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)?