Recovery tests in BIBDs with very small degrees of freedom for interblock errors

When a Balanced Incomplete Block Design (BIBD) is considered with an usual additive mixed model, there is interblock information available to be utilized in inferences on the contrasts of the fixed treatment effects. The recovery problems in estimation have been studied extensively since Yates (1940). However for the null hypothesis there are no differences in treatment effects, a long problem has been to find good exact tests which combines both intrablock and interblock information. Cohen and Sackrowitz (1989) proposed an exact recovery test which has been shown to perform much better than the usual F-test provided that the number of treatments, I, is greater than the number of blocks, J, and the degrees of freedom for errors in intrablock stratum is not much greater than that in interblock stratum. In this note, a class of simple recovery tests is proposed for the case where there is zero degree of freedom for error in interblock stratum (J=I. Furthermore it is found that the Cohen and Sackrowitz test can be modified to reach higher power when J -- I is very small.