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Many statistical methods assume data or a model's residuals are normally distributed. Use this tag for questions about the assumption & testing of normality, or about normality as a *property*. Use [normal-distribution] for questions about the normal distribution per se.
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Checking assumption of normality with multiple subsets of unequal size
There are a lot of normalitytests. For instance the Shapiro-Wilk–test. I would test for each subsets, because this is what you want to know.