Intelligence 30 (2002) 449 – 462
Education, Wechsler’s Full Scale IQ, and g
Roberto Colom*, Francisco J. Abad, Luis F. Garcı́a, Manuel Juan-Espinosa
Facultad de Psicologı́a, Universidad Autónoma de Madrid, 28049 Madrid, Spain
Received 10 May 2000; received in revised form 2 October 2001; accepted 22 April 2002
Abstract
The scientific construct of general intelligence ( g) rests on the correlations among test scores, while
IQ rests on the summation of standardized scores. Although IQ is usually considered a fine-grained
proxy measure of general intelligence, IQ is actually an arbitrary variable (intelligence in general) not a
scientific construct (general intelligence). This study examines the question of whether or not average
Full Scale IQ (FSIQ) differences between groups that differ in their academic level can be attributed to
g, because IQ results from g plus a mixture of specific cognitive abilities and skills. The Spanish
standardization sample of the Wechsler Adult Intelligence Scale (WAIS-III) is analyzed. The sample
comprised 703 females and 666 men aged 15– 94 drawn as representative of the population in forms of
educational level and geographical location. The results support the conclusion that the Wechsler FSIQ
does not directly or exclusively measure g across the full range of the population distribution of
intelligence. There is no significant association between the scientific construct of general intelligence
( g) and the differences in intelligence in general (IQ) assessed by the WAIS-III. Some theoretical
conclusions are stated as consequence of this lack of association.
D 2002 Elsevier Science Inc. All rights reserved.
Keywords: Education; General intelligence; Cognitive abilities; IQ; g; WAIS-III
1. Introduction
One of the most strongly established empirical facts in psychological science is the
positive correlation of all human cognitive abilities (Brody, 1992; Carroll, 1993, 1997;
Jensen, 1998; Mackintosh, 1998; Spearman, 1927). This positive manifold between cognitive
tests is the basis for analytic taxonomies of cognitive abilities. The dimensions found in the
* Corresponding author. Tel.: +34-91-397-41-14; fax: +34-91-397-52-15.
E-mail address: roberto.colom@uam.es (R. Colom).
0160-2896/02/$ – see front matter D 2002 Elsevier Science Inc. All rights reserved.
PII: S 0 1 6 0 - 2 8 9 6 ( 0 2 ) 0 0 1 2 2 - 8
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R. Colom et al. / Intelligence 30 (2002) 449–462
factor analysis of a broad spectrum of cognitive tests can be arranged hierarchically according
to their generality. The general factor ( g) is the most general of all and is common to all
mental abilities.
The proportion of variance explained by g in a cognitive battery (the so-called size of g)
depends on the characteristics of the people tested. When the factor-analytic studies are not
based on representative samples, the g factor extracted is smaller than it would be if extracted
from data for the general population. The most representative are the large samples used to
standardize IQ tests. A theoretically interesting observation is that g accounts for less of the
variance in a cognitive battery for the upper half than for the lower half of the population
distribution of IQ (Abad, Colom, Juan-Espinosa, & Garcı́a, in press; Deary et al., 1996;
Detterman & Daniels, 1989; Jensen, in press). The basis of g is that the correlations among a
variety of cognitive tests are all positive. Since the correlations are smaller in the upper half
than in the lower half of the IQ distribution, it is implied that abilities are more highly
differentiated in the upper half. Therefore, more of the variance consists of group factors
(specific cognitive abilities) and tests specificity, and less consists of g for the upper half of
the IQ distribution.
The size of g can change as a consequence of other facts. One of these possible sources of
change is education. Ceci (1991, 1992) has reviewed the research literature on the effects of
schooling on IQ, leaving little doubt that schooling increases IQ scores. Therefore, IQ
differences could be attributable to schooling differences: people are not necessarily smarter,
but more knowledgeable about the topics included in IQ tests. Particular forms of knowledge
and intellectual skills usually considered marks of intelligent behavior are taught and learned
in schools and these are tapped by intelligence tests. As a matter of fact, schooling powers
intellectual growth (Rowe, 1997). This being true, then the higher the population’s
educational level, the lower will be the size of g, because subtests’ cognitive complexity
becomes lower for more highly educated people. This will have the effect of reducing the
subtests’ g loadings and, ipso facto, the proportion of total variance accounted for by g
(Jensen, 1998).
More educated people will have higher IQ scores than less educated people. But will those
IQ differences be attributable to g? This question calls for an empirical answer. IQ differences
could result from the specific knowledge and skills developed in schools (and tapped by
intelligence tests), but not necessarily from differences in the scientific construct of general
intelligence ( g). As Ceci (1992) notes, ‘‘although schooling helps prop up IQ scores, this is
not equivalent to claiming that it props up intelligence. The latter entails more than the
acquisition of certain modes of cognizing.’’ This is a way of highlighting the distinction
between the construct (general intelligence, g) and the vehicle (intelligence in general, an IQ
test score).
While the scientific construct of general intelligence ( g) rests on the correlations among
test scores, IQ rests on the summation of standardized scores. The simple sum of various test
scores cannot be considered a proper measure of general intelligence ( g), but a measure of
‘‘intelligence in general’’ (IQ). It must be remembered that intelligence in general means g
plus specific cognitive abilities and skills. IQ is a mixture of those abilities and skills:
g + specific cognitive abilites + specific cognitive skills.
R. Colom et al. / Intelligence 30 (2002) 449–462
451
The present study is intended to demonstrate that it is not always valid to infer differences
in g from well-documented differences in most typical IQ tests (like the Wechsler), because
sometimes differences in IQ can reflect ‘‘intelligence in general’’ more than ‘‘general
intelligence’’ defined as g.
2. Method
2.1. Participants and measures
The Wechsler Adult Intelligence Scale (WAIS-III) was standardized in Spain in 1998
(TEA, 1998). The Spanish standardization includes 14 subtests: vocabulary, similarities,
arithmetic, digit span, information, comprehension, letter–number series, picture completion,
coding, block design, matrices, picture arrangement, symbol search, and object assembly.
The standardization sample comprised 703 females and 666 men aged 15–94 (N16 – 19 years =
163, N 20 – 24 years = 153, N25 – 34 years = 272, N 35 – 54 years = 408, N55 – 69 years = 237,
N70 or more years = 136) drawn as a representative sample of the population in forms of
educational level (see below), geographical location (NNorth = 348, NMiddle = 299, NEast = 359,
NSouth = 363), and residence (Nurban = 659, Nrural = 234, Nintermediate = 476). The groups of
interest for this article are the ones corresponding to different academic levels (from lower
to higher): Academic Level 0 (N = 301), Academic Level 1 (N = 432), Academic Level 2
(N = 525), and Academic Level 3 (N = 111). Especially important is the ‘‘nature’’ of the
educational or academic levels. They are not the result of selection in the basis of IQ or
scholastic achievement. The differences in education may be due to differences in educability,
in opportunity, and/or personal choice. The people are simply assigned to a given group
depending on their achieved educational level (details in Table 1).
Table 1 shows the descriptive statistics for every group on the WAIS-III subtests and the
Full Scale IQ (FSIQ).
There are marked differences between people that differ in educational level (Ceci, 1991,
1992; Ceci & Williams, 1997). These differences may translate into IQ differences. Consider
the last row in Table 1: there is a difference of 13 IQ points between the group with Academic
Level 0 and the group with Academic Level 1, a difference of 25 IQ points between the group
with Level 0 and the group with Level 2, a difference of almost 30 IQ points between the
group with Level 0 and the group with Level 3, and so forth.
2.2. Analyses
The analyses are intended to answer the next question: can IQ differences between groups
varying in their academic level be attributed to general intelligence defined as g? The answer
to this question requires the computation of the g column vector for every group, as well as
the column vector defined by the standardized differences among the groups for the subtest in
the battery. If there is a correlation between the two vectors, then the group differences can be
attributed to general intelligence defined as g (Jensen, 1998). If this is not the case, IQ
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R. Colom et al. / Intelligence 30 (2002) 449–462
Table 1
Descriptive statistics for the educational groups on the WAIS-III subtests
WAIS-III subtests
Academic levels
0
Vocabulary
Similarities
Arithmetic
Digit span
Information
Comprehension
Letter – number
Picture completion
Coding
Block design
Matrices
Picture arrangement
Symbol search
Object assembly
FSIQ
1
2
3
Primary and secondary school
High school
College
6 – 13 years
14 – 17 years
18 years +
Mean
S.D.
Mean
S.D.
Mean
S.D.
Mean
S.D.
23.25
10.91
8.96
11.25
10.36
13.23
6.07
12.64
38.66
23.85
8.91
7.07
17.45
20.96
84.09
12.74
5.30
2.64
3.66
4.70
5.84
2.91
5.74
23.99
12.24
4.99
5.24
10.00
9.82
11.57
34.50
15.43
11.41
13.89
14.31
16.77
8.88
17.27
58.48
35.57
14.46
11.54
26.98
28.47
96.98
11.68
5.86
3.29
4.03
5.14
5.34
3.13
4.82
24.33
13.72
5.90
5.49
11.76
10.05
11.75
44.77
20.71
14.18
16.93
19.52
20.80
11.30
20.46
75.49
45.47
19.11
15.22
34.69
34.65
109.00
8.17
5.17
3.44
4.14
4.31
4.95
2.70
2.75
18.31
10.66
4.16
4.26
8.36
8.06
7.58
49.37
22.26
15.33
17.77
21.80
22.94
11.86
21.05
78.68
45.86
19.68
16.14
35.77
33.90
112.29
8.66
5.29
3.75
4.21
3.67
4.50
2.68
3.24
18.68
11.47
4.38
4.17
8.33
8.21
7.73
FSIQ = Full Scale IQ. The third row shows the amount of education associated with different academic levels,
while the fourth row shows the ages associated with grades.
differences must be attributed to the specific cognitive abilities and skills assessed by the
WAIS-III subtests.
First, the standardized differences among the groups are computed. The standardized
differences are shown in Table 2, presented in standard deviation units (d).
Second, the g vectors for the groups are obtained (Table 3). We computed the highly
recommended Schmid–Leiman transformation separately for every academic group (Carroll,
1993). In the Schmid–Leiman transformation, the higher-order factors are allowed to account
for as much of the correlation among the observed variables as they can, while the lowerorder factors are reduced to residual factors uncorrelated with each other and with the higherorder factors. Therefore, each factor represents the independent contribution of the factor in
question (Loehlin, 1992; Schmid & Leiman, 1957).
Three first-order factors were extracted. Then, one second-order factor was extracted from
the correlation matrix between the first-order factors. A principal axis factoring (PAF) was
employed to extract the factors, followed by a Promax rotation (the correlation matrices and
the program used to compute the SL transformations are in Appendix A and Appendix B).
We performed a confirmatory factor analysis to test the likelihood of a model with three
first-order factors and one second-order factor ( g). Contrary to the analyses made by Horn
(1986) with the WAIS, we found plausible a model of strongly correlated first-order factors
and a second-order factor with the Spanish standardization of the WAIS-III (GFI=.924;
R. Colom et al. / Intelligence 30 (2002) 449–462
453
Table 2
Standardized differences (d units) between the educational groups
WAIS-III subtests
d(1 – 2)
d(1 – 3)
d(1 – 4)
d(2 – 3)
d(2 – 4)
d(3 – 4)
rxx
Vocabulary
Similarities
Arithmetic
Digit span
Information
Comprehension
Letter – number
Picture completion
Coding
Block design
Matrices
Picture arrangement
Symbol search
Object assembly
0.88
0.81
0.82
0.69
0.80
0.63
0.93
0.87
0.82
0.90
1.02
0.83
0.87
0.76
2.01
1.87
1.70
1.45
2.03
1.40
1.86
1.74
1.73
1.88
2.22
1.71
1.87
1.52
2.40
2.14
1.96
1.65
2.71
1.86
2.07
1.80
1.86
1.86
2.29
1.92
1.99
1.43
1.02
0.96
0.82
0.74
1.10
0.78
0.83
0.81
0.79
0.81
0.91
0.75
0.76
0.68
1.45
1.22
1.11
0.94
1.68
1.25
1.02
0.92
0.93
0.81
1.00
0.94
0.86
0.59
0.55
0.30
0.32
0.20
0.57
0.45
0.21
0.20
0.17
0.04
0.13
0.22
0.13
0.09
0.95
0.89
0.88
0.89
0.93
0.85
0.91
0.91
0.82
0.94
0.94
0.86
0.77
0.68
For example, d(1 – 2) corresponds to the standardized difference between the group with ‘‘Academic Level 0’’ and
the group with ‘‘Level 1,’’ d(1 – 3) between ‘‘Level 0’’ and ‘‘Level 2,’’ and so forth. Subtest reliabilities are in the
last column.
NFI=.954; CFI=.959; TLI=.949). The correlations among the first-order factors were between
.825 and .834. Therefore, the structure analyzed in the Schmid–Leiman transformation seems
highly plausible.
Table 3
g factors extracted by the Schmid – Leiman transformation
WAIS – III subtests
Vocabulary
Similarities
Arithmetic
Digit span
Information
Comprehension
Letter – number
Picture completion
Coding
Block design
Matrices
Picture arrangement
Symbol search
Object assembly
% Variance
g for the educational groups
Averages g
g1
g2
g3
g4
g1 – 2
g1 – 3
g1 – 4
g2 – 3
g2 – 4
g3 – 4
.637
.633
.660
.709
.627
.637
.794
.658
.711
.735
.753
.736
.725
.658
48
.588
.636
.667
.641
.544
.506
.749
.689
.781
.734
.810
.741
.745
.710
47.21
.451
.487
.524
.509
.425
.415
.615
.392
.443
.587
.585
.545
.463
.521
25.14
.486
.487
.533
.528
.409
.492
.566
.372
.473
.478
.585
.491
.378
.409
23.21
.612
.634
.663
.675
.586
.575
.771
.673
.746
.734
.782
.738
.735
.684
.551
.564
.595
.617
.535
.537
.710
.541
.592
.665
.674
.647
.608
.593
.566
.564
.599
.625
.529
.569
.689
.534
.603
.619
.674
.625
.578
.547
.523
.566
.599
.578
.488
.462
.685
.560
.634
.664
.706
.650
.620
.622
.539
.566
.603
.587
.481
.499
.663
.553
.645
.619
.706
.628
.590
.579
.468
.487
.528
.518
.417
.455
.591
.382
.458
.535
.585
.518
.422
.468
g1 = Academic Level 0, g2 = Level 1, g3 = Level 2, g4 = Level 3. Average g loadings are also shown ( g1 – 2 =
average g for the groups with Academic Level 0 and with Level 1, g1 – 3 = average g for the groups with Level 0
and with Level 2, and so forth).
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R. Colom et al. / Intelligence 30 (2002) 449–462
Third, it was checked if the g vectors are the same irrespective of the educational group.
This was done through the congruence coefficient (Cattell, 1978; Jensen, 1998).
Fourth, the degree of relationship between the g and d vectors was computed (Colom,
Garcı́a, Juan-Espinosa, & Abad, 2002; Colom, Juan-Espinosa, Abad, & Garcı́a, 2000; Jensen,
1998; Rushton, 1998). This procedure is especially useful for comparing the vectors defined
by the g loadings of a variety of tests and the standardized group differences in those tests
(see Jensen, 1998 for details). The statistical test of the hypothesis concerning group
differences is the correlation between the vector of the tests’ g loadings and the vector of
standardized differences between the groups on each of the WAIS-III subtests (d), taking the
subtests’ reliability coefficients into account. The Pearson r and Spearman’s rank-order
correlation are suitable measures of the degree of relationship between those vectors.
Finally, the degree of association between the g vector (for the complete standardization
sample) and the vector defined by the correlation between education and the subtests’ scores
(both ignoring age differences and controlling for age differences) was computed. The
column vector for g and the column vectors for the correlation between education and the
subtests’ scores are shown in Table 5.
There are a couple of technical questions that remain to be discussed.
First, why do we not use a composite measure of g? The answer is straightforward: g factor
scores are not a pure measure of the g factor of the test battery from which it was extracted.
An individual’s g factor score is calculated as a g-weighted mean of the individual’s
standardized scores on each of the subtests. Therefore, it is contaminated by other factors
(and/or test specificity), either increasing or decreasing the mean difference, depending on the
types of subtests in the battery (Colom et al., 2000; Jensen, 1998).
Second, why do we not use structural equation modeling and look at group differences on
mean g factor scores? Because mean g factors scores obtained in a structural equation
modeling are contaminated by non-g sources of variance (see Bollen, 1989, pp. 305–306, for
a statistical justification), as they are in the exploratory factor analysis.
3. Results
Table 2 shows the standardized differences (d) among the four educational groups for the
WAIS-III subtests. Subtests’ reliabilities (rxx) are also shown.
Table 3 shows the g vectors for every group. One key observation is the percentage of
variance explained by g: almost 50% of the variance is explained by g in the group with
Academic Level 0 and in the group with Level 1, whereas only 25% of the variance is
explained by g in the group with Level 2 and in the group with Level 3. Thus, the higher the
academic level, the less variance is explained by g.
The congruence coefficients computed from the g factor loadings in Table 3 are all higher
than +.99. Because the groups show virtual identity of the g factor, the average loadings were
computed (the average g loadings are shown in Table 3).
The partial correlations (controlling for subtests’ reliabilities) between the vector of g
loadings and the vector of standardized group differences (d) are shown in Table 4. The
R. Colom et al. / Intelligence 30 (2002) 449–462
455
Table 4
Correlations between ‘‘general intelligence’’ ( g vectors) and ‘‘intelligence in general’’ (d vectors)
Educational
levels
0–1
0–2
0–3
1–2
1–3
2–3
Partial correlation
controlling for
reliability
Without partialling out reliability
+.750
+.212
.280
.437
.712
.479
+.599
+.086
.007
.187
.411
.209
( P=.003)
( P=.486)
( P=.353)
( P=.135)
( P=.006)
( P=.097)
Spearman’s r
( P=.024)
( P=.771)
( P=.982)
( P=.522)
( P=.144)
( P=.473)
Pearson’s r
+.652
+.230
.039
.384
.571
.318
( P=.011)
( P=.428)
( P=.896)
( P=.175)
( P=.033)
( P=.268)
g and d vectors corrected
for attenuation
Spearman’s r
Pearson’s r
+.727
+.064
.174
.284
.481
.385
+.661
+.128
.358
.522
.764
.466
( P=.003)
( P=.829)
( P=.553)
( P=.326)
( P=.081)
( P=.175)
( P=.010)
( P=.663)
( P=.209)
( P=.056)
( P=.001)
( P=.093)
correlations suggest that IQ differences among the educational groups cannot be attributed
to g.
Searching for possible artifacts, two other analyses were performed. First, the correlations
between g loadings and d values were computed, without partialling out reliability
coefficients. The main question to answer is: how much difference does it make to partial
out reliability? If it makes a lot of difference it risks artifact, because there should be little or
nonintrinsic correlation between g loadings (or d values) and subtest reliabilities. If there is a
large correlation and this makes the partial r very different from the nonpartialled r, it could
be called a ‘‘bad luck’’ artifact. The new values are shown in Table 4: the same result
emerges. Second, the g d correlations were computed on g and d after these were corrected
for attenuation. The correction is obtained by dividing g and d by the square root of the test
reliability. The corrected values are in Table 4. We have again the same result: the
Table 5
g factor extracted from the correlation matrix computed on the complete standardization sample
WAIS-III subtests
g
r.1
r.2
Vocabulary
Similarities
Arithmetic
Digit span
Information
Comprehension
Letter – number
Picture completion
Coding
Block design
Matrices
Picture arrangement
Symbol search
Object assembly
.753
.743
.731
.723
.725
.674
.818
.740
.770
.782
.829
.776
.765
.726
.638
.588
.553
.495
.640
.522
.573
.563
.544
.550
.609
.541
.548
.473
.552
.465
.437
.335
.578
.448
.404
.398
.361
.372
.456
.373
.371
.296
Also shown are the column vectors defined by the correlation between the variable ‘‘education’’ and the subtests’
scores (r.1 = ignoring age differences; r.2 = partial correlation controlling for age differences).
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R. Colom et al. / Intelligence 30 (2002) 449–462
standardized differences among the educational groups cannot be attributed to general
intelligence defined as g.
Finally, Table 5 shows the column vector defined by the g loadings of the complete
standardization sample and the column vectors defined by the correlations among the variable
education and subtests’ scores. The degree of correlation between these vectors is a fine
pathway for answering the question of whether the correlation between education and
subtest’s performance can be explained by g. The partial correlation (controlling for subtests’
reliabilities) between g and r.1 (ignoring age differences) is=+.191 ( P=.530), while the partial
correlation between g and r.2 (controlling for age differences) is = .359 ( P=.228). Hence,
the correlation between education and subtest’s performance cannot be attributed to g. It is
noteworthy that age has no role in the absence of relationship between g and the vector
defined by the r between education and subtest performance.
4. Discussion
There is a long tradition claiming that IQ reflects ‘‘general intelligence’’ (Jensen, 1980,
1998). However, while IQ results from the summation of standardized scores in several tests,
the scientific construct of general intelligence defined as g rests on the correlations among test
scores. IQ results from a mixture of g, specific cognitive abilities, and specific cognitive
skills. General intelligence defined as g is an important ingredient of an IQ score, but IQ is
not only g.
The present study found that the higher the educational level, the lower the loadings at the
g factor derived from the WAIS-III subtests. Furthermore, more education goes with a higher
IQ, but a higher IQ is not necessarily a reflection of a higher g, because the group differences
are not significantly associated with g.
The fact that FSIQ measures ‘‘intelligence in general,’’ but not always ‘‘general intelligence’’ has some implications.
First, it could help to explain the differentiation phenomenon: the average correlation
among a variety of cognitive tests is smaller in the upper half than in the lower half of the IQ
population distribution. Why? According to our results, it is because more educated people
are found in the upper half of the intelligence distribution. Although the g factor is the same
irrespective of the educational groups, there are differences in their relative magnitude. The
reduction of the g loading of a given cognitive task implies a reduction of its reasoning
requirements (Jensen, 1998). The same WAIS-III subtest is less complex for more educated
people. Therefore, (a) the less the amount of education, the more cognitively complex are the
tests, (b) less complexity goes with a lower g loading of the cognitive tests, and (c) a lower g
loading of the tests produces a less amount of g variance. However, Jensen (in press) finds the
differentiation effect in children of comparable education, so educational level is not the only
cause.
Second, the Wechsler is not sensitive to some instances of the so-called Jensen effects (the
positive association between g factor loadings and a huge number of psychological and
biological variables—scholastic achievement, work-place performance, brain size, brain
R. Colom et al. / Intelligence 30 (2002) 449–462
457
glucose metabolic rate, and so forth; see Rushton, 1998). The secular rise in tests scores is a
primary exemplar of this fact (Colom, Andrés-Pueyo, & Juan-Espinosa, 1998; Colom &
Garcı́a-López, in press; Colom, Juan-Espinosa, & Garcı́a, 2001; Flynn, 1987, 1999a; Neisser,
1998; Neisser et al., 1996). The rise has been greater on tests of fluid intelligence (Gf) than on
tests of crystallized intelligence (Gc). Several theories have attempted to account for the rise,
one of them being the effects of extended schooling. Flynn (1999b) as well as Colom et al.
(2001) demonstrated that the rise is not genuine when Gc is considered. The results obtained
from the Wechsler suggest that the secular rise is not genuine. Why? According to our results,
because (a) more widespread schooling stimulates IQ gains, (b) Wechsler scores are
especially sensitive to the improvement in the skills stimulated by the school system, but
(c) the rise in the Wechsler scores is not associated with g (Rushton, 1999), because the
Wechsler has a Gc bias (Flynn, 1999b; Lynn, 1994).
Finally, the changes in the g loadings across the range of educational level could be an
explanation of the relatively low correlations usually found between measures of human
information processing and psychometric measures of cognitive ability (Juan-Espinosa,
Abad, Colom, & Fernández-Truchaud, 2000). Rarely does the association surpass the socalled ‘‘0.3 barrier.’’ Studies of individual differences in cognition have not included a finegrained representation of low ability people (Detterman & Daniels, 1989). Studies of the
relationships between information processing variables and psychometric abilities are mostly
based on psychology undergraduates. Thus, the low correlations usually found in those
studies can be a by-product of inadequate measures of psychometric cognitive ability for the
upper half of the IQ distribution. They are ‘‘inadequate’’ in the sense that they do not have
enough complexity for high-educated people.
In summary, we found that IQ differences between groups varying in their academic level
are not attributable to g. IQ differences between people more or less educated could arise
mainly from differences in specific cognitive abilities and specific skills taught in schools and
claimed for the WAIS-III subtests. The main message is that it is not always reasonable to
infer g differences from IQ differences. IQ differences reflect ‘‘intelligence in general’’
( g + specific abilities + specific skills) and not only ‘‘general intelligence’’ ( g). Therefore, IQ
differences could result mainly from differences in specific abilities and skills acquired
through formal education.
The present study reports marked IQ differences between groups that differ in amount of
education, but those IQ differences were not directly associated with g. However, we must
acknowledge that (a) g could have a role undetected in the present study, and (b) it is
necessary to replicate the present findings with other samples and intelligence batteries.
Acknowledgements
This article has profited from several insightful comments and suggestions provided by
Nathan Brody, Arthur R. Jensen, John B. Carroll, James Flynn, and Earl B. Hunt. We
gratefully acknowledge their contributions. The research referred to in this article was
supported by research grants funded by the Spanish ‘‘Ministerio de Educación y Cultura.’’
458
R. Colom et al. / Intelligence 30 (2002) 449–462
Grant nos. PB98-0066 and BSO2000-0043. We are grateful to TEA for providing the
database analyzed in the present study, with special thanks to Dr. Nicolás Seisdedos.
Appendix A. Correlation matrices
A.1. Correlation matrices for the groups with Academic Level 0 (top half) and with Academic
Level 1 (bottom half)
Subtests
1
2
3
4
5
6
7
8
9
10
11
12
13
14
(1) Vocabulary
(2) Similarities
(3) Arithmetic
(4) Digit span
(5) Information
(6) Comprehension
(7) Letter – number
(8) Picture
completion
(9) Coding
(10) Block design
(11) Matrices
(12) Picture
arrangement
(13) Symbol
search
(14) Object
assembly
–
.661
.483
.367
.525
.622
.434
.445
.610
–
.510
.421
.531
.578
.482
.521
.493
.489
–
.532
.544
.403
.602
.464
.531
.514
.570
–
.303
.364
.663
.465
.551
.484
.518
.543
–
.506
.408
.454
.654
.569
.494
.507
.579
–
.390
.381
.495
.562
.616
.695
.543
.559
–
.533
.449
.501
.468
.493
.473
.499
.557
–
.502
.432
.504
.539
.451
.430
.629
.529
.505
.506
.455
.593
.533
.452
.618
.604
.519
.548
.607
.559
.479
.508
.646
.585
.429
.490
.468
.541
.475
.468
.646
.588
.438
.443
.477
.548
.444
.423
.657
.546
.494
.430
.404
.531
.402
.457
.504
.550
.453
.407
.507
.453
.511
.451
.568
.494
.525
.541
.618
.502
.566
.446
.506
.486
.364
.455
.477
.475
.373
.295
.399
.404
.643
.595
.626
.571
.591 –
.629 .607 .631 .717 .586
.600 .636 –
.655 .670 .629 .708
.636 .704 .711 –
.709 .624 .579
.622 .628 .596 .704 –
.675 .633
.436 .461 .536 .489 .338 .367 .612 .532 .793 .592 .682 .626
–
.438 .461 .446 .475 .405 .374 .545 .567 .593 .667 .652 .658 .595
.595
–
A.2. Correlation matrices for the groups with Academic Level 2 (top half) and with Academic
Level 3 (bottom half)
Subtests
1
2
3
4
5
6
7
8
9
10
11
12
13
14
(1) Vocabulary
(2) Similarities
(3) Arithmetic
(4) Digit span
(5) Information
(6) Comprehension
(7) Letter – number
(8) Picture
completion
(9) Coding
–
.616
.376
.260
.580
.577
.357
.135
.550
–
.363
.227
.468
.524
.277
.199
.285
.275
–
.397
.454
.375
.284
.292
.251
.324
.398
–
.260
.305
.683
.269
.467
.424
.419
.273
–
.479
.213
.102
.550
.561
.305
.206
.483
–
.309
.214
.308
.257
.455
.658
.247
.269
–
.151
.251
.301
.270
.167
.213
.233
.159
–
.200
.200
.228
.253
.062
.120
.351
.247
.230
.308
.392
.275
.304
.183
.321
.337
.247
.340
.451
.327
.239
.211
.328
.381
.347
.361
.298
.286
.329
.375
.382
.335
.201
.196
.269
.261
.114
.107
.345
.188
.194
.255
.307
.271
.248
.177
.331
.241
–
.282 .327 .332 .536 .304
.212 .220 .295 .403 .056 .240 .490 .262
R. Colom et al. / Intelligence 30 (2002) 449–462
(10) Block design
(11) Matrices
(12) Picture
arrangement
(13) Symbol
search
(14) Object
assembly
459
.178 .311 .459 .292 .140 .193 .189 .449 .336 –
.531 .431 .353 .566
.193 .279 .633 .404 .279 .344 .263 .482 .366 .635 –
.438 .354 .421
.234 .384 .417 .277 .246 .335 .256 .404 .303 .396 .656 –
.283 .371
.098 .189 .239 .201 .028 .203 .246 .264 .558 .377 .373 .308
–
.358
.095 .310 .321 .250 .157 .207 .103 .388 .245 .615 .503 .435 .415
–
A.3. Correlation matrix for the complete standardization sample
Subtests
1
2
3
4
5
(1) Vocabulary
(2) Similarities
(3) Arithmetic
(4) Digit span
(5) Information
(6) Comprehension
(7) Letter – number
(8) Picture
completion
(9) Coding
(10) Block design
(11) Matrices
(12) Picture
arrangement
(13) Symbol
search
(14) Object
assembly
–
.755
.608
.555
.715
.729
.627
.616
–
.596
.566
.678
.697
.612
.621
–
.614
.661
.554
.669
.567
–
.543 –
.503 .671 –
.759 .603 .567 –
.538 .599 .552 .612
–
.606
.598
.657
.613
.582
.605
.668
.623
.576
.625
.699
.585
.590
.567
.609
.568
.643 –
.679 .668 –
.711 .711 .769 –
.677 .672 .692 .753
.532
.616
.634
.616
6
.502
.496
.564
.574
7
.689
.655
.692
.665
8
9
10
11
12
13
–
.588 .570 .584 .563 .533 .494 .675 .623 .787 .673 .717 .670
–
.560 .554 .537 .540 .538 .490 .597 .619 .627 .742 .689 .673 .649
Appendix B. Schmid–Leiman transformation (SPSS 7.5 Sintax)
B.1. First–order factor analysis
FACTOR
/VARIABLES
/MISSING
LISTWISE/ANALYSIS
/PRINT INITIAL CORRELATION EXTRACTION ROTATION
/CRITERIA FACTORS(3) ITERATE(25)
/EXTRACTION PAF
14
–
460
R. Colom et al. / Intelligence 30 (2002) 449–462
/CRITERIA ITERATE(25)
/ROTATION PROMAX(4)
/METHOD = CORRELATION.
B.2. Second-order factor analysis
FACTOR
/matrix = in(cor=*)
/MISSING LISTWISE
/PRINT INITIAL EXTRACTION ROTATION
/CRITERIA factors(1) ITERATE(25)
/EXTRACTION paf
/CRITERIA ITERATE(25)
/ROTATION PROMAX(4).
B.3. Schmid–Leiman
matrix.
GET pattern
/FILE = ‘‘pattern.sav’’.
GET comun
/FILE = ‘‘comun.sav’’.
GET pattern2
/FILE = ‘‘pattern2.sav’’.
compute uni2 = 1-comun.
print uni2.
compute uni2d = mdiag(uni2).
print uni2d.
compute unid = sqrt(uni2d).
print unid.
compute p1SL = pattern * unid.
print p1SL.
compute p2SL=(pattern * pattern2).
print p2SL.
end matrix.
Pattern.sav ! SPSS file with the variable’s loadings on the first-order factors (from the
pattern matrix).
Comun.sav ! SPSS file with the first-order factors’ communalities.
Pattern2.sav ! SPSS file with the first-order factor loadings on the second-order factor.
P1SL ! matrix with the Schmid–Leiman variables’ loadings on the first-order factors.
P2SL ! matrix with the Schmid – Leiman variables’ loadings on the second-order
factors.
R. Colom et al. / Intelligence 30 (2002) 449–462
461
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