Sample size and power estimation for studies with health related quality of life outcomes: a comparison of four methods using the SF-36

Table 2 CPSW Study [7] Observed Effect Sizes for Control vs. Intervention Groups

SF-36 Dimension	Group	n	mean	sd	Mean Diff δ	Δ _Normal	P_Noether Parametric	Pr(Y > X) Non-parametric
Physical	Control	241	89.9	14.5	2.6	0.17	0.548	0.561
Function	Intervention	254	87.3	15.8
Role	Control	241	74.3	38.1	9.1	0.23	0.566	0.568
Physical	Intervention	254	65.2	39.5
Bodily	Control	241	75.6	23.7	4	0.17	0.547	0.552
Pain	Intervention	254	71.6	23.8
General	Control	241	77.7	17.7	2.4	0.13	0.537	0.542
Health	Intervention	254	75.3	18.5
Vitality	Control	241	51.1	20.7	1.3	0.06	0.517	0.514
	Intervention	254	49.8	21.7
Social	Control	241	81.6	22.7	4.7	0.20	0.556	0.561
Function	Intervention	254	76.9	24.2
Role	Control	241	77.9	36.4	1.1	0.03	0.509	0.515
Emotional	Intervention	254	76.8	35.5
Mental	Control	241	72.9	17.2	-0.2	-0.01	0.497	0.499
Health	Intervention	254	73.1	16.7

Effect size Δ _Normal = mean difference divided by the pooled standard deviation. Effect size p_Noether Pr(Y_Control > X_Intervention), based on U/nm, where U = MW test statistic (with allowance for ties). Parametric estimate of Pr (Y > X) based on equation 1.

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