July 11, 2005

Documentation of power for comparing two means

Minn M. Soe, MD, MPH, MCTM : msoe@sph.emory.edu

Kevin M. Sullivan, PhD, MPH, MHA: cdckms@sph.emory.edu

In several situations, a predetermined sample size is available for a study, and how much power the study will have for detecting a specific difference of means needs to be estimated. This module estimates the power for studies that compare two sample means. The data input screen is as follows:

The input values requested are:

· Confidence intervals (%) that can be chosen are 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 98, 99, 99.5, 99.8, 99.9, 99.95, 99.98 & 99.99, and they are two-sided.

· Enter individual means (or) difference between 2 group means.

· Enter the available sample sizes for two groups.

· Enter standard deviation (or) variance of individual sample mean.

The result of the calculation is shown next:

The interpretation of power in this study is as follows: If, in truth, mean of Group 1 differs from that of Group 2 given the above values, this study would have 55.52% chance of detecting a difference without the continuity correction.

The formula for the estimation of power is as follows:

The notation for the formulae are:

= sample size of Group 1

= standard deviation of Group 1

= standard deviation of Group 2

= difference of group means

= ratio of sample size: Group 2/ Group 1
Z1-α/2 = the two-sided Z value (eg. Z=1.96 for 95% confidence interval).

Reference:

Bernard Rosner. Fundamentals of Biostatistics (5th edition). (based on equation 8.28)

Acknowledgement:

Default values were obtained from example 8.32 (pg. 309) described in 'Fundamentals of Biostatistics' (5th edition) by Bernard Rosner.