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I know there are a lot of questions along this vein, but none seem applicable to the data I have.

Essentially I have run a one-way ANOVA using a variable composed of 4 different groups (A:D) and the scores of each participants in these groups on a test. I don't know how/ if I should remove the 3 points highlighted on the Cooks Distance plot- do you remove them from the initial data set, or can you just remove them from the data? I'm not even sure if it is necessary to remove them, as various places give different thresholds for points being problematic.

Cooks distance plot for my anova

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In the 1-way ANOVA case, Cook's distance may be a bit of overkill. Essentially, the question is whether or not any values are "outliers" within each separate group.  (The regression model for the ANOVA is just estimating the group means, and in turn, the residuals are just the distance of each individual from their group means.)  Cook's D does have the benefit of "standardizing" all the residuals across all groups (as opposed to asking if a value is flagged as an outlier within each group).

My suggestion would be to ask a slightly different question:  ¿is there any reason to think the variance differs across your groups?  If you do a test for homoscedasticity with and without the flagged values, and if neither flag an issue...you probably are fine.

Hope this helps.

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  • $\begingroup$ Hi thank you for your answer. Initially when I did check for homoscedasticity, the conditions were met. Does that mean that the outliers are not a cause for concern? $\endgroup$
    – Blythe
    Commented Mar 21, 2018 at 20:41
  • $\begingroup$ That would be a reasonable conclusion if the variances weren't flagged as significantly different. Furthermore, if neither of the observations are flagged as outliers within their own groups, then you really don't have a violation of any of the key assumptions for the ANOVA test. $\endgroup$
    – Gregg H
    Commented Mar 21, 2018 at 21:16

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