Applied linear statistical models by Kutner et al. states the following concerning departures from the normality assumption of ANOVA models: Kurtosis of the error distribution (either more or less peaked than a normal distribution) is more important than skewness of the distribution in terms of the effects on inferences.
I'm a bit puzzled by this statement and did not manage to find any related information, either in the book or online. I'm confused because I also learned that QQ-plots with heavy tails are an indication that the normality assumption is "good enough" for linear regression models, whereas skewed QQ-plots are more of a concern (i.e. a transformation might be appropriate).
Am I correct that the same reasoning goes for ANOVA and that their choice of words (more important in terms of the effects on inferences) was just chosen poorly? I.e. a skewed distribution has more severe consequences and should be avoided, whereas a small amount of kurtosis can be acceptable.
EDIT: As adressed by rolando2, it's hard to state that one is more important than the other in all cases, but I'm merely looking for some general insight. My main issue is that I was taught that in simple linear regression, QQ-plots with heavier tails (=kurtosis?) are OK, since the F-test is quite robust against this. On the other hand, skewed QQ-plots (parabola-shaped) are usually a bigger concern. This seems to go directly against the guidelines my textbook provides for ANOVA, even though ANOVA models can be converted to regression models and should have the same assumptions.
I'm convinced I'm overlooking something or I have a false assumption, but I cannot figure out what it might be.