math project

that if there is a great deal of heterogeneity in experimental units, the value of the variance parameter σ2 in the one-way model will be large. In the presence of a systematic pattern to this variability, the effect of blocking is to filter out the variation due to the heterogeneity in the experimental material in the two-way model appropriate for a randomized block experiment, thus leading to a smaller value of the variance parameter σ2. Therefore, blocking when appropriate and justified increases the chance of detecting departures from H0. So, blocking entails a potential gain in terms of power, while also entailing a potential loss in precision (see page 529 for a discussion of this.) Simulate two datasets for the same single-factor experiment, one where blocking leads to gains in power and one where blocking leads to loss of precision. Illustrate the comparison for 2, 3, and 4 blocks respectively.