X-linked genetic differences between male and females have been posited to cause greater variance in cognitive ability in males. Males with only one X chromosome tend to express the genes on the X chromosome more fully than females, who express an "average" of their two X chromosomes due to X-inactivation. Greater variability in expression of genes on the X chromosome could account for greater variability in male cognitive ability. This would affect both the high and low ends of the cognitive ability distribution, but the possibility of high-end impact has drawn the most attention and controversy. The objective of this paper was to outline a method to test for empirical evidence that greater X-chromosomal variation in males is associated with greater variation in cognitive ability in males at the high end of the distribution. The method utilizes exogenous variation in the maternal X chromosome of twins to test the effect of sex on within-pair variation. We applied this method to g composite test scores at age 10 using data from the Twins Early Development Study. Twin-pair zygosity was used as an instrument reflecting whether twins had different maternal X chromosomes. We estimated differences in the association between variation in the maternal X chromosome in males and females and within-pair variation in test scores using a difference in differences specification of a linear regression model. We found no evidence supporting the proposition that the "averaging" effect of X-inactivation in females resulted in greater variation in male cognitive ability. There was evidence of differential selection for cognitive ability in the sample, however, indicating that the value of our study was primarily to introduce a novel method of addressing the question.