Empirical comparison of distance equations using discrete traits.

The use of the Grewal-Smith statistic in measuring biological distance among skeletal population samples has been questioned since it was first applied to human populations. Recently, in an attempt to stabilize the variance of the Grewal-Smith statistic for use with non-metric analysis, Sjøhivold ('73) and Green and Suchey ('76) have introduced corrections and alternative transformations which may enhance the meaning of biological distance among population samples. Their recommendations improve the statistics for specific variable ranges; i.e., small sample size and low trait frequencies. Thirteen equations representing Grewal-Smith, Freeman-Tukey, Anscombe, and Bartlett transformations and/or corrections, were compared using rank order correlation statistics on actual biological distances generated by real population data as presented in existing literature. Results from testing these actual distance models show little variation between equations based on the populational data sets used. Based on these findings, the distance model resulting from the Grewal-Smith statistic is not inferior to the more sophisticated models, although the latter may be superior allowing specific improvements for small sample size and/or low trait frequencies.