The data set in DS 14.1.1 shows the results of an experiment performed to test the machinery used to measure the hardness of a material. The hardness of a material is measured by pushing a tip into the material with a specified force. The depth h of the resulting indentation is then measured. A laboratory purchases a machine that has three different tips that are supposed to provide identical results. The purpose of the experiment is to investigate whether the different tips can in fact be taken to produce identical results. Three types of material are used and four replicate measurements of indentation are obtained for each experimental configuration.
(a) Construct the analysis of variance table.
(b) Plot the residuals for each of the three tips. Why is it useful to do this? Does it tell you anything interesting?