Testing for Normality
Many inferential statistical procedures require that data be normally distributed. Here are a few ways to check if this is the case.
Note that the conventional wisdom that these tests must be applied before using normal theory statistical procedures is debated (see here and here). Unless the sample size is very small, it is probably best to proceed with the statistical procedures when the data are approximately normal. Assessing approximate normality might best be accomplished using the graphical methods below.
Histograms or density plots
These test AGAINST the null hypothesis that the data tested are normal. Low p values reject the null hypothesis, meaning that the data cannot be assumed to be normal. High p values fail to reject the null, and the data may (or may not) be normally distributed.