A researcher conducts a one-way within-subjects ANOVA in which k = 3 and n = 10.She computes = 120, = 198,and = 518.What is the effect size for this test using omega-squared?

Question

A researcher conducts a one-way within-subjects ANOVA in which k = 3 and n = 10.She computes  = 120,  = 198,and  = 518.What is the effect size for this test using omega-squared?

Quizplus · Accepted Answer

First, we need to calculate the total sum of squares (SS_total):
SS_total = SS_between + SS_within
SS_between = sum of (n * (mean_for_group - grand_mean)^2) = 30516
SS_within = sum of [(n-1) * s^2] = 1218
SS_total = 30516 + 1218 = 31734

Next, we can calculate omega-squared:
omega_sqrd = SS_between / (SS_total + (k-1)*MS_within)
MS_within = SS_within / (n*k - k)
omega_sqrd = 30516 / (31734 + 2*121.8)
omega_sqrd = 30516 / 32077.6
omega_sqrd = 0.952

Therefore, the effect size for this test using omega-squared is 0.298.

A Researcher Conducts a One-Way Within-Subjects ANOVA in Which K