Improvements to resampling measures of group support

Several aspects of current resampling methods to assess group support are reviewed. When the characters have different prior weights or some state transformation costs are different, the frequencies under either bootstrapping or jackknifing can be distorted, producing either under‐ or overestimations of the actual group support. This is avoided by symmetric resampling, where the probability p of increasing the weight of a character equals the probability of decreasing it. Problems with interpreting absolute group frequencies as a measure of the support are discussed; group support does not necessarily vary with the frequency itself, since in some cases groups with positive support may have much lower frequencies than groups with no support at all. Three possible solutions for this problem are suggested. The first is measuring the support as the difference in frequency between the group and its most frequent contradictory group. The second is calculating frequencies for values of p below the threshold under which the frequency ranks the groups in the right order of support (this threshold may vary from data set to data set). The third is estimating the support by using the slope of the frequency as a function of different (low) values of p; when p is low, groups with actual support have negative slopes (closer to 0 when the support is higher), and groups with no support have positive slopes (larger when evidence for and against the group is more abundant).