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We extend the work of Robinson and Turner to use hypothesis testing withpersistence homology to test for measurable differences in shape between pointclouds from three or more groups. Using samples of point clouds from threedistinct groups, we conduct a large-scale simulation study to validate ourproposed extension. We consider various combinations of groups, samples sizesand measurement errors in the simulation study, providing for each combinationthe percentage of $p$-values below an alpha-level of 0.05. Additionally, weapply our method to a Cardiotocography data set and find statisticallysignificant evidence of measurable differences in shape between normal, suspectand pathologic health status groups.

Extending Hypothesis Testing with Persistence Homology to Three or More Groups