Comparing Z-scores & log transformed data

Question

I have data for multiple cohorts - some cohort level data has been normalized via Z-scores, and some has been normalized via log transformations. (Agh.) Is there any way to compare them? Can I convert the Z-scores back to raw data, then log transform them? (I do have the mean & SD for the raw data of the Z-scored cohorts).

Also - I saw this post: How to log transform Z-scores?, but as I have multiple cohorts I need to be sure that the data is all on the same scale / transformed in the same way.

Any thoughts would be helpful.

Answer 1

Converting to a common metric (either log- or Z-scores) seems like the best strategy-- you should be able to recover the original scores exactly as you'd expect -- take exp(log-scores) and mean + (sd*Z-scores). If the data is inherited, it may be worth inquiring why a previous analyst chose one metric over the other (does the data quite skewed?) before you choose whether to convert all cohorts to one or the other.