I have a data with distribution like chisq-squared one. But ANOVA and t-test need the data to be normal distributed. So I want to do the Box-cox transformation to the data, but my concern is will the analysis result hold for the original data?
2026-03-30 07:07:40.1774854460
Will statistical analysis of transformed data hold for the original one?
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Yes and no:
If you successfully transform your data so that it looks normal, then the ANOVA will apply to the transformed mean only, not the "back-transformed mean" (this is called transformation bias). This caution will apply to any estimates of moments of a distribution. However, percentiles are not affected by such transformations. Since the median and mean of the normal distribution coincide, if your ANOVA test on the transformed data comes back significant, then you can conclude that the medians of the original data are different, but not the means.