Residual error: All ANOVA models have residual variation defined by the variation amongst sampling units within each sample. This is always given by the last mean square in ANOVA tables, and denoted 'ε' (epsilon) in the descriptions of fully replicated models where it represents the error variance for at least some of the treatment effects. Models without full replication may have no degrees of freedom for measuring residual variation (e.g., randomised block, split plot, and repeated measures models).


Error variance is the random variation in the response against which an effect is tested, containing all of the same components of variation estimated in the population except for the test effect. The validity of ANOVA depends on three assumptions about the error variance: (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.


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.