12.75 Testing several contrasts from the dandruff study. Refer to Exercise 12.72. There are several natural contrasts in this experiment that describe comparisons of interest to the experimenters. They are (1) Placebo versus the average of the other three treatments, (2) Keto versus the average of the two Pyr treatments, and (3) PyrI versus PyrII.

  1. (a) Express each of these three contrasts in terms of the means (μ’s) of the treatments.

  2. (b) Give estimates with standard errors for each of the contrasts.

  3. (c) Perform the significance tests for the contrasts. Summarize the results of your tests and your conclusions.