First we will do a small-scale Monte Carlo study of 500 random assignments using each of the two designs when the response variable is strongly related to the other variable. We let the correlation between them be k1 = .8. The details of how to use the Minitab macro Xdesign.mac or the R function Xdesign are in Appendix 3 and Appendix 4, respectively.

Look at the boxplots and summary statistics.

i. Does it appear that, on average, all groups have the same underlying mean value for the other (lurking) variable when we use a completely randomized design?

ii. Does it appear that, on average, all groups have the same underlying mean value for the other (blocking) variable when we use a randomized block design?

iii. Does the distribution of the other variable over the treatment groups appear to be the same for the two designs? Explain any difference.

iv. Which design is controlling for the other variable more effectively?

Explain.

v. Does it appear that, on average, all groups have the same underlying mean value for the response variable when we use a completely randomized design?

vi. Does it appear that, on average, all groups have the same underlying mean value for the response variable when we use a randomized block design?

vii. Does the distribution of the response variable over the treatment groups appear to be the same for the two designs? Explain any difference.

viii. Which design will give us a better chance for detecting a small difference in treatment effects? Explain.

ix. Is blocking on the other variable effective when the response variable is strongly related to the other variable?