My dataset consists of 68 groups, each with 4 data points inside it.
As means of a robustness test, I am looking to see how the type of average/mean I use impacts the analysis that I will make.
In this case, I am using five types of means which are (1) a harmonized mean, (2) a geometric mean, (3) an arithmetic mean, (4) a trimmed arithmetic mean, and (5) a winsorized arithmetic mean.
After reading, I understand that the common practice for winsorizing is by first selecting a value of x% - of which the top x% percentile and bottom x% percentile that will be then winsorized. However, I was wondering if the following approach would be better suited to my case:
Doing a Grubbs' / Dixon's test to identify outliers in each group, and then winsorizing those outliers. Would this be better than selecting a certain x%? This is because I only have four data points.
Side Note (Open to any comments)
I understand that Grubbs and Dixon both operate under the assumption of normally distributed data, so I have also conducted a normality test (Shapiro-Wilk) for all 68 groups. However, I have also read a study (https://www.osti.gov/biblio/5478051-note-robustness-dixon-ratio-test-small-samples-testing-outliers) that mentioned Dixon's Q-test can operate on non-normal distributed data given a small samples (3-5). Hence, a. For groups that are normally distributed, I apply the Grubbs test to find for outliers. b. For groups that are non-normally distributed, I apply the Q-test to find for outliers.