1. Drug experiment An experiment designed as a split-plot design was described by W.M. Wooding in the Journal of Quality Technology in 1973. The experiment concerned the evaluation of eight drugs (factor A at a = 8 levels) for the treatment of arthritis. A second factor was the dose of the drug (factor B at b = 2 levels), and the third factor was the length of time (factor C at c = 2 levels) that a measurement was taken after injection by a substance known to cause an inflammatory reaction. The experimental units used in the study were n = 64 rats. The response was the amount of fluid (in milliliters) measured in the pleural cavity of an animal after having been administered a particular treatment combination. In many pharmacological studies, time of day has an effect on the response due to changing laboratory conditions, etc. Consequently, the experiment was divided into blocks, whole plots and split plots. The blocks were of size 32, each set of 32 observations being measured on a single day. Each treatment combination was measured once per day. Each day was then subdivided into 4 whole plots of size 8, where the eight measurements within a whole plot were taken fairly close together in time. Since the effect of the drug (A) was of primary importance, and since the effects of B and C were of interest only in the form of an interaction with A, the main effects of B and C and the BC interaction were confounded with the whole plots. The data are shown in Table 19.32, and the experimenter used the logarithms of the data in his analysis. Notice that the design for A on the split plots is a randomized block design, and the design for the BC combinations on the whole plots is also a randomized block design.

(a) Write out a model for this experiment.

(b) Calculate an analysis of variance table using the logarithms of the data. Distinguish between the effects measured on the whole plots and those measured on the split plots. Identify the whole-plot error and split-plot error.

(c) Test any hypotheses of interest and state your conclusions clearly.

(d) Examine interaction plots of any important interactions. Calculate a set of 95% confidence intervals for the differences between pairs of drugs. State your conclusions.