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$begingroup$ I have additional boxplots of residuals with categorical variables in my query above. They don't appear to display something outstanding. $endgroup$

Again, you won't ever be able to prove you have Ordinarily dispersed residuals regardless of whether the residuals are all particularly on the line, but when you see QQ-plots as in Determine 3.twelve you could ascertain that there is distinct proof of violations in the normality assumption.

There are 2 plots in Determine three.9 with handy information and facts for examining the equal variance assumption. The “Residuals vs Fitted” panel in the best still left panel displays the residuals ((e_ ij = y_ ij -widehat y _ ij )) within the y-axis along with the equipped values ((widehat y _ ij )) about the x-axis. This allows you to see When the variability from the observations differs through the groups being a perform of the mean on the teams, due to the fact each of the observations in exactly the same team get the identical equipped worth – the mean with the group. On this plot, the details seem to have quite identical spreads with the equipped values for your 7 teams with equipped values at 114 up to 122 cm. The “Scale-Site” plot within the decreased left panel has precisely the same x-axis of equipped values however the y-axis has the square-root of absolutely the price of the standardized residuals. The standardization scales the residuals to have a variance of 1 so allow you to in other shows to secure a sense of the amount of typical deviations you're far from the signify during the residual distribution.

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With such a big facts established in this article and only minor considerations Along with the normality assumption, the inferences created with the means ought to be reputable and we will get equivalent final results from parametric and nonparametric methods. If we had only fifteen observations for every team and a slightly skewed residual distribution, then we might wish to appeal to the permutation method of have extra trusted success, although the look ended up balanced.

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$begingroup$ The list of illustrations in The best way to interpret a QQ plot involves the basic condition in the issue. Namely, the finishes of the line of details convert counter-clockwise relative to the middle.

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