I am busy reading through some online course material, and was flying through the section on correlation. To my great surprise, I came across the following paragraph just below a graphic of a normal probability plot of correlation residuals (highlighting is my own):
"As you can see the Normal probability plot of residuals evaluates the Normally Distributed response assumption. The residuals should lay near the straight line to within a fat pencil. Looking at a Normal probability plot to determine Normality takes a little practice. Technically speaking however it is inappropriate to generate an Anderson-Darling or any other Normality test that generates a Pvalue to determine Normality. The reason is residuals are not independent and do not meet a basic assumption for using the Normality tests. Dr. Douglas Montgomery of Arizona State University coined the phrase “fat pencil test” much to the chagrin of many of his colleagues."
Firstly I was really shocked to see this in print; my understanding is that one should only use a normality test (e.g. K-S, Lilliefors, SW) to evaluate normality of residuals. But then I have tried to verify the statement regarding normality tests being technically inappropriate to assess normality of residuals but I cannot find anything conclusive.
Hi , Dougan. The contents seem to be cited from another product but not Statistica. Here is the link that seems to contain those contents. I understand you are asking the validity of using normal probability plot to assess residual normality compared with using normality test. Under Statistica|Descriptive statistics, there are options to obtain both the normality test statistics and the normal probability plot. Unfortunately, we at technical support team are not legally defended to offer any statistical consulting regarding which method you should choose. We are here to assist you with software related questions. We have a Professional Service Team that offers billable statistical consulting service. If you are interested in , I can have them to contact you. In addition, you may want to consider other resources/forum targeted for general statistical questions.