An independent-measures research study compares three treatment conditions using a sample of n = 5 in each treatment.For this study,the three samples have SS₁ = 10,SS₂ = 20,and SS₃ = 15.What value would be obtained for MSwᵢthᵢn?
A)45/14
B)45/12
C)10/2
D)10/3

Question

Quizplus · Accepted Answer

MS_within (Mean Square within groups) is calculated by dividing the sum of the squares within each group (SS_within) by the degrees of freedom within groups (df_within). SS_within is the sum of SS₁, SS₂, and SS₃, which equals 45 (10+20+15). The degrees of freedom within groups is calculated as n(total) - k, where n(total) is the total number of observations and k is the number of groups. Here, n(total) = 5*3 = 15 (since there are 3 groups with 5 observations each), and k = 3, so df_within = 15 - 3 = 12. Therefore, MS_within = SS_within / df_within = 45 / 12.

An Independent-Measures Research Study Compares Three Treatment Conditions Using a Sample