LAUSR

Allocation of treatments to experimental units (EUs) is done at random. In the presence of a concomitant variable (e.g., initial body weight; iBW), one strategy is to block WUs into iBW groups. However, in some scientific manuscripts, EUs are sorted by iBW and then allocated to treatments (e.g., treatments “A” and “B”) based on iBW, such that the lightest EU receives “A,” the second and third lightest receive “B,” etc. Although this strategy guarantees similar iBW between treatments, this ignores the random process required for statistical analysis of the data. We aimed to quantify the impact of lack of randomization on the statistical power and type I error of completely randomized designs (CRD). Data were simulated for ADG using two treatments (“A” having 50 g/d more than “B,” and MSE=1250 g2/d2). Data were simulated for different replicates per treatment (RepsPerTreat; from 3 to 18, every 3). We used two scenarios for the correlations between iBW and ADG (ρ ADG,iBW): 0 and 0.5. Treatments were allocated to EUs at random (CRD) or according to the order of EUs based on iBW (completely non-randomized design; CNRD). The model included the fixed-effects of intercept and treatment. For ρ ADG,iBW=0, results showed that CRD had greater statistical power (POW) than CNRD for RepsPerTreat from 3 to 9, whereas CNRD had greater from 12 to 18. For ρ ADG,iBW=0.5, CNRD had an even greater POW than CRD starting at 9 RepsPerTreat. Although the type I error (ERROR) of CRD were close to 5% across all scenarios with different RepsPerTreat, CNRD had consistently greater and lower ERROR than CRD with =0 and 0.5, respectively. Having ERROR deviating from 5% is not expected. Visual inspection of the F-values of these models when the null hypothesis was true showed that a distribution other than the theoretical F-distribution, indicating that the statistical test is not valid. Sorting EUs by iBW does not guarantee greater statistical power but results in invalid F-tests.