This calculator is useful for tests concerning whether the means of two groups are different. Suppose the two groups are 'A' and 'B', and we collect a sample from both groups -- i.e. we have two samples. We perform a two-sample test to determine whether the mean in group A, $\mu_A$, is different from the mean in group B, $\mu_B$. The hypotheses are
This calculator uses the following formulas to compute sample size and power, respectively:
R code to implement these functions:
muA=132.86 muB=127.44 kappa=2 sdA=15.34 sdB=18.23 alpha=0.05 beta=0.20 (nA=(sdA^2+sdB^2/kappa)*((qnorm(1-alpha)+qnorm(1-beta))/(muA-muB))^2) ceiling(nA) # 85 z=(muA-muB)/sqrt(sdA^2+sdB^2/kappa)*sqrt(nA) (Power=pnorm(z-qnorm(1-alpha))) ## Note: Rosner example on p.303 is for 2-sided test. ## These formulas give the numbers in that example ## after dividing alpha by 2, to get 2-sided alpha.
Rosner B. 2010. Fundamentals of Biostatistics. 7th Ed. Brooks/Cole. page 302 and 303.
Chow S, Shao J, Wang H. 2008. Sample Size Calculations in Clinical Research. 2nd Ed. Chapman & Hall/CRC Biostatistics Series. page 58.