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Design of experiments chooses experimental units, treatments, replication, blocks in experimental design and randomization so that scientifically useful treatment contrasts can be estimated with meaningful standard errors. Allocation determines which measurements supply independent treatment information.

Use two crossed sets of blocks in experimental design: volunteers as rows and afternoons as columns. Volunteer blocks control persistent ability, drawing style and prior experience; afternoon blocks control conditions shared that day, including common task difficulty and general practice over time. Neither partition is nested in the other.

Give every volunteer each program twice, and use each program twice each afternoon. The row-column design is then balanced for both block systems. In the additive modelthe program contrasts are orthogonal to both centered block spaces. This controls additive volunteer and afternoon effects; it does not automatically eliminate individual learning differences or carryover effects.

First agree the scientific question and primary response variable. Ask the vet about the disease's course, the proposed mechanism and duration of each treatment, the eligible population, baseline severity, and what outcome and follow-up time would represent worthwhile improvement. Is the disease transmissible, is recovery reversible, and can treating one cow affect another's outcome? These answers determine whether a crossover design is credible, whether the experimental unit should be a cow or a whole herd, and whether individual randomization would leave interference between groups. Agree welfare and rescue arrangements with the vet when deciding which comparisons are feasible; the statistical plan cannot determine these from an unfamiliar disease name.

Second agree feasible allocation and adequate independent replication. Discuss numbers of available cows and herds, variation in the chosen outcome, a scientifically meaningful treatment difference, and the desired statistical power. Use these to plan sample size, rather than choosing a number solely from convenience. Discuss herd, lactation stage and initial severity as potential blocks in experimental design, then specify randomization, comparable management, concealed allocation and blinded outcome assessment where feasible. Repeated milk or health records from the same cow are observational units, not extra independent experimental units; pseudoreplication would give misleading standard errors. Availability of enough independent cows or herds, together with expected variation, governs the precision actually achievable.