Johnson and Leone describe an experiment conducted to investigate warping of copper plates. The two factors studied were temperature and the copper content of the plates. The response variable is the amount of warping. The data are as follows: Consider a two-factor factorial experiment. Develop a formula for finding a 100 (1 - α)% confidence interval on the difference between any two means for either a row or column factor. Apply this formula to find a 95% CI on the difference in mean warping at the levels of copper content 60 and 80%
Copper Content (%)
Temperature(°C) 40 60 80 100
50 17, 20 16, 21 24, 22 28, 27
75 12, 9 18, 13 17, 12 27, 31
100 16, 12 18, 21 25, 23 30, 23
125 21, 17 23, 21 23, 22 29, 31
(a) Is there any indication that either factor affects the amount of warping? Is there any interaction between the factors? Use a = 0.05.
(b) Analyze the residuals from this experiment.
(c) Plot the average warping at each level of copper content and compare the levels using Fisher's LSD method. Describe the differences in the effects of the different levels of copper content on warping. If low warping is desirable, what level of copper content would you specify?
(d) Suppose that temperature cannot be easily controlled in the environment in which the copper plates are to be used. Does this change your answer for part (c)?