Advice on testing the null hypothesis that a sample is drawn from a normal distribution

The normal distribution remains the most widely used statistical model, so it is only natural that researchers will frequently be required to consider whether a sample of data appears to have been drawn from a normal distribution. Commonly used statistical packages offer a range of alternative formal statistical tests of the null hypothesis of normality, with inference being drawn on the basis of a calculated P value. Here we review the statistical literature on the performance of these tests and briefly survey current usage of them in recently published papers, with a view to offering advice on good practice. We find that authors in Animal Behaviour seem to be using such testing most commonly in situations in which it is inadvisable (or at best unnecessary) involving pretesting to select parametric or nonparametric analyses, and making little use of it in model-fitting situations in which it might be of value. Of the many alternative tests, we recommend the routine use of either the Shapiro-Wilk or Chen-Shapiro tests; these are almost always superior to commonly used alternatives such as the Kolmogorov-Smirnov test, often by a substantial margin. We describe how both our recommended tests can be implemented. In contrast to current practice as indicated by our survey, we recommend that the results of these tests are reported in more detail (providing both the calculated sample statistic and the associated P value). Finally, we emphasize that even the higher-performing tests of normality have low power (generally below 0.5 and often much lower) when sample sizes are less than 50, as is often the case in our field.