Under what circumstances would you use a randomized complete block analysis of variance design instead of a one-way analysis of variance?

Question

What will be an ideal response?

Answer 1

Analysis of variance is a statistical tool that is used in cases where we are interested in testing whether three or more populations have the same mean. One-way analysis of variance is used when the samples from the populations are independent and we are not interested in controlling for a second factor that might adversely influence the analysis. With one-way, we test only whether the population means are all equal. However, there are cases in which we will be interested in controlling for a second factor that could have an adverse influence on our results. In these cases, we will want to use the concept of paired samples. The second factor (called the blocking factor) can have multiple levels. In the randomized complete block design (without replication), one observation is obtained for each combination of the two-factors. There are actually two hypotheses tests of interest: the primary test to see whether the populations of interest have different means, and the secondary test to determine whether we were justified in blocking. If the hypothesis test for blocking shows that we're justified in controlling for the second factor, then we look to the primary hypothesis test. If blocking is not determined to be effective, this means that we could (should) have selected independent samples. There is a cost in terms of lost degrees of freedom and it becomes more likely that we will not reject the primary hypothesis. It may be necessary to re-do the experiment as a one-way design if blocking is deemed not effective and the primary null hypothesis is not rejected.