Meta-analyses reporting sex differences in personality and emotion or cross-cultural analyses that report significant sex differences often include samples of thousands of cases, while smaller studies conducted with n = 100 or n = 50 may fail to report sex differences for the same variables, even though means and standard deviations for these variables are similar across studies. This is because large sample sizes are associated with greater power in statistical hypothesis testing than small ones. Power is defined as the ability to reject correctly the null hypothesis (i.e., reject it when this hypothesis is wrong in the population), and power rises in proportion to the square root of sample size n. If sex differences in personality and emotion were large, then the null hypothesis of equality could be rejected with the use of relatively small samples, but if the differences are small (and it has been demonstrated several times that they are), the null hypothesis of equality of the sexes could not be rejected in small-n projects without sufficient power.
Not rejecting the null is not equivalent to proving that two groups are equal, and a lack of power raises the researcher's risk of committing a type II error (failing to reject the null when the null is false in the population).
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