Interpretation of univariate test for normality

[Omenski]

How do I interpret test for normality results using SAS? I have ran the univariate for my data and obtained the results attached. From the probability which is the criteria for accepting or rejecting the normality test? Which of the three methods is best to use? Thanks

[PaigeMiller]

Most of us will not download Microsoft Office documents, as they are a security threat. Please paste your results right into your reply.

[PGStats · Accepted solution]

There is no best method. Each test looks at different aspects of distributions. Thus the minimum p-value among the tests is the one to consider. It tells you about some aspect in witch your distribution differs the most from the normal distribution.

But please consider the pitfalls of normality testing explained here. Most specifically:

"If you want to test the normality assumptions for 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. Because 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, the PROBPLOT statement, and the QQPLOT statement can be very helpful. For small sample sizes, power is low for detecting larger departures from normality that might be important. To increase the test’s ability to detect such deviations, you might 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 can help you assess the severity of the deviations from normality."

[Omenski]

Thanks for the information highly appreciated

[Rick_SAS]

For almost all statistical tests, you should REJECT the null hypothesis when the p-value is smaller than your significance criterion (typically 0.05 or 0.01). The null hypothesis for these tests is that the observed data comes from a normal distribution (with an unknown mean and variance). 

So "small p-value" ==> the evidence does not support the hypothesis that the data are normal.

"Large p-value" ==> we cannot discount the hypothesis that data are normal.

As to which is better, that question has been asked in many papers and books. Often they give similar results. The Wikipedia article for these tests states some of the advantages/disadvantages of the tests. For example, start with the Anderson-Darling test.

[Omenski]

Thanks guidance highly appreciated