Question

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.

Answer 1

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