Activity 41
MATH 216: Statistical Thinking
Activity 1
Question: “If the F-statistic is close to 0, what does this suggest about the variability between groups compared to the variability within groups?”
Options:
- The variability between groups is much larger than within groups.
- The variability between groups is much smaller than within groups.
- The variability between groups is similar to the variability within groups.
Activity 2
Given the ANOVA table below, calculate the missing values for A, B, C, D, and E.
| Source | df | SS | MS | F |
|---|---|---|---|---|
| Groups | A |
169.05 | C |
E |
| Error | 11 | B |
D |
|
| Total | 13 | 302.02 |
Activity 3:
Complete the ANOVA table for an experiment with 4 groups and 24 total observations:
| Source | df | SS | MS | F |
|---|---|---|---|---|
| Groups | 3 | 240 | ? | ? |
| Error | ? | ? | 18 | |
| Total | 23 | 600 |
Activity 4:
Given \(F = 3\), fill in the missing values:
| Source | df | SS | MS | F |
|---|---|---|---|---|
| Groups | 2 | 180 | ? | 3 |
| Error | ? | ? | 30 | |
| Total | 20 | 720 |
Activity 5: Frisbee ANOVA Hypothesis Testing
Scenario: Using the Frisbee grip experiment data (Distance ~ Grip), answer the following:
Question 1: Hypothesis Testing
- State the null and alternative hypotheses for testing if grip type affects throwing distance.
- Interpret the F-statistic (2.045) and p-value (0.154) in context.
Question 2: Assumptions
The researchers checked these diagnostics:
- Group sizes: \(n_{\text{Normal}}=8\), \(n_{\text{Noodle}}=8\), \(n_{\text{Talon}}=8\)
- Standard deviations: \(s_{\text{Normal}}=6.1\), \(s_{\text{Noodle}}=7.2\), \(s_{\text{Talon}}=5.9\)
- Verify the equal variance assumption using the “2x rule.”
- Explain when normality is still plausible despite small \(n_i\).