a total sample 2N would be needed to detect a true difference 8 between H and uc with power(1-B)and significant level a by formula 4Z+Zo 2N=
◼ A total sample 2N would be needed to detect a true difference between I and C with power (1-) and significant level by formula: ( ) 2 2 2 4 2 Z Z N + =
Example 1 An investigator wish to estimate the sample size necessary to detect a 10 mg/dl difference in cholesterol level in a diet intervention group compared to the control group The variance from other data is estimated to be(50 mg/dl For a two sided 5% significance level, Za=1.96, and for 90% power, ZB-1.282 2N=4(1.96+1282)2(50)2/102=1050
Example 1 ◼ An investigator wish to estimate the sample size necessary to detect a 10 mg/dl difference in cholesterol level in a diet intervention group compared to the control group. The variance from other data is estimated to be (50 mg/dl). For a two sided 5% significance level, Z=1.96, and for 90% power, Z=1.282. ◼ 2N=4(1.96+1.282)2(50) 2/102=1050
EXamplela Baseline adjustment An investigator interested in the mean levels of change might want to test whether diet intervention lowers serum cholesterol from baseline levels when compare with a control H:A。-Δ 0 H:△。-△,≠ 00 A 0=20mg/dl, 8=10mg/dI 2N=4(1.96+1282)2(20)2/102=170
Example1a Baseline Adjustment ◼ An investigator interested in the mean levels of change might want to test whether diet intervention lowers serum cholesterol from baseline levels when compare with a control. ◼ H0: =0 ◼ HA: 0 ◼ =20mg/dl, =10mg/dl ◼ 2N=4(1.96+1.282)2(20) 2/102=170 c − I c − I
A Professional statement a sample size of 85 in each group will have 90%o power to detect a difference in means of 10.0 assuming that the common standard deviation is 20.0 using a two group t-test with a 0.05 two-sided significant level
A Professional Statement ◼ A sample size of 85 in each group will have 90% power to detect a difference in means of 10.0 assuming that the common standard deviation is 20.0 using a two group t-test with a 0.05 two-sided significant level
Values of f(a,b) to be used in formula for sample size calculation β( Type II error) 0.05 0.1 0.2 0.5 (lype 0.1 108 8.6 6.2 2.7 error) 0.05 13.0 105 7.9 3.8 0.02 15.8 13.0 100 0.01 17.8 149 17 (zn+2z0)=f(a,)
Values of f(,) to be used in formula for sample size calculation (Type II error) 0.05 0.1 0.2 0.5 (Type I error) 0.1 0.05 0.02 0.01 10.8 13.0 15.8 17.8 8.6 10.5 13.0 14.9 6.2 7.9 10.0 11.7 2.7 3.8 5.4 6.6 ( ) ( , ) 2 Z + Z = f