A few quick definitions:
An error is the difference between an observed value and the "true" value
A residual is the difference between an observed value and the "predicted" value
Let's say we have three samples and want to conduct a 1-way ANOVA:
$$H_0: \mu_1 = \mu_2 = \mu_3 = \mu$$
In order words, our null hypothesis is that all 3 samples were taken from the same population with mean $\mu$. Thus, $\mu$ is the "true" value. And I guess the grand mean of all the samples, $\bar{Y}$, is the "predicted" value.
According to Wikipedia, one of the assumptions of ANOVA is that the distributions of the residuals are normal. I have a few clarifying questions:
Which residuals are these? Is it: $(Y_{ij}-\bar{Y})^2$? Or the residuals within each sample: $(Y_{ij}-\bar{Y_j})^2$? Or both?
Why is the assumption that the residuals are normally distributed and not the sample values themselves? In other words, why is the assumption that $(Y_{ij}-\bar{Y})^2$ is normally distributed, but not $Y_{ij}$?
