Question

If the effect size for a four-group study was .5, the sum of square between was 100, and the mean square within was 5, how many participants were in the study?

Answer 1

effect size = sum of square between / sum of square total = 0.5

=> 100 / sum of square total = 0.5

=> sum of square total = 100 / 0.5 = 200

sum of square within =  sum of square total - sum of square between = 200 - 100 = 100

mean square within = sum of square within / (n - k)

where n is number of participants and k is number of groups

5 = 100 / (n - 4)

=> (n - 4) = 100/5

=> n - 4 = 20

=> n = 20 + 4 = 24

Thus, there were 24 participants in the study.