Seven experimental treatments, A, B, C, D, E, F and G, are to be compared in a replicated experiment. However, the experimental units form natural groups of six, so one treatment must be omitted from each group.

(a) Devise a balanced incomplete block design within these constraints. How many replications are required to achieve balance?

(b) Invent values for the response variable from this experiment, and perform the appropriate analysis of variance.

(c) Confirm that the efficiency factor in this analysis agrees with Equation 8.1, and that SEDifference for the treatment means agrees with Equation 8.2.

(d) Show that if one block is omitted from the experiment it can no longer be simply analysed by analysis of variance, but that it can still be analysed by mixed modelling.

(e) Obtain the treatment means from the analysis of variance of the complete experiment: (i) with recovery of interblock information (ii) without recovery of interblock information.

(f) Obtain the same two sets of means from mixed-model analyses.