Question

We are going to study the difference in means of two independent samples. We assume the difference in mean between these two samples 6.0 (assuming: mu1=16 and mu2=10), and the standard deviation (among all patients in two groups) is 10. Our hypothesis is H0: mu1 = mu2 vs Ha: mu1 not equal to mu2. To achieve a power of 80% to test the difference of 6.0, how many patients in total should we recruit? The significance level is 0.05, and we assume attrition = 10%

Answer 1

We are going to study the difference in means of two independent samples. We assume the difference in mean between these two samples 6.0 (assuming: mu1=16 and mu2=10), and the standard deviation (among all patients in two groups) is 10. Our hypothesis is H0: mu1 = mu2 vs Ha: mu1 not equal to mu2. To achieve a power of 80% to test the difference of 6.0, how many patients in total should we recruit? The significance level is 0.05, and we assume attrition = 10%

  

Sample size calculation

For 0.05 level, z = 1.96

d = 6

sd=10

for 80% power, for β =0.20, z = 0.842

= 43.6

The sample size for each group =44

Total sample size for two groups=88

Accounting for 10% attrition, (100/90)*88 =97.78

= 98 ( rounded)

The required sample size = 98