Exercise 8.35 describes a study examining hippocampus volume in the brain between controls who have never played football, football players with no history of concussion, and football players with a history of concussion. The data are available in FootballBrain. Use StatKey or other technology to conduct an ANOVA randomization test to determine whether there is a significant difference in mean hippocampus volume between the three categories.

(a) What is the F-statistic for the observed data?

(b) Generate one randomization sample. What is the F-statistic for that sample?

(c) Generate a full randomization distribution and find the p-value. (If you have also completed Exercise 8.35, compare this result with the p-value obtained using a theoretical F-distribution.)

(d) What is the conclusion of the test?

Data From Exercise 8.35:
A study examining a possible relationship of football playing and concussions on hippocampus volume, in \(\mu \mathrm{L}\), in the brain. The study included three groups: controls who had never played football (Control), football players with no history of concussions (FBNoConcuss), and football players with a history of concussions (FBConcuss). The data is available in FootballBrain, and the side-by-side boxplots shown in Exercise 2.143 indicate that the conditions for using the F-distribution appear to be met.

Data From Exercise 2.143:

Transcribed Image Text:

Total Hippocampus Volume 10000 9000 8000 7000 6000 5000 4000 Control Football No Concussion Group Football With Concussion