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I've got a variable with psychological data (N=75) which is distributed pretty symmetrical, but has very few cases with very extreme values, more extreme to the left tail. But nevertheless this data is valid. The analysis I will do, is a simple t-test. Due to the fact that the extreme cases on the left tail influence significance, but are valid, instead of removing the extreme values (actually, removing these is considered to be too invasive), I would like to winsorize the variable, use bootstrapping to care for not totally met assumptions, do the t-test. Then afterwards I would like to do a sensitivity analysis by conducting the t-test again with un-winsorized data, so the result can be taken into account and being discussed.

Is this approach a valid and reasonable one? Or should I do it vice versa and conducting the main analysis with un-winsorized data and then the sensitivity analysis with the winsorized values?

Note: in literature, some scientists recommend dichotomizing the variable, but my colleagues said, that in our sample the values are pretty well distributed – except the few extremes.

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  • $\begingroup$ Isn't winsorizing more of an EDA (exploratory data analysis) method than a method for robust inference? That's its use in the DescTools R package for example. $\endgroup$
    – dipetkov
    Mar 16 at 14:43
  • $\begingroup$ Here are some alternatives to consider: (a) Bayesian t-test; see eg. Bayesian equivalent of two sample t-test?; (b) robust regression; see eg Robust regression - a better understanding. It's not clear to me if you have two groups or not. If there are no groups & you want to estimate a central location robustly, you can do that with an intercept-only regression, say robustbase::lmrob(y ~ 1). $\endgroup$
    – dipetkov
    Mar 16 at 14:43
  • $\begingroup$ More about winsorizing: Use and misuse of Winsorization. One last comment: You can bootstrap without winsorizing, that's another option for doing a robust analysis. $\endgroup$
    – dipetkov
    Mar 16 at 16:45

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