Journal of Gerontology 1977. Vol. 32. No. 5. 578-585
The Organization of Spatial Abilities in Older Men and Women Donna Cohen, PhD,1 K. Warner Schaie, PhD, 2 , 3 and Kathy Gribbin, PhD2
A LTHOUGH spatio-visual abilities are l \ well-documented in younger persons, they have been relatively neglected in gerontological research. The superiority of males as children and young adults in tasks which involve visual perception and the use of spatial relationships has been well acknowledged (Anastasi, 1964; Garai & Scheinfeld, 1968; Maccoby, 1966; Maccoby & Jacklin, 1974; Macfarland-Smith, 1964; Tyler, 1965; Werdelin, 1961). By contrast, women perform at a more proficient level than men on reasoning tasks (other than symbolic reasoning) as well as subtests with high verbal loadings (cf. reviews, Broverman, Klaiber, Kobayashi, & Vogel, 1968; Garai & Scheinfeld, 1964; Maccoby & Jacklin, 1974). Sex differences in spatial dimensions (Nesselroade, Schaie, & Baltes, 1972; Schaie & Strother, 1968), arithmetic (Doppelt & Wallace, 1955), and verbal abilities (Blum, Fosshage, & Jarvik, 1972) have been demonstrated in older as well as younger persons. A provocative observation from cross-sectional data is
'Dcpt. of Psychiatry & Behavioral Sciences. Univ. of Washington. Seattle 9S195. anil Geriatric Research Educational and Clinical Center. Seattle/American Lake VA Hospitals. : Andrus Gerontology Center. Univ. of Southern California. Los Armeies 90007. "Dept. of Psychology. Univ. of Southern California. Los Angeles 90007.
578
that older men appear to maintain their superiority over older women even when their performance on spatio-visual tasks is observed to be less proficient than for younger men (Schaie & Strother, 1968). Although recent longitudinal data testify to the stability of a general spatial or visualization factor in older persons (Nesselroade et al., 1972) making the decrement issue controversial (see Baltes & Schaie, 1976; Horn & Donaldson, 1976) confirmation of significant sex differences on spatial tasks have remained unchallenged, at least in the few instances where they have been studied in older populations. Buffrey and Gray (1972), in an excellent review of sex differences, suggest that detailed information is needed on the types of tasks on which the sexes show superior performance. Indeed, where spatial functions have been measured in older persons, seldom has more than one test been administered, and the numbers of young-old and old-old are relatively small. Furthermore, data are needed from aged populations using data of known factorial composition. In such a way, similarities and differences in the cognitive structures of older men and women can be studied. The present study investigates sex differences in cognitive performance and the organization of spatial abilities in a population of
Downloaded from http://geronj.oxfordjournals.org/ at University of Michigan on September 1, 2015
The objective of this study was to test the cognitive identity of older male and female populations with reference to raw score, component structure, and component score measures of spatial and verbal performance. One hundred women (average age, 70.2) and 96 men (average age, 69.0) were administered three verbal and six nonverbal cognitive subtests. The equivalence of four-factor principal component analyses of the male and female correlation matrices, corrected for restriction of range, were tested with the multiple group method of factor analysis. High coefficients of congruence for the three spatial and single verbal factors argue strongly for similar cognitive structures. Multivariate analysis of the factor scores, however, showed a significant mean difference between the older men and women. But when Joreskog's procedures are applied to test the equivalence of covariance structures, the best fit was obtained for a model involving equivalence of factor means, factor structure, factor coefficients and factor correlations.
ORGANIZATION OF SPATIAL ABILITIES
579
4
Downloaded from http://geronj.oxfordjournals.org/ at University of Michigan on September 1, 2015
men and women 60 years and older. Both the Test Instruments level of ability as well as the interrelationship The following tests were administered in a of performance scores are analyzed in order counterbalanced design to control order efto evaluate whether or not cognitive identity fects. Vocabulary from the Wechsler Adult between the sexes can be demonstrated. More Intelligence Scale (WAIS); Word Reasoning precisely, the following hypotheses were and Space subtests from the 1963 adult version tested: of the Primary Mental Abilities (PMA) battery; (1) The cognitive structure of spatial abil- Word Fluency, Form A (Christensen & Guilities reflected in the interrelationships among ford, 1958); Making Objects, Form A (Gerthe performance scores will be different in shon, Gardner, Merrifield, & Guilford, 1963); older men and women. Different underlying Match Problems V (Merrifield & Guilford, factors will be required to explain the rela- 1969); Gottschaldt Hidden Figures4; and two tionships among spatial variables in the two tests developed by J. P. Guilford and his assosexes. Furthermore, men will show a higher ciates, Close-ups, (Guilford, 1969b) and Circle reliability for spatial tests upon which inter- Continuations (Guilford, 1969a). The Closepart correlations are calculated. Ups test requires the subject to identify objects (2) If level of performance is analyzed, in photographs which were taken very near older men will perform at a more proficient the object. Circle Continuations evaluates level than older women on spatio-visual tasks, the ability to complete a portion of a circle whereas women will outscore men on verbal visually; given an arch and five dots, the subfluency and verbal reasoning dimensions. ject must select the dot that would lie on the completed circle. METHOD Except for the vocabulary subtest, which was used to equate male and female populaSubjects tions on general verbal ability, the remainder Two hundred-fifty volunteers were recruited of the battery was selected to include tests from numerous senior citizen organizations of known factorial composition, on which throughout the greater Los Angeles area, and either men or women were known to excel. all participants were white, English-speaking The over-representation of "male" tasks in community residents. Fifty-four subjects were the realm of visuo-spatial abilities is coneliminated because they could not complete or sistent with the goal to examine the interrelarefused to complete the test battery. The re- tionship of figural dimensions in men and maining 196 subjects had adequate vision for women. Most of the tests have not been used the tests, as assessed by a questionnaire and to any great extent in the elderly. They repsatisfactory performance reading a Snellen resent ability dimensions which should be chart. These include 100 women (average age relatively independent or orthogonal to each 70.2 years) and 96 men (average age 69.0 other (Guilford, 1967). years). Participants had to have completed at A number of tests designed by Guilford least 12 years of schooling or to have achieved and his associates were used for this research a minimum vocabulary score of 65 on the because the morphological conceptualization Wechsler Adult Intelligence Scale subtest. of intelligence, the Structure-of-Intellect model (S-I), permits a precise specification Procedure of different spatial or figural factors. Many of A test battery consisting of nine subtests the subtests, developed on samples of bright was administered to small groups over one children and young adults, are generally quite or two testing sessions in familiar settings, difficult. A pilot investigation included three usually a room in their club or organization additional subtests which were found to be headquarters. Each group had met with the too difficult as well as too long. These subtests, investigator at least once before the testing the Guilford-Zimmerman Spatial Orientation, sessions to review sample material and to ask Guilford-Zimmerman Spatial Visualization, questions. Instructions were repeated two or three times, and testing did not proceed until The Gottschaldt Hidden Figures test is available from Dr. Richard S. everyone understood both instructions and Ciutchfield. Institute of Personality Assessment and Research, Univ. of California at Berkeley. the sample problems.
COHEN, SCHAIE, AND GRIBBIN
580
and Spatial Comprehension tests were subsequently eliminated.
5 Although the multiple-group methods (Harman. 1960) c;m provide simple structure factors without rotation, the present method includes rotation to eliminate order of extraction effects.
Table 1 lists the raw score means and standard deviations separately by sex and for the total group. Descriptive statistics for the men and women by age categories are available from the senior author by request. The sex groups were well-matched for verbal abilities since the data indicates that men and women performed equally well on the WAIS vocabulary and the PMA word reasoning subtest. Tests of significance using Wilk's lambda criterion and canonical correlations indicated that men and women differed in level of performance (F = 2.31,/? < 0.05). Equivalence of Correlation Matrices The first hypothesis to be tested is that the two correlation matrices (corrected for restriction of range) are random deviations from a common universe correlation matrix, i.e., that the two matrices are equivalent except for random error of measurement. A simple method to test this hypothesis by means of the Kolmogorov-Smirnov test of the deviation of the differences between corresponding pairs of correlations in the two matrices from the distribution function generated from the normal error curves has been described by Schaie (1958). The Kolmogorov-Smirnov test yielded a significant deviation from the expected chance distribution (p < .01). The null hypothesis can therefore be rejected since there appears to be a significant difference in the cognitive structure of men and women at least at the phenotypic level.
Table 1. Mean Raw Scores and Standard Deviations of Men and Women on Subtests of the Cognitive Battery.* Standard Deviations
Mean Scores
Vocabulary Word Reasoning Word Fluency Space Close-ups Circle Continuation Match Problems Hidden Figures Making Objects
Men
Women
Total Sample
63.8 17.0 36.1 25.7 12.2 9.7 8.0 7.7 32.6
64.5 17.4 41.0 21.6 12.0 9.6 6.4 6.6 35.1
64.2 17.2 38.6 23.6 12.1 9.6 7.2 7.2 33.9
Men
Women
Total Sample
11.0 4.7 14.8 14.5 4.6 4.3 4.5 5.6 14.0
13.0 5.4 14.5 15.1 3.8 3.8 4.4 4.8 12.6
12.0 5.1 15.8 14.9 4.2 4.0 4.5 5.2 13.3
Tests of significance using Wilks Lambda criterion and canonical correlations indicate F = 2.3, df HYP = 9.00, df ERR = 186.0, p = 0.02, r = 0.32.
Downloaded from http://geronj.oxfordjournals.org/ at University of Michigan on September 1, 2015
Data Analysis Descriptive statistics for the nine cognitive subtests were computed for the entire population as well as separately for the sexes. Since the variance for the men was systematically higher across all six nonverbal tests, male and female correlation matrices were rescaled for restriction of range using the joint sample variance as the estimate of the unrestricted (Guilford & Fruchter, 1973). Interconnection matrices were tested for equivalence to determine whether they were random deviations from a universe correlation matrix. A principal component solution indicated four nonerror factors for both the male and female correlation matrices. The multiple group method of factor analysis with rotation to the best simple structure (Horst & Schaie, 1956) was then used to obtain target solutions for the men and women.5 Coefficients of congruence were computed as well as other statistics. Factor scores were then evaluated in a multivariate analysis of variance to examine sex differences in level of performance. Finally, the model suggested by the principal components analysis of the correlation matrices was tested by means of Joreskog's (1971) procedures.
RESULTS
ORGANIZATION OF SPATIAL ABILITIES
581
Table. 2. Hypothesized Pattern of Component Loadings. Components Subtest
Component I
C o m p o n e n t III
Component IV
0 0 0 0 1 0 0 0 1
1 1 1 0 0 0 0
0 0 0 0 0 1 1
0
0
0
0
Vocabulary Word Reasoning Word Fluency Space Close-Up Circle Continuations Match Problems Hidden Figures Making Objects
Table 3. Final Solution of Component Matrix for the Older Men Using Multiple Group Component Analysis with Rotation to Simple Structures.
Subtest
Component I
Component II
Vocabulary Word Reasoning Word Fluency Space Close-Up Circle Continuations Match Problems Hidden Figures Making Objects
-.01 -.07 .07 .74 -.05 -.01 .03 .65 .07
.05 .02 .06 .05 .73 .11 .12 .07 .64
Components C
jonent III .68 .68 .56 -.02 -.10 .01 .02 .01 .12
Component IV -.02 .03 .02 -.06 .07 .70 .78 .08 -.08
Table 4. Final Solution of Component Matrix for the Older Women Using Multiple Group Component Analysis with Rotation to Simple Structures. Components Subtest Vocabulary Word Reasoning Word Fluency Space Close-Ups Circle Continuations Match Problems Hidden Figures Making Objects
Component I
Component II
Component III
Component IV
-.03 .08 -.06 .72 -.09
.05 -.12 .10
.71 .66 .60 -.02 -.03 -.04 .04 .00 .05
-.00 .08 -.08 -.06 .08 .67 .70 .08 -.06
.02 .00 .63 .13
Multiple Group Component Analysis Four components were extracted using a principal components model. The equimax solutions for men and women were rotated to a common target expressed by the hypothesis matrix in Table 2 by means of the multiple group method with rotation to simple structure (Horst & Schaie, 1956). Tables 3 and 4 give the reference structure matrices
-.02 .83 .14 -.12 .06 .76
and correlations for men and women, respectively. The coefficients of congruence between corresponding components for men and women were so high for the single verbal (Component III, 0.995) and the three spatial dimensions (Component I, 0.963; Component II, 0.984; Component IV, 0.970) that further rotation to similarity was unnecessary. Phi coefficients presented in Table 5 suggest
Downloaded from http://geronj.oxfordjournals.org/ at University of Michigan on September 1, 2015
Component II
582
COHEN, SCHAIE, AND GR1BB1N
Table 6. Multivariate Analysis of Variance of Sex Differences on Component Scores.
Table 5. Component Intercorrelations (Phi coefficients). Women l 1 2 3 4
3
2
4
1.00 .51 .46 .16
Component I
1.00 .43 .38
1.00 .36
1 1 2 3 4
1.00 .49 .59
.16
2
3
4
R 21
Univariate F Tests* 555.83* 165.38 453.39* 480.60*
JTests of significance using Wilks Lambda criterion and canonical calculations. *p .05 **p .01
1.00 .43 .38
1.00 .36
1.00
very similar component intercorrelations across sex, the one exception being a slightly higher correlation between the verbal and the spatial relations component in men. The component structures derived for both samples argue for cognitive identity in older men and women. The verbal comprehension (vocabulary), reasoning, and fluency subtests grouped together to form a semantic dimension (Component III) as expected. A spatial relations factor (Component I) grouped the Space subtest, measuring the ability to recognize spatial patterns rotated in one dimension, and Hidden Figures, assessing the ability to evaluate spatial configurations in a distracting perceptual field. Component II, a spatial visualization dimension requiring the ability to identify visual configurations and generate spatial solutions, included CloseUps and Making Objects. Component IV, a spatial flexibility cluster of Match Problems and Circle Continuations, identifies the ability to analyze spatial fields and generate solutions judging spatial distance and alternate spatial configurations. Whereas the component structure argues convincingly for the cognitive identity between the sexes, multivariate analysis of the component scores revealed a significant difference in level of performance (F = 3.72, p < 0.0061, see Table 6). The men performed at a more proficient level than women on the visuospatial components, whereas, by contrast, the women numerically outscored the men on the verbal dimension.
Component Scores (expressed as T scores, M == 501 S.D. = 10) for Older Men and Women Standard Component Mean Deviation
I II III IV
Men
Women
Men
Women
51.7 49.0 48.4 51.6
48.4 50.9 51.5 48.4
10.3 10.8
9 .5 9..2 10.,4 9..7
9.4
10.2
Further Tests of Structural Equivalence Traditional approaches to comparative factor analysis have been criticized because they require the strong assumption of equivalent metrics for the correlation matrices whose equivalence is to be tested. In the foregoing section we argued that the differences in variability on the observed measures in men and women were experimental artifacts and should therefore be corrected, while the mean differences were arbitrary and should therefore be standardized as part of the correlation procedure. Due to the recent availability of the COFAMM computer program (Joreskog & Sorbom, 1976), it is now possible to examine whether the arbitrary standardization of metric has or has not led to spurious conclusions regarding structural equivalence. That is, we can now examine the equivalence of the covariance matrices for men and women (thus preserving the original metrics), under various assumptions regarding the equivalence of factor structure (Joreskog, 1971), and/or factor means (Sorbom, 1974), as well as to test systematically a sequence of alternate models to determine which one would provide the best fit to our data (also cf. Joreskog, 1974).
Downloaded from http://geronj.oxfordjournals.org/ at University of Michigan on September 1, 2015
j
5.70 1.65 4.54 4.88
HI IV
1.00
Men 0
F (4,191) 3.72**
Sex
J
¥>
ORGANIZATION OF SPATIAL ABILITIES
Table 7. Results of the COFAMM Analyses. Model
df
Chi-Square
118.3 96.6 92.1 81.3
.001 .002 .003 .006
85.6 60.5 60.7 45.9
.05 .17 .10
M o d e l s permitting differences in factor m e a n s (0 m y df) HI
Xm = Xf, m = f, i|/m = i/»f
H2
\ m = Xf,
The Organization of Spatial Abilities in Older Men and Women Donna Cohen, PhD,1 K. Warner Schaie, PhD, 2 , 3 and Kathy Gribbin, PhD2
A LTHOUGH spatio-visual abilities are l \ well-documented in younger persons, they have been relatively neglected in gerontological research. The superiority of males as children and young adults in tasks which involve visual perception and the use of spatial relationships has been well acknowledged (Anastasi, 1964; Garai & Scheinfeld, 1968; Maccoby, 1966; Maccoby & Jacklin, 1974; Macfarland-Smith, 1964; Tyler, 1965; Werdelin, 1961). By contrast, women perform at a more proficient level than men on reasoning tasks (other than symbolic reasoning) as well as subtests with high verbal loadings (cf. reviews, Broverman, Klaiber, Kobayashi, & Vogel, 1968; Garai & Scheinfeld, 1964; Maccoby & Jacklin, 1974). Sex differences in spatial dimensions (Nesselroade, Schaie, & Baltes, 1972; Schaie & Strother, 1968), arithmetic (Doppelt & Wallace, 1955), and verbal abilities (Blum, Fosshage, & Jarvik, 1972) have been demonstrated in older as well as younger persons. A provocative observation from cross-sectional data is
'Dcpt. of Psychiatry & Behavioral Sciences. Univ. of Washington. Seattle 9S195. anil Geriatric Research Educational and Clinical Center. Seattle/American Lake VA Hospitals. : Andrus Gerontology Center. Univ. of Southern California. Los Armeies 90007. "Dept. of Psychology. Univ. of Southern California. Los Angeles 90007.
578
that older men appear to maintain their superiority over older women even when their performance on spatio-visual tasks is observed to be less proficient than for younger men (Schaie & Strother, 1968). Although recent longitudinal data testify to the stability of a general spatial or visualization factor in older persons (Nesselroade et al., 1972) making the decrement issue controversial (see Baltes & Schaie, 1976; Horn & Donaldson, 1976) confirmation of significant sex differences on spatial tasks have remained unchallenged, at least in the few instances where they have been studied in older populations. Buffrey and Gray (1972), in an excellent review of sex differences, suggest that detailed information is needed on the types of tasks on which the sexes show superior performance. Indeed, where spatial functions have been measured in older persons, seldom has more than one test been administered, and the numbers of young-old and old-old are relatively small. Furthermore, data are needed from aged populations using data of known factorial composition. In such a way, similarities and differences in the cognitive structures of older men and women can be studied. The present study investigates sex differences in cognitive performance and the organization of spatial abilities in a population of
Downloaded from http://geronj.oxfordjournals.org/ at University of Michigan on September 1, 2015
The objective of this study was to test the cognitive identity of older male and female populations with reference to raw score, component structure, and component score measures of spatial and verbal performance. One hundred women (average age, 70.2) and 96 men (average age, 69.0) were administered three verbal and six nonverbal cognitive subtests. The equivalence of four-factor principal component analyses of the male and female correlation matrices, corrected for restriction of range, were tested with the multiple group method of factor analysis. High coefficients of congruence for the three spatial and single verbal factors argue strongly for similar cognitive structures. Multivariate analysis of the factor scores, however, showed a significant mean difference between the older men and women. But when Joreskog's procedures are applied to test the equivalence of covariance structures, the best fit was obtained for a model involving equivalence of factor means, factor structure, factor coefficients and factor correlations.
ORGANIZATION OF SPATIAL ABILITIES
579
4
Downloaded from http://geronj.oxfordjournals.org/ at University of Michigan on September 1, 2015
men and women 60 years and older. Both the Test Instruments level of ability as well as the interrelationship The following tests were administered in a of performance scores are analyzed in order counterbalanced design to control order efto evaluate whether or not cognitive identity fects. Vocabulary from the Wechsler Adult between the sexes can be demonstrated. More Intelligence Scale (WAIS); Word Reasoning precisely, the following hypotheses were and Space subtests from the 1963 adult version tested: of the Primary Mental Abilities (PMA) battery; (1) The cognitive structure of spatial abil- Word Fluency, Form A (Christensen & Guilities reflected in the interrelationships among ford, 1958); Making Objects, Form A (Gerthe performance scores will be different in shon, Gardner, Merrifield, & Guilford, 1963); older men and women. Different underlying Match Problems V (Merrifield & Guilford, factors will be required to explain the rela- 1969); Gottschaldt Hidden Figures4; and two tionships among spatial variables in the two tests developed by J. P. Guilford and his assosexes. Furthermore, men will show a higher ciates, Close-ups, (Guilford, 1969b) and Circle reliability for spatial tests upon which inter- Continuations (Guilford, 1969a). The Closepart correlations are calculated. Ups test requires the subject to identify objects (2) If level of performance is analyzed, in photographs which were taken very near older men will perform at a more proficient the object. Circle Continuations evaluates level than older women on spatio-visual tasks, the ability to complete a portion of a circle whereas women will outscore men on verbal visually; given an arch and five dots, the subfluency and verbal reasoning dimensions. ject must select the dot that would lie on the completed circle. METHOD Except for the vocabulary subtest, which was used to equate male and female populaSubjects tions on general verbal ability, the remainder Two hundred-fifty volunteers were recruited of the battery was selected to include tests from numerous senior citizen organizations of known factorial composition, on which throughout the greater Los Angeles area, and either men or women were known to excel. all participants were white, English-speaking The over-representation of "male" tasks in community residents. Fifty-four subjects were the realm of visuo-spatial abilities is coneliminated because they could not complete or sistent with the goal to examine the interrelarefused to complete the test battery. The re- tionship of figural dimensions in men and maining 196 subjects had adequate vision for women. Most of the tests have not been used the tests, as assessed by a questionnaire and to any great extent in the elderly. They repsatisfactory performance reading a Snellen resent ability dimensions which should be chart. These include 100 women (average age relatively independent or orthogonal to each 70.2 years) and 96 men (average age 69.0 other (Guilford, 1967). years). Participants had to have completed at A number of tests designed by Guilford least 12 years of schooling or to have achieved and his associates were used for this research a minimum vocabulary score of 65 on the because the morphological conceptualization Wechsler Adult Intelligence Scale subtest. of intelligence, the Structure-of-Intellect model (S-I), permits a precise specification Procedure of different spatial or figural factors. Many of A test battery consisting of nine subtests the subtests, developed on samples of bright was administered to small groups over one children and young adults, are generally quite or two testing sessions in familiar settings, difficult. A pilot investigation included three usually a room in their club or organization additional subtests which were found to be headquarters. Each group had met with the too difficult as well as too long. These subtests, investigator at least once before the testing the Guilford-Zimmerman Spatial Orientation, sessions to review sample material and to ask Guilford-Zimmerman Spatial Visualization, questions. Instructions were repeated two or three times, and testing did not proceed until The Gottschaldt Hidden Figures test is available from Dr. Richard S. everyone understood both instructions and Ciutchfield. Institute of Personality Assessment and Research, Univ. of California at Berkeley. the sample problems.
COHEN, SCHAIE, AND GRIBBIN
580
and Spatial Comprehension tests were subsequently eliminated.
5 Although the multiple-group methods (Harman. 1960) c;m provide simple structure factors without rotation, the present method includes rotation to eliminate order of extraction effects.
Table 1 lists the raw score means and standard deviations separately by sex and for the total group. Descriptive statistics for the men and women by age categories are available from the senior author by request. The sex groups were well-matched for verbal abilities since the data indicates that men and women performed equally well on the WAIS vocabulary and the PMA word reasoning subtest. Tests of significance using Wilk's lambda criterion and canonical correlations indicated that men and women differed in level of performance (F = 2.31,/? < 0.05). Equivalence of Correlation Matrices The first hypothesis to be tested is that the two correlation matrices (corrected for restriction of range) are random deviations from a common universe correlation matrix, i.e., that the two matrices are equivalent except for random error of measurement. A simple method to test this hypothesis by means of the Kolmogorov-Smirnov test of the deviation of the differences between corresponding pairs of correlations in the two matrices from the distribution function generated from the normal error curves has been described by Schaie (1958). The Kolmogorov-Smirnov test yielded a significant deviation from the expected chance distribution (p < .01). The null hypothesis can therefore be rejected since there appears to be a significant difference in the cognitive structure of men and women at least at the phenotypic level.
Table 1. Mean Raw Scores and Standard Deviations of Men and Women on Subtests of the Cognitive Battery.* Standard Deviations
Mean Scores
Vocabulary Word Reasoning Word Fluency Space Close-ups Circle Continuation Match Problems Hidden Figures Making Objects
Men
Women
Total Sample
63.8 17.0 36.1 25.7 12.2 9.7 8.0 7.7 32.6
64.5 17.4 41.0 21.6 12.0 9.6 6.4 6.6 35.1
64.2 17.2 38.6 23.6 12.1 9.6 7.2 7.2 33.9
Men
Women
Total Sample
11.0 4.7 14.8 14.5 4.6 4.3 4.5 5.6 14.0
13.0 5.4 14.5 15.1 3.8 3.8 4.4 4.8 12.6
12.0 5.1 15.8 14.9 4.2 4.0 4.5 5.2 13.3
Tests of significance using Wilks Lambda criterion and canonical correlations indicate F = 2.3, df HYP = 9.00, df ERR = 186.0, p = 0.02, r = 0.32.
Downloaded from http://geronj.oxfordjournals.org/ at University of Michigan on September 1, 2015
Data Analysis Descriptive statistics for the nine cognitive subtests were computed for the entire population as well as separately for the sexes. Since the variance for the men was systematically higher across all six nonverbal tests, male and female correlation matrices were rescaled for restriction of range using the joint sample variance as the estimate of the unrestricted (Guilford & Fruchter, 1973). Interconnection matrices were tested for equivalence to determine whether they were random deviations from a universe correlation matrix. A principal component solution indicated four nonerror factors for both the male and female correlation matrices. The multiple group method of factor analysis with rotation to the best simple structure (Horst & Schaie, 1956) was then used to obtain target solutions for the men and women.5 Coefficients of congruence were computed as well as other statistics. Factor scores were then evaluated in a multivariate analysis of variance to examine sex differences in level of performance. Finally, the model suggested by the principal components analysis of the correlation matrices was tested by means of Joreskog's (1971) procedures.
RESULTS
ORGANIZATION OF SPATIAL ABILITIES
581
Table. 2. Hypothesized Pattern of Component Loadings. Components Subtest
Component I
C o m p o n e n t III
Component IV
0 0 0 0 1 0 0 0 1
1 1 1 0 0 0 0
0 0 0 0 0 1 1
0
0
0
0
Vocabulary Word Reasoning Word Fluency Space Close-Up Circle Continuations Match Problems Hidden Figures Making Objects
Table 3. Final Solution of Component Matrix for the Older Men Using Multiple Group Component Analysis with Rotation to Simple Structures.
Subtest
Component I
Component II
Vocabulary Word Reasoning Word Fluency Space Close-Up Circle Continuations Match Problems Hidden Figures Making Objects
-.01 -.07 .07 .74 -.05 -.01 .03 .65 .07
.05 .02 .06 .05 .73 .11 .12 .07 .64
Components C
jonent III .68 .68 .56 -.02 -.10 .01 .02 .01 .12
Component IV -.02 .03 .02 -.06 .07 .70 .78 .08 -.08
Table 4. Final Solution of Component Matrix for the Older Women Using Multiple Group Component Analysis with Rotation to Simple Structures. Components Subtest Vocabulary Word Reasoning Word Fluency Space Close-Ups Circle Continuations Match Problems Hidden Figures Making Objects
Component I
Component II
Component III
Component IV
-.03 .08 -.06 .72 -.09
.05 -.12 .10
.71 .66 .60 -.02 -.03 -.04 .04 .00 .05
-.00 .08 -.08 -.06 .08 .67 .70 .08 -.06
.02 .00 .63 .13
Multiple Group Component Analysis Four components were extracted using a principal components model. The equimax solutions for men and women were rotated to a common target expressed by the hypothesis matrix in Table 2 by means of the multiple group method with rotation to simple structure (Horst & Schaie, 1956). Tables 3 and 4 give the reference structure matrices
-.02 .83 .14 -.12 .06 .76
and correlations for men and women, respectively. The coefficients of congruence between corresponding components for men and women were so high for the single verbal (Component III, 0.995) and the three spatial dimensions (Component I, 0.963; Component II, 0.984; Component IV, 0.970) that further rotation to similarity was unnecessary. Phi coefficients presented in Table 5 suggest
Downloaded from http://geronj.oxfordjournals.org/ at University of Michigan on September 1, 2015
Component II
582
COHEN, SCHAIE, AND GR1BB1N
Table 6. Multivariate Analysis of Variance of Sex Differences on Component Scores.
Table 5. Component Intercorrelations (Phi coefficients). Women l 1 2 3 4
3
2
4
1.00 .51 .46 .16
Component I
1.00 .43 .38
1.00 .36
1 1 2 3 4
1.00 .49 .59
.16
2
3
4
R 21
Univariate F Tests* 555.83* 165.38 453.39* 480.60*
JTests of significance using Wilks Lambda criterion and canonical calculations. *p .05 **p .01
1.00 .43 .38
1.00 .36
1.00
very similar component intercorrelations across sex, the one exception being a slightly higher correlation between the verbal and the spatial relations component in men. The component structures derived for both samples argue for cognitive identity in older men and women. The verbal comprehension (vocabulary), reasoning, and fluency subtests grouped together to form a semantic dimension (Component III) as expected. A spatial relations factor (Component I) grouped the Space subtest, measuring the ability to recognize spatial patterns rotated in one dimension, and Hidden Figures, assessing the ability to evaluate spatial configurations in a distracting perceptual field. Component II, a spatial visualization dimension requiring the ability to identify visual configurations and generate spatial solutions, included CloseUps and Making Objects. Component IV, a spatial flexibility cluster of Match Problems and Circle Continuations, identifies the ability to analyze spatial fields and generate solutions judging spatial distance and alternate spatial configurations. Whereas the component structure argues convincingly for the cognitive identity between the sexes, multivariate analysis of the component scores revealed a significant difference in level of performance (F = 3.72, p < 0.0061, see Table 6). The men performed at a more proficient level than women on the visuospatial components, whereas, by contrast, the women numerically outscored the men on the verbal dimension.
Component Scores (expressed as T scores, M == 501 S.D. = 10) for Older Men and Women Standard Component Mean Deviation
I II III IV
Men
Women
Men
Women
51.7 49.0 48.4 51.6
48.4 50.9 51.5 48.4
10.3 10.8
9 .5 9..2 10.,4 9..7
9.4
10.2
Further Tests of Structural Equivalence Traditional approaches to comparative factor analysis have been criticized because they require the strong assumption of equivalent metrics for the correlation matrices whose equivalence is to be tested. In the foregoing section we argued that the differences in variability on the observed measures in men and women were experimental artifacts and should therefore be corrected, while the mean differences were arbitrary and should therefore be standardized as part of the correlation procedure. Due to the recent availability of the COFAMM computer program (Joreskog & Sorbom, 1976), it is now possible to examine whether the arbitrary standardization of metric has or has not led to spurious conclusions regarding structural equivalence. That is, we can now examine the equivalence of the covariance matrices for men and women (thus preserving the original metrics), under various assumptions regarding the equivalence of factor structure (Joreskog, 1971), and/or factor means (Sorbom, 1974), as well as to test systematically a sequence of alternate models to determine which one would provide the best fit to our data (also cf. Joreskog, 1974).
Downloaded from http://geronj.oxfordjournals.org/ at University of Michigan on September 1, 2015
j
5.70 1.65 4.54 4.88
HI IV
1.00
Men 0
F (4,191) 3.72**
Sex
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ORGANIZATION OF SPATIAL ABILITIES
Table 7. Results of the COFAMM Analyses. Model
df
Chi-Square
118.3 96.6 92.1 81.3
.001 .002 .003 .006
85.6 60.5 60.7 45.9
.05 .17 .10
M o d e l s permitting differences in factor m e a n s (0 m y df) HI
Xm = Xf, m = f, i|/m = i/»f
H2
\ m = Xf,
