In Wolter (1985) the problem of estimating variances when the data are contaminated by measurement (or response) errors was considered for linear estimators. Under a simple additive error model it was shown that design-unbiased variance estimators are in general biased as estimators of total variance and that in certain circumstances this bias can be important. It was also shown that with additional conditions a random group variance estimator can shift the bias entirely to the sampling error component, generally with an accompanying reduction in the total variance.