Alternative Methods For Dealing With Nonnormality And Heteroscedasticity In Paleontological Data

Although numerical methods are highly useful in paleontological studies, potential problems arise with application of parametric statistical methods to paleontological data. Most common statistical tests assume data are normally distributed and that multiple populations have equal variances (homoscedasticity). Paleontological data frequently do not satisfy these assumptions, thereby affecting results of tests and potentially misleading scientific interpretations. Nonparametric tests should be used when assumptions of parametric tests are violated. Normal scores tests, which utilize expected normal deviates (rankits) substituted for original data, are the most powerful nonparametric tests. Despite their potential utility, normal scores tests have received little attention, primarily because of difficulties encountered with rankit conversion. Recent advances in microcomputer technology provide viable methods for rankit conversion, thus making normal scores tests accessible for routine application. Normal scores tests provide a practical method of dealing with nonnormality and heteroscedasticity common in paleontological data.