Statistical Glossary

Normality tests are tests of whether a set of data is distributed in a way that is consistent with a normal distribution. Typically, they are tests of a null hypothesis that the data are drawn from a normal population, specifically a goodness-of-fit test. Hence, while it is possible to reach a definitive conclusion that a set of data is not normally-distributed (by rejecting the null hypothesis), the most one can say if the null hypothesis is not rejected is that the data could possibly come from a normally distributed population. See Lilliefors test for normality.