This question has been answered before. See also: http://stats.stackexchange.com/questions/2492/is-normality-testing-essentially-useless and http://stats.stackexchange.com/questions/3514/what-is-the-normality-test-for-binary-data. You should make sure your question has not already been asked and answered before posting it as a new question.
– Marquis de CarabasJul 04 '15 at 10:01
1
If it's categorical data, it can't be normal.... Only variables that are least approximately continuous could possibly be (close to) normal. If this is unclear, please explain what you mean by "categorical" and/or give examples of categorical variables.
– Nick CoxJul 04 '15 at 10:12
The very best test is easy to compute, has an extremely low false positive rate in most settings, and a fabulous false negative rate of zero: without even looking at the data, conclude that the underlying distribution is non-normal.
– whuberJul 04 '15 at 14:52