Design and analysis of pen studies in the animal sciences.

Increasingly, research is being performed in which animals subjected to a common treatment are also housed in a common pen. Issues have been raised regarding the proper planning of experiments and conduct of statistical analyses in these instances. This paper reviews the problems associated with ignoring animal grouping during data analyses, and examples are provided for appropriate methods to use when animals are grouped in pens. Using animals as the error term when treatments are applied to pens can result in biased estimates of treatment effects when pens are of unequal sizes and animals are moved in and out of the pens. It always results in biased probability statements regarding their significance. The pen effect includes systematic effects other than that of the treatment, which is why pens must be replicated and randomized. In essence, pen studies have an implicit split-plot design in which the main plots (pens) receive the treatments of interest, whereas the subplots (cows) receive all the same subplot treatment. Using the subplot error to test main-plot treatment effects creates inflated degrees of freedom and uses the wrong denominator mean square to test the effect; hence, severely biasing the test of significance for the treatment effects and resulting in an invalid causal inference base. The interactions of pens with the fixed-effect elements of the treatment design are the correct error terms for those fixed-effects factors applied to the pens. The same statistical designs used with animals as experimental units can be used with pens. The number of experimental units to achieve a given power can be, and generally is, considerably less with pens because the variance among pens is generally less than the variance of cows within pens. Pens must be replicated, randomized, and included in the statistical model to ensure valid statistical inference.