Abstract
Consider a Balanced Incomplete Blocks Design (BIBD) for a mixed two way model with interactions and p observations per cell. A sufficient condition is given under which recovery of interblock information is obtainable for inferences concerning treatment contrasts. The condition is considerably weaker than the previously known condition for analyzing such BIBDs given by Kapadia, Kvanli, and Lee (1988). The condition suffices to preserve the covariance structure of the observation vector when no interactions are present. The condition not only suffices to preserve the structure for BIBDs but also for any block design in which the mixed model is assumed. For the BIBD case a test for the presence of a random interaction is given. In addition, consider a K-random factor design under a mixed model which includes random interactions between blocking factors and treatments. Another set of sufficient conditions is given under which the covariance structure of the observation vector is preserved from the model with no interactions.
Published Version
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