Is it better to compare Z-scores between two groups, or the actual (non-normalized) scores?     Let's say I have reading scores from two schools, and these scores have had z-scores calculated, normalized to a larger external population's scores. (Therefore each Z-score indicates where the student's score would lie within the larger population if they were members of that population).  Should I compare the Z-scores of students between these two schools, or would it be better to compare the actual (untransformed) reading scores between the two schools?  I did it both ways with t-tests and got slightly different t-values and resulting p-values.