race differences and the spearman hypothesis
TRANSCRIPT
INTELLIGENCE 9, 275--283 (1985)
Race Differences and the Spearman Hypothesis
LLOYD G. HUMPHREYS
Department of Psychology University of Illinois
603 East Daniel Champaign, IL 61820
Certain published data have been reviewed and new data presented relevant to the so- called Spearman hypothesis concerning the racial differences on cognitive tests of black and white Americans. In the published data, the correlation between the profiles of low socio-economic and high socio-economic status (SES) whites became - .90 when sex, area of the country, and grade/age were controlled. This nearly mirror- image relationship suggests that the residual across-the-board difference between the two groups is primarily on the general factor in intelligence. In contrast, the same correlation between blacks and the low SES whites was only - . 19. This indicated not only independence of the profiles but the presence of multiple causes of differences in addition to a possible contribution of the general factor. These published interpreta- tions have now been confirmed by obtaining correlations between general factor loadings and the group differences for most of the same tests. For the SES dichotomy in whites this correlation is .86. For blacks and the low SES whites it is . 17. When the two distributions of differences are correlated, a value of .42 is obtained. The Spear- man hypothesis appears to apply primarily to differences in socio-economic status rather than race. Furthermore, one cannot assume a large genetic component for each set of differences. Nor can one argue that the possibility of a large environmental component for each set indicates common environmental causes.
I N T R O D U C T I O N
J e n s e n (1980) has s u m m a r i z e d e v i d e n c e in suppor t o f the hypo thes i s , a t t r ibuted
to S p e a r m a n , tha t the m e a n d i f f e r ence o n cogn i t i ve m e a s u r e s b e t w e e n b l ack and
whi te A m e r i c a n s is d i rec t ly re la ted to the load ings o f those measu re s on the
genera l fac tor in in te l l igence . In the m o s t r ecen t p r e sen t a t i on o f data r e l evan t to
the hypo thes i s ( J ensen , 1983) , he has c o n t i n u e d to o v e r l o o k u n o r t h o d o x bu t
c o n v i n c i n g e v i d e n c e tha t ques t i ons the hypo thes i s ( H u m p h r e y s , F l e i s h m a n , &
Lin , 1977). The ana lyses o f these au thors i n v o l v e d the degree o f c o n g r u e n c e
The data analyzed in this report were obtained from the Project Talent Data Bank. The acquisition of the data was supported by a grant from the Spencer Foundation. Computations were supported by the Campus Research Board.
Correspondence and requests for reprints should be sent to the author at the address listed above.
275
276 HUMPHREYS
between profiles of group means of cognitive measures. Some new analyses of the same data employing different and more orthodox methodologies have now been completed. These analyses also question the validity of the hypothesis. Before presenting the new analyses, however, it is desirable to recapitulate the methodology and results of the earlier study. It is also useful to look closely at the methodology that Jensen has employed.
Methodological Problems Jensen's procedure has been to compute a correlation between general-factor loadings and mean-race differences in standard units for a particular selection of measures. The number of measures is usually fairly small and limited in variety. Not only are there problems relative to the selection of the measures, but there are psychometric difficulties as well. If the tests vary widely in reliability, the correlation that checks the hypothesis is inflated spuriously. (Jensen [1983] corrected his data for reliability differences.) If some of the tests are too easy and some too difficult for either one of the two groups, the correlation will be attenuated by the varying size of the units of measurement from group to group.
The hypothesis also requires, unless the theory is very weak, a correlation between the two distributions approaching unit. A supposedly significant cor- relation is not sufficient. Even the test of significance is inadequate. The units of sampling, the tests, are not independently and randomly sampled from a defined population. The usual confidence interval cannot be placed around a given sam- ple statistic. One cannot determine with confidence whether the sample value is reasonably close to any specified population correlation. The more familiar sampling errors of means based on the size of the random sample of persons from some defined population becomes the equivalent of measurement error in the test of the Spearman hypothesis. The number of tests in the correlation does have an effect, as does the level of intercorrelations of the tests, but these effects are difficult to gauge.
Given these problems, a desirable data set for testing the hypothesis should have the following characteristics. The sample of persons should be large and representative of a wide range of talent. There should be a large and hetero- geneous set of cognitive tests with a wide range of loadings on the general factor. These tests should be as homogeneous as possible in their reliabilities. The units of measurement should be approximately equal in the ranges of scores occupied by the two races.
Published Data: Methodology Humphreys, Fleishman, and Lin (1977) used the data of Humphreys, Lin, and Fleishman (1976) who had been concerned with race by sex interactions in cognitive measures. More than 100,000 cases of all-black and all-white high schools in the Project Talent Data Bank constituted the set of data. Means and standard deviations of raw scores for 24 demographic groups were the first statistics obtained. The 24 groups were defined by sex, area (south and non-
RACE DIFFERENCES 277
south), high school grade (upper and lower), low and high socio-economic status (SES) whites, and blacks undifferentiated by SES, and composed a non- orthogonal 2 × 2 x 2 x 3 factorial design. The low-white group was approx- imately equal to the black group on the Talent SES composite, and represented about 20% of the total white distribution while the high-white group contained the remaining 80%.
The raw score means and standard deviations were highly correlated, mostly positively, in the 24 groups. This result indicated floor and, to a lesser extent, ceiling effects. For the 74 cognitive tests and composites a transformation using only the covariances of means and standard deviations, as described in Humphreys et al. (1976), reduced these correlations to approximately zero. The transformation had the effect of reducing the size of most of the interactions between race and sex, but many remained. Ideosyncratic transformations that would have abolished all sex-by-race interactions would have introduced interac- tions between other demographic variables. The transformation also equalized black and white variances, which is a reasonable outcome for two human popula- tions. There is a wide range of reliabil'ities of the individual measures in these data, as described by Flanagan et al. (1964), but they are otherwise excellent for a study of race differences.
The research pertinent to the Spearman hypothesis utilized these transformed data to compute the intercorrelations among the profiles formed by the means of the 24 groups over the set of different test scores. Each test distribution, as a result of the transformation, had a mean of zero and a SD of 1.00 in the entire sample. Such correlations have ipsative properties, but the constraints are not severe when 24 variables are involved. The mean correlation in the 24-by-24 matrix is - V23, but the possible range of values is from - 1.00 to slightly less than + 1.00.
Published Data: Findings In this matrix, the large positive correlations among profiles are found between groups that differ only with respect to area or grade. Under these conditions the correlations are mostly in the high 80s. A difference in any other variable, of which sex is the most potent, produces smaller correlations between profiles. When only sex differs, the correlations between profiles tend to be slightly negative.
When sex, area, grade, and SES differ simultaneously in the white sample, the mean correlation between profiles is - . 90 . As profiles approach the mirror image of each other ( -1 .00) , an explanation of the separation, in terms of multiple factors operating independently of each other, becomes highly improba- ble. Only if the two groups are separated on a single factor, the general factor in intelligence, can the mirror-image outcome be explained satisfactorily.
The across-the-board difference in these profiles has independent contribu- tions from section of the country, age/grade, and SES, but only a trivial amount from sex. In standard-score units, the contributions are approximately 0.20,
278 HUMPHREYS
0.35, and 0.40, respectively. The approximation to the mirror-image relationship suggests that there are only trivial residual factors to be taken into account in estimating the separation of the groups on the general factor. Rural/urban resi- dence might well be such a factor.
In contrast, the mean correlation between black and Iow-SES white profiles, when sex, area, and grade also differ as before, is only - .19 . Not only are the shapes of these profiles of means almost independent of each other, but there are unknown determinants of differences between means for the two racial groups. Differences occur on factors that are independent of the general factor.
However, there are larger across-the-board differences in these profiles re- quiring explanation than in the all-white sample. The independent contribution of race in standard-score units is .55, while area is 0.17, age/grade is 0.30, and sex, again, has a trivial contribution. The .55, however, cannot be used to estimate a residual, independent contribution of the general factor in intelligence until the factors have been discovered that will produce an approximation to the mirror-image relationship. After this point has been reached one can look for an independent across-the-board difference that represents the general factor.
Even when the black profile is compared with the high SES white group with sex, grade, and area varying as before, the mean correlation is - . 61 , indicating only 37% of common variance. This is far short of the mirror-image relationship required before variation on a single factor becomes tenable. Because the dif- ferences in individual test means are much larger in this comparison, the condi- tions for a large negative correlation are more favorable than in the comparison of the high and low white groups. The black and high white comparison has the advantage of a wider range of talent, but the size of the correlation falls far short of -1 .00 . Apparently, the obtained profile correlation is determined more by SES than by race.
In all of these correlations between profiles, differences in reliability from one measure or another do make a contribution to the size of the correlations. The negative correlations that are critical in the argument are spuriously high by some unknown amount. This effect, however, is not differential with respect to the groups being compared. Thus, the small negative correlation between black and low SES white profiles would be closer to zero in the absence of reliability differentials.
Admittedly, this analysis did not use a routine methodology and the in- ferences that follow from the profile correlations may not be obvious at first sight. However, the following conclusions are supported by the outcomes re- ported. The residual across-the-board difference between low and high SES whites is largely a general-factor difference. Furthermore, to the extent that there is a genetic component to individual differences in general intelligence, it be- comes plausible that white social classes differ genetically. Because the dif- ferences in profiles of blacks and low SES whites are determined by multiple factors that were not controlled, the observed across-the-board difference be- tween the groups does not necessarily include a contribution from the general
RACE DIFFERENCES 279
factor. The extent to which the discovery and measurement of these unknown determinants would reduce the independent contribution of the general factor to the race differences is unknown.
New Analyses: Methodology If the logic of the preceding argument concerning correlations between group profiles is accurate, a more traditional analysis should produce parallel conclu- sions. Although a factor analysis of Project Talent tests with rotation to a general factor has not been done on intercorrelations based on individuals, there is a published analysis based on the intercorrelations of school means (Humphreys, Parsons, & Park, 1979). The use of school means did not affect the definition of the general factor. All tests analyzed had nonzero correlations with that factor. The loadings ranged from a low of 0.25 for Hunting information to a high of 0.96 for Vocabulary, and the relative size of loadings in between were those expected on a priori grounds. The SES variable had a loading of 0.76, an appropriate level in comparison to the 0.96 of Vocabulary. Use of school means allowed the variance of the general factor in the intercorrelations of group means to be substantially enhanced, and the variance of primary-group factors to be substan- tially decreased, in comparison to expectations based on samples of individuals.
The racial composition of the schools was that of the nation in 1960. Fifty- five test means were factor analyzed, and 54 were identical to 54 of the 74 variables that were used in the profile correlations. Factor loadings for means of girls were also available, but sex differences were small. Only the boys' loadings will be used in these computations.
Race and SES differences on the tests were obtained from the study of sex-by- race interactions of Humphreys et al. (1976). These authors had computed two analyses of variance, each a 2 x 2 × 2 × 2 nonorthogonal, factorial design. One involved blacks and low SES whites, sex, area, and age/grade. The second substituted high SES whites for the blacks. Main effects and interactions were orthogonalized by computing partial correlations for each source of variation with all others held constant. Thus, there were 15 partial correlations between each component of the ANOVA and each test. The appropriate partial correla- tions measure the size of the race difference and the size of the SES difference. Again, the range of group differences is somewhat increased by variation in reliabilities. The correlation between the race partials and the general-factor loadings tests the Spearman hypothesis by a more standard methodology. The correlation between the SES partials and the general-factor loadings checks the earlier interpretation of the profile correlations for the white groups.
RESULTS
The correlation between the general-factor loadings and the group differences are .17 and .86 for race and SES, respectively. These values are highly con- gruent with the profile correlations and validate the interpretations made. The
280 HUMPHREYS
reversals in signs are the effects of the methodologies and have no other signifi- cance.
Extreme scores do, of course, have a marked effect on correlations. Removal of five of the 54 observations would increase the first correlation and decrease the second, but an appreciable difference in the same direction would still exist. The Spearman hypothesis, as it has been interpreted by Jensen and his students, does not specify any domain other than those variables with loadings on the general factor. Previous studies of the hypothesis have used a more homoge- neous set of tests than those available in Project Talent. Disconfirmation of the hypothesis requires only one large set of tests, all loaded to some degree on the general factor and based on large samples to provide stability of the observations.
Additional data to supplement these analyses can also be brought to bear on the issues of overlap, or lack thereof, in the determinants of SES and race differences. Although low SES whites are common to both samples, the size of a given contribution to the variance of a dependent variable in one sample is linearly independent of the parallel source of variation in the other sample. There are 74 dependent variables and a total of 15 main effects and interactions for each test. It is possible, therefore, to compute correlations among main effects and interactions with each correlation based on 74 data points. Because complex interactions made little contribution to total variance in the research of Hum- phreys et al. (1976), only the intercorrelations of race/SES, sex, area, age/grade, and their six first-order interactions will be presented. As described earlier, each contribution to the variance of a dependent variable was statistically independent of all of the others. It follows, therefore, that a large correlation between any two sources of variation computed across the 74 tests is not artifactual. High correla- tions indicate psychological communality to determinants of differences.
The 20 x 20 correlation matrix involving 10 sources of variation in two different samples is presented in Table 1. There is a one-to-one correspondence in the designations of the variables except for the substitution of SES for Race in the second sample. Signs of the correlations are based on the following coding of the dichotomies: Male, upper grades, and south were each assigned plus one; blacks in contrast to low SES whites and low SES whites in contrast to high whites were also assigned plus one.
The secondary diagonal containing the correlations between the same or sim- ilar sources of variation in the two samples contains a parallel to same trait, different method correlations. Some of these are very large. The relative size of sex differences is the same (r = .99) whether they are computed in a mixed- racial or a mixed-social status sample. Differences in means arising from matura- tion and education are almost as highly correlated from sample-to-sample (r = .95) as the sex differences. Area differences, in contrast, are somewhat more dependent (r = .85) on the groups compared. Certain interactions are also sim- ilar from one sample to the other. The correlation for sex by grade is .92, for area by grade .77, and for sex by area .68.
TA
BL
E
1
Inte
rco
rrel
atio
ns
of
Mai
n E
ffec
ts a
nd
Fir
st-O
rder
In
tera
ctio
ns
Bas
ed o
n P
arti
al C
orr
elat
ion
s w
ith
74
Dep
end
ent
Var
iab
les
in S
amp
les
Def
ined
by
Rac
e an
d S
oci
o-E
con
om
ic S
tatu
s
1 2
3 4
5 6
7 8
9 10
11
12
13
14
15
16
17
18
19
Rac
e 1
Sex
2 -2
6
Are
a 3
34
-04
G
rade
4
-60
-2
3
-40
R
xS
5
26
-77
-2
0
19
Rx
A
6 -
19
41
08
-19
-2
4
Rx
G
7 26
02
08
-4
1
-09
-0
2
Sx
A
8 00
-5
3
07
22
28
-02
-2
7
Sx
G
9 -3
2
77
01
-16
-7
3
27
32
-51
A
xG
10
-1
9
-19
-0
6
36
19
-36
-2
1
01
SES
II
42
-04
77
-5
1
-13
-0
1
-03
05
Se
x 12
-2
8
99
00
-21
-8
5
37
05
-52
A
rea
13
45
-20
85
-3
3
-06
-4
3
08
03
Gra
de
14
-57
-2
0
-39
95
18
-1
5
-60
25
S
ES
xS
15
22
-4
1
07
-03
50
03
-1
5
45
SE
Sx
A
16
-36
-3
2
-14
43
18
10
-0
2
31
SE
Sx
G
17
-39
07
03
39
-0
7
-05
-2
3
-02
S
xA
18
-1
0
-29
-0
5
29
24
20
-23
68
S
xG
19
-3
3
61
-07
-
14
-63
20
34
-4
1
Ax
G
20
-19
-2
7
-13
38
19
-4
8
-06
01
-19
-1
1
08
81
-21
-0
3
-12
12
74
-1
6
-19
31
-4
9
-19
-6
2
11
19
-52
-1
0
-20
-3
9
-28
-1
1
39
12
05
-36
-1
2
-13
-3
2
92
-24
-2
3
68
-18
77
-1
2
-26
-33
08
-0
3
-31
43
-0
6
06
26
18
-14
-1
8
35
46
45
06
-18
-1
4
-70
02
-3
1
-36
15
31
11
-2
2
36
-11
-1
8
TA
BL
E 2
Dis
trib
uti
on
of
Co
rrel
atio
ns
wit
h t
he
Tw
o F
ou
r-W
ay I
nte
ract
ion
s in
Sam
ple
s D
efin
ed b
y R
ace
and
SE
S
Lo
wer
Bo
un
d o
f In
terv
al
-.3
5
-.3
0
- .2
5 -
.20
-.
15
-. 1
0 -.
05
.0
0
+ .
05
+
. 10
+
. 15
+
.2
0
+ .
25
+ .
30
t,~
Fre
qu
ency
1
0 1
5 8
4 10
3
8 7
2 5
1 1
282 HUMPHREYS
The correlation between race and SES differences of .42 is much smaller than the correlations for sex and grade in this sample of tests. As in the preceding ways of treating these data, little communality of the determinants of race and SES differences is indicated. Is it reasonable to conclude that .42 is greater than zero? The usual statistical analysis is not applicable for the reasons noted earlier, but an empirical approach can be substituted for the statistical one. In both samples the four-way interaction had little more variation across the 74 tests than would be expected from random samples drawn from a population correlation of zero. The distribution of all correlations involving this interaction with the ex- ception of the one in the secondary diagonal is presented in Table 2. The actual range of correlations is from - . 3 1 to +.32, the median is essentially zero, and the SD i s . 14. The distribution shows more variability than one would expect if sampling were independent and random. A zero correlation between race and SES differences in a heterogeneous set of tests can be rejected with the use of this empirically determined standard error with, p < .01. By the same logic, a population correlation of .70 can be rejected. There is some overlap of the determinants of race and SES differences, but the amount is far less than for the determinants of sex, grade, and even area differences.
There are additional correlations in Table 1 that support a good deal of uniqueness among the determinants of race and SES. The three interactions involving race and SES have the smallest correlations in the secondary diagonal. Sex, in contrast, has relatively large correlations in the two samples when it interacts with area and grade. One might well infer that the correlation of .50 between the race-by-sex and the SES-by-sex interactions represents an effect of sex, rather than race, or SES. SES differences and area differences are more highly correlated (r=.77, .74) than race differences and area differences (r =.45, .34). Sex differences are more highly correlated with race-by-sex dif- ferences ( r=.77, .85) than sex differences with SES-by-sex differences (r =.41, .52).
These other differences in correlations involving race and SES suggest that a population value of .7 at the high end of my estimated confidence interval is unlikely. The correlations viewed as a whole indicate nonzero but modest com- munality between race differences, when the races are ~ipproximately equal in SES, and SES differences in the white population.
DISCUSSION
In one sense the Spearman hypothesis has nothing to do with the issue of a possible genetic contribution to race and SES differences. On the other hand, when claims are made that individual differences on the general factor in intel- ligence are 70% to 80% heritable, the causes of race and SES differences inevita- bly become an issue. These data indicate that race differences, with SES con- trolled, and SES differences, with race controlled, on a very heterogeneous set of
RACE DIFFERENCES 283
cognitive tests have relatively few determinants in common. If SES differences on cognitive tests are highly determined by a genetic contribution to Spearman's general factor, a plausible hypothesis, it follows that the same hypothesis cannot be invoked for race differences of the size and kind that are observed in these data. Of course, the genetic component could be small in both sets of dif- ferences. If so, there is relatively little overlap in the environmental determi- nants. Environmental explanations phrased in terms of economic deprivation are inadequate, but more complex environmental explanations are possible.
Jensen has found support for the Spearman hypothesis in limited sets of tests. It is highly probable that he would find equal or stronger support in the same tests for socio-economic differences in the white population. In a limited set, one would not necessarily expect the correlation between the general-factor loading and the size of the SES difference to be higher than the racial comparison. In the present analyses, many more tests with a wider variety of content have been used. The profiles of means on cognitive tests of blacks and low SES whites are almost independent of each other. The correlation between these race differences and the general-factor loadings of the tests is only slightly greater than zero. In contrast, profiles of low and high SES white approach the mirror-image rela- tionship. The correlations between these SES differences and the general-factor loadings of the tests is almost .90. Finally, the correlation between the two sets of differences is only .42, and their correlations with other main effects and interactions also indicate absence of high communality. The conclusion is ines- capable that the across-the-board difference between SES groups occurs pri- marily on the general factor. It also seems inescapable that there are major determinants of race differences that are independent of the general factor.
REFERENCES
Flanagan, J. C., Davis, F. B., Dailey, J. T., Shaycoft, M. F., Orr, D. B., Goldberg, I., & Neyman, C.A. (1964). The American High School Student. Final report for Cooperative Research Project #635, U.S.O.E.. Pittsburgh: Project Talent Office, University of Pittsburgh.
Humphreys, L. G., Fleishman, A., & Lin, P. (1977). Causes of racial and socio-economic dif- ferences in cognitive tests. Journal of Research in Personality, 11, 191-208.
Humphreys, L. G., Lin, P., & Fleishman, A. (1976). The sex by race interaction in cognitive measures. Journal of Research in Personality, 10, 42-58.
Humphreys, L. G., Parsons, C. K., & Park, C. K. (1979). Dimensions involved in differences among school means of cognitive measures. Journal of Educational Measurement, 16, 53-76.
Jensen, A. R. (1980). Bias in mental testing. New York: The Free Press. Jensen, A. R. (1983). The nature of the white-black difference on various psychometric tests. The
91st Annual Convention of the American Psychological Association, Anaheim, CA.