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I checked my data to know if they're normally distributed using SPSS. Test of Normality table However, I saw that KS test and SW test gives different significance values. They give conflicting significance values, KS test says that one is normally distributed while SW test says it not, and vice versa. Which test of normality will I follow?

sammyyy
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    Why do you want to know that your variables are normally distributed – Maarten Buis Oct 10 '17 at 14:13
  • I want to compare their means. Specifically, I want to determine if there are differences between the means of the three groups (Indigenous, Non-indigenous-public, Non-indigenous-private) – sammyyy Oct 10 '17 at 14:21
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    Most of the methods for comparing means would probably be robust against small departures from normality so as @MaartenBuis wisely remarks, why bother? – mdewey Oct 10 '17 at 15:31
  • Knowing if the data is normal or not would be my basis in choosing the proper test that will be used. Am I right or wrong. Please enlighten me. :) – sammyyy Oct 10 '17 at 15:42
  • This is closely related to [Conflicting Normality Tests](https://stats.stackexchange.com/questions/81477/conflicting-normality-tests) and arguably a duplicate of it. – Silverfish Oct 10 '17 at 19:29

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