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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?
Jeromy Anglim
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Carol Jaensch
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  • The construction of z-scores *guarantees* some will be negative. You can't take their logarithms. The answers to the remaining questions depend on what you intend to do with the transformed data. – whuber Oct 13 '11 at 21:45
  • @Carol I've assumed that condition is within-subjects and groups is between subjects. is this correct? – Jeromy Anglim Oct 13 '11 at 22:13
  • Thanks for the many comments. Yes - condition is within subject and groups is between subject. – Carol Jaensch Oct 14 '11 at 15:43

2 Answers2

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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.

Peter Flom
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There are a few things that you could want to do. The following discusses some plausible scenarios.

Comment on Log transforming z-scores

Creating overall rating averaged across conditions

  1. log transform all ratings
  2. compute z-score for each condition, but use the mean and standard deviation of all groups combined but each condition separately.
  3. 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:

  1. log transform all ratings
  2. Compute z-score for all ratings using means and standard deviations of all groups combined and for all conditions combined.
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Jeromy Anglim
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  • Thanks again, Jeromy. The data will be used for GLM mixed effect in R. I think your last solution is probably the best, although I am not convinced that Z-scores should be computed across all ratings. If the z-scores represent a value against a particular population, shouldn't I split it by group, given that one group (eg adults) may perform differently than another (eg young children), and therefore represent a different population? – Carol Jaensch Oct 14 '11 at 15:55