During my calculations I need to use square roots but z-scores can be negative.
Is there a trick to transform them into positive value without missing the usefulness of z-scores?
What if I have not a single distribution but more than one to compare each other?
Edit for details
I have two ranks calculated using z-scores (they rank student performance using different metrics) and I want to make a geometric average between the two rank, but as z-scores has negative values I cannot perform square root on negative results.
Eg: if student Foo has a score of 2 on the first rank and a score of -2 on the other i cannot make the square root of -4.
If there is a method to convert the scores into positive values I can perform geometric average.
For example when I use percentage I add one to the value divided by 100 (eg -80% and +50% become 0,8 and 1,5). Is there a trick like this that works on z-scores?