Section D.7 Discussion
This example demonstrates a strength of bootstrap resampling—it is easy to explore multiple test statistics and consider which is most relevant to the hypothesis in question.
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If we compare standard deviations of height, men are more variable, but that’s not too surprising—men are taller, and almost any process that makes bigger things probably makes more variable things, too.
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Coefficient of variation might be a better way to compare things with different sizes. By that standard, men are still slightly more variable, but the difference is so small, it’s hard to imagine it being practically significant.
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When we use more robust statistics that are less influenced by outliers—like MAD or IQR—the results are reversed: women’s heights are slightly more variable.
So whether men are more variable than women in height depends on how we measure variability. With robust statistics, the result is reversed. In any case, the differences are so small they have no practical consequences.
