This is the variation that is not explained by the model in terms of the factors.
Block variance is only present when blocks are included in the design. This is variation that is attributed to something changing that is not a factor in the experiment. It is removed from the tests and \(R^2\) approximations.
Re-setting a hard to change factor provides a source of variation. The test for the whole plot effects is a function of both the group and residual variances. When the group variance is zero, the whole-plot model is explaining all of the variation between groups. If this occurs the analysis will be equivalent to a randomized design.
Each run creates a source of variation separate from and in addition to the above sources. The test for subplot effects is a function of the residual variance along with the covariance with the groups.
The sum of the above sources of variation.
The estimated variance components have a standard error associated with them. The standard error is used to compute the variance confidence intervals. For blocks and groups the intervals are based upon a normal distribution. For the residual, the interval is a \(\chi^2\) based interval.