Data set: Cookies
Two students wanted to determine if people could taste the difference in chocolate chip cookies with varying amounts of sugar and varying amount of freshness. Nine batches were made, following the recipe on the chocolate chip bag as closely as possible except for the amount of sugar. Each batch was randomly assigned to one of three treatments: half the suggested amount of sugar, the suggested amount of sugar, and double the suggested amount of sugar. On the day the nine batches of cookies were baked, the researchers handed out five cookies from each batch (a total of 45 cookies) to people in their dorm and asked them to rate the cookies from 1 through 10, with 1 being inedible and 10 being the best cookie they ever had. The researchers stored the rest of the cookies for a day. On the second day, the researchers handed out five more cookies from each of the original nine batches to students in their dorm and asked them to rate them from 1 through 10. The researchers did the same thing on the third day. Split-plot designs are often used when time is a second factor. The whole- plot factor (Sugar) is randomly assigned to whole- plot units (Batch), and then these same units (Batches) are measured at several time points (Day). This is called a split plot in time, as the split plots are the time points within the units. The factor Day is confounded with any other effect that occurs over time. For example, suppose this study was conducted on a Saturday, Sunday, and Monday. Students may have been more stressed on Monday and unknowingly tended to give lower scores on Monday. Or more parents may have been around on the weekend and may have been more positive than students when rating the cookies.
a. Specify whether each factor in the study is fixed or random and whether each factor is crossed or nested.
b. Calculate an appropriate ANOVA for this study using Taste 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.