Interpreting statistical significance in hominin dimorphism: Power and Type I error rates for resampling tests of univariate and missing-data multivariate size dimorphism estimation methods in the fossil record.

The degree of sexual size dimorphism in fossil hominins is important evidence for the evaluation of evolutionary hypotheses, but it is also difficult/impossible to measure directly. Multiple methods have been developed to estimate dimorphism in univariate and multivariate datasets, including when data are missing. This paper introduces 'dimorph', an R package that implements many of these methods and associated resampling-based significance tests and evaluates their performance in terms of Type I error rates and power. Tests evaluated here are those that appear most commonly in the hominin literature: testing whether a fossil sample is significantly more dimorphic than a comparative sample of known dimorphism. Univariate and multivariate methods are applied to metric data from four extant hominoid species: Gorilla gorilla, Homo sapiens, Pan troglodytes, and Hylobates lar. Each species is represented by 47 female and 47 male adult individuals, from which 10 linear postcranial measurements are collected. Data are resampled at a broad range of sample sizes (n = 4 to n = 82), sex ratios (proportion of females range from 0 to 1), and in the case of missing-data methods, proportions of missing data (0-0.9). Type I error rates and power are evaluated by the proportion of tests correctly or incorrectly rejecting null hypotheses regarding dimorphism difference within pairs of samples drawn from these four species, in which one sample stands in for a fossil sample. Results indicate low Type I error rates for all methods, whereas power is variable across methods but often low at sample sizes common to fossil analyses. Recommendations are made for the best significance tests. Additionally, previous work using lack of significant difference as evidence for similarity in dimorphism between fossils and extant species should be re-examined to determine whether those studies have enough power to detect known differences among extant taxa.