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I had a question that involves the basic assumptions of t-tests and anova models. I know there are assumptions of normality but wasn't sure where they need to be applied to.

I see most people explain that the normality assumption is related to the residuals and the standard way to see this is to make a qqplot with the residuals.

Could the normality assumption also or instead be applied to the predictors? For example, creating a qqplot for the data for each group in an anova, or would that not matter?

I wrote a quick example to show what I'm talking about...

dat<- data.frame(Class=c(rep("A", 5), rep("B", 5), rep("C", 5)), Value=rnorm(15))

#now does it make sense if i do this for each class
#or does it need to be the model residuals

qqnorm(subset(dat, dat$Class=="A")$Value)
qqline(subset(dat, dat$Class=="A")$Value)
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  • $\begingroup$ if your predictors are normal, that means they are noise and probably not very good predictors. $\endgroup$ – aginensky Jun 9 '17 at 17:45
  • $\begingroup$ I phrased this a bit wrong. I'm meant testing if the response is normal by predictor level. So if in my example, I'm looking at normality in the Value by Class level $\endgroup$ – intern Jun 9 '17 at 18:16
  • $\begingroup$ Your DV should be normally distributed, yes. But there's no reason—or at least none that I'm aware of—to look at it split up by condition. If the distribution varies by condition, you're going to likely violate homogeneity of variance anyways. $\endgroup$ – Mark White Jun 10 '17 at 5:05
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    $\begingroup$ @aginensky, I see no reason why that should be the case. Relevance of predictors is determined not by their marginal distribution but by the connection between their distribution and the distribution of the dependent variable, thus conditional distr. of the dep. var. conditioning on the indep. var. $\endgroup$ – Richard Hardy Jun 10 '17 at 15:47
  • $\begingroup$ @ Hardy. One of us is mis-understanding OP. I took him to mean y ~ N(m,s). Given that, I think my comment is valid. $\endgroup$ – aginensky Jun 10 '17 at 15:56

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