I have a 2x3 between-subjects design. I want to run two-way ANOVA but have no normality and no homogeneity. I have 3 variables and 103 observations in total.

  1. Factor 1 - attentional bias (CFT): G0 n.38; G1 n.31; G2 n.34
  2. Factor 2 - body dissatisfaction (EDI): G0 n.61; G1 n.42
  3. Dependent Variable - Disgust

Regarding the violation of normality, I found that ANOVA is considered a robust test even in the case of a deviation from normality. Regarding the violation of homogeneity, is there any method to run Anova anyway? enter image description here

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1 Answer 1


ANOVA is equivalent to regression. So, you can use regression methods that do not assume normality or homogeneity of errors. Two such methods are quantile regression and robust regression.

As an aside, why are the IVs categorical? From their names, both vary on some sort of continuum and would be better measured with a scale (0 to 100 or whatever) than by grouping them into (apparently) three and two groups, respectively.

  • 3
    $\begingroup$ +1. It's a perpetual bugaboo that violation of normality and homogeneity of errors are roadblocks. On another note, congrats on your 100k! $\endgroup$ Commented Jul 24, 2023 at 10:12
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    $\begingroup$ Most of the time when statisticians talk about the robustness of ANOVA to violations of assumptions they are thinking of preserving the type I assertion probability $\alpha$, and forgetting that power ($1 - \beta$) can be badly hurt by assumption violations. But at any rate, one of the most robust minimal-assumption methods is semiparametric ordinal regression which is invariant to transformations of $Y$ and for the logit link is equivalent to the Kruskal-Wallis test for one-way ANOVA. And congratulations Peter on 100k! $\endgroup$ Commented Jul 24, 2023 at 11:19

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