Question

# Following is a one-way ANOVA. 30 participants were randomly assigned into three different groups, with 10...

Following is a one-way ANOVA. 30 participants were randomly assigned into three different groups, with 10 participants in each group. The means and sample standard deviations for each group are shown below

 n X_bar Sample standard deviation Group 1 10 18 1.5 Group 2 10 14 2 Group 3 10 22 3

What is the value of η 2 for this ANOVA? Round your answer to two decimal places.

What is the value of ω 2 for this ANOVA? Round your answer to two decimal places.

 paint ni x̅i S2i ni*(Xi-Xgrand)2 (ni-1)*S2i Group 1 10 18.000 2.250 0.000 20.25 Group 2 10 14.000 4.000 160.000 36.00 Group 3 10 22.000 9.000 160.000 81.00 grand mean= 18.000 320.000 137.25 SSTr SSE Source of variation SS df MS F between 320.00 2 160.00 31.475 within 137.25 27 5.08 total 457.25 29

1)

2 =SSbg/SSttoal =320/457.25 =0.70

 ω2 =(k-1)*(F-1)/((k-1)*(F-1)+nk) =0.67

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