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I am conducting a 2 (stimulus type) x 2 (response mode) within-subjects ANOVA on Response Times on a computer task and I am having trouble making a decision about a particular kind of outlier.

I have one participant for whom each of the four means used in the analysis are not outliers.

However, the difference between Response Time means between the two stimulus types for this participant is 3 SDs above the mean for the sample. Including this one participant influences my results quite a bit as they are showing a main effect for stimulus type.

Is there a process to identify and remove outliers such as this?

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  • $\begingroup$ In this case you may want to define outliers via the residuals of your ANOVA. E.g. see: stats.stackexchange.com/questions/173269/… $\endgroup$ – mzunhammer Jul 12 '17 at 10:24
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    $\begingroup$ Perhaps this person is the most interesting finding in your experiment? So why remove? $\endgroup$ – mdewey Jul 12 '17 at 10:39
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You can identify such a case from the usual plots associated with regression, which identify influential cases.

However, unless the data is incorrectly recorded, I would not remove the person. Instead, use a regression method that deals better with outliers, such as quantile regression or robust regression.

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