Bethea et al. (1985) reported data on an experiment to determine the effectiveness of four adhesive systems for bonding insulation to a chamber. The adhesives were applied both with and without a primer. Tests of peel-strength were conducted on two different thicknesses Table 16.19: Steel bar lengths.
Heat treatment W Heat treatment L Machine A B C D A B C D 6 7 1 6 4 6 −1 4 Time 1 9 9 2 6 6 5 0 5 1 5 0 7 0 3 0 5 3 5 4 3 1 4 1 4 6 8 3 7 3 6 2 9 Time 2 3 7 2 9 1 4 0 4 1 4 1 11 1 1 −1 6 −1 8 0 6 −2 3 1 3 5 10 −1 10 6 8 0 4 Time 3 4 11 2 5 0 7 −2 3 9 6 6 4 3 10 4 7 6 4 1 8 7 0 −4 0 Table 16.20: Peel-strength of various adhesive systems.
Adhesive Adhesive 1 2 3 4 1 2 3 4 60 57 19.8 52 73 52 32.0 77 63 52 19.5 53 79 56 33.0 78 With 57 55 19.7 44 76 57 32.0 70 Primer 53 59 21.6 48 69 58 34.0 74 56 56 21.1 48 78 52 31.0 74 57 54 19.3 53 74 53 27.3 81 59 51 29.4 49 78 52 37.8 77 48 44 32.2 59 72 42 36.7 76 Without 51 42 37.1 55 72 51 35.4 79 Primer 49 54 31.5 54 75 47 40.2 78 45 47 31.3 49 71 57 40.7 79 48 56 33.0 58 72 45 42.6 79 Thickness A Thickness B of rubber. Using two thicknesses of rubber was not part of the original experimental design. The existence of this factor was only discovered by inquiring about a curious pattern of numbers in the laboratory report. The data are presented in Table 16.20. Another disturbing aspect of these data is that the values for adhesive system 3 are reported with an extra digit. Presumably, a large number of rubber pieces were available and the treatments were randomly assigned to these pieces, but, given the other disturbing elements in these data, I wouldn’t bet the house on it. A subset of these data was examined earlier in Exercise 12.7.6.

(a) Give an appropriate model. List all the assumptions made in the model.

(b) Check the assumptions of the model and adjust the analysis appropriately.

(c) Analyze the data. Give an appropriate analysis of variance table. Examine appropriate contrasts.