The following from the UNIVARIATE chapter of the SAS Procedures Guide explains how to interpret the results of the NORMAL option tests:
- You determine whether to reject the null hypothesis by examining the probability that is associated with a test statistic. When the p-value is less than the predetermined critical value (alpha value), you reject the null hypothesis and conclude that the data does not come from the theoretical distribution.
- If you want to test the normality assumptions that underlie analysis of variance methods, beware of using a statistical test for normality alone. A test's ability to reject the null hypothesis (known as the power of the test) increases with the sample size. As the sample size becomes larger, increasingly smaller departures from normality can be detected. Since small deviations from normality do not severely affect the validity of analysis of variance tests, it is important to examine other statistics and plots to make a final assessment of normality. The skewness and kurtosis measures and the plots that are provided by the PLOTS option, the HISTOGRAM statement, PROBPLOT statement, and QQPLOT statement can be very helpful. For small sample sizes, power is low for detecting larger departures from normality that may be important. To increase the test's ability to detect such deviations, you may want to declare significance at higher levels, such as 0.15 or 0.20, rather than the often-used 0.05 level. Again, consulting plots and additional statistics will help you assess the severity of the deviations from normality.