I measured behavioral data (human body inclination) of two different groups (each, 15 subjects) in three different moments (sessions), the data was not normal (Shapiro-Wilk test) and did not respect homogeneity of variance (Levens' test). I ran non-parametric test (Mann-Whitny U test for independent comparisons and Friedman and Wilcoxon sign-rank test for paired sample comparisons).
The reviewer of my article asked me to transform data to be normal and then run parametric test (rmANOVA). I applied many transformation, only one of them was good: the LMS approach proposed by Cole and Green (1992). It is also known as LMS quantile regression with the Box-Cox transformation to normality as well as it is known as Box-Cox Cole-Green (BCCN) transformation. The formula is: Z = ((y/μ)^L-1) / (S*L), where L is a constant parameter, μ is the mean value and S is generalized coefficient of variation (i.e., σ/μ and σ is standard deviation). It is not so common transformation.
My question is: can I use any kind of transformation in the literature to transform data to meet the assumptions of parametric test in statistical analysis like rmANOVA? Or, I should just use the transformations that are famous in the field that I am working?
Many thanks in advance for your comments!
Cole TJ, Green PJ. Smoothing reference centile curves: the LMS method and penalized likelihood. Stat. Med. 1992;11:1305–1319.
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