# Transforming Cohen's d effect sizes into unit changes

I want to calculate unit changes (or percentile changes) from an intervention for a continuous outcome variable where I have the pre and post test means and standard deviations. From that I can calculate a Cohen's d, but I want to use the result for a CBA and therefore have to transform Cohen's d to unit changes. I am looking at symptoms for different mental disorders, and not specifically diagnosis/non-diagnosis.

An idea is to use a cut-off on the normal distribution, for instance 90th percentile, which then determines diagnosis/non-diagnosis. Is it a sound approach to (from a z-score table) start at the 90th percentile, see where I end up in the distribution after the given effect size (Cohen's d), and thereby find the percentile change from the intervention for the 90th percentile of the sample population?

If yes, can I then turn that percentile into percentages by dividing the percentile change by .5 and multiply it by 100?