# Can one apply different transformations to the same variable within different analyses?

My stats questions concerns the appropriateness of using different transformations of the same variable within different analyses (within the same larger study).

My research involves emotional expression as a dependent variable. I'm looking at 1) baseline differences between healthy controls (HCs) and individuals with a disease and 2) treatment effects within the disease group (Treatment Groups: HC-no-treatment, Disease-no-treatment, Disease-treatment 1, Disease-treatment 2). Each subject was assessed at baseline, post-treatment, and follow-up.

Research Aim 1. Baseline Differences Between Health Status Groups (Healthy Controls and Disease).
When looking at the emotion expression data, at baseline, by health status group (2: healthy controls and Disease), the raw data is not normally distributed (based on Shapiro-Wilk). Because square root transformation normalizes the distribution, I was planning on using a t-test (as opposed to Mann-Whitney) to assess baseline differences between the healthy control and disease groups.

Research Aim 2. Treatment Effects. When looking at the emotion expression data, by treatment group (HC, disease-no-treatment, disease-treatment1, disease-treatment2) at each time (baseline, post, follow-up), the raw is not normally distributed (based on Shapiro-Wilk). For these groupings, the square root transformation does NOT normalize the distribution. However, a log10 transformation does normalize the distribution.

Main Question: Can I use a square root transformation for Aim 1 and a different transformation for Aim 2 (e.g.,log10 in a mixed model ANOVA, or raw data if I end up using nonparametric stats for Aim 2)?

• "the raw data is not normally distributed" - why would this matter? What assumes raw data is normal? Mar 21, 2013 at 23:07
• By "raw data" I meant dependent variable, without applying any transformation. Does the t-test not assume normality of the dependent variable?
– dav
Apr 9, 2013 at 20:45
• It assumes the distribution of the dependent variable in the populations are conditionally normal - what is it that is being checked for normality? What kind(s) of non-normality do you observe? Note that when you transform the data, you're no longer estimating differences in means. Even if the t-test were unsuitable, depending on what you want to achieve you may be better off doing something other than transformation. Apr 9, 2013 at 21:16