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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'?

ajpat
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    No, as mentioned here (https://stackoverflow.com/questions/32479024/inverse-of-z-normalize-z-score-function-on-matlab) – Ahorn May 29 '20 at 13:08
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    No, information is lost in the transformation. If you don't record the original mean and sd, there is no going back. (Imagine the case of a single data point - if I give you a `4`, and tell you "Hey, I started with a number `x`, I subtracted a number `m`, and then divided by a number `s`, and `(x - m) / s = 4`. What was the original `x`?", there is no way you can answer without knowing both `m` and `s`. – Gregor Thomas May 29 '20 at 13:08
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    @GregorThomas Thank you for the clear explanation! – ajpat May 29 '20 at 13:35

1 Answers1

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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.

Tom Price
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