ANOVA question

[thaumaturgy]

I have a large data set and I find that my distribution of residuals has a "heavy tail" distribution. the normal quantile plot looks like this:



So my question is: when I run the ANOVA and I get an F-statistic and p-value for the linear regression, can I assume that with a heavy-tailed distribution of error terms that this will conservatively INFLATE the p-value meaning that if I see a significant p-value for the F test on the regression that if anything this is a CONSERVATIVE estimation?

That with heavy-tailed distribution of residuals am I more or less likely to conclude a non-zero slope?


Thanks!
-Chris

[Masteras]

the t distribution looks like the normal distribution only that it has heavier tails. Now since you have a large data set, the central limit theorem applies. So you are ok. But if you have any doubt, use non paramteric regression and see what you get, or perhaps bootstrap, or M or S robust regression (available for Splus)