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I am undergraduate student and I have a problem in my research. Recently, my supervisor told me that if using secondary data no need to perform normality test, why? It is got any citation or previous research prove this?

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The need to perform a normality test has nothing to do with the data source, in general. And the reasons for doing normality tests (which are sometimes not sensitive enough to detect non-normality) are few, especially once your know about nonparametric/robust methods. Nonparametric (rank-based) methods are often more powerful than parametric methods that rely on normality assumptions.

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