Fig. 3

Pairwise scatterplots exploring associations between Kruskal–Wallis (KW) P value with other measures. The panels here present a selection of pairwise plots to illustrate the relationships between the imbalance metric we used in our randomization algorithm, the KW test P value, and additional candidate imbalance metrics explored. Each plot includes 5000 observations from the resampled scenarios using 1:3:3 allocation as in our present study. In each plot, there is often a non-linear relationship. For example, the first plot illustrating min(KW P value) in comparison with the multivariate analysis of variance (MANOVA) demonstrates a somewhat noisy relationship between the two whereby the min(KW P value) tends to be lower than the overall MANOVA P value, but the two are related. The comparison of the min(KW P value) versus the min(Wilcoxon rank-sum [WRS] P value) shows a more pronounced relationship and a clearer, non-linear pattern. All metrics of imbalance as determined are highly related; broadly, the more global tests (e.g., MANOVA) tended to be less conservative (i.e., have larger P value) than the corresponding more specific tests based on more than one comparison (e.g., WRS). The line y = x has been added for reference