PSII-7 Type I error rates of two strategies to analyze a randomized complete block design within multiple sites

It is not unusual to come across randomized complete block designs (RCBD) replicated over a small number of sites in swine nutrition trials. For example, pens could be blocked by location or by initial body weight within three rooms or barns. One possibility is to analyze this design with the assumption of no treatment by site interaction which implies treatment differences are similar across all sites. This assumption might not always seem reasonable and site by treatment interaction could be included in the analysis to account for these differences should they exist. However, the site by treatment mean square becomes the error term for evaluating treatment. The objective of this study was to provide a recommendation of a practical strategy based on Type I error rates estimated from a simulation study. Scenarios with and without site by treatment interaction were considered with three sites and equal means across four treatments. The variance component for the error was set to 1 and the rest were either selected to be equal (σ2s = σ2b = σ2s*t =1) or one of them was set to 10. For the scenarios with no site by treatment interaction, σ2s*t = 0, for a total of 7 scenarios. Each scenario was simulated 10,000 times. For each simulation, both strategies were applied. The Kenward-Rodger approximation (KR) to the denominator degrees of freedom was also considered. Type I errors were estimated as the proportion of simulations with a significant treatment effect with α = 0.05. Overall, there was no evidence Type I error rates were inflated when the site by treatment interaction was omitted, even when σ2s*t = 10. The KR had no effect. In contrast, including the interaction term leads to a highly conservative Type I error rate far below the 5% level which results in a reduction of power; however, using KR mitigated the conservativeness.