If you have a data vector you are given that contains only z-scored variables is it possible to reverse the z-score values to get the original measure without using the original measure? In R Program:
a = runif(100)
az = (a - mean(a))/sd(a)
Can you get back 'a' using JUST 'az'?
No, it is not possible. The reverse transformation requires knowledge of the summary statistics mean(a) and sd(a), which cannot be recovered from the standardized scores.