Cranial Capacity and IQ

by R.T. Osborne

from Mankind Quarterly April, 1992

As was the case in much of his other research, Sir Francis Galton (1888) was the first to report a quantitative relationship between human cranial capacity and mental ability. Galton's subjects were 1095 Cambridge undergraduates. The statistical techniques available to him in 1888 did not include Pearson's correlation coefficient nor an objective Binet-type measure of intelligence. Galton computed head capacity simply by multiplying head length by breadth by height. No adjustment was made for thickness of the skull. Mental ability was estimated from average college marks. He found the relationship to be low and insignificant. Years later when Galton's 1888 data were reworked the correlation between head capacity and college marks was found to be in the range of rs reported by Pearson (1902, 1906, 1926), Pearl (1906) and many others.

From Galton's early paper to Lynn's series of studies in 1989-1990 there were at least 38 published investigations of the relationship of human head measurements to mental ability but only about one in four used cranial capacity as a head measurement despite the fact that in 1901 Dr. Alice Lee had developed a formula for determining cranial capacity which corrected for thickness of the skull. In the present study, which correlates mental ability with head capacity, Lee's formula was applied to head measurements of 476 subjects from the Georgia Twin Study (Osborne 1980). At the suggestion of Richard Lynn (personal communication) two additional correlations were computed, mental ability rs. head circumference and mental ability vs. cranial capacity with height and weight controlled.

The Georgia Twin Study database contains 127 measures of physical, mental and personal characteristics for 238 pairs of twins. In this analysis only the following variables will be used; age, race, sex, height, weight, head length, head width, head circumference, and IQ obtained from the average of the twelve mental tests of the Basic Battery of the twin study. The 476 subjects ranged in age from 12 to 18 but 2 subjects age 12 were placed in the 13-year-old group and 26 age 18 were combined with 70 subjects age 17 to yield a total of 96 for the oldest age group. There were 100 subjects age 16, 96 age 15, 116 age 14, and 68 in the 13-year-old group, including the two 12-year-olds who were assigned to the group. Of the 476 subjects 106 were white males, 84 black males, 118 white females and 168 black females. It should be mentioned here that in the total group of 476 subjects there are 50 pairs of unlike-sexed twins. For this reason the number of subjects in an age-sex analysis does not always yield an even number as would be the case if all the twins were like-sexed. For example, there are five subjects in the 13-year group of white males. At least one of these subjects has his twin in the white female group. In addition to the 50 pairs of unlike sexed twins, 20 pairs of white males were DZ, 21 MZ; 11 pairs of black males were DZ, 18 MZ. Of the white females 21 pairs were DZ, 26 MZ. Twenty eight pairs of black females were DZ, 43 MZ. The complete break-down by age, race and sex is given in Table 1.

Head capacity was determined by Lee's formula which requires head height. Since this measure was not one of the 127 twin-study variables, head height was estimated from a table prepared by Berry and Porteus (1920) and reproduced by Penrose as Appendix 2 (Penrose 1963).

From Table 1 it is seen that in the first phase of the analysis correlations were computed by age, for four race-sex groups. Because of the small numbers in some of the categories little credence can be placed in the rs. However, the correlations for the total race-sex groups compare favorably with recent studies of head measurements as they relate to mental ability. Among the mostly positive rs the insignificant and even negative rs at the 16-year level stand out. These subjects are all age 16; this is not a collapsed age bracket as we have at ages 13 and 17. The 16-year-old white males, black males and black females show this deviation in rs from adjacent ages. All the correlations in the table for white females are positive and compare favorably with the total rs by sex. Since the subjects' ages were not determined until after the tests were administered there is no way some 16-year-olds could have been singled out for special or different treatment from 15-year-olds or 17-year-olds. In the case of black males the small number of cases might have been a factor but not in the case of black females nor white Since Galton's 1888 study there have been at least 21 published studies examining the quantitative relationship between head measurements and mental ability. The first significant correlational study was Pearson's 1902 Royal Society paper, which he published again in 1926 in Annals of Eugenics. Results of studies before 1902 for the most part here reported as differences in means.

There has been little agreement among investigators as to which cranial measurements yielded the best estimate of cranial capacity. They varied from simple head width to brain weight/spinal cord weight ratio. Head circumference was the most frequently used head measurement, Correlations ranged from .02 in one of Lynn's studies (1989) to .41 (Wienberg 1974). Cephalic index consistently produced a very low or negative correlation with mental ability. Galton estimated cranial capacity by multiplying head length by head height by head breadth but he had no method of estimating the relationship between the variables except to show mean differences. Since Galton's Cambridge study numerous other investigators have used cranial capacity to compute head measurements-mental ability correlations. The range of rs for these studies was from .08 (Reed, 1923) to .14 (Passingham 1979).

In Table 1 correlations between head capacity and mental ability and head circumference and IQ are shown by age for four different sex-race groups and for the total group by sex. Also given for the five groups are the rs between IQ and head capacity with height and weight partialed out. From the table a trend of consistent age differences in correlations is not apparent unless it would be that of the white females who show slightly decreasing rs with increasing age. When only total groups are considered; i.e., all white males, black males, white females and black females, the rs between IQ and head capacity are higher than any reported in the literature. When the two races are compared, rs for females are significantly higher than those for males. The pattern does not hold when comparing total group rs for head circumference and IQ. Black males rs > than black females and white females rs > than white males. As would be expected when partial r's are computed between head capacity and IQ with height and weight partialed out the rs are attenuated when compared with those between head capacity and IQ alone.

While the database for this study was the 238 sets of twins from the Georgia Twin Study (Osborne 1980) intraclass correlations or other twin statistics were not computed. Each member of a twin pair was treated as an individual for our analysis. Positive correlations were found between head size as measured by head capacity and IQ and by head circumference and IQ. The rs were significant when the subjects were grouped by race and by sex. When the subjects were analyzed by age, race and sex the groups were too small to yield a pattern of meaningful correlations.

This article supports the recent studies of Lynn (1989, 1990) and Broman (1987) which found a positive association between human head size and intelligence. Lynn interprets this finding as an explanation for the rapid evolution of brain size in hominids during the last $-2 million years. Our finding that head capacity-IQ correlations rs hold up equally for males and females and for both blacks and whites is the unique contribution of this paper.


Correlations between Mental Ability, Head Capacity and Head Circumference by Age, Race and Sex Correlation between IQ and AGE Number Head Measurements

(a.) (b.) (c.)

White Males135.451-.072-.345






Black Males1320.106.228.071






White Females1311.716.632.484






Black Females1332.045-.245.086






Total Group By Sex



(a.) Pearson r (IQ vs. Head Capacity)

(b.) Pearson r (IQ vs. Head Circumference)

(c.) Partial rs (IQ vs. Head Capacity) Ht. and Wgt. partialed out.


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Broman, S., Nichols, P. L., Shaughnessy, P., Kennedy, W. 1987 Retardation in Young Children, Hillsdale, N.J.: Erlbaum.

Galton, F. 1888 Head Growth in Students at the University of Cambridge, Nature, 38; 14-15.

Lee, Alice and Pearson, K. 1901 A First Study of the Correlation of the Human Skull, Phil. Trans. Royal Society, 196 (Series A): 225-264.

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Reed, R, W., Mulligan, J. H. 1923 Relation of Cranial Capacity to Intelligence, Jour. Royal Anthropological Inst., 53:322-332.

Weinberg, W. A., Dietz, S. G., Penick, E. C., McAlister, W. M. 1974 Intelligence, Reading Achievement, Physical Size, and Social Class, J. Pediatrics, 85: 482-489.

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