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Intelligence and Educational Achievement

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This 5-year prospective longitudinal study of 70,000 + English children examined the association between psychometric intelligence at age 11 years and educational achievement in national examinations in 25 academic subjects at age 16. The correlation between a latent intelligence trait (Spearman's g from CAT2E) and a latent trait of educational achievement (GCSE scores) was 0.81. General intelligence contributed to success on all 25 subjects. Variance accounted for ranged from 58.6% in Mathematics and 48% in English to 18.1% in Art and Design. Girls showed no advantage in g, but performed significantly better on all subjects except Physics. This was not due to their better verbal ability. At age 16, obtaining five or more GCSEs at grades A⁎–C is an important criterion. 61% of girls and 50% of boys achieved this. For those at the mean level of g at age 11, 58% achieved this; a standard deviation increase or decrease in g altered the values to 91% and 16%, respectively.
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Intelligence and educational achievement
Ian J. Deary
a,
, Steve Strand
b
, Pauline Smith
c
, Cres Fernandes
c
a
Department of Psychology, University of Edinburgh, 7 George Square, Edinburgh EH8 9JZ, Scotland, UK
b
Centre for Educational Development, Appraisal and Research, University of Warwick, UK
c
NFER-Nelson, London, UK
Received 26 October 2005; received in revised form 3 February 2006; accepted 17 February 2006
Available online 6 March 2006
Abstract
This 5-year prospective longitudinal study of 70,000+ English children examined the association between psychometric
intelligence at age 11 years and educational achievement in national examinations in 25 academic subjects at age 16. The
correlation between a latent intelligence trait (Spearman's gfrom CAT2E) and a latent trait of educational achievement (GCSE
scores) was 0.81. General intelligence contributed to success on all 25 subjects. Variance accounted for ranged from 58.6% in
Mathematics and 48% in English to 18.1% in Art and Design. Girls showed no advantage in g, but performed significantly better
on all subjects except Physics. This was not due to their better verbal ability. At age 16, obtaining five or more GCSEs at grades
AC is an important criterion. 61% of girls and 50% of boys achieved this. For those at the mean level of gat age 11, 58%
achieved this; a standard deviation increase or decrease in galtered the values to 91% and 16%, respectively.
© 2006 Elsevier Inc. All rights reserved.
Keywords: Intelligence; IQ; CAT; Education; GCSE
1. Introduction
Ability testing is one of the most widespread yet most
controversial exports from academic psychology to the
real world, intended to provide an objective measure of
the individual differences in cognitive abilities that
undoubtedly exist within society. Firm evidence that
psychometric test scores accurately predict real-world
success would have considerable import at the practical
and the theoretical levels. It would justify the use of such
tests as educational and occupational selection tools and
as dependent variables in studies of possible genetic and
neurophysiological correlates of cognitive ability differ-
ences. Predicting individual differences in educational
outcomes was the raison dêtre for the first broad test of
cognitive ability (Binet, 1905; Zenderland, 1998). The
discovery of general intelligence involved, in part, using
individual differences in school examination scores
(Spearman, 1904). Alongside occupational outcomes
(Schmidt & Hunter, 1998), educational outcomes are the
major target for the predictive validity of cognitive
ability tests.
What, then, is the association between cognitive
ability and educational achievement? There is broad
agreement that there is a moderate to strong correlation
between the two. Jencks et al.'s (1979, p. 102) detailed
account of eight samples from six longitudinal studies
reported correlations ranging from 0.40 to 0.63 between
cognitive test scores and amount of education obtained.
More recent overviews are provided by various authors
and reach similar conclusions (Bartels, Rietveld, Van
Intelligence 35 (2007) 13 21
Corresponding author.
E-mail address: I.Deary@ed.ac.uk (I.J. Deary).
0160-2896/$ - see front matter © 2006 Elsevier Inc. All rights reserved.
doi:10.1016/j.intell.2006.02.001
Vaal, & Boomsma, 2002b; Brody, 1992; Jensen, 1998;
Neisser et al., 1996; Sternberg, Grigorenko, & Bundy,
2001). For example, Mackintosh's (1998) survey
reckoned that there is a correlation between 0.4 and
0.7 between IQ scores and school performance grades.
More specifically for the present study, Mackintosh
stated that, in Britain, the correlation between 11-year-
old IQ scores and later educational attainment, including
performance on school examinations at age 16, is about
0.5.
The present study will provide a better estimate of the
true association between intelligence and education by
having multiple cognitive tests as predictors and multiple
educational outcomes, applied to a massive representa-
tive sample. This echoes Spearman's (1904) original
examination of the correlation between the latent trait
from several school examination results and the latent
trait from discrimination tests. For example, using just
two ability tests and scores from four school examination
areas (languages, science, mathsphysics, and human-
ities), there was a correlation of 0.53 between ability and
education latent traits (Rinderman & Neubauer, 2004).
Another major issue addressed by the current study is
the gender gap in educational outcomes. Boys perform
less well in school assessments than girls, despite
similar scores on cognitive tests (e.g. Fergusson &
Horwood, 1997). The similarity of boys and girls on
cognitive test scores at age 11 is quite well established.
In studies involving an entire Scottish population
(Deary, Thorpe, Wilson, Starr, & Whalley, 2003), or
massive representative samples from the United King-
dom (Strand, Deary, & Smith, in press), boys and girls at
11 years of age show no appreciable differences in mean
general cognitive ability. However, girls score slightly
higher on verbal ability and boys have a slightly larger
standard deviation on general and specific ability scores.
Here, we aim to determine whether the sex difference in
verbal ability (after accounting for g) explains any of the
sex difference in school assessment performances.
After 100 years of studying the cognitive ability
education association, there is still a need for a definitive,
prospective study, one which assesses initial cognitive
ability and later educational attainment with compre-
hensive assessments. Here, we report such a study, using
a large, representative, 5-year prospective examination
of over 70,000 children in England. The present study
asks: (1) what is the association between general
cognitive ability and overall educational attainment in
25 different courses?; (2) what is the association between
a latent cognitive ability trait (general intelligence or g)
and a latent educational outcome trait?; (3) what is the
effect of sex on examination performance, and is it
accounted for by general cognitive and/or verbal
abilities?; (4) in epidemiological terms, what is the
effect size of cognitive ability on educational attainment?
2. Methods
2.1. The Cognitive Abilities Test (CAT)
The CAT is the most widely used test of reasoning
abilities in the UK, with close to one million school
students assessed each academic year. The data reported
here relate to the CAT second edition (CAT2E)
(Thorndike, Hagen, & France, 1986). CAT2E has 10
separate subtests, which are aggregated into three
batteries, providing standardised measures of verbal,
quantitative, and nonverbal reasoning abilities. An
average of the three standardised scores, the mean
CAT score, is also calculated. The tests are described in
detail in Strand (2004) and in the test manual.
The CAT2E spans the age range 7:0615:09 years
and is divided into six levels of difficulty, Level A
through to Level F. Level D is typically used in the first
year of secondary school (year 7). The results are most
often reported as standard age scores, with a mean of
100 and standard deviation of 15. The tests have very
high levels of reliability. The internal consistency
(KR21) estimates of the Level D batteries are:
verbal = 0.94, quantitative = 0.90, and nonverbal = 0.92
(Thorndike et al., 1986). The KR21s of the 10 subtests
range from 0.74 to 0.86 with a mean of 0.80 (Thorndike
et al., 1986). The testretest correlations are also high
(Sax, 1984; Strand, 2004). For example, the Pearson
correlation coefficients between age 10 + and 13+
(N= 10.644) were: verbal = 0.87, quantitative = 0.79,
nonverbal = 0.76, and mean CAT score = 0.89 (Strand,
2004).
A third edition of the CAT (CAT3) was launched in
June 2001 and is now more widely used than CAT2E.
However, an extensive equating study involving over
10,000 pupils allows CAT2E scores to be converted to
CAT3 equivalents or vice versa (Smith, Fernandes, &
Strand, 2001).
Here, we have taken the age-standardised scores for
the three batteries of the CAT2E and subjected them to
principal axis factoring. Inspection of the scree slope
clearly indicated a single factor. The first unrotated
general ability factor (Spearman's g) accounted for
69.6% of the variance. A gfactor score was computed
and stored for each subject. Boys and girls did not differ
significantly in gscores, even with about 35,000 in each
group (Cohen's d= 0.01) (see also Strand et al., in
press). We then created a residual verbal factor,
14 I.J. Deary et al. / Intelligence 35 (2007) 1321
unrelated to the gscore, using linear regression with the
verbal reasoning standard age score as the dependent
variable and gas the independent variable and saving
the standardised residuals. Girls scored better in the
residual verbal factor (Cohen's d= 0.25). The gand
verbal scores have means of 1 and standard deviations of
0. The verbal score was used specifically in addition to g
because it showed sex differences (Strand et al., in press)
and contributed additional variance to the educational
outcomes.
2.2. National GCSE/GNVQ public examination results
Pupils in England sit national public examinations at
age 15/16 years. The entire country's pupils sit the same
examination, apart from the small number with
moderate to severe learning difficulties who are
educated in special schools. These are typically General
Certificate of Secondary Education (GCSE) examina-
tions, which are offered in a wide range of subjects and
are graded from Adown to G (and U for ungraded) in
each subject. For the purposes of the present analyses,
these are scored from 8 to 0, respectively. A small
proportion of entries are also made for General National
Vocational Qualifications (GNVQs). These can be
awarded at distinction, merit, or pass levels. A detailed
set of score equivalencies are defined by the govern-
ment, which allow GCSE/GNVQ results to be expressed
on a common scale as points scoresand allow the
calculation of the Best 8performance score as an
overall measure of attainment (Autumn Package, 2002).
The Best 8performance score gives the pupils' points
score in the eight highest scoring units studied, whether
they be GCSE full course, GCSE short course, GNVQ
foundation, or GNVQ intermediate examinations. Here,
we examine the results from 25 different GCSE/GNVQ
topics. We have divided them into groupings of arts and
humanities, science, social sciences, and practical (Table
2). We also study the total points gained by each student
and the points gained from their Best 8topics. In
addition, we examine the binary variable of whether or
not students gained 5 or more scores at grades Ato C,
which is used widely in England as a performance
criterion, e.g. for ranking school performances.
2.3. The present study's datasets and the matching
process
CAT is processed through a national service which
provides computer scoring and analysis of pupils'
answer sheets. Consent is asked from schools to retain
these data for further research on monitoring CAT norms
or developing indicators and 94% of users consent to
this use. CAT test scores from administrations in the
1997/98 academic year, mostly in SeptemberNovem-
ber 1997, were matched to the national GCSE 2002
dataset. Thus, a dataset of matched autumn 1997 CAT
results and May 2002 GCSE results was created. After
the matching was complete, individual records were
given a unique ID code and all identifying information
on pupils' names was deleted from the file to assure
confidentiality for individual pupils and schools.
CAT scores were found for over 80,000 of the pupils
in the national GCSE dataset, with pupils drawn from a
total of 973 secondary schools across 103 Local
Education Authorities. Table 1 compares the GCSE
results at age 16 for the CAT-matched sample with the
national averages derived from the full national dataset.
The GCSE/GNVQ performance score for the CAT
matched sample does not differ substantially from the
national average in either mean or standard deviation.
There are also are no significant differences in the
proportion of higher grades awarded in the three core
GCSE subjects of English, mathematics, or science.
Given the matched CAT sample constitutes over one-
fifth (22%) of the total national dataset, this is not
surprising. For the present analyses, we selected only
those pupils who took the CAT2E Level D test (the vast
majority) and only those students who attended
mainstream state secondary schools (again, the vast
majority). This gave a maximum data set of N= 74,403
(37,509 girls, 36,894 boys). The difference between this
and the number in Table 1 is accounted for by pupils
who were missing one or more scores from the CAT.
3. Results
3.1. The association between intelligence and
education
The correlations between the CAT's gfactor and
individual GCSE subject scores were all positive and
Table 1
Comparison of the matched sample against the population average for
GCSE/GNVQ outcomes
Measure CAT-matched
sample
Full national
dataset
GCSE/GNVQ Best 8points:
mean (S.D.)
37.3 (13.4) 36.8 (14.0)
English: % entries graded AC 62% 61%
Maths: % entries graded AC 54% 53%
Science: % entries graded AC 54% 53%
Sample size 80,074 361,335
15I.J. Deary et al. / Intelligence 35 (2007) 1321
medium to large in effect size (Table 2). The correlation
with overall GCSE points score was 0.69 and with
GCSE Best 8 was 0.72. In the arts and humanities group,
the highest correlation was with English (0.67). Most
others were around 0.6, with Religious Education and
Drama lower, around 0.5. In the science group,
Mathematics correlated highest, at 0.77, and the
individual sciences (Physics, Chemistry, and Biology),
which are taken by much smaller numbers of students,
correlated around 0.5. This group is characterised by
high ability and restriction of range; for example, in the
pupils who took physics, the mean and S.D. of gare
0.96 and 0.64 compared with 0.0 and 1.0 in the entire
sample. In the social sciences, Geography and History
correlated above 0.6 and others around 0.5. In the
practical subjects, all correlations were between 0.43
and 0.54, with Physical Education (r= 0.55) and Music
(r= 0.54) highest. They are similar to the correlations
with the CAT total score for previous data (Smith et al.,
2001) and for selected school subjects with these data
(Strand, in press).
The next analysis addressed the question about the
true correlation between the latent traits of ability
assessed in the CAT2E and educational performance in
Table 2
Sex comparisons in cognitive ability and GCSE scores, and correlations between general cognitive ability (g) and the residual verbal factor and GCSE
scores
Cognitive Ability Test or GCSE subject Malefemale comparisons Correlations
Boys' mean (S.D., N) Girls' mean (S.D., N)pfor difference
(Cohen's d)
CAT gCAT residual
verbal
a
Cognitive Abilities Test
gfactor
b
0.007 (0.965, 34,850) 0.004 (0.912, 35,680) 0.096 (0.01)
Residual verbal factor
b
0.126 (1.026, 34,850) 0.122 (0.958, 35,680) <0.001 (0.25) 0.00
Overall score
GCSE total points 39.5 (18.8, 36,894) 45.1 (18.2, 37,509) <0.001 (0.30) 0.69 (70,530) 0.13
GCSE Best 8 35.4 (13.5, 35,848) 39.4 (12.8, 36,759) <0.001 (0.30) 0.72 (68,904) 0.14
Arts and Humanities
English 4.52 (1.53, 34,947) 5.13 (1.41, 36,328) <0.001 (0.41) 0.67 (67,677) 0.22
English literature 4.60 (1.61, 31,316) 5.22 (1.44, 34,317) <0.001 (0.41) 0.59 (62,416) 0.20
Drama 4.97 (1.52, 4022) 5.53 (1.38, 7537) <0.001 (0.39) 0.47 (10,997) 0.14
Religious Education 4.16 (2.07, 5887) 4.96 (1.93, 8211) <0.001 (0.40) 0.52 (13,572) 0.16
French 4.04 (1.69, 17,876) 4.74 (1.69, 20,213) <0.001 (0.41) 0.64 (36,370) 0.20
German 4.28 (1.62, 8135) 4.93 (1.60, 9491) <0.001 (0.40) 0.61 (16,638) 0.18
Spanish 3.92 (1.82, 2734) 4.71 (1.76, 3983) < 0.001 (0.44) 0.62 (6501) 0.18
Science
Mathematics 4.48 (1.73, 35,371) 4.54 (1.71, 36,390) < 0.001 (0.03) 0.77 (68,125) 0.00
Double Science 4.52 (1.60, 30,831) 4.63 (1.61, 31,918) < 0.001 (0.07) 0.68 (59,518) 0.12
Single Science 2.95 (1.45, 2661) 3.30 (1.48, 2928) <0.001 (0.24) 0.60 (5331) 0.02
Physics 5.83 (1.35, 1555) 5.78 (1.39, 1268) 0.33 (0.04) 0.50 (2733) 0.09
Chemistry 5.61 (1.33, 1539) 5.92 (1.26, 1272) <0.001 (0.24) 0.46 (2720) 0.08
Biology 5.84 (1.22, 1568) 6.07 (1.21, 1292) <0.001 (0.19) 0.51 (2764) 0.14
Social Sciences
Geography 4.55 (1.77, 15,014) 4.88 (1.80, 12,430) < 0.001 (0.18) 0.65 (26,081) 0.16
History 4.62 (1.95, 11,697) 5.02 (1.91, 12,220) <0.001 (0.21) 0.63 (22,764) 0.18
Business 4.49 (1.77, 6591) 4.72 (1.74, 5184) <0.001 (0.13) 0.56 (11,188) 0.11
Information Technology 4.43 (1.87, 5747) 4.79 (1.83, 3840) <0.001 (0.19) 0.47 (9350) 0.07
Information Technology short course 3.79 (1.88, 4144) 4.39 (1.90, 5217) <0.001 (0.32) 0.48 (8931) 0.11
Practical
Art and Design 4.59 (1.62, 6486) 5.54 (1.49, 9397) < 0.001 (0.61) 0.43 (15,104) 0.09
Music 5.11 (1.97, 2221) 5.48 (1.70, 3224) <0.001 (0.20) 0.54 (5208) 0.16
Physical Education 4.87 (1.53, 9802) 5.03 (1.65, 4696) <0.001 (0.10) 0.55 (13,846) 0.07
DT-Food 4.14 (1.68, 3605) 4.84 (1.65, 10,626) < 0.001 (0.42) 0.52 (13,493) 0.08
DT-Graphics 4.24 (1.80, 8387) 5.06 (1.67, 6745) <0.001 (0.47) 0.45 (14,328) 0.07
DT-Resistant Materials 4.18 (1.67, 11,361) 4.88 (1.69, 3499) <0.001 (0.42) 0.48 (14,059) 0.06
DT-Textiles 3.68 (1.86, 201) 5.00 (1.65, 6557) <0.001 (0.75) 0.52 (6390) 0.09
a
This is the residual of the CAT verbal score after regression with the CAT gfactor entered as the independent variable; ns for this column are the
same as those for the column immediately to the right.
b
These variables are in standard units (mean= 0, S.D. = 1).
16 I.J. Deary et al. / Intelligence 35 (2007) 1321
GCSE exams. For this, we used structural equation
modelling (EQS; Bentler, 1995)toestimatethe
correlation between a latent trait of mental ability and
educational examination scores. Students take different
combinations of school subjects, so we analysed the
largest possible complete data set. There were 13,248
students with full CAT2E data, and GCSE scores on
English, English Literature, Mathematics, Double
Science, French, and Geography. (All analyses were
repeated with the 12,519 students who did History
rather than Geography and there were trivial differences
in the outcomes.) The analysis in the full sample
demonstrated that there was a single factor underlying
performance on the CAT's three batteries (see Methods).
The results from the six GCSE subjects were subjected
to principal axis factoring. A single factor was found,
accounting for 71.8% of the variance. Therefore, the
simple model in Fig. 1 was fitted to the data, with the
question being: what is the correlation between the two
latent traits? The fit of the overall model is not of prime
consideration here. However, for the model shown in
Fig. 1, the average of the off-diagonal standardised
residuals = 0.04, the chi-square = 7799.0 (df =26,
p< 0.001), and the comparative fit index = 0.920. Note
the high values of the path coefficients between the
manifest and latent traits. The correlation between gand
general educational achievement was 0.81.
3.2. Sex differences in educational attainment
Girls performed better than boys on overall GCSE
points scores, with a Cohen's dof 0.30 (Table 2). There
were significant sex differences (p< 0.001) in all GCSE
scores except Physics. Girls performed better in every
topic except Physics. The effect sizes of the sex
differences were often substantial. The Arts and Human-
ities group had Cohen's dvalues tightly grouped around
0.4. The practical subjects group had some large effects,
for example Art and Design had a Cohen's dof 0.61. The
Science and Social Science subjects showed smaller
differences. The difference in Mathematics was very small
(Cohen's d=0.03).
Girls and boys did not differ in g, but girls scored
higher on the residual verbal factor. Might this explain
the girls' better performance on GCSEs? The correla-
tions between the residual verbal factor and GCSE
subjects were all positive and of small effect size,
demonstrating that verbal ability, orthogonal to g,
contributes some additional variance to examination
performance (Table 2). The correlation with overall
GCSE points was 0.13. The only subject for which this
ability had no contribution was Mathematics, where the
correlation was zero. The largest correlations were in the
Arts and Humanities group where correlations were
around 0.2, and there were similar-sized correlations
with History, Geography, and Music.
The next step applied general linear modelling
(ANCOVA) to the GCSE scores to discover the relative
contributions of the predictors. Sex (male, female) was a
fixed effect. The CAT's gand residual verbal factors
were covariates. Age was also a covariate. The
contributions from each of these effects to the overall
GCSE scores and to each topic individually are shown
in Table 3, and are expressed as partial η
2
values
(proportion of variance accounted for). Age made very
little contribution and is not discussed further. The g
factor contributes 53.5% of the variance to GCSE Best
8 scores and 49.2% of the variance to total GCSE scores.
All of the contributions to individual courses are
moderate to large in size. The highest contributions
are to Mathematics (58.9%) and English (48.3%). The
lowest contribution is to Art and Design (18.2%), and
the practical subjects generally have lower values than
the more traditional academic subjects, most of which
have values greater than 40%. The residual verbal factor
accounted for about an additional 3% of the variance in
overall GCSE scores, and makes additional contribu-
tions between about 2% and 7% in the Arts and
Humanities, and only 0% to less than 3% in the
Sciences. Verbal ability did contribute a very small but
significant amount to Physics performance, on which
the sexes did not differ. The contribution to practical
subjects is small, mostly around or below 1% of the
variance. In the Social Sciences, History and Geography
had contributions from the residual verbal factor of
about an additional 4%.
Sex contributes 3.2% of the variance to overall
GCSE scores and 3.7% to GCSE Best 8 scores (Table 3).
English
English Lit.
Maths
Science
Geography
French
CAT
Verbal
CAT
Non-verbal
CAT
Quantitative
F1
F2
.86
.82
.84
.87
.88
.80
.83
.81
.73
.81
Fig. 1. Structural equation model (confirmatory factor analysis) to
examine the correlation between latent traits of intelligence and
educational achievement.
17I.J. Deary et al. / Intelligence 35 (2007) 1321
The contributions of sex to the GCSE scores showed
differences between subjects. The contributions to Arts
and Humanities were between 3.4% and 7.4%. The
contributions to Science were all very low, with only
Chemistry and Biology above 1%, and Mathematics and
Double Science at or below 0.1%. The Social Sciences
had contributions from sex at about an additional 1% to
2% of the variance. The practical subjects were mixed,
with the notable results being the contributions of 5.7%
to Design and Technology-Graphics and 8.0% to Art
and Design. To quantify the extent to which the effects
of sex were caused by girls' having better residual
verbal scores, the same models were re-run for all
subjects, but without the residual verbal factor in the
model (results not shown). The results did produce some
increase in the effect of sex but, in all cases, this is
around or below 10% of the effect of sex seen in the
model with the residual verbal factor. Therefore, girls'
better scores on the verbal factor account for only a very
small part of their better scores on GCSE examinations.
3.3. Intelligence and education: an epidemiological
approach
Whether or not students gain five or more GCSE
scores at grades from Ato C is important. For example,
the Department for Education and Skills (DfES) use this
binary variable as a key outcome in school performance
tables. Such thresholds are also common for students
personally, because they can be the bases of entry to
further education and training. There were 39,193
students who met this criterion, and 30,646 who did
not. Logistic regression was used with gscores as a
predictor of this criterion. The exponent of βwas used to
obtain the odds ratio of meeting the criterion for a
standard deviation increase in the gscore. The result was
that a standard deviation increase in gwas associated
with an increased odds of 7.32 (p< 0.001, 95% CI = 7.10
to 7.54). Practically, this means that, at a mean value of
the gscore, 58% achieved this criterion. On the other
hand, 91% those scoring 1 S.D. higher on gachieved
this and only 16% of those scoring 1 S.D. lower on gdid
so. The predicted values from this univariate logistic
regression model were used to conduct a Receiver
Operating Characteristic curve analysis, with the
criterion as the outcome (five grades at Ato C) and g
as the predictor. The area under the curve was 0.859
(p< 0.001, 95% CI = 0.857 to 0.862). Values over 0.8
indicate good predictors.
A multivariate logistic regression was run with the
same criterion as the outcome and g, the residual verbal
factor, sex, and age as the predictor variables. The
resulting odds ratios, controlling for the other variables
in the model, were as follows: g= 8.09 (p< 0.001, 95%
CI = 7.84 to 8.34), residual verbal factor = 1.43
(p<0.001, 95% CI = 1.40 to 1.46), sex= 1.96
(p< 0.001, 95% CI = 1.88 to 2.04), and age = 1.014
(p< 0.001, 95% CI = 1.009 to 1.019). 61% of girls and
only 50% of boys achieved the criterion. The predicted
values from this multivariate logistic regression model
were used to conduct a Receiver Operating Character-
istic curve analysis, with the criterion at the outcome
(five grades at Ato C) and g, the residual verbal factor,
Table 3
General linear modelling of GCSE scores
Subject η
2
values from general linear
model
N
CAT
g
CAT
residual
verbal
a
Age Sex
Overall score
GCSE total points 0.492 0.027 0.000 0.032 70,530
GCSE Best 8 0.535 0.032 0.001 0.037 68,904
Arts and Humanities
English 0.483 0.072 0.001 0.065 67,677
English literature 0.383 0.049 0.001 0.060 62,416
Drama 0.226 0.018 0.001 0.034 10,997
Religious Education 0.303 0.032 0.000
b
0.065 13,572
French 0.448 0.053 0.000 0.074 36,370
German 0.402 0.040 0.000
b
0.062 16,638
Spanish 0.413 0.040 0.001
b
0.073 6501
Science
Mathematics 0.589 0.000 0.000
b
0.001 68,125
Double Science 0.465 0.026 0.000 0.000 59,518
Single Science 0.361 0.017 0.000
b
0.004 5331
Physics 0.244 0.005 0.000
b
0.000
b
2733
Chemistry 0.215 0.002 0.000
b
0.019 2720
Biology 0.264 0.013 0.000
b
0.012 2764
Social Sciences
Geography 0.443 0.039 0.001 0.011 26,081
History 0.406 0.041 0.001 0.014 22,764
Business 0.336 0.026 0.000
b
0.011 11,188
Information Technology 0.228 0.005 0.000
b
0.016 9350
Information Technology
short course
0.234 0.009 0.000
b
0.030 8931
Practical
Art and Design 0.182 0.001 0.001 0.080 15,104
Music 0.288 0.016 0.001
b
0.008 5208
Physical Education 0.303 0.013 0.005 0.000
b
13,846
DT-Food 0.294 0.015 0.000
b
0.045 13,493
DT-Graphics 0.211 0.001 0.000
b
0.057 14,328
DT-Resistant Materials 0.223 0.004 0.001 0.021 14,059
DT-Textiles 0.263 0.008 0.001
b
0.012 6390
Values shown are η
2
for each fixed effect and covariate in the model.
a
This is the residual of the CAT verbal score after regression with
the CAT gfactor entered as the independent variable.
b
These effects have p-values >0.01 (even in some cases where the
η
2
value is signified as 0.000). All other effects have p-values =0.01.
18 I.J. Deary et al. / Intelligence 35 (2007) 1321
sex and age as the predictors. The area under the curve
was 0.873 (p< 0.001, 95% CI = 0.870 to 0.875), only a
little greater than when gwas used alone, but
significantly so, because the 95% confidence intervals
of the two models do not overlap.
4. Discussion
Cognitive ability tests taken at age 11 correlate
0.81 with national school examinations taken at age
16. Thus, the main finding here is the large
contribution of general mental ability to educational
achievement overall, and to all 25 individual subjects,
though these showed substantial differences. The
additional contribution of a residual verbal ability
was significant, about an order of magnitude less; its
contribution ranged from zero in Mathematics to 7.1%
of the variance in English. Girls performed signifi-
cantly better than boys on all subjects except Physics.
Adjusting for g, there was a contribution from sex to
examination performance that was about the same
magnitude as the residual verbal factor. The effect of
sex, too, varied markedly in magnitude across
examination subjects and was not accounted for by
the better verbal ability of girls. Obtaining five GCSEs
at grades between Aand C is an important
educational outcome in England. A student with an
average cognitive ability test score has a 58% chance
of obtaining this; a person one standard deviation
higher in ability has a 91% chance.
The data used here have a number of strengths. The
sample is very large and probably representative. The
cognitive test battery assesses a range of abilities in 10
individual subtests. The timing of the test was optimal:
at the beginning of secondary education when there
has not yet been subject-specific teaching in the
educational outcomes at secondary level. The pro-
spective longitudinal nature of the study is a strength.
The range of educational topics assessed is compre-
hensive. The examinations are national, almost all
schoolchildren in England take them, and their timing
is such that no children have yet left school. Thus, the
cognitive ability assessments and the later educational
attainments were taken when almost all children were
still in school.
A possible weakness is the lack of family back-
ground data. However, as Mackintosh (1998, p. 46)
argues, the association between family background and
educational attainments is not high enough to account
for the association between cognitive ability and
education. Moreover, both twin and adoption studies
consistently find that the contribution of shared
environment (principally family background) is small
at the childhood ages relevant to the present study
(Bartels, Rietveld, Van Baal, & Boomsma, 2002a; Petrill
et al., 2004). There are various possible causes of the
cognitive abilityeducational achievement association.
Bartels et al. (2002b) found a strong genetic correlation
between cognitive ability (measured at 5, 7, 10, and 12
years) and educational achievement at age 12. In an
overview, Petrill and Wilkerson (2000) concluded that
genetics and shared and non-shared environmental
factors all influence intelligence and education, with
genetics being important in the correlation between
them, and non-shared environment being important in
discrepancies between intelligence and educational
attainments.
Whereas the correlations indicate that around 50% to
60% of the variance in GCSE examination points score
can be statistically explained by the prior gfactor, by the
same token a large proportion of the variance is not
accounted for by g. Some of the remaining variance in
GCSE scores will be measurement error, but some will
be systematic. Thus, non-gfactors have a substantial
impact on educational attainment. These may include:
school attendance and engagement; pupils' personality
traits, motivation and effort; the extent of parental
support; and the provision of appropriate learning
experiences, teaching quality, school ethos, and struc-
ture among other possible factors (Petrides, Chamorro-
Premuzic, Frederickson, & Furnham, 2005; Strand,
2003).
There was a moderately large gender gap in
educational outcomes in the present data, with differ-
ent-sized effects in different school subjects. Girls have
an advantage on verbal ability on the CAT (Strand et al.,
in press) and the residual verbal ability score used here
did contribute to educational outcomes at about the
same level as sex. However, sex differences in the
educational outcomes were not accounted for by
residual verbal ability scores. This accords with others'
results and it has been suggested that this is due in large
part to the different classroom behaviours of boys and
girls (Fergusson & Horwood, 1997). It is also possible
that girls have a type of verbal advantage in GCSE that
is not captured by CAT verbal subtests. Such abilities
might include verbal fluency and/or the ability to
express thoughts in connected prose, and/or better
memory for information that was presented in verbal
form (orally, by teachers, or by reading textbooks).
GCSE public examinations rely heavily on essays and
other modes of assessment requiring extended writing.
We also know that largest sex differences reflect girls'
superiority in the area of writing. For example, Cole
19I.J. Deary et al. / Intelligence 35 (2007) 1321
(1997) reported an analysis of multiple US national
datasets for school students assessed at age 9, 14, and 17
on a wide variety of tests. There was no sex difference
on verbal reasoning/vocabulary (d=0.05), a small
advantage in verbal-reading (d= 0.20), a medium female
advantage in verbal-language use (d= 0.40), and the
largest difference for verbal-writing (d= 0.60). It is also
possible that sex differences in GCSE reflect wider
factors related to motivation and effort, such as girls'
greater likelihood to complete and submit coursework
(OHMCI, 1997), gendered patterns of subject choice
(Arnot, David, & Weiner, 1996), and/or gendered
allocation to tiered subjects (Elwood, 1995). Salisbury,
Rees, and Gorard (1999) provide a review of the
literature in this area.
Spearman (1904) suggested that the general factor
from school subjects would be almost perfectly
correlated with general intelligence. In fact, the
correlation is above 0.8, even when the cognitive ability
measurements were taken 5 years before the school
exams. Beyond that, in English school examinations,
there is further advantage to girls and to those with
relatively strong verbal skills (after gis controlled).
These data establish the validity of gfor this important
life outcome.
Acknowledgements
Ian Deary is the recipient of a Royal Society-Wolfson
Research Merit Award. A version of this paper was
presented by Ian Deary as the Spearman Centenary
Lecture to the International Society for Intelligence
Research in New Orleans, USA, in December 2004.
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