3% 15.4% 1.9% 7.2%
Number of subjects, 10; number of sections, 3; number of experiments,
27; number of associations, 407.
GROUP VI
What modification of influence takes place when an auditory impression
in the form of a word of abstract nature (the pure abstract words are
taken later) is given in comparison with a concrete noun? The tables
indicate that we are now able partly to overcome the disadvantage
of first position by the advantage of concrete content. 24% of the
associations are the result of total fusion; there are eight cases of
total fusion throughout the series, and seven where total fusion took
place before the third word and continued. There are two cases where
the first was followed throughout, and but one where the second was
followed exclusively. The tables indicate that there were very few
words. Some of the subjects claim, "These words did not seem equally
rich in associations. I was not at all conscious of the one while the
other was in consciousness." (H.) The most characteristic feature here
was, as Br. also indicates, "Great amount of rivalry at the beginning
of the series"; while Bs. states, "There was a lot of confusion and
a feeling of groping for words." Br. adds later, "For some seconds
association seemed obstructed. Then by an effort the process was
started which followed an involuntary course. A kind of confused
presence of both words." Another subject adds, "There was a long blank
after the words were said in which both words were balancing off in
the fringe of consciousness and the mind expectant, passively waiting
for an association to turn up. The hesitant period seemed marked by an
attempt at a synthesis of these two words in some way."
SUBJECT XIX
Lamp--Justice.
| chimney lamp.
| white lamp chimney.
| yellow white chimney.
| flame yellow.
| nickel lamp plus the other words.
- scales justice.
- purple robe justice.
As the tables indicate, there was frequently a strong tendency here for
the abstract terms to fuse. As H. noticed, "It does not tend to call up
associations of its own stripe, but in some way becomes concrete."
TABLE VI. TWO WORDS: CONCRETE--ABSTRACT SPOKEN
Time--15 seconds.
Characters--same as Table I.
(I) Desert--Hate
A. | | | + + +
M. | | | | - -
F. + + +
H. | - | | | | | | |
Ro. | | - - | | | |
Bl. + + + + + + +
By. | | | + + + + + +
Bs. - | | | | |
Br. | | | + +
(1) Desert--Hate.
(2) Lamp--Justice.
(3) Pen--Fatigue,
(4) Gate--Fear.
TABLE VI--_continued_
| - + α β
A. { 10 2 6 0 0
{ 55.5% 11.2% 33.3%
M. { 7 8 10 0 0
{ 28.0% 32.0% 40.0%
F. { 3 8 5 0 0
{ 18.7% 50.1% 31.2%