In repeated dose administration toxicity studies, which are regulatory requirements for the safety evaluation of drugs, pesticides, etc., the analysis of between-group differences is typically carried out using either parametric or nonparametric statistical methods. The choice of the method depends on whether the data distributions within the groups are normal or not, and or are homogeneous. In theory, testing for normality is important because many parametric tests, such as the t-test and ANOVA, assume that the data within each group follows a normal distribution. However, in repeated dose administration toxicity studies, the data are not always explicitly tested for normality. One reason for this is that there is no universally accepted threshold for deciding whether data is “normal enough” for parametric tests. Another reason is the power of normality tests varies depending on the sample size. In repeated dose administration studies, the number of animals in each group is often small (5–20). In such cases, normality tests may not provide meaningful results due to low statistical power, and the decision to use a parametric or nonparametric test often relies on other considerations, such as variance. It is a common practice to use equal-variance tests (for example Bartlett’s test, Levene’s test, etc.) to determine whether parametric or nonparametric methods should be used for analyzing data. In repeated dose administration toxicity studies for assessing normality the Shapiro-Wilk’s W (Shapiro-Wilk) test is recommended.