Using transformed data in Cohen's d effect size calculations

Question

I have used a Log10 transformation on my data to transform some non-parametric data to normally distributed so that I could run a Pearsons correlation. Field (2013) states that only problematic variables need to be transformed to attempt to achieve normality, so this is what I did, and a pearsons correlation between my normal and transformed to nomrmality datasets and all seemed well.

However, now I want to calculate Cohen's d effect size using this data. I have averaged (mean) and calculated St. Dev for the data and have used this in the Cohen's d calculation (http://www.uccs.edu/~lbecker/), but obviously, comparing means and st.dev of transformed data (i.e. usually in minus figures) vs not transformed data is giving me some very strong effects.

If I compare non-logged data then the effect doesn't come from the same dataset as the data used in the pearsons correlation, but if I use the logged data, the effect sizes I am generating seem to be far too large.

Any thoughts/suggestions appreciated.

Answer 1

First, data can't be parametric or non-parametric, only models or tests can be.

Second, Pearson's correlation does not assume normality. Whether you want to use Pearson's or Spearman's rank correlation or some other measure depends on what you are trying to do.

Third, in my view, you should only transform data for substantive reasons, not statistical ones. If your data make more sense on the original scale, then leave them alone and find an appropriate method for dealing with them.

Fourth, you don't say what you are using Cohen's D for, but assuming it is a comparison of means, then, yes, clearly, you cannot compare the log of the variable to the variable itself and get anything meaningful. But why are you doing a t-test? If you did a t-test, why are you doing correlation?