Incorporating Previous Results Into the Analysis of General Balanced Designed Experiments

When previous results are available about quantities of interest in a designed experiment they should be incorporated into the analysis. We suppose that estimates of treatment effects and variance components and their precisions are available from previous data but not necessarily the full data. A prior-posterior method is described which incorporates these previous estimates directly into the analysis of a current set of data. General but concise formula are derived for the class of generally balanced designs. Previous results are represented by a multivariate normal prior for the treatment means and independent inverse chi-squared distributions for the variance components. Joint and marginal posterior modes and a measure of dispersion are proposed as combined or updated estimates. These posterior summary statistics have highly interpretable forms and are readily computed.