3. It is not always easy to compare the size of various differences. The ideal way would be to have effect sizes for gender and other differences so the size of the difference could be directly compared. Unfortunately, the data necessary to calculate effect sizes are not always presented. However, some comparison is usually possible. For example Harold Stevenson, Shin-Ying Lee, and James Stigler reported that sex differences in China, Japan and the U.S. in three grades were nonsignificant, but data are not given separately for each gender making it impossible to calculate effect sizes for gender. The effect sizes for differences between countries range from a low of .05 to a high of 1.29. The largest country differences at each grade level are .88 (Kindergarten), .76 (Grade 1), and 1.29 (Grade 5). Although effect sizes for gender cannot be calculated, given that they are statistically nonsignificant and that the number of subjects are large (over 200 students in each country at each grade level), the effect sizes would be smaller than all but one of the nine comparisons between countries. Jinni Xu and Edwin Farrell present some of the most complete data comparing mathematics achievement across schools in China. The smallest effect sizes for gender are .004 and .046. The largest effect sizes for gender are .34 and .43. The smallest effect size differences between schools are .05 and .49. The largest effect sizes are 2.16 and 3.03. Two other studies make size of difference comparisons using statistics other than effect sizes. In a comparison of mathematics achievement across eight countries, Corrina Ethington used a median polish analysis and found gender effects in all cases to be smaller than country effects. For example for the whole test the gender effect was .16. The smallest country effect was 1.41 (France) and the largest country effect was 13.07 (Japan). Sandra Marshall compared students' mathematics achievement in California ethnic groups (Hispanic, Oriental, and Caucasian), social class (unskilled, semi- skilled, semi-professional, and professional), kind of problem (computation and story problems), and gender. Comparing the probability of a correct response across groups, she found that average gender differences ranged from zero to 5%. Social class differences ranged from 6% to 27%. Ethnic differences ranged from 8% to 30%.

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