Question Description
How Many Chews Does It Take to Eat a Mini Candy Bar?
According to the data, somewhere between 4 and 35. Yes, that’s a big difference! The real answer is that it depends on several things. Whether those things make a significant difference or not is can be determined using one-factor and two-factor ANOVA.
When this course was taught on campus, the instructor brings in bags of mini 3 Musketeers and Milky Way candy for the class to evaluate. Each student chewed each candy separately and counted the number of chews until they are ready to swallow the candy. Unfortunately, the candy doesn’t transfer well over the internet, so we’ll be using previous data for this exercise.
Using the tables on the next page, answer the following questions: 1. We usually run a two-factor ANOVA on this data using the factors gender and candy type. What other factors might we use? 2. Do you think there will be any difference in the ANOVA results if we run a one-factor ANOVA using only one of the two factors (gender and candy type) rather than a two-factor ANOVA? Why or why not? 3. Fill out Tables 1, 2, and 3 on the next page. 4. Based on question 3, are there any significant differences in any of the analyses? If so, what are they and how do you know there are significant differences? If not, how do you know there are no significant differences? 5. Were you surprised by the results of questions 3 and 4? Why or why not?
Table 1: One-Factor ANOVA, Factor: Candy Type Source of Variation Sum of Squares DoF
Mean Square F0 Candy 608.4 1 Error 38 Total 2058.0
Fa,n1,n2: Number of candies: Number of genders:
Table 2: One-Factor ANOVA, Factor: Gender Source of Variation Sum of Squares DoF
Mean Square F0 Gender 509.2 1 Error 1548.8 40.76 Total 39
Fa,n1,n2: Number of candies: Number of genders:
Table 3: Two-Factor ANOVA, Factors: Gender and Candy Type Source of Variation Sum of Squares DoF Mean Square F0 Candy 608.4 608.40 Gender 509.2 1 Interaction 1 8.55 Error 36 Total 2058.0
Fa,n1,n2: Fa,n1,n2: Fa,n1,n2: Number of candies: Number of genders:
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