I am wondering whether I can use z-scores to analyse variance and compare means - as though they were raw scores.

The project: Participants are divided into 4 different intervention conditions. I have pre- and post-intervention anxiety and depression scores, however participants did not use the same anxiety assessments or depression assessments for the duration of the data collection. Eg. with depression, half the participants used the PHQ9 to measure depression, half used the BDI.

Can I analyse the variance and compare the means using z-scores eg. a depression pre-treatment z-score which comprises PHQ and BDI pre-treatment scores (and the same for anxiety)? If not, is there another way I can compare the effect of the different conditions on outcome?

I have been trying to figure this out for days and have done lots of reading and online searching. So far all I've figured out is that I probably can't analyse variance like this (something to do with main effects being lost?). I don't know if this is correct, or what analysis I should do, if I can't use combined z-scores for the analyisis.

Thank you in advance, any help with this is appreciated,

Seon