One Sample Test

statistical advice: One common, though misguided technique is to pre-screen variables used in other parametric analyses using this test. For example, one might check the normality of the residuals of a regression as a diagnostic technique. Hypothesis testing is fundimentally the wrong tool to use. At small sample sizes normality hypothesis tests will be insignificant even in the presence of large deviations from normality due to lack of power. At large sample sizes, data that is nearly normal (nothing is ever exactly normal) will trigger a significant normality test because the test has the power to detect even the smallest deviations from normality. These are precisely the opposite types of miscategorizations that an analyst wishes to make. Most statistical tests are robust to large departures from normality provided the sample size is large enough. So normality matters most in the situations where you have no statistical power to detect it.

A better alternative to normality testing is to examine the histogram. Is it skewed or roughly symmetrical? Are its tails fat? If your sample is small and your variable is skewed you can try switching to non-parametric methods or transforming the variable so it looks more normal. Alternatively if you can program, you can run simulations to assess the procedure's sensitivity to departures from normality.