Suppose that the overall F -test obtained from performing a multi-way ANOVA to c
ID: 3227242 • Letter: S
Question
Suppose that the overall F-test obtained from performing a multi-way ANOVA to compare sub-maximal cycling exercise for 30 minutes across adolescents, adults, and the elderly in rural and city subsamples resulted in a p-value that was statistically significant for city versus rural but not for age. Which of the following is true?
The variability within the rural/city area groups is very large compared to between-group variability and the opposite for age.
The ratio of the between and within variability was not sufficiently large for rural/city area.
The variability between the rural/city area groups is larger than the one within each area; however the variability between age groups is the same.
The F-statistic was larger than the critical value obtained from the F-distribution for age.
a.The variability within the rural/city area groups is very large compared to between-group variability and the opposite for age.
b.The ratio of the between and within variability was not sufficiently large for rural/city area.
c.The variability between the rural/city area groups is larger than the one within each area; however the variability between age groups is the same.
d.The F-statistic was larger than the critical value obtained from the F-distribution for age.
Explanation / Answer
F Statistic = variance of the group means / mean of the within group variances.
THe correct answer is A.
1)The variability within the rural/city area groups is very large compared to between-group variability. Hence,we get a significant stastic . For the age case, we get a lower F-stastic and hence the within group variabilty is low
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