McNemar’s test and Simpson’s Paradox (and the “hot hand” in basketball)

hot hand basketball

(I wrote this paper in 2007 for a Statistics class I took while trying to do a PhD. I am sharing it here for posterity.)

McNemar’s test is a non-parametric method used on nominal data to determine whether the row and column marginal frequencies are equal. It is applied to 2×2 contingency tables with a dichotomous trait with matched pairs of subjects.

Simpson’s paradox is a statistical paradox in which the successes of several groups seem to be reversed when the groups are combined. This seemingly impossible result is encountered often in social science statistics, and occurs when a weighting variable, which is not relevant to the individual group assessment, must be used in the combined assessment.

The paper evaluates the potential effect of Simpson’s paradox in McNemar’s test results and conclusions.

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