Invited review: Assessing experimental designs for research conducted on commercial dairies

Statistical power of test versus number of experimental units for effect sizes (△) equal to 0.75 (○), 1.00 (●), 1.25 (□), 1.50 (■), 1.75 (♢), 2.00 (♦), 2.25(△), or 2.50 (▴) for comparing 2 treatments in a a) completely randomized design, b) single crossover design, and c) randomized complete block design with subsampling.

Statistical power of test for comparing 2 treatments for differences in incidence rates of binary responses given an incidence rate of 0.05 for 1 treatment and various incidence rates for the second treatment (0.10 ○, 0.15 ●, 0.20 □, 0.25 ■, 0.30 ♢, 0.35 ♦, 0.40 △, and 0.45 ▴) as a function of number of individually treated cows per treatment.

Statistical power of test for comparing 2 treatments for differences in incidence rates of binary responses given an incidence rate of 0.05 for 1 treatment and various incidence rates for the second treatment (0.10 ○, 0.15 ●, 0.20 □, 0.25 ■, 0.30 ♢, 0.35 ♦, 0.40 △, and 0.45 ▴) as a function of the number of pens per treatment. Experimental variability and number of cows (d) per pen set equal to a) , d=24, b) , d=48, c) , d=24, d) , d=48, e) , d=24, and f) , d=48.

Empirical ranges (curves) of observed incidence rates of binary responses between experimental units (e.g., pens) based on overall incidence rates of p=0.05 (solid line), p=0.25 (short-dash line), and p=0.50 (long dash line) as a function of the experimental variability on the underlying liability scale.