Question

3. Suppose you are a researcher studying treatments for depression. Imagine three treatment groups (anti-depressant, therapy, and placebo) are being compared using Analysis of Variance.

What effect would each of the following have on an F score (make it smaller, make it larger, or cause no change)?

Explain why.

(Note: If you have trouble, look at the slides and consider the formula F = variance between groups/variance within groups, and consider what would influence that ratio).

a. A large within-group error.

b. One group with a mean that is two standard deviations away from the other groups.

c. A great deal of overlap between two groups.

d. Adding a bunch of outliers (extreme scores) to all three groups being compared.

Answer 1

a) A large within-group error would make the F-score smaller as F = variance between groups/within groups.

b) One group with a mean that is two sd away from the other groups would mean that the variance between groups is high. Hence, F score would be larger.

c) If there is a great deal of overlap between two groups, between group variance will be less. Hence, the F score would be smaller

d) If we add a bunch of outliers, the within group variance would increase. Hence, the F score would get smaller.