If you have two groups (i.e. treated versus untreated) you would like to compare with a parametric analysis, should you determine if the dependent variable is normally distributed across all samples or is the normal distribution assumption apply to the distribution within groups and not between groups? It seems like the normality should be determined within groups because each sample set is theoretically from an independent population (one population being treated and one population being untreated). Any thoughts from the biostatistics community?
You are correct, the assumption for things like the t-test is that the residuals are normally distributed. If the two populations differ in means, then the distribution of the combined groups might be bi-modal (depending on how different the means are) even if both are normally distributed on their own.
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Yes, the normality should be examined within group. If they're not normal, you might want to consider performing tests which do not assume normality. Otherwise, you can try to transform your data to make them normally distributed.
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