= Solution
A \b[<completely randomized design>] uses $2m$ eligible animals, randomly selecting $m$ to receive $P$ and assigning the remainder to $Q$. Use comparable follow-up and assess the same <response variable> in both groups. Its advantage is simplicity and freedom from previous-treatment <carryover effects>; its disadvantage is that between-animal variation enters the residual and can make a <treatment contrast> imprecise.
A \b[<randomized complete block design> with matched pairs] first forms $m$ pairs using pre-treatment characteristics such as initial disease severity, age or breed. Independently choose which animal in each pair receives $P$, with its partner receiving $Q$. The <experimental units> are animals; pairs are blocks. The average within-pair difference estimates the <treatment contrast>, and positive within-pair similarity can reduce its <variance>. Its advantage is control of known heterogeneity; its disadvantage is the need for useful matching, with fewer residual <statistical degrees of freedom> and little gain if the matching variables are uninformative. Do not construct pairs using outcomes observed after assignment.
A \b[two-period <crossover design>] randomly assigns half the animals to sequence $PQ$ and half to $QP$. Each animal receives both treatments in separate periods, with a scientifically justified interval between them and the same outcome assessment after each period. Animal blocks remove persistent between-animal differences, while the two sequences balance treatment against period. Its advantage is potentially high precision from within-animal comparisons; its disadvantage is vulnerability to <carryover effects>, changing disease state and irreversible effects. It is suitable only when comparing the treatments in both periods remains meaningful and residual effects of the first treatment are adequately controlled. A two-period <crossover design> does not by itself disentangle arbitrary treatment-specific <carryover effects>.
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