I was taught in applied stats to verify the assumption of normality on my variables separated by group. For example, if I'm studying a continuous variable like weight (g) in two groups of subjects: A and B, and I'll use a t-test to test a hypothesis of the difference in means, I'd proceed to use plots and summaries (kurtosis, skewness) or even the least favored (Shapiro-Wilk, Kolmogorov-Smirnov, etc.) to assess normality.
If I do this and found one of the groups to deviate significantly from normality, I'd think of another approach to analyze the data or keep with normality after approximating through transformations. However, if I instead input the same data in a linear regression model with 'group' as an independent variable, I then reassess the distribution of my residuals, the normality assumption now holds.
- I know that the residuals are combined, but what are the fundamental differences between the two approaches?
- Wouldn't be wiser to use the last one?
- Why was this taught this way, is there a more appropriate way?
I also learned that several statistical tests have underlying linear models, so hence the question.