COVARIANCE ADJUSTMENT IN STUDIES INVOLVING OBSERVATIONAL FACTORS OR COVARIATES INFLUENCED BY TREATMENTS

We extend the definition of adjusted treatment means in the analysis of covariance to deal with the case where some of the covariates are influenced by treatments or where some of the factors are observational. In these cases, comparison of treatment means adjusted to a common value of the covariate may be inappropriate. Partially adjusted means are defined and it is shown that special cases include the usual adjusted means (adjusted to a common value for each of the covariates) and unadjusted means. In fact, in a multifactorial experiment, one can, by appropriate choice of adjustment, compare adjusted means for one factor but unadjusted means for the second factor. Partially adjusted means can be computed by any linear models software which will estimate linear combinations of the parameters