# Assessing normality for ANOVA

More of a general statistics question rather than about R specifically, but I didn't know where to post this, so if anyone can help, it would be hugely appreciated!

I am trying to assess the conditions for ANOVA, specifically the condition in question that residuals must be normally distributed. I first did a boxplot to visually assess the data and from the boxplot, the residuals do not look normal, or at least each group's residuals are not centered on zero:

After seeing the boxplots, I did a normal quantile plot to investigate further, and from the normal quantile plot the data does appear to be normal. I would post a screenshot but I'm limited to one photo per post, this was my code:

qqnorm(m\$residuals, pch=16)
qqline(m\$residuals, col="red", lwd=3)

From what I understand, it appears that my residuals are normally distributed, but do not have a mean of zero. What I am wondering is if zero mean is a condition for ANOVA? I know that residuals have to be normally distributed but do they also have to have zero mean?

If you are plotting the residuals of each subgroup from the global mean, you would expect the residuals to not be centered around zero if the groups are "significantly" different. ANOVA is intended to answer, "are the groups means different"? Think about a simple case where the whole data set has three sub-populations: A = rnorm(n = 30, mean = 0, sd = 1), B = rnorm(n= 30, mean = 10, sd = 1), C = rnorm(n = 30, mean = 20, sd = 1). An ANOVA test will show that the three groups are not the same. The residuals from the grand mean will be very different from normal; they will be trimodal. Each subgroup is normal.

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