A 24
complete factorial experiment was performed to study four factors on the taste of brownies.
The factors and their levels are given in Table 1. Six persons were asked to provide scores for each
batch of brownies and the average score for each batch is given in Table 2 together with the order of
the runs.
1. Estimate the main and interaction effects.
2. Use Daniel’s, Length’s, and Dong’s methods to determine the significant effects.
3. Which, if any, effects are significant at level α = 0.10?
4. Fit a model containing only the significant effects to the data, plot the residuals, and state your
conclusions.
5. Show a plot of the yields (average scores) versus run order.
6. Can the plot provide a possible explanation for the significant effects?
Table 1: Factor levels for cookie experiment
Factor Low level (–) High level (+)
Oven temperature (A) 300 degrees 400 degrees
Cooking oil (B) vegetable oil coconut oil
Mixing method (C) hand mixing with spoon electric mixer
Amount of sugar (D) 1 cup 2 cups
Table 2: Results from brownie experiment
Run Factor A Factor B Factor C Factor D Average
order Temperature Oil Mixing Sugar score
3 − − − − 15.3
9 + − − − 7.6
12 − + − − 11.2
6 + + − − 13.0
14 − − + − 10.8
16 + − + − 14.0
7 − + + − 17.8
1 + + + − 13.2
11 − − − + 9.0
13 + − − + 17.3
5 − + − + 11.0
15 + + − + 8.8
2 − − + + 15.0
8 + − + + 12.8
10 − + + + 13.0
4 + + + + 18.6
