Inter-block Information: to Recover or Not to Recover It?

Comparing standard errors of treatment differences using fixed or random block effects with the approximation of Kackar and Harville helps in choosing the preferable assumption for blocks in the analysis of field experiments. Blocked designs are common in plant breeding field trials. Depending on the precision of variance estimates, recovery of inter-block information via random block effects may be worthwhile. A challenge in practice is to decide when recovery of information should be pursued. To investigate this question, a series of sugar beet trials laid out as α-designs were analysed assuming fixed or random block effects. Additionally, small trials laid out as α-designs or partially replicated designs were simulated and analysed assuming fixed or random block effects. Nine decision rules, including the Kackar-Harville adjustment, were used for choosing the better assumption regarding the block effects. In general, use of the Kackar-Harville adjustment works well and is recommended for partially replicated designs. For α-designs, using inter-block information is preferable for designs with four or more blocks.