Refer to Exercise 12.31. Suppose that a completely

Chapter 12, Problem 33SE

(choose chapter or problem)

Refer to Exercise 12.31. Suppose that a completely randomized design is employed for the comparison of the two treatment means. Then, a response could be modeled by the expression

\(Y_{i j}=\mu_{1}+P_{y}+\varepsilon_{y}\)

but the "pair effect"  (which will still affect an experimental unit) will be randomly selected and will likely differ from one of the  observations to another. Further, in contrast to the matched-pairs experiment, the pair effects will not cancel when you calculate \(\left(\overline{Y_{1}}-\overline{Y_{2}}\right)\). Compare \(V\left(\overline{Y_{1}}-\overline{Y_{2}}\right)=V(\bar{D})\) for this design with the matched-pairs design of Exercise . Why is the variance for the completely randomized design usually larger?

Equation transcription:

Text transcription:

Y{i j}=mu{1}+P{y}+varepsilon{y}

(overline{Y{1}}-overline{Y{2}})

V(overline{Y{1}}-overline{Y{2}})=V(bar{D})