A note on two-sample tests for comparing intra-individual genetic sequence diversity between populations

Gilbert, Rossini, and Shankarappa (2005, Biometrics 61, 106-117) present four U-statistic based tests to compare genetic diversity between different samples. The proposed tests improved upon previously used methods by accounting for the correlations in the data. We find, however, that the same correlations introduce an unacceptable bias in the sample estimators used for the variance and covariance of the inter-sequence genetic distances for modest sample sizes. Here, we compute unbiased estimators for these and test the resulting improvement using simulated data. We also show that, contrary to the claims in Gilbert et al., it is not always possible to apply the Welch-Satterthwaite approximate t-test, and we provide explicit formulas for the degrees of freedom to be used when, on the other hand, such approximation is indeed possible.