Normality tests (H0: "the distribution is exactely normal in the population from

which the data are sampled") always show deviations from normality, if sample size

is so large. Mind that for linear regression or analysis of variance, not the dependent

variable should be normally distributed, but the prediction errors from the model (the

residuals). But you can safely ignore this if sample size is large (n > 50 or so).

So you can do a oneway ANOVA here. The question remains, why you want

to do an analysis with such a huge sample size. Even in the smallest subgroup here,

the standard error of the mean is very tiny ( SD / 45 for n=2048), so you could

just use the descriptive statistics. p-values tell you nothing about the size or

relevance of an effect.

With kind regards

Karabiner