The data in the next  are the results of an experiment to investigate the sources of variability in testing the strength of Portland cement. A sample of cement was divided into small samples for testing. The cement was “gauged” (mixed with water) by three different men called gaugers, and then it was cast into cubes. Three men, called breakers, later tested the cubes for compressive strength. The measurements are in pounds per square inch. Each gauger gauged 12 cubes, which were then divided into three sets of four, and each breaker tested one set of four cubes from each gauger. All the tests were carried out on the same machine. The purpose of the experiment was to identify the source of and measure the variability among gaugers and breakers. (a) Compute the estimated cell means and display your results in the format. (b) Plot the estimated cell means of the breakers (factor B) against the the three levels of gaugers (factor A)  for an example). Does the graph suggest the existence of an interaction? (c) Test for the existence of main effects and interactions by constructing the ANOVA . (d) Check the model assumptions by graphing sui residual plots.

(Source: O.L. Davies and P.L. Goldsmith (eds.) (1972), Statistical Methods in Research and Production, 4th ed., Edinburgh, Oliver and Boyd, p. 154; quoted in D.J. Hand (1994), p. 24.)