[Paleopsych] Intelligence: Michael A. McDaniel: Big-brained people are smarter: A meta-analysis of the relationship between in vivo brain volume and intelligence

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Michael A. McDaniel: Big-brained people are smarter: A meta-analysis of the 
relationship between in vivo brain volume and intelligence
Intelligence
Volume 33, Issue 4 , July-August 2005, Pages 337-346

Michael A. McDaniel
Department of Management, Virginia Commonwealth University, PO Box 84400, 
Richmond, VA 23284-4000, USA

Received 30 December 2003;  revised 7 September 2004;  accepted 11 November 
2004.  Available online 12 February 2005.

Abstract

The relationship between brain volume and intelligence has been a topic of a 
scientific debate since at least the 1830s. To address the debate, a 
meta-analysis of the relationship between in vivo brain volume and intelligence 
was conducted. Based on 37 samples across 1530 people, the population 
correlation was estimated at 0.33. The correlation is higher for females than 
males. It is also higher for adults than children. For all age and sex groups, 
it is clear that brain volume is positively correlated with intelligence.

Keywords: Brain; Intelligence; MRI scan IQ

Article Outline

1. Introduction
2. Methods

2.1. Literature review
2.2. Decision rules
2.3. Analysis approach
3. Results
4. Discussion

4.1. Data reporting and availability issues
4.2. Additional research
5. Conclusion
References


1. Introduction

In 1836, Frederick Tiedmann wrote that there exists “an indisputable connection 
between the size of the brain and the mental energy displayed by the individual 
man” (as cited in Hamilton, 1935). Since that time, the quest for the 
biological basis of intelligence has been pursued by many. Various narrative 
reviews (Rushton & Ankney, 1996, Rushton & Ankney, 2000 and Vernon et al., 
2000) and a meta-analysis (Nguyen & McDaniel, 2000 ) have documented a 
non-trivial positive relationship between brain volume and intelligence in 
non-clinical samples. In the brain volume literature, there are two general 
categories of brain volume measures. The first category consists of measures of 
the external size of the head, such as the circumference of the head. The 
second category consists of measures of the in vivo brain volume, typically 
assessed through an MRI scan. For external head measures, Vernon et al. (2000) 
reported the population correlation between head size and intelligence to be 
0.19. Nguyen and McDaniel (2000) reported population correlations from 0.17 to 
0.26 for three different sub-categories of external head size measures. Studies 
assessing the correlation between in vivo brain volume and intelligence are 
more rare. Vernon et al. (2000) reported data on 15 such correlations and 
obtained a population correlation of 0.33. Nguyen and McDaniel (2000) reported 
the same population correlation based on 14 correlations. Gignac, Vernon, and 
Wickett (2003) reported data published in 2000 or earlier with a mean 
correlation of 0.37. Since 2000, much more data relating brain volume and 
intelligence have become available due to the increased use of MRI-based brain 
assessments. The purpose of this meta-analysis is to cumulate our knowledge 
concerning the magnitude of the correlation between in vivo brain volume and 
intelligence in order to answer the long-standing question on this topic. In 
addition, potential sex and age moderators of the relationship are evaluated.

2. Methods

2.1. Literature review

A review of all known past literature was conducted using PsychInfo and Medline 
as well as citation index searches of popular past reviews. Studies containing 
relevant data were reviewed to identify citations to other relevant research. 
Often, studies were found in which the authors collected MRI-assessed brain 
volume and intelligence data but did not report the correlation between these 
measures because the correlation between brain volume and intelligence was not 
the focus of the study, and/or because the publication standards for the 
journal did not require a correlation matrix among all variables. For such 
studies, the correlations were requested from the authors.

After preliminary findings were obtained, over 50 authors were contacted who: 
(1) had published in the area of brain volume and intelligence, (2) had 
provided commentaries on such literature, or (3) were known to have an interest 
in the relation between brain volume and intelligence. These researchers were 
provided with the preliminary findings and were asked to scan the references to 
determine if any relevant research had been omitted. These researchers were 
also asked if they knew of any data sets containing both MRI-assessed brain 
volume and intelligence that might be relevant to the study.

2.2. Decision rules

The analysis included all correlations between in vivo measures of full brain 
volume and intelligence that met the decision rules. It did not include studies 
if they only measured partial brain volume, for example only frontal gray 
matter volume (Thompson et al., 2001 ). All intelligence measures were 
standardized tests of general cognitive ability and primarily were full-scale 
IQ measures or the Ravens Progressive Matrices Test . We did not include data 
from studies that estimated full-scale IQ from other measures such as the New 
Adult Reading Test. Some studies reported data on more than one sample. Only 
one correlation between brain volume and intelligence for a given sample was 
reported, but whenever possible, data were coded separately by age (children 
vs. adults) and by sex. Thus, if a sample recorded a correlation for all 
members of the sample and correlations separately by sex, the correlation for 
each sex group was included, but the correlation for all members in the sample 
was not included. Thus, all correlations contributing to the meta-analysis are 
from independent samples. All sample members were non-clinical. Often the 
sample was the non-clinical control group in a clinical study.

Whereas the Gignac et al. (2003) paper is the most recently published review on 
this topic, it is useful to compare that data set with the data set used in the 
this study. This paper incorporates 23 additional samples raising the total 
number of coefficients available for analysis from 14 to 37. Some of the 23 
sample difference is due to differing decision rules. For this paper, 
correlations are reported separately by sex for six studies (Andreasen et al., 
1993, Gur et al., 1999, Ivanovic et al., 2004, Reiss et al., 1996, Tan et al., 
1999 and Willerman, 1991 ) while Gignac et al. reported a single correlation 
for males and females combined for five of the studies and did not include data 
from Ivanovic et al. (2004). This reduced the number of different samples to 
18. Gignac et al. included data from 96 individuals (Pennington et al., 2000 ) 
of whom at least half had reading disabilities. This sample was excluded from 
the present study because it did not meet this paper's decision rule for 
clinically normal subjects. Also, Gignac et al. had included a study by Tramo 
(1998). That study was excluded from the present analysis because it lacked a 
measure of full brain volume. This increased the number of unique samples in 
this study to 20. These 20 coefficients from independent samples were drawn 
from 11 sources (Aylward et al., 2002, Castellanos et al., 1994, Frangou et 
al., 2004, Garde et al., 2000, Giedd, 2003, Ivanovic et al., 2004, Kareken et 
al., 1995, MacLullich et al., 2002, Nosarti et al., 2002, Shapleske et al., 
2002 and Staff, 2002 ) not included in the Gignac et al. review. The increased 
number of samples over the Gignac et al. review and the decision rule to record 
data separately by age and sex, permitted the evaluation of both age and sex 
moderators.

2.3. Analysis approach

The psychometric meta-analysis approach (Hunter & Schmidt, 1990 and Hunter & 
Schmidt, 2004 ) was used. This approach estimates the population correlation by 
correcting the observed correlations for downward bias due to various artifacts 
including measurement error and range restriction. Whereas both intelligence 
measures and MRI-based measures of in vivo brain volume have reliabilities in 
the 0.90s, correlations were not corrected for measurement error in either 
variable. However, 16 of the 37 samples reported standard deviation for the 
intelligence measure. Of these 16 samples, 13 reported the standard deviation 
of the intelligence measures to be below the population standard deviation of 
15. The average (median) of the standard deviations was 12.9 indicating that 
the observed correlations were, on average, underestimates of the population 
correlation due to restriction of range on the intelligence measures.

The analyses are presented in two ways. First, the observed correlations were 
cumulated without any corrections for range restriction/enhancement. The 
resulting mean correlation would likely be an underestimate of the population 
parameter due to range restriction. Next, the observed correlations were 
corrected individually for range restriction (three correlations were corrected 
for range enhancement because the standard deviation of the intelligence 
measure was larger than the population standard deviation of 15). For those 
coefficients where the degree of range restriction was not known, the value of 
12.9 (the median of the known values) was used. The resulting mean correlation 
corrected for range restriction is offered as the best estimate of the 
population parameter. Those who are not comfortable with the interpolation of 
the range restriction data and/or the range restriction corrections may 
interpret the mean observed correlation with knowledge that it is likely an 
underestimate of the population parameter. Those who are comfortable with the 
range restriction corrections may interpret the mean of the corrected 
correlations as a reasonable estimate of the population parameter. The pattern 
of the reported moderators is evident in both the observed and corrected means.

3. Results

The results of the analysis based on 37 correlations that met the decision 
criteria (Andreasen et al., 1993, Aylward et al., 2002, Castellanos et al., 
1994, Egan et al., 1995, Flashman et al., 1998, Frangou et al., 2004, Garde et 
al., 2000, Giedd, 2003, Gur et al., 1999, Ivanovic et al., 2004, Kareken et 
al., 1995, MacLullich et al., 2002, Nosarti et al., 2002, Pennington et al., 
2000, Raz et al., 1993, Reiss et al., 1996, Schoenemann et al., 2000, Shapleske 
et al., 2002, Staff, 2002, Tan et al., 1999, Wickett et al., 1994 and Willerman 
et al., 1991) are reported in Table 1 . The results for the correlations 
corrected for the downward bias of range restriction will be discussed in this 
paper, although results for uncorrected correlations are also shown in the 
table. The best unbiased estimate of the population correlation between brain 
volume and intelligence is 0.33 (Table 2).

Table 1.

Comparison of the data reported by Gignac et al. (2003) and the current study
Included in Gignac et al. (2003) Included in current study N r Sex/race/age 
information
Aylward et al. (2002) No Yesa 46 ?0.13 Male, white, children
Aylward et al. (2002) No Yesa 30 0.08 Mixed sex, white, adults
Andreasen et al. (1993) Yes, data based on sample containing both males and 
females Yes, data reported separately by sex 37 0.40 Male, unknown race, adults
30 0.44 Female, unknown race, adults
Castellanos et al. (1994) No Yes 46 0.33 Male, unknown race, children
Egan et al., 1994 and Egan et al., 1995 Yes, used 1994 datab Yes, used 1995 
datab 40 0.31 Mostly maleb, unknown race, adults
Flashman et al. (1998) Yes Yes 90 0.25 Mixed sex, unknown race, adults
Frangou et al. (2004) No Yes 40 0.41 Mixed sex, unknown race, mostly childrenc
Garde et al. (2000) No Yesa 46 0.07 Male, white, adults
22 0.22 Female, white, adults
Giedd (2003) No Yes 7 ?0.67 Female, not white and not black, children
8 0.46 Female, black, children
39 0.34 Female, white, children
7 0.17 Male, black, children
63 0.27 Male, white, children
7 0.67 Male, not white and not black, children
Gur et al. (1999) Yes, data based on sample containing both males and females 
Yes, data reported separately by sex 40 0.39 Male, unknown race, adults
40 0.40 Female, unknown race, adults
Ivanovic et al. (2004) No Yes 47 0.55 Male, unknown race, adults
49 0.37 Female, unknown race, adults
Kareken et al. (1995) No Yesa 68 0.30 Mixed sex, unknown race, adults
MacLullich et al. (2002) No Yes 97 0.39 Male, white, adults
Nosarti et al. (2002) No Yesa 42 0.37 Mixed sex, white, children
Pennington et al. (2000) Yesd Yes 36 0.31 Mixed sex, mixed race, children
Raz et al. (1993) Yes Yes 29 0.43 Mixed sex, unknown race, adults
Reiss et al. (1996) Yes, data based on sample containing both males and females 
Yes,a data reported separately by sex 12 0.52 Male, whitee, children
57 0.37 Female, white,e children
Schoenemann et al. (2000) Yesf Yesf 72 0.21 Female, unknown race, adults
Shapleske et al. (2002) No Yesa 23 0.13 Male, white, adults
3 ?0.86 Male, black, adults
Staff (2002) No Yes 106 ?0.08 Mixed sex, white, adults
Tan et al. (1999) Yes, data based on sample containing both males and females 
Yes, data reported separately by sex 49 0.28 Male, white, adults
54 0.62 Female, white, adults
Tramo et al. (1998) Yes, the authors used a forebrain volume measure No, There 
is no full brain volume measure in this study – – –
Wickett et al. (1994) Yes Yes 40 0.40 Female, unknown race, adults
Wickett et al. (2000) Yes Yes 68 0.35 Male, unknown race, adults
Willerman et al. (1991) Yes, data based on sample containing both males and 
females Yes, data reported separately by sex 20 0.51 Male, unknown race, adults
20 0.33 Female unknown race adults

Note: Correlation coefficients in this table were rounded to two decimal 
places. The statistical analysis did not use rounded correlation coefficients.
a Data from this study were supplemented by communication with the author(s). 
This communication resulted in correlations that were not reported in the 
original study.
b In Egan et al. (1994), the sample was described as 48 males and two females. 
Egan et al. (1995) reported corrected analyses using a sample of 40. This 
sample of 40, being a subset of the 48 could have had no more than 2 females 
and was classified as a male sample in the analysis.
c The sample used by Frangou et al. (2004) had an age range of 12 to 21. Based 
on the mean and standard deviation of age, it appeared that most of the sample 
was under 18. We classified the sample as “children.”
d Gignac et al. (2003) also included a correlation from a sample of twins where 
at least one of each twin pair had a learning disability. The current study 
excluded the sample because it was not considered clinically normal.
e  In personal communication to the author (10/17/2002), Dr. Reiss described 
the race of the sample as being “great majority white.”
f Gignac et al. (2003) reported a correlation of 0.45 which was the partial 
correlation between the first principal component of a battery of test and 
brain volume controlling for age and simple reaction time. The author used the 
correlation between brain volume and the Ravens which was provided to us by Dr. 
Schoenemann on November 14, 2002.

Table 2.

Meta-analytic results for in vivo brain volume and intelligence
Distribution Number of studies Sample size Observed mean correlation Mean 
correlation corrected for range restriction
All correlations 37 1530 0.29 0.33

Analyses by whether the degree of range restriction was interpolated
Interpolation 21 963 0.29 0.32
No interpolation 16 567 0.30 0.34

Analyses by sex
Females 12 438 0.36 0.40
Males 17 651 0.30 0.34
Mixed sex 8 441 0.21 0.25

Analyses by age
Adults 24 1120 0.30 0.33
Children 13 410 0.28 0.33

Analyses by age and sex
Female adults 8 327 0.38 0.41
Female children 4 111 0.30 0.37
Male adults 11 470 0.34 0.38
Male children 6 181 0.21 0.22

It is possible that the correlation between brain volume and intelligence in 
studies that provided standard deviations of intelligence is systematically 
higher or lower than the studies that did not report standard deviations of 
intelligence. If this were the case, the interpolation of the standard 
deviations for those studies that did not report standard deviations might lead 
to biased estimates of the unattenuated correlation between brain volume and 
intelligence. To assess this potential problem, the author analyzed the data 
partitioned by whether the standard deviation was reported in the study or 
whether it was interpolated. The similarity of the observed correlations (0.29 
and 0.30) suggested that the studies that reported standard deviations for 
intelligence were not systematically different in their average observed 
correlation. Thus, it is reasonable to interpolate the missing standard 
deviations from the known standard deviations.

When the data were subdivided by sex, one obtains three sub-distributions: 
samples of males, samples of females, and samples that contained both males and 
females. The relationship between brain volume and intelligence shows a clear 
sex moderator with the correlation being larger for females than males (0.40 
vs. 0.34). For studies in which both males and females were combined in the 
same sample, the correlation is 0.25. Assuming this correlation is not an 
anomaly due to sampling error, it argues for separate reporting of results by 
sex.

The data were then subdivided by age into adult and child samples. The analyses 
restricted to age alone showed no evidence of a moderating effect; however, the 
mixed sex samples and the uneven distribution of age across sex clouded an 
effect that is evident when the data were divided hierarchically by sex and 
then by age. Female adult samples showed a somewhat larger population 
correlation than female children samples (0.41 vs. 0.37). Male adult samples 
showed a larger population correlation than male children samples (0.38 vs. 
0.22). The hierarchical sex/age results also confirm the sex moderator. Female 
adult samples showed a higher population correlation than male adult samples 
(0.41 vs. 0.38). Female children samples showed a higher population correlation 
than male children samples (0.37 vs. 0.22).

An anonymous reviewer requested a significance test on the sex difference. Most 
applications of psychometric meta-analysis (Hunter & Schmidt, 2004 ) do not 
incorporate statistical significance tests. This is in part because the 
meta-analysis seeks to estimate population parameters and statistical tests are 
designed for sample data. This is also in part due to the fact that statistical 
tests do not answer the questions that most users think they answer (Cohen, 
1994 and Hunter & Schmidt, 2004 ). However, in deference to the reviewer, 
statistical significance tests are reported here. Statistical tests in 
meta-analysis focus on whether the observed variance in the distribution of 
effect sizes is different from the variance one would expect from sampling 
error alone. A chi-square significance test on the distribution of 37 effect 
sizes was statistically significant (p<0.0003) indicating that some of the 
variance in the distribution is not due to sampling error and thus might be due 
to moderators. Thus, on the basis of the statistical significance test, the 
moderator analyses for interpolation, age, and sex were warranted. With respect 
to the sex moderator analysis, the significance test was not statistically 
significant for females (p<0.065) but was significant for males (p<0.014) and 
for the mixed sex samples (p <0.017). One interpretation of these significance 
tests is that there are no moderators within the effect size distribution for 
females but there are moderators with the distribution of males and within the 
distribution of mixed-sex samples. Based on this interpretation, the age within 
sex analyses for females was not warranted while the age within sex analysis 
was warranted for the males and the mixed-sex samples. However, the 
significance of the chi-square analyses is a function of the sample size. At 
least by meta-analysis standards, all these sample sizes are small. Thus, a 
second interpretation, and the one favored by the author, is that the 
distribution of effect sizes from female samples needs more data to reach 
significance. Based on this interpretation, the search for age within sex 
analyses for females is reasonable and should be replicated as more data 
cumulate.

4. Discussion

This study's best estimate of the correlation between brain volume and 
intelligence is 0.33. The correlation is higher for females than males. It is 
higher for adults than children. Regardless of the subgroups examined, the 
correlation between brain volume and intelligence is always positive. It is 
very clear that brain volume and intelligence are related.
4.1. Data reporting and availability issues

There is much cause for concern regarding the reporting practices of research 
in this area. Few studies reported means and standard deviations and a 
zero-order correlation matrix among the variables. The lack of reported 
standard deviations makes it impossible to estimate precisely the effect of 
range restriction in these data. The lack of a correlation matrix results in 
excluding data from this analysis and thus increases publication bias concerns. 
Publication bias analyses for these data were not conducted because some 
procedures assume that the results are homogeneous (i.e., lacking moderators) 
(Terrin, Schmid, Lau, & Olkin, 2003 ). These data clearly show evidence of both 
sex and age moderators. The data distributions subdivided by both sex and age 
may be homogeneous but the number of correlations in these distributions was 
judged too few to conduct meaningful publication bias analyses. As future data 
accumulate, these analyses should be re-conducted and publication bias analyses 
should be pursued.

Given the evidence of age and sex moderators in these data, more research 
reporting results separately by age and sex is warranted. Potential race 
moderators were not examined due to the relative lack of non-Caucasians in the 
samples and the failure to report correlations separately by race.

4.2. Additional research

In addition to more research with better reporting, two additional areas 
deserve greater research attention. The first area is an examination of the 
brain volume and intelligence relationship at a more refined level of analysis 
than total brain volume. For example, although Staff's (2002) results indicated 
a small negative correlation between brain volume and intelligence, the 
fraction of brain volume that was gray matter was correlated 0.35 with 
intelligence. Likewise MacLullich et al. (2002) examined the relationship 
between regional brain volumes (e.g., left and right hippocampus, left and 
right frontal lobe, left and right temporal lobe) with intelligence. The author 
had considered including in this meta-analysis an analysis of regional brain 
volumes with intelligence but there were too few studies to analyze. The second 
area worthy of increased attention is the genetic contribution to the brain 
volume and intelligence relationship. The research in this area is both recent 
and rapidly growing (Molloy et al., 2002, Pennington et al., 2000, Posthuma et 
al., 2002, Posthuma et al., 2003, Schoenemann et al., 2000 and Thompson et al., 
2001). These two research areas will help us to better understand the causal 
relationship between brain volume and intelligence.

5. Conclusion

This paper contributes to the literature in three ways. First, the study more 
than doubles the number of unique samples that address the in vivo brain volume 
and intelligence relationship. Second, it also contributes by testing age and 
sex moderators of the relationship. The relationship is stronger for females 
than males and is stronger for adults than children. Finally, it resolves a 169 
year-old debate. Tiedmann (1836) was correct to conclude that intelligence and 
brain volume are meaningfully related.

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