Resolving network clusters disparity based on dissimilarity measurements with nonmetric analysis of variance

Classic ANOVA (cA) tests the explanatory power of a partitioning on a set of objects. More fit for clusters proximity analysis, nonparametric ANOVA (npA) extends to a case where instead of the object values themselves, their mutual distances are available. However, extending the cA applicability, the metric conditions in npA are limiting. Based on the central limit theorem (CLT), here we introduce nonmetric ANOVA (nmA) that by relaxing the metric properties between objects, allows an ANOVA-like statistical testing of a network clusters disparity. We present a parametric test statistic which under the null hypothesis of no differences between the competing clusters means, follows an exact F-distribution. We apply our method on three diverse biological examples, discuss its parallel performance, and note the specific use of each method tailored by the inherent data properties. The R code is provided at github.com/AmiryousefiLab/nmANOVA.