Hey Respected Members
I am performing a regression analysis to check the normality of the residual data.
I performed TWO normality tests such as the Shapiro-Wilk normality test and the Anderson-Darling normality test.
With the Shapiro-Wilk normality test, the p-value is less than 0.05. Whereas, with the Anderson-Darling normality test, the p-value is greater than 0.5.
How should I interpret the result now?
Well, first A large p-value for the S-W test favors a normal population see:
Shapiro–Wilk test - Wikipedia Many PhD students miss this in their statistics courses. Now for A-D test See: Interpret all statistics and graphs for Normality Test - Minitab Wikipedia Express Large values of the A-D stat. favor non-normal distributions. Thus in summary:
Null HypothesisThe null hypothesis states that the data follow a normal distribution.Alternative HypothesisThe alternative hypothesis states that the data do not follow a normal distribution.
P-value
The p-value is a probability that measures the evidence against the null hypothesis. Lower probabilities provide stronger evidence against the null hypothesis.
Interpretation
The p-value is a probability that measures the evidence against the null hypothesis. Lower probabilities provide stronger evidence against the null hypothesis. Thus large p-values favor the non-normal distribution. Your p-value was large which favors which favors non-normal. A small p-value of S-W favors non-normal. your results:
S-W pnon-normal
A-D p>0.05 => non-normal
There is no contradiction . Your population is most likely non-normal.
Best wishes, David Booth
Thanks to the Wikipedia authors.
Based on your results for AD - accept the null hypothesis and assume that the errors has a normal distribution.SW - the opposite applies.
You may want to employ Ryan-Joiner test (which is a a simpler alternative to SW)
where, if p-value > 0.1=AD test.
There are different aspects in which a frequency distribution can deviate from a distribution model (it can have a different skew, a different kurtosis, fatter or thinner tails, is can have different modes, there can be a difference in som higher-order moment etc.). Different tests have a different sensitivity to detect particular deviations.
Since you consider SW "significant", you conclude that yourdata are sufficient to demonstarte the deviation of your data from the normal model the SW-test is testing (is most sensitive for). The deviation tested most sensitively by the AD test is not conclusive, so you would need more data to demonstrate the deviation regarding the properties the AD-test is most sensitive to. The fun part is that we actuallydon't really know what there properties are the two tests are particularily sensitive to.
As I understood you are using the normality tests to check the assumptionsof a (normal) regression analysis. This is bollocks. You see from my explanation abouve that the whole testing is completely useless for that purpose. Pradeep's suggestion to "accept the null hypothesis" if p>0.05 is based on a severely flawed logic about tests. There is no justification to accept a null hypothesis by the p-value of a significance test. Never ever. The only question a test can adress is: "do I have enough data to demonstrate that the (null-)hypothesis is sufficiently implausible?". The aim is to reject the hypothesis. If this is not possible, the data are inconclusive (regarding the tested hypothesis). So testing assumption this way is a no-go: if p
