ESTIMATION OF CONTRAST VARIANCES IN LINEAR-MODELS

A common problem in the reporting of statistical analyses is the presentation of standard errors of nonindependent effects. In particular, it is desirable to provide a useful indication of the covariance structure of the parameter estimates. The problem is considered for several cases. First, in an analysis of covariance situation, we derive upper and lower bounds for the standard error of an arbitrary linear contrast of treatment effects; the method allows for unequal numbers of replicates as well as generalized linear models. We also show how extra covariates may be incorporated and discuss the choice of a point estimate for the standard error within the interval.