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I performed an analysis a while ago, and the experiment was blocked for production day (3 different production days). Two of the production days had terrible outliers, and after looking at the Cook's Distance for the residuals I decided to simply analyze a single block.
The conclusion contained the caveat that the analysis represents an idealized scenario in which the reasons for the outliers have been discovered and controlled. The analysis was considered a success, but what is really gnawing at me is that I could not find ANY other analysis that was conducted in such a manner.

I would like to know the thoughts of the folks on this site, what do you think about this approach? The details and justification are severely truncated here, so just looking for thoughts about the concept when the caveat is included.

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    $\begingroup$ Perhaps the reason you don’t see others doing it this way is that you’re one of the few to be honest about your methodology. (I think others will do this and not report it.) Outliers tend to be misunderstood, and when you’re in a diverse environment, it is amazing how statisticians and non-statisticians differ in viewing extreme observations. $\endgroup$
    – Dave
    Commented Feb 14, 2021 at 15:45

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Usually in an empirical study, people would indeed often drop these blocks while showing in a robustness check that disregarding them does not change the interpretation of the results.

In the robustness check, you can for example apply a simpler but outlier-robust tests on the two disregarded blocks (such as a sign or rank test) or even more advanced methods such as quantile regression which are less sensitive to outliers, and might be even valid in case of truncation in the dependent variable compared to, for example, linear regression.

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