When using T-test to compare two group means, say group A and group B, I usually transform data to normal distribution if possible.
Before doing that, if the sample size is enough, I usually use Q-Q plot to see if the data set is normally distributed. Maybe I've been doing this wrong for many years, but what I usually do (and have been taught) is draw Q-Q plot for the whole variable (ignoring group A or group B). But what T-test assumes is that A and B are from normal distribution separately. And it is true that even when both A and B is from normal distribution with different means, the Q-Q plot of whole variable is not on the straight line.
My question is that what do you usually do to test normality? Q-Q plot together or separately? shapiro wilk test together or separately? Anderson Darling test together or separately?
If together, then two normal distribution will result a non-normal distribution. If separate, what would you do to transform them? Transform them using one method together? Thank you!