How to sequence z-score creation and log transformation in an experiment with multiple groups and conditions? In a psycholinguistic task, participants listened to and viewed stimuli, and were asked to make acceptability judgements  on them:


*

*4 conditions 

*4 groups 

*Rating scale from 1-5


I have been advised to use z scores and log transformation (for R) on the ratings scores:
Questions:


*

*Should the ratings be computed into Z scores before log transformation?

*Should computation (whether z or log first) be done by group or for the whole data set?

*Should computation (whether z or log first) be done by condition or for the whole data set?

 A: I can't see any reason to log transform AFTER making z-scores; it COULD be right to log transform and then take z-scores of the logged data. I'm not as sure on the other questions, but my intuition would be to log transform everything, then take z-scores, then do the analysis. That way, a change of 1 in a variable is the same amount in every group.
A: There are a few things that you could want to do. The following discusses some plausible scenarios.
Comment on Log transforming z-scores


*

*In order to log transform z-scores, you would need to add a constant to the z-score, in order to ensure that the values of the z-score are all greater than zero. See my answer to this question on log transforming z-scores. It is unlikely that this is what you want to do.


Creating overall rating averaged across conditions


*

*log transform all ratings

*compute z-score for each condition, but use the mean and standard deviation of all groups combined but each condition separately.

*get the mean of each condition z-score.


This would provide one way of looking at differences between groups where in some sense each condition is weighted equally in the composite.
z-scores to aid interpretation of group * condition effects
Alternatively, if you wanted to look at effect of condition, then I imagine the z-score would be purely a tool to make the metric of the dependent variable a little more interpretable. In that case the procedure might look like:


*

*log transform all ratings

*Compute z-score for all ratings using means and standard deviations of all groups combined and for all conditions combined.

