17.3 Beyond Hypothesis Testing

If a chi-square analysis had supported the hot-hand theory, we would want to know more about this particular finding. For example, we might ask how large a difference the hot hand made to a particular athlete’s performance and we might want to see the difference in a graph. Most nonparametric hypothesis tests do not have associated effect-size measures, but chi square does. We’ll introduce Cramer’s V, the effect size for chi square, as one method to determine how large a finding is. We’ll then show how to depict chi-square findings visually in a graph so that we can see how large the effect is. We’ll also demonstrate how to calculate relative risk, another way to understand the size of an effect by quantifying the chances of a given outcome. Finally, we’ll show how to conduct a type of post hoc test that can be used to determine exactly where any differences lie among the cells of a chi-square design.