Lowering sample size in comparative analyses can indicate a correlation where there is none: example from Rensch's rule in primates.

The fact that characters may co-vary in organism groups because of shared ancestry and not always because of functional correlations was the initial rationale for developing phylogenetic comparative methods. Here we point out a case where similarity due to shared ancestry can produce an undesired effect when conducting an independent contrasts analysis. Under special circumstances, using a low sample size will produce results indicating an evolutionary correlation between characters where an analysis of the same pattern utilizing a larger sample size will show that this correlation does not exist. This is the opposite effect of increased sample size to that expected; normally an increased sample size increases the chance of finding a correlation. The situation where the problem occurs is when co-variation between the two continuous characters analysed is clumped in clades; e.g. when some phylogenetically conservative factors affect both characters simultaneously. In such a case, the correlation between the two characters becomes contingent on the number of clades sharing this conservative factor that are included in the analysis, in relation to the number of species contained within these clades. Removing species scattered evenly over the phylogeny will in this case remove the exact variation that diffuses the evolutionary correlation between the two characters - the variation contained within the clades sharing the conservative factor. We exemplify this problem by discussing a parallel in nature where the described problem may be of importance. This concerns the question of the presence or absence of Rensch's rule in primates.