Extending hypothesis testing with persistent homology to three or more groups

Abstract

We extend the work of Robinson and Turner to use hypothesis testing with persistent homology to test for measurable differences in shape between the spaces of three or more groups. We conduct a large-scale simulation study to validate our proposed extension, considering various combinations of groups, sample sizes and measurement errors. For each such combination, the percentage of p-values below an $\alpha$-level of 0.05 is provided. Additionally, we apply our method to a cardiotocography data set and find statistically significant evidence of measurable differences in shape between the spaces corresponding to normal, suspect and pathologic health status groups.