Normality Test

Given a sample from some population, the normality test is intended to assess the following assertion:

The sample is selected from a population that is normally distributed.

SAS provides the normal option to be used with proc univariate to conduct a normality test. Pages 137 through 139 of your SAS text provides syntactic details as well as some insight into the interpretation of the statistic and p-value produced but does not present a decision rule for the p-value. Following is the decision rule that should be used:

  1. If the p-value is less than or equal to 0.05 reject the assertion and conclude that the sample could not have been selected from a normal distribution.
  2. If the p-value is greater than 0.05 then you have insufficient evidence to question the assertion and so you should treat the assertion as reasonable.

Note: See the material on hypothesis testing for a more formal treatment of this topic.