Should blocks be fixed or random?
Many studies include some form of blocking in the study design. Block effects are rarely of intrinsic interest; instead they are included in a model so that that model reflects the study design. I consider the question of how these block effects should be modeled: as fixed effects or as random effects. I discuss the consequences of the choice, including the recovery of inter-block information when available, give a simple example to illustrate the connection between recovery of inter-block information and pooling two estimators of a treatment effect, and give an example where fitting a model with random block effects can lead to the wrong answer. I suggest that block effects should be modeled as fixed effects unless there are compelling reasons to do otherwise.
This proceeding is from Dixon, P.M. Should blocks be fixed or random? 2016 Conference on Applied Statistics in Agriculture Proceedings, May 1-3, Manhattan Kansas. Kansas State University. doi: 10.4148/2475-7772.1474.