subject k(i) gets formulation R, ε if response Y is from formulation T and ε if response Y is from formulation R. The means of T and R are then µ and µ , respectively. Then Var[s ] = σ , the between-subject variance for T , Var[s ] = σ , the between-subject variance for R, Var[s ] = σ , the subject-by-formulation interaction variance, Cov[s ] = ρσ σBR = σ , Var[ε ] = σ and Var[ε ] = σ . Further, we assume that all ε’s are pairwise independent, both within and between subjects. For the special case [ of equal group sizes (n Var[µˆ ] = [ σ − 2σ + ] (σ +σ )/2 /N = σ + (σ )/2 /N where N = 4n. The variances and interactions needed to assess IBE can easily be ob-tained by fitting an appropriate mixed model using proc mixed in SAS. The necessary SAS code for our example will be given below. However, before doing that we need some preliminary results. Using the SAS code we will obtain estimates σˆ , ωˆ , σˆ and σˆ , where ω is the between-subject covariance of R and T, and was earlier denoted by σ . These are normally distributed in the limit with a variance-covariance matrix appropriate to the structure of the fitted model. The model is fitted using REML (restricted maximum likelihood, see Section 6.3 of Chapter 6) and this can be done with SAS proc mixed with the REML option. In addition we fit an unstructured covariance structure using the type =UN option in proc mixed. The estimates of the vari-