[R] Problems with normality req. for ANOVA

[wwreith]

I am conducting an experiment with four independent variables each of which
has three or more factor levels. The sample size is quite large i.e. several
thousand. The dependent variable data does not pass a normality test but
"visually" looks close to normal so is there a way to compute the affect
this would have on the p-value for ANOVA or is there a way to perform an
nonparametric test in R that will handle this many independent variables.
Simply saying ANOVA is robust to small departures from normality is not
going to be good enough for my client. I need to compute an error amount for
ANOVA or find a nonparametric equivalent. 

Thanks,

William 
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