When should we apply normality tests? For which types of the variables should we apply the normality test? For example dependent variables, independent variables, or control variables, etc?
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Readers here may find this thread of interest: [what-if-residuals-are-normally-distributed-but-y-is-not](http://stats.stackexchange.com/questions/12262/). – gung - Reinstate Monica Mar 14 '13 at 05:04
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In many contexts (e.g., multiple regression) it is the distribution of the residuals that is the relevant assumption (see here for a discussion).
Your question also raises the general issue of the relevance of normality testing. See this previous question: Is normality testing 'essentially useless'?
However, more broadly, doing exploratory data analysis (e.g., plots, summary statistics, etc.) to understand the distribution of all your variables is important.
Jeromy Anglim
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I agree with Jeromy. There is no sense to categorize application of normality testing in terms of types of variables. What matters is when normality becomes a modeling issue. There are many pros and cons associated with normality testing that are discussed in other posts on this site including the one Jeromy mentioned. – Michael R. Chernick Aug 23 '12 at 10:57
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+1 for "However, more broadly, doing exploratory data analysis (e.g., plots, summary statistics, etc.) to understand the distribution of all your variables is important". – gung - Reinstate Monica Mar 14 '13 at 04:53