A study has three groups, each with an equal number of participants. The population variance is estimated from the variance within each group, giving three estimates, 54.4, 48.6, and 50.9. What is the within-group estimate of the population variance?
A)(54.4 + 48.6 + 50.9)/(3-1)= 76.95
B)(54.4 + 48.6 + 50.9)/3 = 51.3
C)(54.4 + 48.6 + 50.9)/(3 + 1)= 38.48
D)(54.4 + 48.6 + 50.9)/(3 + 2)= 30.78

Question

Quizplus · Accepted Answer

The within-group estimate of the population variance is calculated by taking the average of the variances within each group. Therefore, the correct calculation is (54.4 + 48.6 + 50.9)/3 = 51.3. Option A is incorrect because it includes an incorrect formula and incorrectly assumes the number of participants and groups. Option C and D are incorrect because they use incorrect formulas and do not consider the number of groups accurately.

A Study Has Three Groups, Each with an Equal Number