To Block or Not to Block: The Tale of Initial Weight in Swine Nutrition Trials

A traditional way to account for individual BW variability in swine nutrition trials is to block animals by initial weight (IW) – this is known as complete randomized block design (CRBD). In this design, animals are stratified into groups based on the distribution of the IW data, where the number of groups is defined by the researcher. Furthermore, increasing the number of blocks removes residual degrees-of-freedom, which can potentially decrease statistical power (POW). In contrast, IW could be used as a covariate in complete randomized designs (CRD), while consuming one degree-of-freedom. The objective of this study was to compare POW of CRBD and CRD using stochastic simulation. We evaluated the effect of a dietary treatment (Control or Test) on ADG. Effect of the Test Diet was set to 10g/d. Different scenarios were evaluated: 5 correlations between IW and ADG (0, 0.25, 0.50, 0.75, and 0.99); 5 residual variances (25 to 125, by 25 g²/d²); and 6 replicates/treatment (6 to 21, by 3 pigs), for a total of 150 scenarios. Each scenario was simulated 1,000 times. For each simulation, animals were either randomly assigned to diets (CRD) or ranked by IW, classified into 1 of 3 blocking groups, and then randomly assigned to diets within blocks (CRBD). POW was calculated using P<0.05 for Diet effect. For all scenarios, POW increased as the number of replicates/treatment increased, and as the residual variance decreased. The overall average POW of CRD and CRBD were 75.4% and 74.5%, respectively. Albeit similar, greater variability in POW was observed for CRBD compared to CRD, with CV of 22.6% and 19.3%, respectively. For correlations of 0, 0.25, and 0.5, POW were similar (76% for CRBD and 75.5% for CRD). For higher correlations differences were greater, with 73.3% (CRBD) and 75.2% (CRD), and 71.1% (CRBD) and 75.2% (CRD), for correlations 0.75 and 0.99, respectively. Residual variances were unbiasedly estimated using CRD, but they were increasingly overestimated from correlation 0 (slope=1.01) to 0.99 (slope=1.22) using CRBD. In conclusion, no increase in statistical power was observed by using CRBD in place of CRD. In addition, when the correlation between IW and ADG was greater than 0.5, CRD showed greater power than CRBD. Finally, bias estimates of error variance were obtained using CRBD. These results indicate that CRD using IW as a covariate in the model may yield similar or better results than CRBD when using IW as a blocking factor.