The Wikipedia page on ANOVA lists three assumptions, namely:
- Independence of cases – this is an assumption of the model that simplifies the statistical analysis.
- Normality – the distributions of the residuals are normal.
- Equality (or "homogeneity") of variances, called homoscedasticity...
Point of interest here is the second assumption. Several sources list the assumption differently. Some say normality of the raw data, some claim of residuals.
Several questions pop up:
- are normality and normal distribution of residuals the same person (based on Wikipedia entry, I would claim normality is a property, and does not pertain residuals directly (but can be a property of residuals (deeply nested text within brackets, freaky)))?
- if not, which assumption should hold? One? Both?
- if the assumption of normally distributed residuals is the right one, are we making a grave mistake by checking only the histogram of raw values for normality?