Using the Shapiro Wilks test my data proved normally distributed, the Anderson darling test proved the same data was not normal, which test result do I go with when testing for normality? (My sample size is 40).
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Neither test "proved" anything. You are better off plotting your data so you can understand *how* they are distributed and then relate that to what you ultimately want to do with your data (testing Normality almost never is the final objective of data analysis). Use a Normal QQ plot. – whuber Feb 09 '21 at 14:54
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[some answers here](https://stats.stackexchange.com/questions/90697/is-shapiro-wilk-the-best-normality-test-why-might-it-be-better-than-other-tests?rq=1) – John L Feb 09 '21 at 16:10