We can often use an analysis of variance with data that are not well matched to a linear regression, using dummy variables to avoid the need to model a curved relationship. In this example, a bakery ran an experiment to measure the effect of different recipes on the volume of commercial bread loaves (measured in milliliters). Customers generally prefer larger-looking loaves rather than smaller loaves, even if the net weights are the same. In this experiment, the bakery varied the level of potassium bromate from 0 to 4 milligrams.16
(a) Consider the linear regression of loaf volume on the amount of potassium bromate. Do the data appear to meet the assumptions required by the simple regression model?
(b) Do the data appear to meet the conditions required for fitting an ANOVA? (Determine this visually, before fitting the ANOVA.)
(c) Fit an ANOVA by treating the amounts of potassium bromate as identifying five categories. Can the bakery affect the volume of its loaves by varying the amount of this ingredient?
(d) If your software provides it, give the 95% Tukey confidence interval for the difference in volume produced with no potassium bromate and 2 milligrams of potassium bromate. Is there a statistically significant difference in volume?
(e) Give the 95% Bonferroni confidence interval for the difference in volume produced with no potassium bromate and 2 milligrams of potassium bromate. Is there a statistically significant difference in volume?
(f) Explain any differences between the conclusions of part (c) and the conclusions of parts (d) and (e).