Some Designs and Analyses for Temporally Independent Experiments Involving Correlated Bivariate Responses

Abstract

Designs and analyses are derived for experiments with two experimental units where responses are correlated within and independent among time periods. Fisher's information function for the treatment parameter is maximized to obtain most informative designs for estimating a treatment effect. In the absence of pre-test or historical data on the two units, the most informative design is always a balanced crossover. With historical data, the design is either a continued covariate or an augmented crossover. Efficient analyses of continued covariate and balanced crossover designs are shown to be examples of maximum likelihood (ML) estimation and the analysis of covariance. For the augmented crossover designs, (ML) methods and Wilks' lambda criterion are used to provide efficient large sample procedures. It is shown that use of a most informative design and efficient analysis instead of more familiar designs and analyses can result in a sizable decrease in the variance of the treatment effect estimator.