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Causes of racial and socioeconomic differences in cognitive tests
JOURNAL
OF
RESEARCH
IN
PERSONALITY
11,
191-208
(1977)
Causes of Racial and Socioeconomic Differences in Cognitive Tests LLOYDG. HUMPHREY%ALLEN I. FLEISHMAN,AND PANGCHIEH LIN University
of Illinois,
UrbanaChampaign
Correlations among profiles of means based upon 75 cognitive variables from Project TALENT are presented for groups defined by race, socioeconomic status, sex, area of the country, and grade in high school. Sex makes by far the largest contribution to differences in shape of profiles. Race and socioeconomic status, in turn, make much larger contributions to differences than grade and area. Sex differences in shapes of profiles are a function primarily of race and, to a lesser extent, of social class. Race differences are larger than socioeconomic differences and the former, in particular, are also a function of sex. Black males differ more from white patterns than black females. There is lack of substantial overlap in the causes of race and socioeconomic differences in shape of cognitive profiles.
The heredity-environment discussions of the origins of human intelligence have, over the years, generated a great deal more heat than light. Extremists of both persuasions have not infrequently discussed the issues more in the tone of religious zealots than of scientists. In one respect, however, knowledgeable hereditarians have had a more defensible position: they start from a theory from which moderately specific predictions are made that are subject to disproof. For example, similarities in intelligence among individuals related genetically to varying degrees are generally congruent with the theory. Environmentalists, on the other hand, have done little to develop a theory from which predictions subject to disconfirmation can be made. The hypothesis that social and economic privilege leads to higher intelligence is not very satisfactory theoretically since it does not lead to a prediction more precise than a nonzero relationship between measures of children’s intelligence and of the privileged position of the family. Why, from the environmentalist’s point of view, is this correlation about .30 when privilege is defined by family income, increases to .40 when a more complex measure of socio-economic status This research was supported by a grant from the Spencer Foundation. thank the Foundation for its support. They also gratefully acknowledge Charles Parsons to some of the analyses. Requests for reprints should Lloyd G. Humphreys, 425 Psychology Building, University of Illinois, 61820. 191 Copyright All rights
Q 1977 by Academic Press. Inc. of reproduction in any form reserved.
The authors wish to the contribution of be addressed to: Dr. Champaign, Illinois
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is used, and becomes SO if the I.Q. of one parent is the definition of privilege? All of these correlations seem low in terms of an extreme environmental position. Nowhere is this defect in theory more apparent than when race and social class differences are discussed. Blacks score lower than whites, and lower class children score lower than middle class children, but merely to conclude that both of the high scoring groups are more privileged is more political than psychological. In this instance the hereditarian is on ground that is only somewhat more solid than the environmentalist. While the former’s prediction of a class difference in a somewhat meritocratic society is sound, once a large genetic contribution to individual differences within groups is assumed, there is substantial uncertainty in extending this proposition to a racial group that has been subjected to massive discrimination. It is still possible, however, that both race and class differences are in whole or in part genetic in origin. but hereditarians have produced little in the way of testable hypotheses concerning the nature of these differences. Human intelligence is both general and multifactored. Has genetic selection been on general intelligence or has it operated differentially on group factors? Has selection been parallel for race and social class, with the difference being one of degree only, or has selection operated differently in white and black populations? The present authors have recently reported on a study of race by sex interactions among a large number of cognitive variables from Project TALENT (Humphreys, Lin, and Fleishman, 1976). This research was undertaken to check on and extend Jensen’s findings and hypotheses (1971) concerning this interaction. Although correlational statistics were used, ‘the analysis was otherwise traditional in that the dependent variables were analyzed one by one. In contrast the present analysis looks at patterns across the entire set of dependent variables by means of correlations among the profiles of subgroup means. The systematic nature of the several interactions is revealed more clearly by the profile correlations than by the analyses of variance. These results also narrow the number of plausible hypotheses, both genetic and environmental, that account for mean differences on cognitive measures. NATURE
OF THE DATA
Subjects were approximately 100,000 students whose records were in the Project TALENT Data Bank. Since individual reports of race were not obtained in 1960, race was defined by presence in an all-black or all-white high school as reported by the principal. Blacks totalled approximately 15,000, whites 85,000. Groups were also categorized as South or non-South, as 9th and 10th graders or I lth and 12th graders, and as male
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or female. A composite measure of socio-economic status was also obtained on each student in the sample. The white group was truncated on this measure into a low group of approximately 15,000 cases and a high group of approximately 70,000. Thus, there are three levels of race-SES, two of area, two of grade, and two of sex for a total of 24 demographic groups. Means and standard deviations of the measure of SES are presented in Table 1 for ah subgroups. Truncation explains the small standard deviations of the white groups. If these two groups were retested on a parallel form of the index, the mean of the lower group would increase somewhat, and its standard deviation would increase markedly. Somewhat smaller effects on distribution statistics would be observed in the
DEFINITION
OF SUBGROUPS
TABLE I AND SAMPLE STATISTICS COMPOSITE
FOR THE SOCIOECONOMIC
Blacks Grades
9 and 10
S,
5588 99.73 7.62 12535 100.86 7.61 4946 98.93 7.27 11987 100.81 7.31 5019 100.61 8.04
I1539 92.27 10.93 15834 97.63 9.80 11753 90.86 10.50 15375 97.52 9.55 9089 93.78 II.09
N x S, N South J? S, N non-South x SZ Totals N x S*
648 90.62 9.48 2924 88.09 9.75 867 92.27 8.92 15876 88.43 9.83
1618 83.88 3.89 2019 82.60 4.36 1560 84.28 3.60 17275 82.91 4.43
11358 101.34 7.47 4841 99.49 7.23 I1426 101.25 7.32 67700 100.65 7.50
13624 98.75 9.36 9784 92.60 10.41 13853 98.78 9.06 100851 95.69 10.45
non-South
Grades
1 I and 12
Male
S, N South k S, N non-South J? S, N South k
non-South
Female
Totals
2814 81.97 4.76 2371 83.35 4.34 2872 82.06 4.70 2204 83.63 4.14 1817 82.55 4.43
Male
Female
High SES Whites
3137 88.21 10.24 928 90.40 9.62 3935 87.13 9.71 1184 90.13 9.31 2253 87.61 9.64
South
N 2 S.Z N ,?
Low SES Whites
STATUS
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HUMPHREY&
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high white group; the mean of the latter would decrease somewhat and its standard deviation would increase. On the parallel form, the low white group would be quite comparable to the black group as a whole in terms of the index used. Dependent variables were the information, achievement, and aptitude tests administered in Project TALENT, including several different composites developed in the Project. Since raw score means and standard deviations were, in most cases, highly correlated, a transformation, described in the previous report, was used. Following the transformation, 75 variables met the criterion used to assess homogeneity of variance. In order to obtain the correlations among profiles of test score means it is necessary to have each of the 75 cognitive measures in the same metric. The transformation used to obtain equal units of measurement produced within group standard deviations of unity, but each measure had a different arbitrary origin. It was necessary, therefore, to scale each cognitive measure about its own mean in the transformed units of measurement. The basic score matrix has 24 columns, one for each demographic group, and 75 rows, one for each dependent variable. Each entry is a group mean. Each row has a mean of zero and a standard deviation greater than unity by an amount reflecting the variability of the subgroup means in the row. The intercorrelations of the 24 subgroups of necessity have a mean of -l/23 because the score matrix is now double-centered. Computations of correlations equated the means of the columns. This restriction has very little effect on the size of any one correlation, however. It also means that across-the-board differences between subgroups in level of cognitive achievement do not affect the correlations. RESULTS Table 2 presents the 24 x 24 table of intercorrelations. Even though a matrix of this size is not easy to comprehend in detail, containing as it does 276 correlations, its availability to the reader will allow readier comprehension of the analyses that follow. Also, since there is no obvious way in which to summarize such data, it will allow the interested reader to conduct his own analyses. Some of the features of this matrix can be noted at this point. First, there is a very satisfactory and interesting range of values of Y. Clearly, the double centering did have only the slightest biasing effect on the individual profile relationships. Second, there is no way to attach a standard error to these correlations and no need to do so. The sample consists of measures of psychological characteristics. There is no defined population from which the sample was drawn, and the units in the sample are not independent of each other. The scores do, however, have very
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high reliability since each mean is based upon a relatively large N. If the study were repeated with samples of students drawn from the same populations at the same time period and with similar cognitive measures, the present results would be replicable. Component Analysis It is almost a reflex response among many psychologists to factor a matrix of correlations such as this one and to rotate factors having latent roots greater than unity. The present authors, however, approached this matter more cautiously since it is far from certain that factor analysis is the analytical method of choice. It was decided that component analysis for these data was more meaningful and more defensible than factor analysis. It was further decided that there are meaningful components having latent roots less than unity. Thus, loadings on the first seven components, along with the latent roots, are presented in Table 3. TABLE UNROTATED
PRINCIPAL
COMPONENTS
THE
Groupsa I BLMS 2 BLMN 3 BLFS 4 BLFN 5 BUMS 6 BUMN 7 BUFS 8 BUFN 9 W,LMS IO W,LMN II W,LFS I2 W,LFN 13 W,UMS 14 W,UMN 15 W,UFS 16 W,UFN 17 W,LMS I8 WZLMN I9 W,LFS 20 WpLFN 21 W,UMS 22 W,UMN 23 WJFS 24 W,UFN Latent Roots
COGNITIVE
3
DESCRIBING PROFILES
THE
INTERCORRELATIONS
OF
OF 24 GROUPS
I
II
III
IV
V
VI
VII
07 07 56 68 01 -03 73 83 -58 -81 76 88 -73 -92 84 83 -90 -96 93 75 -91 -88 85 66 13.06
-97 -92 -81 -69 -96 -87 -64 -46 -69 -47 -44 -14 -30 -06 01 34 -34 10 08 55 I7 41 41 71 7.65
-09 -29 -01 -12 -02 -35 06 -II 37 I3 38 19 58 29 51 28 09 -16 09 -20 15 -II I7 -10 1.49
-02 06 -04 04 15 24 I2 I7 -18 -24 -21 -34 18 08 18 16 -12 -15 -20 -26 23 II 23 I7 .77
08 10 -02 -03 06 00 -04 -08 -01 18 -12 16 -01 22 00 28 -18 01 -24 04 -22 00 -09 14 .40
I3 -17 I5 -05 II -21 13 -05 01 -08 -02 -07 -03 -05 -08 -02 -04 -06 -09 -04 -02 03 -08 04 .I9
-10 -05 04 I4 -12 -04 06 17 -04 00 06 11 -02 05 -02 -01 -06 02 -10 -06 06 13 -12 -05 .I6
a Abbreviations used are as follows: black (B), low SES white (W,), high SES white (WJ, 9th and 10th grades (L), I lth and 12th grades (U). sexes (M and F), areas (S and N).
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Component I describes sex differences. The principal contrast is between white males and females but with black females being much more like their white counterparts than the black males. The latter have essentially zero loadings on this component. Sex differences make the dominant contribution to variance in these data. Component II represents a contrast between both social class and race. The extremes are defined by blacks and the high SES white groups, but with the low SES white groups, particularly those in the lower high school grades, being more like the blacks than the high SES whites. This component is also quite large, but is only a little more than half the size of the sex difference component. Component III contrasts low SES whites, particularly males, with blacks, particularly females, and with the high SES white males being somewhat more similar to the low SES whites and the high SES white females being somewhat more similar to the blacks. The primary contrast here again involves sex differences, but with an overlay of race and social class. Components IV through VII are quite small, but the pattern of signs for these objectively defined variables is a sufficient basis for concluding that these components are replicable. Component IV contrasts the upper and lower high school grade groups, especially for the whites. Component V contrasts geographical areas for the white groups, with black males being a little more like northern whites and black females being a little more like southern whites. Both VI and VII are very small with VI being an area contrast in blacks and VII a sex contrast in blacks. While the preceding series of small components are both replicable and interpretable, for most descriptive purposes they could be disregarded. For the present data their importance lies in their small size. Area and grade have very small effects on cognitive profiles, although both show appreciable across-the-board differences. The principal sources of variation in profiles are sex, which is primary, followed by race and social class. Cluster Analysis A more informative method of analyzing the correlations in Table 2 involves cluster analyses and the computation of mean correlations (using the z-transformation) within clusters. In these data, in contrast to the usual cluster analysis, the clusters can be defined by the characteristics of the groups rather than by the similarities among the correlations. The 15 possible clusters which exhaust the 276 correlations are described in Table 4. Cluster # 1, for example, involves the 12 correlations between the upper and lower grades in high school that involve the same sex, area, and race-SES groups. Starting with the correlation between groups 1 and 5 in the triangular matrix for blacks, move down this
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COMPOSITION
4
OF 15 SUBSETS OF CORRELATIONS DEFINED GROUPS WHOSE PROFILES ARE CONTRASTED
Groups contrasted (1) (2) (3) (4) (5) (6) (7) (8) (9) (IO) (1 I) (12)
AND LIN
Grades in High School Areas of the Country Males and Females Races and SES Groups Grades and Areas Grades and Sexes Areas and Sexes Grades, Races, and SES Areas, Races, and SES Sexes, Races, and SES Grades, Areas, and Sexes Grades, Areas, Races, and SES (13) Grades, Sexes, Races, and SES (14) Areas, Sexes, Races, and SES (IS) All Groups
BY THE
Number of correlations
No.
Contrasted within groups
Number of groups
I I 1 3 2 2 2 6 6 6 4 12
Sex, Area, Race-SES Sex, Grade, Race-SES Area, Grade, Race-SES Sex, Area, Grade Sex, Race-SES Area, Race-SES Grade, Race-SES Sex, Area Sex, Grade Area, Grade Race-SES Sex
I2 12 12 8 6 6 6 4 4 4 3 2
I? 12 12 24 I2 I2 I2 24 24 24 12 24
12
Area
2
24
12
Grade
2
24
I
24
24
secondary diagonal through the 8th row to obtain four correlations. Now move to the correlation between 9 and 13 in the triangular matrix for low SES whites and pick up four more correlations along the secondary diagonal. The last four correlations to enter this cluster are obtained from the triangular matrix for high SES whites, starting with the correlation between 17 and 21. The formation of cluster #5 starts with the correlation between groups 1 and 6, moves to 2 and 5, 3 and 8, 4 and 7, and then moves down to the two white triangular matrices for the parallel selection of the groups to be added. In this cluster both areas and levels of high school grades are simultaneously contrasted, but the correlations involve groups that remain homogeneous in both sex and race-SES. Table 4 also indicates the number of correlations between the groups contrasted and the number of groups within which the correlations are computed. The product of contrasts and groups provides the total number of correlations in a cluster. The sequence of the clusters in this table follows the logic of the factorially designed analysis of variance which was used in the earlier report. The first four clusters are somewhat analogous to main effects, for the between group correlation, but it is not possible to remove the influence of other independent variables from a
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particular comparison. It is possible, however, to obtain subtotals and means within the remaining groups. These can reveal an interaction between variables with respect to group profile similarity; i.e., a difference in degree of profile similarity as a function of level on another independent variable. The means for the clusters involving the three independent variables of sex, area, and grade are presented in Table 5. It is seen that grade and
MEAN
CORRELATIONS
TABLE FOR THE CONTRASTS
Correlation between groups
Correlahons
(II) Grades, Areas. Sexes
F
S
N
88
87
88
87
xx
88
xx
- 07 78
78
7x
-26
00
-?I
GRADE,
AREA,
-I4
AND SEX
groups
Cimder
M 88
-23 -38
within
AP.ZiS
SeXS
(1) Grades (2) Areas 13) Sexes (5) Grades and Areas (6) Grades and Sexes (7) Areas and Sexes
5 INVOLVING
RXeS-SES
L
U
88 - 02
X8 -I?
-23
-24
- 30
I3
W,
w>
93 Y? 69 xx 65 62 60
79 87 -37 69 - 57 - J? -61
84 x5 - 59 72 -73 -71 -82
area have relatively little interaction with the other variables. The low SES whites may differ more from the lower to the upper grades than the other two race-SES groups, but the difference is small. It also appears in some comparisons that the effects of grade and area are additive. If one assumes a reliability of any one profile in the high nineties, the drop to .78 for the effects of grade and area combined is about what would be expected from the respective drops to .88 of the two variables in isolation. It is also clear from this table that sex is a much more potent producer of dissimilarities in cognitive profiles than either of the other variables. The correlation between males and females is -.07. Sex also interacts dramatically with race-SES. The correlation between black males and females is a substantial positive value (.69) while that between the sexes for high SES whites is almost as large in the negative direction (-.59). Low SES whites also show a negative correlation between profiles of the sexes, but the opposition is not quite as extreme as for the higher SES group. The addition of area and grade to sex in forming a contrast has a smaller effect than would be predicted from their individual contributions to dissimilarity. The seeming additivity of effects has disappeared. For example, there is relatively little drop in the similarity between black males and females when sex, area, and grade are combined, but the effects are more pronounced for the white students, particularly those
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with high SES. Only within the latter group are the effects of area and grade in line with initial expectations. Table 6 focuses on the race-SE!3 contrasts. Race-SES does not produce as much dissimilarity as sex but is much more potent than either area or TABLE MEAN
Correlation
CORRELATIONS
between
FOR
THE
CONTRASTS
groups
6 INVOLVING
Correlations Sexes
(41 B and W, B and W2 W, and W, (8) B and W, B and W, W, and Wz (9) B and W, B and W, W, and W, (10) B and W, B and W, W, and W, (12) B and W, B and W, W, and W, (13) B and W, B and W, W, and W, (14) B and W, B and W, W, and W2 (15) B and W, B and W, W, and W,
52 12 78 47 09 65 47 09 73 -14 -55 -66 42 06 54 -18 -59 -80 -15 -58 -76 -19 -61 -90
RACES
within
AND
SES GROUPS
groups
Areas
Grades
M
F
s
N
L
U
33 -08 78 29 -11 67 27 -I? 73
66 31 78 62 28 63 63 30 73
61 24 80 57 21 65
41 00 76 36 -03 65
63 19 76
39 0.5 80
58 16 71 14 -38 -70
34 02 75 -40 -68 -63
12 -42 -79
-40 -72 -74
24 -15 58
10 -37 -56
-36 -69 -74
05 -41 -72
-39 -73 -86
57 27 51
grade. Furthermore, the effect of the race-SES variable depends upon which two of the three groups are contrasted. When other variables are used to produce maximum demographic similarity (contrast #4), blacks and high SES whites have profiles that are almost independent of each other, and low whites are closer to high whites than they are to blacks. When the contrast involves all independent variables (#15), the relationship between blacks and low SES whites is almost zero. In this situation high and low SES whites have profiles that are almost mirror images of each other.
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Table 6 also shows that there are interactions between the contrast of blacks and low SES whites and the other demographic variables. These between racial profiles are more similar in females, the South, and in the lower high school grades than in males, the North, and the upper high school grades. These interactions continue as grade and area (#8 and #9) are added to the contrast. The same interactions are relatively minor, on the other hand, for the other two race-SES contrasts; these latter profile similarities are little affected by levels of the other independent variable or variables. When sex is contrasted simultaneously with race-SES, interactions occur with both grade and area for the contrasts of blacks with both white groups. The dissimilarity is greater in the North than in the South and greater in the upper than in the lower high school grades. The area interaction, as a matter of fact, extends to the low and high SES white contrast with the opposition between the groups being greater in the North than in the South. Sex not only has the largest “main effect,” but it also is involved in the largest and most complex interactions. DISCUSSION A Factor
Model
of Cognitive
Abilities
The implications of these data for genetic or environmental causes of cognitive differences can be discussed most meaningfully in terms of a factor model of cognitive abilities. The hierarchical model of Vernon (1950), which differs only slightly from that of Cattell (1971), is useful for this purpose. Both authors recognize either explicitly (Vernon) or implicitly (Cattell) a general factor in human abilities. Vernon breaks out from the general factor three major group factors: verbal-educational, practicalmechanical, and speed of intellectual response. Cattell has counterparts for these three that are similar though not identical. The major group factors are followed by minor group factors, such as Thurstone’s primary mental abilities, and ultimately by nonerror specifics. One of us (Humphreys, 1962, 1967) has discussed this model in more detail. Races, classes, age cohorts, and area residents all show across-theboard differences. These can be described as largely due to differences on scores on the general factor. A sex difference on general factor scores, however, could only be tiny at most. Whether there is such a difference, as well as its direction, requires a dependable higher order factor analysis of a carefully selected test battery. Drawing inferences about sex differences on scores on a general factor from across-the-board differences on an arbitrary selection of tests is very tenuous, But test selection cannot be advanced for the other differences mentioned because, as one views the
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heterogeneous nature of the Project TALENT tests, it is difficult to conceive of a different set of 75 measures that would produce radically different results. The nature of the general factor in human abilities has been variously interpreted, but these interpretations can be categorized either as unitary trait or faculty theories, on the one hand, or overlapping element theories on the other. The prototypes of these two are Spearmen’s mental energy (1927) and Thomson’s overlapping independent neural connections (1951). Thomson also discussed, as have later theorists of this persuasion (Thorndike, 1926; Tryon, 1935), independent stimulus-response bonds, skills, and specific experiences. Obvious additions to the list of possible independent elements are the genes. Theories in the Thomson tradition have several advantages over those of Spearman. They are simpler in a very important sense since they do not posit an entity within the organism. They are also congruent with knowledge concerning genetics, neural anatomy, and the highly varied response repertoire of the human subject. There are individual differences in the genes, in neural structure and function, and in short and long term memory and in problem solving. This is the sum and substance of the concept of general intelligence. There is not only an assumption that intelligence is polygenetic in origin but that the concept itself is polyneural and polybehavioral. Thus the acquisition of larger amounts of information about hunting, fishing, farming, domestic science, and mechanics is as indicative of general intelligence as the acquisition of large amounts of more academic information. When there are across-the-board differences between groups, it is plausible to assume a difference in means on the general factor. One does not look for specific genes that are present or absent in blacks and whites, in lower and higher social classes, or in geographical areas. Instead the hypothesis is that selection has produced different statistical distributions of what are most probably the same genes, undoubtedly a very large number being involved, in the several demographic groups. Environmental explanations of across-the-board differences are not, of course, ruled out by the preceding line of reasoning. This is particularly true for environmental events that have an effect on the organism as a whole and thus affect scores on the general factor. Prenatal, perinatal, and postnatal events of various kinds may have such effects. For example, postnatally, very early lack of appropriate stimulation may be involved, as well as the ingestion of lead, but explanations based upon poor quality school experiences can be ruled out. Much more is required of an explanation of general factor group differences than differences in privilege. Since there is no definitive hierarchical analysis of the Project TAL-
RACIAL
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203
ENT tests, it is useless to speculate concerning the causes of differences on group factors in any detail. Some very general statements can be made. Group factors define a much smaller share of the total variance in a hierarchical solution than they appear to do as first order factors. (See Humphreys, Tucker, & Dachler, 1970, for a methodology of assessing factor contributions.) Since there is less to explain, it is possible that these factors could be entirely environmental in origin. The fact that tests that identify group factors show evidence of heritability is not questioned, but it may well be that the explanation lies in the general factor variance of those tests. It has also been claimed that group factors show evidence of differential degrees of heritability (Vandenberg, 1967; Schoenfeldt, 1968), but this evidence has been questioned by Humphreys (1974). Admittedly, a high degree of differential heritability of group factors would not be congruent with present hypotheses. Genetic contributions to a group factor variance must be placed in the questionable category, but it seems absurd to expect genetic contributions to most specifics. For example, information about hunting, fishing, and the outdoors, all Project TALENT variables, may define a group factor, but differences within this group of tests can and do arise from the specific factor content of each. The possibility of genetic contribution to individual differences in performance, therefore, seems highest for the general factor and least for the specific factors. Projle
Relationships
It is also useful to look theoretically at correlations between profiles in advance of more specific discussion of the results. First, consider that one of the present groups could be randomly split into two groups and mean differences computed on all of the measures in a common metric. If only the two groups were entered in a double-centered matrix and a profile correlation obtained, that correlation would be - 1 .OO. Sampling errors, no matter how small, would produce this result. In a matrix consisting of the present 24 groups, however, the correlation between the two groups randomly selected from the same population would approach 1.00. The two profiles would be much more similar than any two profiles in the present data. A somewhat different outcome would result if a single group were split at the median on the distribution of scores on the general factor and if all of the measures were composed solely of a general factor plus a specific and error. The correlation between the two groups would now approach - 1.OO since the individual test mean differences would be largest on the measures most heavily weighted on the general factor and smallest on those least heavily weighted. Differences in the contributions of measurement error to variance could alone have this effect.
204
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AND
LIN
The realistic situation is, of course, that the individual measures contain variance of group factors, in addition to those specified above, on which the demographic groups differ. When the two groups correlated share the same group factor contributions, but differ in level on the general factor, the expected negative correlation is reduced in size or becomes positive, depending on the relative contributions to variance of the several factors. In contrast, when the two groups differ in level on the general factor and on group factors as well, the contribution of the general factor difference toward an inverse relationship is accentuated by the group factor differences. It is also possible for two groups to be essentially equal on the general factor, but differ on group factors. An obvious example is the sex contrast. There is a wide range of sex differences in both directions on cognitive measures, but with the large majority of differences being approximately zero. Even a small number of large differences in both directions will produce a negative correlation between profiles. When groups differ with respect to sex but are otherwise similar, the inverse tendency is counteracted: the addition of other differences to that of sex accentuates the inverse tendency. The extent, of course, depends on the size of the differences in group factor scores associated with the demographic variables on which the sex group are similar or different. Sex Differences
in Cognitive
Projles
In the virtual absence of an across-the-board difference in this very heterogeneous set of tests, there is no evidence to support any general factor difference between the sexes. Group and specific factor differences are sufficiently large, however, so that sex differences largely dominate the correlations between profiles of means. Males are superior on group factors of mechanical and outdoor sports information while females are superior on factors involving cultural or aesthetic and domestic information. Such sex information profiles have been known for many years (see Terman & Cox, 1936). The evidence for an interaction between race and sex, and between SES and sex, is more dramatic in these data than when interactions were assessed in the usual fashion (Humphreys, Lin, & Fleishman, 1976). The profiles of black males and females show rather substantial similarity while there is an equal or greater degree of opposition between the sex profiles for high SES whites. Low SES whites are intermediate in degree of similarity-dissimilarity, but are closer to the high SES whites than to the blacks. Sex roles in cognitive test profiles are not highly differentiated in this sample of blacks but are much more differentiated in whites, particularly in high SES whites. While these data do not rule out entirely some genetically determined contribution to sex differences in cognitive skills and information, a
RACIAL
DIFFERENCES
IN
COGNITIVE
TESTS
205
predominance of environmental causes seems most reasonable. In the analysis of variance of these same data a biological explanation did not systematically interrelate all of the findings, while environmental pressures to assume sex roles was more promising. (For the full argument, see the reference cited above.) In the present analyses, different degrees of similarity-dissimilarity of the sexes in cognitive profiles as a function of race and social class also argue against a genetic explanation. Social forces rather than biological forces are the more plausible explanatory factors. Race Differences
The most dramatic and unexpected findings concern race differences in the shape of cognitive profiles. When maximum similarity between black and white groups is introduced by computing profile correlations within sex, area, and grade groups, blacks and low SES whites have somewhat similar but far from identical profiles while blacks and high SES whites have unrelated profiles. Since the cluster analyses indicate that general factor differences between groups have only small effects at most, e.g., black profiles remain very similar (Table 5) even though there are acrossthe-board differences introduced by different levels of the area and high school grade variables, black and white profile differences indicate substantial lack of overlap of the causes of profile shapes. Note also that when maximum dissimilarity between black and white groups is introduced by the systematic variation of sex, area, and grade, blacks and low SES whites have profiles that are essentially unrelated while blacks and high SES whites now show a moderate negative correlation between their profiles. Thus it can be concluded that comparable levels of socioeconomic status tend to move profiles toward somewhat greater degrees of similarity, but there are also powerful causal factors that operate differentially for race that are not revealed in these data. Degree of privilege is an inadequate explanation of differences. In the explanation of the sex by race interactions obtained in the traditional fashion, and which were previously referred to, the initial hypothesis concerned the development of black girls. From the known incidence of black families headed by a lone woman and from the proportion of married black women in the labor force, it was assumed that black girls would be more strongly occupationally oriented from an earlier age. On the test side the direction of the interaction was toward smaller race differences among girls on tests showing masculine superiority. Such tests are also, by and large, more occupationally oriented than tests showing female superiority. This explanation was found to be deficient, however, since the traditional interactions were largest in the comparison between blacks and low SES whites.
206
HUMPHREY%
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AND LIN
The present data suggest that the explanation lies primarily with developmental factors among black males. All comparisons involving raceSES in which sex is held constant show that black and white girls have more similar profiles than black and white boys. Where sex varies, it is possible, also, to obtain an interaction not previously reported. These results are presented in Table 7. It is seen that there is more opposition BREAKDOWN
TABLE 7 OF THE RACE-SES BY SEX INTERACTION Contrasted within groups Area, grade
Black males, low SES white females Black females, low SES white males Black males, high SES white females Black females, high SES white males Low SES white males High SES white females Low SES white females High SES white males
05
Area -01
Grade 02
All vary -02
-31
-35
-32
-35
-41
-39
-40
-46
-70
-74
-73
-75
-66
-79
-75
-90
-66
-78
-77
-90
between the profiles of white males and black females than between black males and white females. This is true for all such comparisons and for white groups at both levels of SES. In contrast, when the white groups alone are contrasted, there is no similar difference. Differences in family patterns between black and white groups may indeed be responsible, but the effects appear to be stronger on black males than on black females. Generul Factor Differences
While the profile correlations are independent of across-the-board differences in the sense that mean differences are excluded from the correlations, an earlier discussion indicated one way in which general factor differences could affect profile correlations. Empirically, however, this possible effect makes only a small contribution to the variability of profile correlations in these data. The across-the-board grade difference certainly in part reflects a general factor difference because of the correlation of grade and chronological age, but there are numerous cases in the data in which a grade difference has only a small effect on profile correlations. Since grade also reflects curriculum opportunities, the larger differences due to grade are not maturational.
RACIAL
DIFFERENCES
IN COGNITIVE
TESTS
207
In contrast to the small direct effect of a general factor difference, these profile correlations allow a limited inference about one of the possible general factor differences. This is the one between the two white social class groups. It takes only a small number of demographic variables, sex, area, and grade, in addition to social class to produce profiles sufficiently dissimilar (Y = -.90) that they become almost mirror images of each other. It should not be difficult to find additional variables, such as rural-urban residence that would produce to all intents and purposes mirror images. Dissimilarity can proceed no further. Thus, if there are residual across-the-board differences after the differences on individual measures have been corrected for the idiosyncracies produced by a small number of demographic differences, that residual difference is a general factor difference. Furthermore, if there is a general factor difference, the probability is increased that a portion of the social class difference in whites is genetically determined. In contrast the profile correlations involving blacks are far from indicating a mirror image situation. There is a substantial across-the-board difference between blacks and low SES whites even though they share about the same level of economic privilege. When these groups are allowed to differ to the maximum extent possible in the present study, their profiles are almost completely independent of each other. With enough information from measures that are currently unknown but knowable, presumably this correlation could be pushed toward 1.00. At that point a residual across-the-board difference could be interpreted in the same fashion as was done for the white groups. Further research is needed to develop the measures required. This research must also be guided by something more than the lack of privilege hypothesis. REFERENCES Cattell, R. B. Abilities: Their sfrucfure, groiraflz, und uction. Boston: Houghton Mifflin, 197 I. Humphreys, L. G. The organization of human abilities. American Psychologist. 1962. 17, 475-483. Humphreys, L. G. Critique of Cattell’s “Theory of fluid and crystallized intelligence: a critical experiment.” Jolrrnal ofEd~cationa/ Psycho/ogy, 1967, 58, 129-136. Humphreys, L. G.. Tucker, L. R., & Dachler, P. Evaluating the importance of factors in any given order of factoring. Multivnriate Beho\ziorct/ Research. 1970, 5, 209-215. Humphreys, L. G. The misleading distinction between aptitude and achievement tests. In D. R. Green (Ed.), The Aptifude-Achievement Distinction. Monterey, California: CTB/ McGraw-Hill, 1974, 262-274. Humphreys, L. G. Lin, Pang-Chieh, & Fleishman. A. The sex by race interaction in cognitive measures. Journal of Research in Personality, 1976, 10, 42-58. Jensen, A. R. The race x sex x ability interaction. Chapter 9 in Robert Cancro (Ed.), Intelligence: Genetic and Enr,ironmentol Injluences. New York: Grune and Stratton, 1971. Schoenfeldt, L. F. Hereditary environmental components of the Project TALENT two-day
208
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FLEISHMAN.
AND LIN
test battery. Paper presented at the XVIth International Congress of Applied Psychology, Amsterdam, 1968. Spearman, C. The Abilities oJ’ Man. New York, Macmillan, 1927. Terman, L. M., & Miles. C. C. Sex and Personality. New York, McGraw-Hill, 1936. Thomson, G. The Factor Analysis of Haman Abilities. 5th Edition. New York: Houghton Mifflin, 195 I. Thorndike, E. L. The Measuremenr of Inrelligence. New York: Bureau of Publications, Teachers College, Columbia University, 1926. Tryon, R. C. A theory of psychological components-an alternative to “mathematical factors.” Psychological Review, 1935, 42, 425-454. Vandenberg, S. G. Hereditary factors in psychological variables in man, with a special emphasis on cognition. In J. N. Spuhler (Ed.), Genetic Diversify and Human Behavior. Chicago: Aldine, 1967, 99-133. Vernon, P. E. The Structure of Human Abilities. London: Methuen, 1961.
OF
RESEARCH
IN
PERSONALITY
11,
191-208
(1977)
Causes of Racial and Socioeconomic Differences in Cognitive Tests LLOYDG. HUMPHREY%ALLEN I. FLEISHMAN,AND PANGCHIEH LIN University
of Illinois,
UrbanaChampaign
Correlations among profiles of means based upon 75 cognitive variables from Project TALENT are presented for groups defined by race, socioeconomic status, sex, area of the country, and grade in high school. Sex makes by far the largest contribution to differences in shape of profiles. Race and socioeconomic status, in turn, make much larger contributions to differences than grade and area. Sex differences in shapes of profiles are a function primarily of race and, to a lesser extent, of social class. Race differences are larger than socioeconomic differences and the former, in particular, are also a function of sex. Black males differ more from white patterns than black females. There is lack of substantial overlap in the causes of race and socioeconomic differences in shape of cognitive profiles.
The heredity-environment discussions of the origins of human intelligence have, over the years, generated a great deal more heat than light. Extremists of both persuasions have not infrequently discussed the issues more in the tone of religious zealots than of scientists. In one respect, however, knowledgeable hereditarians have had a more defensible position: they start from a theory from which moderately specific predictions are made that are subject to disproof. For example, similarities in intelligence among individuals related genetically to varying degrees are generally congruent with the theory. Environmentalists, on the other hand, have done little to develop a theory from which predictions subject to disconfirmation can be made. The hypothesis that social and economic privilege leads to higher intelligence is not very satisfactory theoretically since it does not lead to a prediction more precise than a nonzero relationship between measures of children’s intelligence and of the privileged position of the family. Why, from the environmentalist’s point of view, is this correlation about .30 when privilege is defined by family income, increases to .40 when a more complex measure of socio-economic status This research was supported by a grant from the Spencer Foundation. thank the Foundation for its support. They also gratefully acknowledge Charles Parsons to some of the analyses. Requests for reprints should Lloyd G. Humphreys, 425 Psychology Building, University of Illinois, 61820. 191 Copyright All rights
Q 1977 by Academic Press. Inc. of reproduction in any form reserved.
The authors wish to the contribution of be addressed to: Dr. Champaign, Illinois
192
HUMPHREYS,
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LIN
is used, and becomes SO if the I.Q. of one parent is the definition of privilege? All of these correlations seem low in terms of an extreme environmental position. Nowhere is this defect in theory more apparent than when race and social class differences are discussed. Blacks score lower than whites, and lower class children score lower than middle class children, but merely to conclude that both of the high scoring groups are more privileged is more political than psychological. In this instance the hereditarian is on ground that is only somewhat more solid than the environmentalist. While the former’s prediction of a class difference in a somewhat meritocratic society is sound, once a large genetic contribution to individual differences within groups is assumed, there is substantial uncertainty in extending this proposition to a racial group that has been subjected to massive discrimination. It is still possible, however, that both race and class differences are in whole or in part genetic in origin. but hereditarians have produced little in the way of testable hypotheses concerning the nature of these differences. Human intelligence is both general and multifactored. Has genetic selection been on general intelligence or has it operated differentially on group factors? Has selection been parallel for race and social class, with the difference being one of degree only, or has selection operated differently in white and black populations? The present authors have recently reported on a study of race by sex interactions among a large number of cognitive variables from Project TALENT (Humphreys, Lin, and Fleishman, 1976). This research was undertaken to check on and extend Jensen’s findings and hypotheses (1971) concerning this interaction. Although correlational statistics were used, ‘the analysis was otherwise traditional in that the dependent variables were analyzed one by one. In contrast the present analysis looks at patterns across the entire set of dependent variables by means of correlations among the profiles of subgroup means. The systematic nature of the several interactions is revealed more clearly by the profile correlations than by the analyses of variance. These results also narrow the number of plausible hypotheses, both genetic and environmental, that account for mean differences on cognitive measures. NATURE
OF THE DATA
Subjects were approximately 100,000 students whose records were in the Project TALENT Data Bank. Since individual reports of race were not obtained in 1960, race was defined by presence in an all-black or all-white high school as reported by the principal. Blacks totalled approximately 15,000, whites 85,000. Groups were also categorized as South or non-South, as 9th and 10th graders or I lth and 12th graders, and as male
RACIAL
DIFFERENCES
IN
COGNITIVE
193
TESTS
or female. A composite measure of socio-economic status was also obtained on each student in the sample. The white group was truncated on this measure into a low group of approximately 15,000 cases and a high group of approximately 70,000. Thus, there are three levels of race-SES, two of area, two of grade, and two of sex for a total of 24 demographic groups. Means and standard deviations of the measure of SES are presented in Table 1 for ah subgroups. Truncation explains the small standard deviations of the white groups. If these two groups were retested on a parallel form of the index, the mean of the lower group would increase somewhat, and its standard deviation would increase markedly. Somewhat smaller effects on distribution statistics would be observed in the
DEFINITION
OF SUBGROUPS
TABLE I AND SAMPLE STATISTICS COMPOSITE
FOR THE SOCIOECONOMIC
Blacks Grades
9 and 10
S,
5588 99.73 7.62 12535 100.86 7.61 4946 98.93 7.27 11987 100.81 7.31 5019 100.61 8.04
I1539 92.27 10.93 15834 97.63 9.80 11753 90.86 10.50 15375 97.52 9.55 9089 93.78 II.09
N x S, N South J? S, N non-South x SZ Totals N x S*
648 90.62 9.48 2924 88.09 9.75 867 92.27 8.92 15876 88.43 9.83
1618 83.88 3.89 2019 82.60 4.36 1560 84.28 3.60 17275 82.91 4.43
11358 101.34 7.47 4841 99.49 7.23 I1426 101.25 7.32 67700 100.65 7.50
13624 98.75 9.36 9784 92.60 10.41 13853 98.78 9.06 100851 95.69 10.45
non-South
Grades
1 I and 12
Male
S, N South k S, N non-South J? S, N South k
non-South
Female
Totals
2814 81.97 4.76 2371 83.35 4.34 2872 82.06 4.70 2204 83.63 4.14 1817 82.55 4.43
Male
Female
High SES Whites
3137 88.21 10.24 928 90.40 9.62 3935 87.13 9.71 1184 90.13 9.31 2253 87.61 9.64
South
N 2 S.Z N ,?
Low SES Whites
STATUS
194
HUMPHREY&
FLEISHMAN,
AND
LIN
high white group; the mean of the latter would decrease somewhat and its standard deviation would increase. On the parallel form, the low white group would be quite comparable to the black group as a whole in terms of the index used. Dependent variables were the information, achievement, and aptitude tests administered in Project TALENT, including several different composites developed in the Project. Since raw score means and standard deviations were, in most cases, highly correlated, a transformation, described in the previous report, was used. Following the transformation, 75 variables met the criterion used to assess homogeneity of variance. In order to obtain the correlations among profiles of test score means it is necessary to have each of the 75 cognitive measures in the same metric. The transformation used to obtain equal units of measurement produced within group standard deviations of unity, but each measure had a different arbitrary origin. It was necessary, therefore, to scale each cognitive measure about its own mean in the transformed units of measurement. The basic score matrix has 24 columns, one for each demographic group, and 75 rows, one for each dependent variable. Each entry is a group mean. Each row has a mean of zero and a standard deviation greater than unity by an amount reflecting the variability of the subgroup means in the row. The intercorrelations of the 24 subgroups of necessity have a mean of -l/23 because the score matrix is now double-centered. Computations of correlations equated the means of the columns. This restriction has very little effect on the size of any one correlation, however. It also means that across-the-board differences between subgroups in level of cognitive achievement do not affect the correlations. RESULTS Table 2 presents the 24 x 24 table of intercorrelations. Even though a matrix of this size is not easy to comprehend in detail, containing as it does 276 correlations, its availability to the reader will allow readier comprehension of the analyses that follow. Also, since there is no obvious way in which to summarize such data, it will allow the interested reader to conduct his own analyses. Some of the features of this matrix can be noted at this point. First, there is a very satisfactory and interesting range of values of Y. Clearly, the double centering did have only the slightest biasing effect on the individual profile relationships. Second, there is no way to attach a standard error to these correlations and no need to do so. The sample consists of measures of psychological characteristics. There is no defined population from which the sample was drawn, and the units in the sample are not independent of each other. The scores do, however, have very
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196
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FLEISHMAN,
AND
LIN
high reliability since each mean is based upon a relatively large N. If the study were repeated with samples of students drawn from the same populations at the same time period and with similar cognitive measures, the present results would be replicable. Component Analysis It is almost a reflex response among many psychologists to factor a matrix of correlations such as this one and to rotate factors having latent roots greater than unity. The present authors, however, approached this matter more cautiously since it is far from certain that factor analysis is the analytical method of choice. It was decided that component analysis for these data was more meaningful and more defensible than factor analysis. It was further decided that there are meaningful components having latent roots less than unity. Thus, loadings on the first seven components, along with the latent roots, are presented in Table 3. TABLE UNROTATED
PRINCIPAL
COMPONENTS
THE
Groupsa I BLMS 2 BLMN 3 BLFS 4 BLFN 5 BUMS 6 BUMN 7 BUFS 8 BUFN 9 W,LMS IO W,LMN II W,LFS I2 W,LFN 13 W,UMS 14 W,UMN 15 W,UFS 16 W,UFN 17 W,LMS I8 WZLMN I9 W,LFS 20 WpLFN 21 W,UMS 22 W,UMN 23 WJFS 24 W,UFN Latent Roots
COGNITIVE
3
DESCRIBING PROFILES
THE
INTERCORRELATIONS
OF
OF 24 GROUPS
I
II
III
IV
V
VI
VII
07 07 56 68 01 -03 73 83 -58 -81 76 88 -73 -92 84 83 -90 -96 93 75 -91 -88 85 66 13.06
-97 -92 -81 -69 -96 -87 -64 -46 -69 -47 -44 -14 -30 -06 01 34 -34 10 08 55 I7 41 41 71 7.65
-09 -29 -01 -12 -02 -35 06 -II 37 I3 38 19 58 29 51 28 09 -16 09 -20 15 -II I7 -10 1.49
-02 06 -04 04 15 24 I2 I7 -18 -24 -21 -34 18 08 18 16 -12 -15 -20 -26 23 II 23 I7 .77
08 10 -02 -03 06 00 -04 -08 -01 18 -12 16 -01 22 00 28 -18 01 -24 04 -22 00 -09 14 .40
I3 -17 I5 -05 II -21 13 -05 01 -08 -02 -07 -03 -05 -08 -02 -04 -06 -09 -04 -02 03 -08 04 .I9
-10 -05 04 I4 -12 -04 06 17 -04 00 06 11 -02 05 -02 -01 -06 02 -10 -06 06 13 -12 -05 .I6
a Abbreviations used are as follows: black (B), low SES white (W,), high SES white (WJ, 9th and 10th grades (L), I lth and 12th grades (U). sexes (M and F), areas (S and N).
RACIAL
DIFFERENCES
IN
COGNITIVE
TESTS
197
Component I describes sex differences. The principal contrast is between white males and females but with black females being much more like their white counterparts than the black males. The latter have essentially zero loadings on this component. Sex differences make the dominant contribution to variance in these data. Component II represents a contrast between both social class and race. The extremes are defined by blacks and the high SES white groups, but with the low SES white groups, particularly those in the lower high school grades, being more like the blacks than the high SES whites. This component is also quite large, but is only a little more than half the size of the sex difference component. Component III contrasts low SES whites, particularly males, with blacks, particularly females, and with the high SES white males being somewhat more similar to the low SES whites and the high SES white females being somewhat more similar to the blacks. The primary contrast here again involves sex differences, but with an overlay of race and social class. Components IV through VII are quite small, but the pattern of signs for these objectively defined variables is a sufficient basis for concluding that these components are replicable. Component IV contrasts the upper and lower high school grade groups, especially for the whites. Component V contrasts geographical areas for the white groups, with black males being a little more like northern whites and black females being a little more like southern whites. Both VI and VII are very small with VI being an area contrast in blacks and VII a sex contrast in blacks. While the preceding series of small components are both replicable and interpretable, for most descriptive purposes they could be disregarded. For the present data their importance lies in their small size. Area and grade have very small effects on cognitive profiles, although both show appreciable across-the-board differences. The principal sources of variation in profiles are sex, which is primary, followed by race and social class. Cluster Analysis A more informative method of analyzing the correlations in Table 2 involves cluster analyses and the computation of mean correlations (using the z-transformation) within clusters. In these data, in contrast to the usual cluster analysis, the clusters can be defined by the characteristics of the groups rather than by the similarities among the correlations. The 15 possible clusters which exhaust the 276 correlations are described in Table 4. Cluster # 1, for example, involves the 12 correlations between the upper and lower grades in high school that involve the same sex, area, and race-SES groups. Starting with the correlation between groups 1 and 5 in the triangular matrix for blacks, move down this
198
HUMPHREY&
FLEISHMAN, TABLE
COMPOSITION
4
OF 15 SUBSETS OF CORRELATIONS DEFINED GROUPS WHOSE PROFILES ARE CONTRASTED
Groups contrasted (1) (2) (3) (4) (5) (6) (7) (8) (9) (IO) (1 I) (12)
AND LIN
Grades in High School Areas of the Country Males and Females Races and SES Groups Grades and Areas Grades and Sexes Areas and Sexes Grades, Races, and SES Areas, Races, and SES Sexes, Races, and SES Grades, Areas, and Sexes Grades, Areas, Races, and SES (13) Grades, Sexes, Races, and SES (14) Areas, Sexes, Races, and SES (IS) All Groups
BY THE
Number of correlations
No.
Contrasted within groups
Number of groups
I I 1 3 2 2 2 6 6 6 4 12
Sex, Area, Race-SES Sex, Grade, Race-SES Area, Grade, Race-SES Sex, Area, Grade Sex, Race-SES Area, Race-SES Grade, Race-SES Sex, Area Sex, Grade Area, Grade Race-SES Sex
I2 12 12 8 6 6 6 4 4 4 3 2
I? 12 12 24 I2 I2 I2 24 24 24 12 24
12
Area
2
24
12
Grade
2
24
I
24
24
secondary diagonal through the 8th row to obtain four correlations. Now move to the correlation between 9 and 13 in the triangular matrix for low SES whites and pick up four more correlations along the secondary diagonal. The last four correlations to enter this cluster are obtained from the triangular matrix for high SES whites, starting with the correlation between 17 and 21. The formation of cluster #5 starts with the correlation between groups 1 and 6, moves to 2 and 5, 3 and 8, 4 and 7, and then moves down to the two white triangular matrices for the parallel selection of the groups to be added. In this cluster both areas and levels of high school grades are simultaneously contrasted, but the correlations involve groups that remain homogeneous in both sex and race-SES. Table 4 also indicates the number of correlations between the groups contrasted and the number of groups within which the correlations are computed. The product of contrasts and groups provides the total number of correlations in a cluster. The sequence of the clusters in this table follows the logic of the factorially designed analysis of variance which was used in the earlier report. The first four clusters are somewhat analogous to main effects, for the between group correlation, but it is not possible to remove the influence of other independent variables from a
RACIAL
DIFFERENCES
IN
COGNITIVE
199
TESTS
particular comparison. It is possible, however, to obtain subtotals and means within the remaining groups. These can reveal an interaction between variables with respect to group profile similarity; i.e., a difference in degree of profile similarity as a function of level on another independent variable. The means for the clusters involving the three independent variables of sex, area, and grade are presented in Table 5. It is seen that grade and
MEAN
CORRELATIONS
TABLE FOR THE CONTRASTS
Correlation between groups
Correlahons
(II) Grades, Areas. Sexes
F
S
N
88
87
88
87
xx
88
xx
- 07 78
78
7x
-26
00
-?I
GRADE,
AREA,
-I4
AND SEX
groups
Cimder
M 88
-23 -38
within
AP.ZiS
SeXS
(1) Grades (2) Areas 13) Sexes (5) Grades and Areas (6) Grades and Sexes (7) Areas and Sexes
5 INVOLVING
RXeS-SES
L
U
88 - 02
X8 -I?
-23
-24
- 30
I3
W,
w>
93 Y? 69 xx 65 62 60
79 87 -37 69 - 57 - J? -61
84 x5 - 59 72 -73 -71 -82
area have relatively little interaction with the other variables. The low SES whites may differ more from the lower to the upper grades than the other two race-SES groups, but the difference is small. It also appears in some comparisons that the effects of grade and area are additive. If one assumes a reliability of any one profile in the high nineties, the drop to .78 for the effects of grade and area combined is about what would be expected from the respective drops to .88 of the two variables in isolation. It is also clear from this table that sex is a much more potent producer of dissimilarities in cognitive profiles than either of the other variables. The correlation between males and females is -.07. Sex also interacts dramatically with race-SES. The correlation between black males and females is a substantial positive value (.69) while that between the sexes for high SES whites is almost as large in the negative direction (-.59). Low SES whites also show a negative correlation between profiles of the sexes, but the opposition is not quite as extreme as for the higher SES group. The addition of area and grade to sex in forming a contrast has a smaller effect than would be predicted from their individual contributions to dissimilarity. The seeming additivity of effects has disappeared. For example, there is relatively little drop in the similarity between black males and females when sex, area, and grade are combined, but the effects are more pronounced for the white students, particularly those
200
HUMPHREY%
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with high SES. Only within the latter group are the effects of area and grade in line with initial expectations. Table 6 focuses on the race-SE!3 contrasts. Race-SES does not produce as much dissimilarity as sex but is much more potent than either area or TABLE MEAN
Correlation
CORRELATIONS
between
FOR
THE
CONTRASTS
groups
6 INVOLVING
Correlations Sexes
(41 B and W, B and W2 W, and W, (8) B and W, B and W, W, and Wz (9) B and W, B and W, W, and W, (10) B and W, B and W, W, and W, (12) B and W, B and W, W, and W, (13) B and W, B and W, W, and W, (14) B and W, B and W, W, and W2 (15) B and W, B and W, W, and W,
52 12 78 47 09 65 47 09 73 -14 -55 -66 42 06 54 -18 -59 -80 -15 -58 -76 -19 -61 -90
RACES
within
AND
SES GROUPS
groups
Areas
Grades
M
F
s
N
L
U
33 -08 78 29 -11 67 27 -I? 73
66 31 78 62 28 63 63 30 73
61 24 80 57 21 65
41 00 76 36 -03 65
63 19 76
39 0.5 80
58 16 71 14 -38 -70
34 02 75 -40 -68 -63
12 -42 -79
-40 -72 -74
24 -15 58
10 -37 -56
-36 -69 -74
05 -41 -72
-39 -73 -86
57 27 51
grade. Furthermore, the effect of the race-SES variable depends upon which two of the three groups are contrasted. When other variables are used to produce maximum demographic similarity (contrast #4), blacks and high SES whites have profiles that are almost independent of each other, and low whites are closer to high whites than they are to blacks. When the contrast involves all independent variables (#15), the relationship between blacks and low SES whites is almost zero. In this situation high and low SES whites have profiles that are almost mirror images of each other.
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Table 6 also shows that there are interactions between the contrast of blacks and low SES whites and the other demographic variables. These between racial profiles are more similar in females, the South, and in the lower high school grades than in males, the North, and the upper high school grades. These interactions continue as grade and area (#8 and #9) are added to the contrast. The same interactions are relatively minor, on the other hand, for the other two race-SES contrasts; these latter profile similarities are little affected by levels of the other independent variable or variables. When sex is contrasted simultaneously with race-SES, interactions occur with both grade and area for the contrasts of blacks with both white groups. The dissimilarity is greater in the North than in the South and greater in the upper than in the lower high school grades. The area interaction, as a matter of fact, extends to the low and high SES white contrast with the opposition between the groups being greater in the North than in the South. Sex not only has the largest “main effect,” but it also is involved in the largest and most complex interactions. DISCUSSION A Factor
Model
of Cognitive
Abilities
The implications of these data for genetic or environmental causes of cognitive differences can be discussed most meaningfully in terms of a factor model of cognitive abilities. The hierarchical model of Vernon (1950), which differs only slightly from that of Cattell (1971), is useful for this purpose. Both authors recognize either explicitly (Vernon) or implicitly (Cattell) a general factor in human abilities. Vernon breaks out from the general factor three major group factors: verbal-educational, practicalmechanical, and speed of intellectual response. Cattell has counterparts for these three that are similar though not identical. The major group factors are followed by minor group factors, such as Thurstone’s primary mental abilities, and ultimately by nonerror specifics. One of us (Humphreys, 1962, 1967) has discussed this model in more detail. Races, classes, age cohorts, and area residents all show across-theboard differences. These can be described as largely due to differences on scores on the general factor. A sex difference on general factor scores, however, could only be tiny at most. Whether there is such a difference, as well as its direction, requires a dependable higher order factor analysis of a carefully selected test battery. Drawing inferences about sex differences on scores on a general factor from across-the-board differences on an arbitrary selection of tests is very tenuous, But test selection cannot be advanced for the other differences mentioned because, as one views the
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heterogeneous nature of the Project TALENT tests, it is difficult to conceive of a different set of 75 measures that would produce radically different results. The nature of the general factor in human abilities has been variously interpreted, but these interpretations can be categorized either as unitary trait or faculty theories, on the one hand, or overlapping element theories on the other. The prototypes of these two are Spearmen’s mental energy (1927) and Thomson’s overlapping independent neural connections (1951). Thomson also discussed, as have later theorists of this persuasion (Thorndike, 1926; Tryon, 1935), independent stimulus-response bonds, skills, and specific experiences. Obvious additions to the list of possible independent elements are the genes. Theories in the Thomson tradition have several advantages over those of Spearman. They are simpler in a very important sense since they do not posit an entity within the organism. They are also congruent with knowledge concerning genetics, neural anatomy, and the highly varied response repertoire of the human subject. There are individual differences in the genes, in neural structure and function, and in short and long term memory and in problem solving. This is the sum and substance of the concept of general intelligence. There is not only an assumption that intelligence is polygenetic in origin but that the concept itself is polyneural and polybehavioral. Thus the acquisition of larger amounts of information about hunting, fishing, farming, domestic science, and mechanics is as indicative of general intelligence as the acquisition of large amounts of more academic information. When there are across-the-board differences between groups, it is plausible to assume a difference in means on the general factor. One does not look for specific genes that are present or absent in blacks and whites, in lower and higher social classes, or in geographical areas. Instead the hypothesis is that selection has produced different statistical distributions of what are most probably the same genes, undoubtedly a very large number being involved, in the several demographic groups. Environmental explanations of across-the-board differences are not, of course, ruled out by the preceding line of reasoning. This is particularly true for environmental events that have an effect on the organism as a whole and thus affect scores on the general factor. Prenatal, perinatal, and postnatal events of various kinds may have such effects. For example, postnatally, very early lack of appropriate stimulation may be involved, as well as the ingestion of lead, but explanations based upon poor quality school experiences can be ruled out. Much more is required of an explanation of general factor group differences than differences in privilege. Since there is no definitive hierarchical analysis of the Project TAL-
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ENT tests, it is useless to speculate concerning the causes of differences on group factors in any detail. Some very general statements can be made. Group factors define a much smaller share of the total variance in a hierarchical solution than they appear to do as first order factors. (See Humphreys, Tucker, & Dachler, 1970, for a methodology of assessing factor contributions.) Since there is less to explain, it is possible that these factors could be entirely environmental in origin. The fact that tests that identify group factors show evidence of heritability is not questioned, but it may well be that the explanation lies in the general factor variance of those tests. It has also been claimed that group factors show evidence of differential degrees of heritability (Vandenberg, 1967; Schoenfeldt, 1968), but this evidence has been questioned by Humphreys (1974). Admittedly, a high degree of differential heritability of group factors would not be congruent with present hypotheses. Genetic contributions to a group factor variance must be placed in the questionable category, but it seems absurd to expect genetic contributions to most specifics. For example, information about hunting, fishing, and the outdoors, all Project TALENT variables, may define a group factor, but differences within this group of tests can and do arise from the specific factor content of each. The possibility of genetic contribution to individual differences in performance, therefore, seems highest for the general factor and least for the specific factors. Projle
Relationships
It is also useful to look theoretically at correlations between profiles in advance of more specific discussion of the results. First, consider that one of the present groups could be randomly split into two groups and mean differences computed on all of the measures in a common metric. If only the two groups were entered in a double-centered matrix and a profile correlation obtained, that correlation would be - 1 .OO. Sampling errors, no matter how small, would produce this result. In a matrix consisting of the present 24 groups, however, the correlation between the two groups randomly selected from the same population would approach 1.00. The two profiles would be much more similar than any two profiles in the present data. A somewhat different outcome would result if a single group were split at the median on the distribution of scores on the general factor and if all of the measures were composed solely of a general factor plus a specific and error. The correlation between the two groups would now approach - 1.OO since the individual test mean differences would be largest on the measures most heavily weighted on the general factor and smallest on those least heavily weighted. Differences in the contributions of measurement error to variance could alone have this effect.
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The realistic situation is, of course, that the individual measures contain variance of group factors, in addition to those specified above, on which the demographic groups differ. When the two groups correlated share the same group factor contributions, but differ in level on the general factor, the expected negative correlation is reduced in size or becomes positive, depending on the relative contributions to variance of the several factors. In contrast, when the two groups differ in level on the general factor and on group factors as well, the contribution of the general factor difference toward an inverse relationship is accentuated by the group factor differences. It is also possible for two groups to be essentially equal on the general factor, but differ on group factors. An obvious example is the sex contrast. There is a wide range of sex differences in both directions on cognitive measures, but with the large majority of differences being approximately zero. Even a small number of large differences in both directions will produce a negative correlation between profiles. When groups differ with respect to sex but are otherwise similar, the inverse tendency is counteracted: the addition of other differences to that of sex accentuates the inverse tendency. The extent, of course, depends on the size of the differences in group factor scores associated with the demographic variables on which the sex group are similar or different. Sex Differences
in Cognitive
Projles
In the virtual absence of an across-the-board difference in this very heterogeneous set of tests, there is no evidence to support any general factor difference between the sexes. Group and specific factor differences are sufficiently large, however, so that sex differences largely dominate the correlations between profiles of means. Males are superior on group factors of mechanical and outdoor sports information while females are superior on factors involving cultural or aesthetic and domestic information. Such sex information profiles have been known for many years (see Terman & Cox, 1936). The evidence for an interaction between race and sex, and between SES and sex, is more dramatic in these data than when interactions were assessed in the usual fashion (Humphreys, Lin, & Fleishman, 1976). The profiles of black males and females show rather substantial similarity while there is an equal or greater degree of opposition between the sex profiles for high SES whites. Low SES whites are intermediate in degree of similarity-dissimilarity, but are closer to the high SES whites than to the blacks. Sex roles in cognitive test profiles are not highly differentiated in this sample of blacks but are much more differentiated in whites, particularly in high SES whites. While these data do not rule out entirely some genetically determined contribution to sex differences in cognitive skills and information, a
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predominance of environmental causes seems most reasonable. In the analysis of variance of these same data a biological explanation did not systematically interrelate all of the findings, while environmental pressures to assume sex roles was more promising. (For the full argument, see the reference cited above.) In the present analyses, different degrees of similarity-dissimilarity of the sexes in cognitive profiles as a function of race and social class also argue against a genetic explanation. Social forces rather than biological forces are the more plausible explanatory factors. Race Differences
The most dramatic and unexpected findings concern race differences in the shape of cognitive profiles. When maximum similarity between black and white groups is introduced by computing profile correlations within sex, area, and grade groups, blacks and low SES whites have somewhat similar but far from identical profiles while blacks and high SES whites have unrelated profiles. Since the cluster analyses indicate that general factor differences between groups have only small effects at most, e.g., black profiles remain very similar (Table 5) even though there are acrossthe-board differences introduced by different levels of the area and high school grade variables, black and white profile differences indicate substantial lack of overlap of the causes of profile shapes. Note also that when maximum dissimilarity between black and white groups is introduced by the systematic variation of sex, area, and grade, blacks and low SES whites have profiles that are essentially unrelated while blacks and high SES whites now show a moderate negative correlation between their profiles. Thus it can be concluded that comparable levels of socioeconomic status tend to move profiles toward somewhat greater degrees of similarity, but there are also powerful causal factors that operate differentially for race that are not revealed in these data. Degree of privilege is an inadequate explanation of differences. In the explanation of the sex by race interactions obtained in the traditional fashion, and which were previously referred to, the initial hypothesis concerned the development of black girls. From the known incidence of black families headed by a lone woman and from the proportion of married black women in the labor force, it was assumed that black girls would be more strongly occupationally oriented from an earlier age. On the test side the direction of the interaction was toward smaller race differences among girls on tests showing masculine superiority. Such tests are also, by and large, more occupationally oriented than tests showing female superiority. This explanation was found to be deficient, however, since the traditional interactions were largest in the comparison between blacks and low SES whites.
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The present data suggest that the explanation lies primarily with developmental factors among black males. All comparisons involving raceSES in which sex is held constant show that black and white girls have more similar profiles than black and white boys. Where sex varies, it is possible, also, to obtain an interaction not previously reported. These results are presented in Table 7. It is seen that there is more opposition BREAKDOWN
TABLE 7 OF THE RACE-SES BY SEX INTERACTION Contrasted within groups Area, grade
Black males, low SES white females Black females, low SES white males Black males, high SES white females Black females, high SES white males Low SES white males High SES white females Low SES white females High SES white males
05
Area -01
Grade 02
All vary -02
-31
-35
-32
-35
-41
-39
-40
-46
-70
-74
-73
-75
-66
-79
-75
-90
-66
-78
-77
-90
between the profiles of white males and black females than between black males and white females. This is true for all such comparisons and for white groups at both levels of SES. In contrast, when the white groups alone are contrasted, there is no similar difference. Differences in family patterns between black and white groups may indeed be responsible, but the effects appear to be stronger on black males than on black females. Generul Factor Differences
While the profile correlations are independent of across-the-board differences in the sense that mean differences are excluded from the correlations, an earlier discussion indicated one way in which general factor differences could affect profile correlations. Empirically, however, this possible effect makes only a small contribution to the variability of profile correlations in these data. The across-the-board grade difference certainly in part reflects a general factor difference because of the correlation of grade and chronological age, but there are numerous cases in the data in which a grade difference has only a small effect on profile correlations. Since grade also reflects curriculum opportunities, the larger differences due to grade are not maturational.
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In contrast to the small direct effect of a general factor difference, these profile correlations allow a limited inference about one of the possible general factor differences. This is the one between the two white social class groups. It takes only a small number of demographic variables, sex, area, and grade, in addition to social class to produce profiles sufficiently dissimilar (Y = -.90) that they become almost mirror images of each other. It should not be difficult to find additional variables, such as rural-urban residence that would produce to all intents and purposes mirror images. Dissimilarity can proceed no further. Thus, if there are residual across-the-board differences after the differences on individual measures have been corrected for the idiosyncracies produced by a small number of demographic differences, that residual difference is a general factor difference. Furthermore, if there is a general factor difference, the probability is increased that a portion of the social class difference in whites is genetically determined. In contrast the profile correlations involving blacks are far from indicating a mirror image situation. There is a substantial across-the-board difference between blacks and low SES whites even though they share about the same level of economic privilege. When these groups are allowed to differ to the maximum extent possible in the present study, their profiles are almost completely independent of each other. With enough information from measures that are currently unknown but knowable, presumably this correlation could be pushed toward 1.00. At that point a residual across-the-board difference could be interpreted in the same fashion as was done for the white groups. Further research is needed to develop the measures required. This research must also be guided by something more than the lack of privilege hypothesis. REFERENCES Cattell, R. B. Abilities: Their sfrucfure, groiraflz, und uction. Boston: Houghton Mifflin, 197 I. Humphreys, L. G. The organization of human abilities. American Psychologist. 1962. 17, 475-483. Humphreys, L. G. Critique of Cattell’s “Theory of fluid and crystallized intelligence: a critical experiment.” Jolrrnal ofEd~cationa/ Psycho/ogy, 1967, 58, 129-136. Humphreys, L. G.. Tucker, L. R., & Dachler, P. Evaluating the importance of factors in any given order of factoring. Multivnriate Beho\ziorct/ Research. 1970, 5, 209-215. Humphreys, L. G. The misleading distinction between aptitude and achievement tests. In D. R. Green (Ed.), The Aptifude-Achievement Distinction. Monterey, California: CTB/ McGraw-Hill, 1974, 262-274. Humphreys, L. G. Lin, Pang-Chieh, & Fleishman. A. The sex by race interaction in cognitive measures. Journal of Research in Personality, 1976, 10, 42-58. Jensen, A. R. The race x sex x ability interaction. Chapter 9 in Robert Cancro (Ed.), Intelligence: Genetic and Enr,ironmentol Injluences. New York: Grune and Stratton, 1971. Schoenfeldt, L. F. Hereditary environmental components of the Project TALENT two-day
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test battery. Paper presented at the XVIth International Congress of Applied Psychology, Amsterdam, 1968. Spearman, C. The Abilities oJ’ Man. New York, Macmillan, 1927. Terman, L. M., & Miles. C. C. Sex and Personality. New York, McGraw-Hill, 1936. Thomson, G. The Factor Analysis of Haman Abilities. 5th Edition. New York: Houghton Mifflin, 195 I. Thorndike, E. L. The Measuremenr of Inrelligence. New York: Bureau of Publications, Teachers College, Columbia University, 1926. Tryon, R. C. A theory of psychological components-an alternative to “mathematical factors.” Psychological Review, 1935, 42, 425-454. Vandenberg, S. G. Hereditary factors in psychological variables in man, with a special emphasis on cognition. In J. N. Spuhler (Ed.), Genetic Diversify and Human Behavior. Chicago: Aldine, 1967, 99-133. Vernon, P. E. The Structure of Human Abilities. London: Methuen, 1961.