| Shapiro–Wilk test (best) |
normality |
small to moderate sample sizes (up to around 2000 observations) |
known for its power and reliability in detecting deviations from normality |
| Anderson–Darling |
normality |
larger sample sizes |
sensitive to deviations (tails) |
| Kolmogorov-Smirnov |
normality |
any sample size |
sensitive to differences in both location and shape between the sample distribution and the normal distribution |
| Lilliefors |
normality |
when the mean and variance of the population are unknown |
A modification of the Kolmogorov-Smirnov test that provides estimates of parameters from the sample data. |