I need to transform the score of a variable to z-scores, because of two different scales that were used according to the subjects' age. However, there are two groups: control and diseased. Do I compare the variable score to the mean and standard deviation of the control group i.e. z-score = (score - control mean)/SD in control group for each scale?
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It depends on what your purpose is. If you want to compare individuals with different scores within the same treatment group, you would use the mean and standard deviation of the treatment group they're in. If you want to compare the average score between treatment groups, you would use the overall mean and standard deviation. If you standardized within each group, the mean difference would be exactly equal to 0 (i.e., because the means of the Z-score within each group would be equal to 0). To retain the differences between the treatment groups, the Z-scores should be computed with respect to the whole sample.
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$\begingroup$ Thanks. Yes, I want to compare the two groups. Previously I was told that standardization had to be done in reference to the control group. $\endgroup$– JohannaCommented Feb 28, 2019 at 10:41
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$\begingroup$ Then it doesn't matter which mean you subtract from the scores and which standard deviation you divide by the scores, as long as you use the same mean and standard deviations for all units in the sample for each measure. Standardization just changes the units; there is no better or rose mean and standard deviation to use. You can use the mean and standard deviation of the whole sample, or of the control group, or of the treated group. It might be best for you to do what is most commonly done in your discipline. $\endgroup$– NoahCommented Mar 1, 2019 at 7:59