Hi.
I am dealing with data that shows negative skewness and variables that were calculated in different ways: Some of the variables´ composites were calculated from the mean, but others had subscales and the composite was calculated by substracting one subscale from the other which results in a range that crosses the 0 (i.e., positive and negative values).
My question is: Does it make sense to transform the variables in the way that they all have the same lower and upper limits? And can I/ should I then further log-transform them to deal with the non-normality? Do these transformations conflict with running correlations and further analyses on the data?
Thank you.
Hello Carina,
1. It's not necessary to transform variables so that they have common scale limits. In some applications, having variables on a common scale (specifically, the same SD) can be helpful: Cluster analysis in which distance measures are used for the proximity matrix is one example (otherwise, the variable with largest SD dominates the development of the clusters).
2. Negative skewness will be exacerbated, not ameliorated, by apply a log transform. If you first reflect the data (e.g., new score = Max score + 1 - old score), then apply a log (or root) transform, you'll have better success. The direction of the scores, however, is now reversed, so be careful about interpretation.
3. Non-linear transformations can and will affect correlations among variables. Linear transformations (adding/subtracting/multiplying/dividing scores by a constant) do not. Z-scores and common scale limits are examples of linear transforms. Log and root are examples of non-linear transforms.
4. A difference score (subtracting one score from another) is less reliable than either of the scores from which it was created, unless both scores are perfectly reliable.
Good luck with your work.
Just for your information;
Article TO DETERMINE SKEWNESS, MEAN AND DEVIATION WITH A NEW APPROAC...
Hello David Morse, thank you for your answer!
Regarding point 1: We have used scales that require different ways in which they are caluclated. For example, while for some scales, we could simply calculate the mean as a composite, for other scales, subscales had to be substracted from another first, so that overall, the scales range from 1 - 9 (where we could use the mean) to -18/ +23 (where subscales had to be considered). Since the scales are so different, I guess it will hardly be possible to interpret their relationships without adjusting the scales.
On top of that, we witnessed the negative skew in basically all scales. This is why my question consisted of two parts.
If I understand you correctly, I could deal with the scales first (so that they are comparable) and then transform them to deal with non-normality, correct? Regarding the interpretation issue; would I perhaps be better off adjusting the scales and then use non-parametric tests instead?
Thank you.
Hello again Carina,
If you absolutely, positively have to have all variable scores to be on a common scale, I'd suggest thinking about something simple, like z-scores. That, at least, equalizes the SDs.
Transformations can be applied at any point, though if you subsequently apply any non-linear transform, then you need to re-check for whatever distributional attributes you seek. A linear transform, however (e.g., z-scores) will not change distribution shapes (just recenters and fixes SD to specific value).
Finally, consider using bootstrap/resampling methods; going this route allows you to discard your worries about normality of distributions and focus on what's going on in your data set. More statistical packages include this as an option these days.
Good luck with your work.
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