14. Meat cooking experiment (L. Alvarez, M. Burke, R. Chow, S. Lopez, and C. Shirk, 1998)

An experiment was run to investigate the amount of weight lost (in grams) by ground beef hamburgers after grilling or frying, and how much the weight loss is affected by the percentage fat in the beef before cooking. The experiment involved two factors: cooking method (factor A, with two levels frying and grilling, coded 1, 2), and fat content (factor B, with three levels 10, 15, and 20%, coded 1, 2, 3). Thus there were six treatment combinations 11, 12, 13, 21, 22, 23, relabeled as treatment levels 1, 2, …, 6, respectively. Hamburger patties weighing 110 g each were prepared from meat with the required fat content. There were 30 “cooking time slots” which were randomly assigned to the treatments in such a way that each treatment was observed five times (r = 5). The patty weights after cooking are shown in Table 3.14.

(a) Plot the data and comment on the results.

(b) Write down a suitable model for this experiment.

(c) Calculate the least squares estimate of the mean response for each treatment. Show these estimates on the plot obtained in part (a).

(d) Test the null hypothesis that the treatments have the same effect on patty post-cooking weight.

(e) Estimate the contrast τ1 − (τ2 + τ3)/2 which compares the effect on the post-cooked weight of the average of the two higher fat contents versus the leanest meat for the fried hamburger patties.

(f) Calculate the variance associated with the contrast in part (e). How does the value of the variance compare with the variance σ2 of the random error variables?