Brain Size in Cubic Centimeters versus Standardized Test Scores

References:

 1999 GRE scores. Incomes by race and sex http://www.census.gov/hhes/income/income99/99tableb.html Cranial capacities. Correlation when adjusted by height and Hispanic origin. Perspectives of a "liberal"

The credible worldwide TIMSS and TIMSS-R studies demonstrated a wide range of academic skills amongst nations, with 8th grade students in Korea scoring 85 points higher than American 8th graders, 121 points higher than Israeli 8th graders, and 312 points higher than South African 8th graders.  Such a wide variation in scores, coupled with the consistent 15-60 point gap between boys and girls at the 12th grade level, suggests that there is a physiological explanation.  One of the candidates is brain size, though there is so much disinformation regarding the differences in brain sizes between races and  sexes that there  doesn't seem to be a final authority for such figures.  The most credible source for average brain sizes by race and sex is provided by J. Phillipe Rushton of the University of Western Ontario in Canada, who  shows that the average brain size for Asian men is 1,472 cubic centimeters (cc's), which is 21% greater than that for African women at 1,217 cubic cc's.

Should we expect that a 21% variation in brain size could account, at least partially, for a 121% variation in TIMSS scores?   Once brain size is correlated, by race and sex, with the Graduate Record Exam, International Assessment of Education Progress, TIMSS (Third International Math and Science Study), and TIMSS-R scores, we find the following values for r-squared:

 .8795 = GRE Quantitative .8073 = 12th Grade TIMSS Science* .7146 12th Grade TIMSS Math* .5766 = GRE Verbal .5692 = GRE Analytical .587 = 8th Grade TIMSS-R Math .5777 = IAEP Math

 Race & Sex TIMSS Math Cranial Capacity cc's ACT Math GRE Quanti tative NAEP Math Asian Boys 640 1,472 24.4 638 293 Caucasian Boys 588 1,416 22.4 586 286 Asian Girls 550 1,358 22.2 572 279 Indian Boys 500 1,299 19 525 268 Mexican Boys 519 1,326 19.4 517 255 Caucasian Girls 528 1,304 20 514 276 jew boys 476 1,266 18.2 470 255 Indian Girls 440 1,217 18 462 258 Mexican Girls 459 1,250 18.4 451 245 Nigger Boys 469 1,319 17.4 446 247 jew girls 456 1,246 17.7 451 251 Nigger Girls 430 1,217 16.4 404 237

Numbers in Red are estimates.

A partial explanation for the lower correlation for TIMSS-R Math and IAEP Math is that the countries used as examples are not 100% of any race.  Taiwan, France, and Mozambique were used for the IAEP correlation;  and Singapore, the Netherlands, and South Africa were used for the TIMSS-R Math correlation.   While these countries are as close to one race as any other countries, the 3 percent of blacks in the Netherlands, France, and Switzerland, the 15 percent of Whites in Mozambique and South Africa, and a few percent of non-Taiwanese in Taiwan would be expected to skew the results even further than the graphs indicate.   It can be seen from the graphs that correlation of TIMSS and IAEP would be closer to the correlation for GRE if such data were available by race rather than country.

*There are no 12th grade TIMSS scores available for any Asian nation because no Asian nation participated in that portion of the study.  So the 12th grade TIMSS score correlations are based on *estimates* of where Japan would be expected to have scored from reviewing the projected data.  Using these estimates for Japan and the actual scores for Switzerland and South Africa produced a correlation which is between that for GRE Quantitative and GRE Verbal.  It should be noted that their actual score might have been, and most likely would have been, higher than this estimate

Compared to African women, Asian men:

 Have a 21% larger cranial capacity. Score 70% higher on the 12th grade TIMSS. Score 58% higher on GRE quantitative. Earn 188% more.
 Brain Size Cubic Centimeters 12th Grade TIMSS Math 12th Grade TIMSS Science 8th Grade TIMSS-R Math IAEP Math GRE Quantitative GRE Verbal GRE Analytical Annual Incomes Asian men 1,472 590 585 614 73.1 638 490 566 \$55,358 White men 1,416 575 532 545 65.5 586 512 578 \$50,375 Asian women 1,358 480 478 594 72.4 572 484 552 \$37,916 White women 1,308 523 490 535 62.8 514 485 556 \$34,503 African men 1,319 365 367 280 28.8 446 399 429 \$28,075 African women 1,217 348 333 270 27.8 404 388 421 \$19,230

 Character assassination by Stephen Jay Gould, exposed by J. Phillipe Rushton http://www.lrainc.com/swtaboo/stalkers/jpr_gould_paid.html "Consider the following statistically significant comparisons (sexes combined) from recently conducted studies using the four techniques mentioned above. Using brain mass at autopsy, Ho et al. (1990) summarized data for 1,261 individuals. They reported a mean brain weight of 1,323 grams for White Americans and 1,223 grams for Black Americans. Using endocranial volume, Beals et al. (1984) analyzed about 20,000 skulls from around the world and found that East Asians, Europeans, and Africans averaged cranial volumes of 1,415, 1,362, and 1,268 cm3 respectively."

 Using endocranial volume, Beals et al. (1984, page 307, Table 5) analyzed 20,000 crania and found sex-combined brain cases differed by continental area. Excluding Caucasoid areas of Asia (e.g., India) and Africa (e.g., Egypt), 19 East Asian populations averaged 1,415 cm3 (sd = 51), 10 European groups averaged 1,362 cm3 (sd = 35) and 9 African groups averaged 1,268 cm3 (sd = 85). Using external head measure- ments, Rushton (1992) found, in a stratified random sample of 6,325 U.S. Army personnel, measured in 1988 to determine head size for fitting helmets, Asian-Americans, European-Americans, and African-Americans averaged 1,416, 1,380, and 1,359 cm3, respectively (see also, Rushton, 1994).

Within each race, the standard deviations for both sexes will be larger than for a single sex.  Where the standard deviation for Europeans is 35, or 2.6%, it is *possible* that the sd for one sex would be 18, or 1.3%.   The larger standard deviations for Asians and Africans may be due to a bigger difference between men and women than for Europeans.