Assumptions: These are the necessary preconditions for fitting a given type of model to data. No form of generalisation from particular data is possible without assumptions. They provide the context for, and the means of evaluating, scientific statements purporting to truly explain reality. As with any statistical test, ANOVA assumes unbiased sampling from the population of interest. Its other assumptions concern the error variation against which effects are tested by the ANOVA model: (i) that the random variation around fitted values is the same for all sample means of a factor, or across the range of a covariate; (ii) that the residuals contributing to this variation are free to vary independently of each other; (iii) that the residual variation approximates to a normal distribution. Underlying assumptions should be tested where possible, and otherwise acknowledged as not testable for a given reason of design or data deficiency.
Doncaster, C. P. & Davey, A. J. H. (2007) Analysis of Variance and Covariance: How to Choose and Construct Models for the Life Sciences. Cambridge: Cambridge University Press.