Data set: Cookies2
Two students wanted to test whether ingredients (butter, Fleischmann’s corn oil margarine, or unflavored Crisco), cooking time (short or long) or cookie type (chocolate chip or gingersnap) influenced taste ratings. Both main effects and interactions were of interest. Twelve volunteers were found who were each willing to taste 12 cookies in random order (one taste for each of the two cookie types, the three ingredient types, and the two cooking times). Each volunteer ranked all 12 cookies on a scale from 1 to 10 (10 being the best).
a. Specify whether each factor in the study is fixed or random and whether each factor is crossed or nested with all other factors.
b. Calculate an appropriate ANOVA for this study using Rating as the response. State your conclusions, taking into account random sampling and random allocation. Provide appropriate plots.
c. Check the model assumptions. Create a plot to check if the data appear to be skewed or have outliers. Is there reason to doubt the equal variance assumption? Are the error terms approximately normally distributed? d. Draw a Hasse diagram corresponding to this study.
e. If these student researchers had asked your help in designing this study, would you have suggested having 144 people each taste one cookie and rate it? Is there a benefit to having 12 people each taste 12 cookies?