Measure of Strength of Evidence for Visually Observed Differences between Subpopulations

For measuring the strength of visually observed subpopulation differences, the Population Difference Criterion is proposed to assess the statistical significance of visually observed subpopulation differences. It addresses the following challenges: in high-dimensional contexts, distributional models can be dubious; in high-signal contexts, conventional permutation tests give poor pairwise comparisons. We also make two other contributions: Based on a careful analysis we find that a balanced permutation approach is more powerful in high-signal contexts than conventional permutations. Another contribution is the quantification of uncertainty due to permutation variation via a bootstrap confidence interval. The practical usefulness of these ideas is illustrated in the comparison of subpopulations of modern cancer data.