Gender and Math: Putting Differences in Perspective
by Meredith Kimball
The construction of gender differences in mathematics achievement is neither simple nor straightforward. For example, the critical question of how large, or small, is this observed difference can be answered in several ways though typically it has been answered using statistical significance. That is, if the probability of a difference of a certain size is low, the researcher makes the judgment that the difference, if found, is large, or at least large enough to be noteworthy. Because statistical significance depends on sample size, two further specific problems arise. If very large samples are used, very small and meaningless differences will be significant; if small samples are used, even medium-sized and perhaps meaningful differences will not be statistically significant.
In order to overcome these problems, feminist psychologists have been instrumental in developing and applying a technique called meta-analysis. Ignoring the statistical significance of the findings, the first step in a meta-analysis is to calculate an effect size 2 for each measurement of gender difference. The smallest possible effect size is zero, indicating that the two groups are identical on the particular measurement used. By convention, effect sizes of .20 are considered small, .50 medium, and .80 large (Cohen). Although there is no absolute upper limit to an effect size, in the measurement of human group differences effect sizes of 2.0 to 3.0 are about the largest ones found.
Effect sizes can be expressed in more common sense ways. For example, one national U.S. study of mathematics achievement found an effect size favouring males of .23 (small). This means that 56% of the males and 44% of the females were above the median (mid-point) score for the combined male and female samples. In other words, if one female's score were drawn randomly and compared to one randomly drawn male score, the male's score would be higher 56% of the time. Another study of mathematics achievement found an effect size favouring males of .48 (medium). In this case 62% of males and 38% of females scored above the combined mid point and given two randomly drawn scores, the male's score would be higher 63% of the time (McGraw & Wong).
In the empirical studies of mathematics achievement, two types of measurement have been used: standardized tests and classroom grades. By far the greatest bulk of work has been and continues to be concerned with performance on standardized tests. Janet Hyde and her colleagues (1990a) provide the most thorough review of these studies in a meta-analysis of gender differences. Their examination of over 250 effect sizes yielded a small average effect size of .20 that favoured males. The size of the difference varied considerably depending on the context of the study. For example, in samples of precocious adolescents in special accelerated math programs the difference favouring males was larger (.41).