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Psychologica/ Reports, 1960, 7 , 387-398. @ Southern Universities Press 1960
EFFECTS OF ANXIETY LEVEL AND
EXTRAVERSION-INTROVERSION O N PROBABILITY LEARNING'
MICHAEL A. WALLACH A N D RUTHELLEN C. G A H M
/Massachusetts Institute of Technology and T h e Age Center of N e w Enghlzd, Inc.
Suppose an individual has to predict which of two events will occur on
each of a series of tries, and one of these events is more likely than the other
although boch in fact occur in a random sequence. How often will the rare
event be predicted? Two factors might conceivably make for a high rate of
predicting the rare event. It is the purpose of this study to separate them and
examine their possible relationships to aspects of personality in an older sample.
A high rate of predicting the rare event will result if the person assumes
there is some pattern to the rare event's occurrence, and tries to solve the problem of accurately predicting when the rare event will occur (the "problem"
approach). For such a person, trying to "catch" the rare event's occurrence is
a challenge which he accepts: being correct in predicting the rare event is
more imporcant to him than being correct in predicting the frequent event.
On che other hand, a high rate of predicting the rare event also will result if
the person simply isn't sensitive to the infrequency of the rare event and hence
treats it as if it occurs more often than it does (the "50:5OWapproach).
Although boch "problem" and "50:50n approaches lead to more frequent
prediction of the rare alternative, the former is a much more "thoughtful" approach to che task than the latter. Can we discinguish the two in terms of
some additional response measure? Latency of predicting the rare alternative
seems to provide a method. If high frequency of choosing the rare alternative
is due to the "problem" approach, then choice of the rare alternative should
be preceded by a longer latency than choice of the frequent alternative: S should
be especially thoughcful before predicting the rare event since its accurate prediction is the challenge for him; it is the rare event with which his hypotheses
specifically are concerned. Predicting the frequent event, on the other hand, is
more likely to be correct and hence poses less of a problem. If, on the other
hand, high choice frequency for the rare event is due to the "50:50" approach,
then S should be about as fast in predicting the rare alternative as he is in
predicting the frequent one since he is insensitive to the difference between
[hem. Although a frequency measure alone, then, is not sufficient to distinguish
[he "problem" and "50:5OP'approaches, measuring latencies as well as frequencies seems co provide a way of making this discrimination. W e hence may
'This investigation was supported by a research grant (M-2269) from the National Institute of Mental Health, Public Health Service, conducted under the auspices of The
Age Center of New England, Inc. Grateful thanks are due Marguerite Braun, Leonard
R. Green, and Lynne Hamilton, for aid in data analysis.
358
M. A. WALLACH
&
R. C. GAHM
operationally define the "problem" approach in terms of high choice frequency
for the rare event, and also a longer latency of choice for the rare event than
for the frequent one. The "50:50n approach, on the other hand, may be defined in terms of high choice frequency for the rare event, and also as short a
latency of choice for the rare event as for the frequent one.
While clear relationships have been found between probability learning
performance and stimulus condition independent variables (such as the degree
of deviation from 50:50 in the relative frequencies of the two events),' little
understanding has been obtained of how probability learning performance may
vary with personality when stimulus conditions are held constant. Fillenbaum
(1959), for instance, using young adult males, found no correlations beyond
what might be expected by chance between scores on MMPI scales and individual
differences in choice frequency for a rare alternative occurring in a random
sequence with 67:33 as the actual relative frequencies. However, variability
for young adults in cognitive performances of the kind just cited typically is
not large. It may be especially difficult to obtain relationships between personality and probability learning among younger Ss, therefore, because of an
insufficient range of individual differences in the probability learning measures.
The impetus to the present research was the view that work with an older
male sample well might cast light on these apparently elusive relationships between personality and probability learning. The greater variability in cognitive
performances found, on the average, among older as compared with younger
Ss, might reveal relationships between probability learning and personality
that remain concealed in younger individuals.
In particular, it was desired to investigate two aspects of personality
which might be expected to influence the use of the' more deliberative "problem"
approach to probability learning versus the more thoughtless "50: 50" approach.
These aspects are manifest anxiety level and extraversion-introversion. A high
level of anxiety has been found to disrupt attempts at rational, deliberative
solving of complex problems (see, e.g., Easterbrook, 1959). So also we well
might expect extraverts to be more impulsive and less contemplative than introverts. In sum, the presence for older Ss both of high anxiety and of extraversion
might be expected to favor the occurrence of the thoughtless "50:5OWapproach.
On the other hand, the presence for older Ss both of low anxiety and of introversion might be expected to favor the occurrence of the thoughtful, deliberative "problem" approach.
The hypotheses under examination in the present research, then, are that
( a ) high anxiety extraverts in an older male sample will be most likely to show
'See Feather (1959) for a review of such stimulus condition variables, and see Bruner,
Goodnow, and Austin (1956) for some relevant experiments.
ANXIETY, EXTRAVERSION, AND PROBABILITY LEARNING
389
n "S0:SO" approach to probability learning, while ( b ) low anxiety introue~ts
i n an older male sample will be mart likely to show a "problem" npproach.'
METHOD
T h e Exferimental Skzration
A simple binary choice situation was arranged, analogous to ones used
with young adult males by Goodnow ( 1955 ) and others. On each of 100 trials,
S had to predict which of two lights would appear. H e made his prediction
by pressing the button under the light on which he was betting. After each
prediction, the left- or right-hand light immediately went on for one second,
thus informing S which side was correct on that trial.
In actuality the left-hand light was correct on 70 trials and the right-hand
light on 30, with this 70:30 probability being present and order randomized
within each block of 10 trials. Which button S pushed on a trial, and which
light was illuminated on that trial from the automatic program sequence, were
recorded by pen marks on the channels of an Esterline-Angus moving tape.
Later reading of the tape permitted us to count the number of times the righthand button was pushed within a series of trials, and to measure, in terms of
length of tape, the latency between a light's going off and S's next push of the
left- or right-hand button. Because an initial period of familiarization with
the payoff schedule was necessary before scores would become meaningful, it
was decided beforehand to consider frequency and latency measures for the
last 20 trials: that is, Trials 81-100.
The latency score used was a ratio consisting of the mean of an S's latencies
for right-hand choices, divided by the mean of that S's latencies for left-hand
choices. Mean latency for right-hand choices indicated S's reaction speed when
predicting the rare alternative, while mean latency for left-hand choices indicated
the same S's reaction speed when predicting the frequent alternative. Dividing
the former mean by the latter mean hence provided an index of S s latency in
predicting the rare alternative compared to his latency in predicting the frequent one.
Instructions to S directed him to predict which of the two lights would go
on for each trial. S knew that the machine was programmed, so he couldn't
alter or control the lights in any way. His only job was to predict, by pushing
the appropriate button, which light would come on next. The main object of
the test, S was told, was to predict correctly as often as possible.
Personality Variables of Manifest Anxiety and Extraversion-introversion
The group form of the MMPI (Hathaway & McKinley, 1940) was in'Examples of analyzing the personality variables of manifest anxiety and extraversionintroversion in combination may be seen in research by Wallach and Gahm (1960) and
Wallach and Greenberg ( 1960).
390
M. A. WALLACH & R. C. GAHM
dividually administered to each S some time before he went through the probability-learning task. Scale scores then were obtained for each of the MMPI
scales listed by Kassebaum, Couch, and Slater (1959, p. 228), plus certain others
which are of too specialized interest to report here but are described by Slater in
1958.h." Scores for these MMPI scales were intercorrelated for a sample of 129
older males, including Ss in the present srudy plus additional Ss from the same
population. The correlation matrix was factor analyzed by Thurstone's complete
centroid method (Thurscone, 1947), and orthogonal rotations carried out wich
the aim of maximizing the similarity of the two largest faccors to the comparable
two largest factors in the parallel MMPI study by Kassebaum, Couch, and
Slater ( 1959) using male college students.
The two factors, each accounting for more of the total variance than any
other factor, had to do with manifest anxiety and extraversion-introversion. It
is of interest that the two largesc factors emerging in the present older sample
closely matched the two largest factors that emerged from the study of college
students just cited. This finding provides evidence that these aspects of personality structure do not change with increasing age.
O n the first factor, which accounted for about 32% of the total variance,
those scales that were highest loading (.74 or better) were "admission of weaknesses" (Slater" , "anxiety" (Welsh & Dahlstrorn, 1956, pp. 264-281 ), "caudality" (Williams, 1952 ), "dependency" (Navran, 1954), "hypertension correction scale" (described by Slater" "neuroticism" ( Winne, 1951) , "parietal"
scale (Friedman, 1950), "psychasthenia," and "schizophrenia" (Hathaway &
McKinley, 1943), wich negative loadings for "ego functioning" (Hathaway &
McKinley, 1943) and "leadership" (Oettel, 1952). The "admission of weaknesses" scale, developed by Slater5, contains those items from the MMPI for
which a "yes" response means that S admits there is something psychologically
or physically wrong wich him. The presence of this scale, the Welsh "anxiety"
scale, and Winne's "neuroticism" scale, plus the fact that most of the other
scales noted above also are indicative of manifest feelings of "disturbance,"
seemed to make "manifest anxiety" the most appropriate label for this first
factor!
On the second factor, which accounted for about 10% of the total variance,
those scales that were highest loading (.60 or better) were "agreement wich
general assertions" (Slater", an "extraversion index" consisting of hypomania
),
'All statistical treatment of these MMPI data, the factor analysis, and computation of
factor scores, were carried out by Philip E. Slater, to whom we are greatly indebted for
aid in facilitating the present research. These data were processed at the MIT Computation
Center.
"Preliminary report of progress on 'correlates of anxiery' project," unpublished manuicripr by P. E. Slacer, 1958.
It might also be called "neuroticism" (see Eysenck, 1956) or "ego weakness" (see
Kassebaum, Couch, & Slater, 1959).
ANXIETY, EXTRAVERSION, AND PROBABILITY LEARNING
391
score minus depression score (Slater"), "hypomania" (Hathaway & McKinley,
1943), and "sociability" (Gough, 1957), with negative loadings for "repression, denial" (Welsh & Dahlstrom, 1956, pp. 264-281), and "social introversion" (Hathaway & McKinley, 1943). Slater's 1958 sca1e"or
"agreement
wich general assertions" contains those items from the MMPI for which agreement means adherence to generally held preferences, interests, and beliefs about
people and things. The nature of the various scales loading highly on this
second factor seemed to make "extraversion-introversion" the most appropriate
label for it.
Ss' anxiety and extraversion-introversion scores were based on these respective factors rather than on single scales, in order to enhance the reliability
of the measures employed. Individual factor scores were obtained by a method
described in detail by Kassebaum, Couch, and Slater (1959). In brief, the
variables included for computation of factor scores on each of the two factors
were so selected as to satisfy the following double criterion: ( a ) maximizing
the communality of the factor measure in question, and ( b ) minimizing the
saturation on the remaining factors by equalizing the positive and negative
loadings of these variables on each of the remaining factors. When the set of
variables was found which satisfied this double criterion for a factor measure,
the individual scores for each variable (i.e., scale) in the set were converted
into standard scores so that score distributions on the variables in question could
be treated as equivalent. An individual's factor score for anxiety or extraversion
then consisted of the algebraic sum of his standard scores for the variables included in the factor measure in question. The correlation between anxiety
factor scores and extraversion factor scores was - .09 for the 52 older males
in the present study, thus indicating the orthogonality of these two score
dimensions.
Ss were separated into extraverts and introverts by dichotomizing the
distribution of extraversion factor scores as close to the median as possible.
Similarly, Ss were separated into high and low anxiety groups by dichotomizing
the distribution of anxiety factor scores as close to the median as possible.' Four
groups of Ss resulted from these dichotomizations: high anxiety extraverts,
high anxiety introverts, low anxiety extraverts, and low anxiety introverts. As
expected from the orthogonality of these two factors, a similar, although not
identical, number of Ss fell into each of these four groups. These groups contained not the extremes of the anxiety and extraversion-introversion factor score
distributions, bur rather all of the cases.
'Splits could not occur exacdy at the median because, for each of the two distributions
of factor scores, a score for which several Ss were tied overlapped the median, with a
majoriry of the tied Ss falling on one side of it. Each split was made by assigning all
tied Ss to this majority side.
392
M. A. WALLACH
&
R. C. GAHM
These two dichotomized personality dimensions constituted our treatment
variables. Their effects on the dependent variables of frequency and latency
of choice were investigated by 2-by-2 analyses of variance. Because of some
inequalities in the cell sizes for each analysis, Snedecor's Method of Unweighted
Means (Snedecor, 1956, pp. 385-388; Gosslee, 1959) was used in the computation. Since none of the bases of classification involved random sampling, the
fixed constants m d e l (McNemar, 1955, pp. 304-306) provided the suitable
method for selecting the error term in computation of F ratios.
Control Variables
It was desirable to insure that any frequency and latency differences among
the personality groups were not artifacts of intelligence, education, or age differences among these same groups. The intelligence measure used was the
vocabulary subtest from the Wechsler intelligence test for adults (Wechsler,
1944). A vocabulary index was chosen to assess intelligence for two reasons.
First of all, the vocabulary subtest of the Wechsler group has a very high correlation with the score based on the complete Wechsler battery of 11 subtests.
Secondly, vocabulary scores have been reported to show the least decrement with
age of any intelligence test measure (see, for instance, Doppelt & Wallace, 1955;
Strother, Schaie, & Horst, 1957). Since our Ss were of an older age group and
we wished to determine their intellectual comparability to young adults, vocabulary score seemed to be the most appropriate way of doing so.
The vocabulary test was administered individually after S went through
the probability-learning task. Vocabulary scoring was done according to
Wechsler's manual of instructions by each of two independent judges. The
score used was the sum numerical value of S's vocabulary credits. Reliability
of the two judges' sum scores, as determined by an intraclass correlation coefficient (Robinson, 1957; 1959) was .95 for a larger sample of older males and
females including the 52 older males of the present study. Disagreements were
resolved by taking the average of the two discrepant sum scores in question.
Highest attained level of education and date of birth also were known for
all Ss. Education level was measured in terms of years of schooling. Age was
determined to the nearest year by taking an arbitrary current date (the same
date for all Ss) and subtracting from it each S's date of birth.
Subjects
The participants in the present study were 52 older maless Their high
'While che work cited by Fillenbaum, Goodnow, and other researchers on probability
learning has focussed on young adult males, the present research thus utilizes a sample
of older males. That research on probability learning has focussed on males probably
reflects the difficulty of inducing females to understand the nature of the probability
learning task. Indeed, attempts by the present investigators to use older females proved
infeasible for just this reason: interviews indicated that older females were unable to
understand the nature of the experimental task.
ANXIETY, EXTRAVERSION, AND PROBABILITY LEARNING
393
intellectual and educational status made them comparable in these respects to
male college srudents. Mean age was 70.6 (SO = 7.0). With regard to
Wechsler vocabulary test score, the mean was 34.8 (SD = 5.0):
Finally, mean
level of education was 13.6 years of schooling (SD = 3.0),'or an average of
1.G years of college.
RESULTS
AND DISCUSSION
Table 1 presents the means and Table 2 the analysis of variance for frequency of choice of the rare alternative during the last 20 trials, i.e., Trials 81TABLE 1
MEAN FREQUENCIES
OF CHOICEOF RAREALTERNATIVE
DURINGTHE LAST20
.TRIALS FOR PERSONALITY
GROUPS(N= 5 2 )
-
-
-
Groups
-
-
-
Extraversion
- -
-
--
Introversion
High anxiety
8.07
4.67
Low anxiety
6.33
8.14
*Group sizes in this and all following tables are 12, 14, 14, and 12, for high anxiety
introverts, high anxiety extraverts, low anxiety introverts, and low anxiety extraverts,
respectively.
100, for the four personality groups. Scores are approximately normally distributed and variances are homogeneous by Bartlett's test (Walker & Lev, 1953,
pp. 193-194). The only significant F value is for the interaction of anxiety and
extraversion. Frequency of choice of the rare alternative is higher for anxious
extraverts and nonanxious introverts than the frequency of the rare alternative's
actual occurrence. For the remaining two personality groups, however, frequency of choice of the rare alternative matches or is lower than the frequency
of its actuaI occurrence. With 1 and 48 degrees of freedom, the P for this
interaction is 5.92 ( p < .03).
TABLE 2
ANALYSISOF VARIANCE,
FREQUENCIES
OF CHOICEOF RAREALTERNATIVEDURING
THE
LAST20 TRIALS FOR PERSONALITY GROUPS(N= 52)
-
Source
Extraversion
Anxiety
Interaction
Within cells
-
-
df
Mean square
F
1
8.02
9.83
87.79
14.83
0.54
0.66
5.92
1
1
48
n.s.
n.~.
< .03
Wata on college students reported by Dana (1957) and others indicate that our older Ss'
scores tend, if anything, to exceed those of young adult college srudents.
M. A. WALLACH & R. C. GAHM
394
The latency ratio score means and analysis of variance are presented in
Tables 3 and 4, respectively, for the four personality groups during the last
TABLE 3
MEANLATENCY
RATIOSCORES
FOR SPEED OF CHOICE
OF THE ALTERNATIVES
DURINGTHE LAST 20 TRIALSFOR PERSONALITY
GROUPS(N= 52)
Groups
Extraversion
Introversion
High anxiety
1.01
1.27
1.08
1.53
Low anxietv
-.
'Each S's ratio score consists of the mean latency of his right-hand responses divided by
the mean latency of his left-hand responses during these 20 trials.
-
-
20 trials. An S s latency ratio score is the mean lacency of his right-hand responses during those 20 trials divided by the mean latency of his left-hand responses during the same series of 20 trials.1° The more a latency ratio score
exceeds one, the greater is S's latency in predicting the rare in contrast to the
frequent alternative. We find a significanc effecc for the extraversion-introversion dimension, introverts being slower in predictions of the rare in contrast
to the frequent alternative than extraverts. As variances proved heterogeneous
by Barcletc's test, a square root transformation was applied and led to homoTABLE 4
ANALYSISOF VARIANCE,
LATENCY
RATIO SCORES
FOR SPEED OF CHOICEOF THE
A L T E R N A ~ EDURING
S
THE LAST20 TRIALS
FOR PERSONALITY
GROUPS( N = 52) *
Source
df
Mean squase
F
P
Extraversion
1
2.70
6.2 1
< .03
n.s.
Anxiety
1
0.69
1.58
Interaction
1
0.24
0.54
n.s.
Within cells
48
0.43
'While the means in Table 3 are raw scores, a square root transformation was applied
for the analysis of variance in order to avoid heterogeneity of variances. Before the
transformation, decimal points were moved one digit to the ;ighc and scores carried out
to rwo figures beyond the new decimal point.
geneous variances by that test. The analysis of variance on transformed scores,
which were approximately normally distributed, yielded an F of 6.21 ( 1 and 48
df, p < .03) for extraversion-introversion, with no other effect significant. The
finding of larger latency ratio scores for introverts is heavily contributed to
by the low-anxiety introverts, who show the largest latency ratios of all four
groups. High-anxiety extraverts, on the other hand, show the smallest lacency
ratios of all the groups.
I'n the case of two Ss (one in each of two groups), no right-hand responses were given
during Trials 8 1 to 100. The mean right-hand latency term for their latency ratio score
was estimated as the grand mean of the mean right-hand latency scores for all Ss during
Trials 81 to 100. Such a procedure provides the most conservative estimate one could
make.
ANXIETY, EXTRAVERSION, AND PROBABILITY LEARNING
395
These frequency and latency results constitute our main findings. What
light do they shed on our initial questions of separating "problem" and "50:50"
approaches to the probability-learning task and finding hypothesized personality
correlates of each? From the means of Table 1, we note that high anxiety
extraverts and low anxiety introverts both predict the rare alternative more
frequently than it occurs, and more often than the other groups. Turning now
to the means of Table 3, we find that a sizeable difference in latency ratio
scores discriminates high-anxiety extraverts from low-anxiety introverts, even
though both predict the rare event very often. High-anxiety extraverts have
the smallest latency ratio scores of all four groups; indeed, they predict the rare
alternative just about as quickly as they predict the frequent alternative. Lowanxiety introverts, on the other hand, have the largest latency ratio scores of
all four groups, taking about 50% longer in predicting the rare alternative
than they d o in predicting the frequent one.
The probability-learning behaviors of high-anxiety extraverts and lowanxiety introverts thus meet our operational definitions for the "50:50" and
"problem" approaches, respectively. While high anxiety extraverts predicc the
rare evenc with high frequency, their latency in predicting it is short-no longer
than when they predict the frequent event. This is the behavior in terms of
which we defined the "50:50" approach. According to this approach, S simply
isn't sensitive to the infrequency of the rare event, and treats it as if i t occurs
more often than it does because, in effect, he doesn't really know any better.
On the other hand, while low-anxiety introverts also predict the rare evenc with
just as high a frequency, their latency in predicting it is long-half again longer
than when they predicc the frequent event. This is the behavior in terms of
which we defined the "problem" approach, according to which S assumes the
rate event occurs in some pattern and tries to solve the problem of accurately
predicting when the rare event will occur.
Our expectations were confirmed, furthermore, with regard to which
personality group would exhibit each approach. High anxiery should disrupt
attempts at problem-solving, and extraversion should represent a relatively
impulsive, non-contemplative attitude also inimical to problem-solving. Ss
for whom both high anxiety and extraversion are present hence should be most
likely to exhibit the impulsive, thoughtless behavior of the "50:50" approach,
and this was the case. On the other hand, low anxiety should provide a supportive context for attempts at problem-solving, and introversion should represent an attitude of deliberation and contemplation also favorable to problemsolving. Ss who are low in anxiety and introverted hence should be most likely
to show the deliberative, thoughtful behavior of the "problem" approach, and
this too was the case.
In order to determine whether the relationships we have reported were in-
396
M. A . WALLACH & R. C. GAHM
fluenced by intelligence, education, or age differences, analyses of variance
were performed using the same four personality groups. The dependent variables tested were vocabulary score, education, and age, respectively, in three
separate two-way analyses of variance. In none of the analyses did the F for
interaction, rows, or columns even approach significance. W e therefore may
conclude that no vocabulary score, education, or age differences are influencing
the relationships obtained.
SUMMARYAND CONCLUSIONS
The purpose of the present research was to use older males as Ss in an
attempt to determine relationships between personality and approaches to a
probability-learning situation. While attempts to obtain such relationships
with young
.
- adult males have met with little success, it was felt that the wider
range of individual differences in cognitive performances typically found in
older as compared with younger Ss might reveal relationships between personality and probability learning that remain concealed in younger adults.
The probability-learning situation required S to predict which of two
alternatives would occur on each of many tries, one of these alternatives occurring less frequently than the other but in a random sequence. Two approaches which involved a high rate of predicting the rare event were isolated
as dependent variables whose relations with personality were to be assessed.
In one approach, S supposes that there is some pactern to the rare alternative's
occurrence and tries to solve the problem of accurately predicting when the rare
event will occur (the "problem" approach); while in the other, S simply fails
to discriminate just how infrequently the rare event occurs (the "50:50" approach).' Although both approaches should lead to high frequency of predicting
the rare event, we reasoned that the "problem" approach should result in longer
latencies for predicting the rare event than for predicting the frequent event
(since accurate prediction of the rare event is perceived as the main challenge),
while che "50:50Mapproach should result in about the same latencies for predicting the rare as for predicting the frequent event (since S is insensitive to
the difference between them).
High manifest anxiety was expected co disrupt, and low manifest anxiety
to facilitate, attempts at deliberative problem-solving. So also extraverts were
expected to be more impulsive and thoughtless, introverts more contemplative
and thoughtful. Presence both of high anxiety and extraversion hence was expected to favor the occurrence of the thoughtless "50:50" approach to the
probability learning task, while presence both of low anxiety and introversion
was expected to favor the occurrence of the more thoughtful "problem" approach. These expectations were confirmed in an experiment with 52 older
males.
ANXIETY, EXTRAVERSION, AND PROBABILITY LEARNING
377
Our main conclusions are as follows: ( a ) Light can be shed on relationships .between personality and probability learning by using an age sample
whose probability-learning performances provide a wider range of individual
differences than typically is the case with young adults. ( b ) It is of importance
to use combined rather than single procedures for the assessment of probability
learning and of personality. In the present study, frequency and latency of
choice were jointly used as probability learning indices; and manifest anxiety
and extraversion-introversion were jointly used as personality indices.
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