Sample Size Estimation

John Eng, M.D.
Johns Hopkins University School of Medicine, Baltimore, Maryland, USA

Instructions:  This page calculates the sample size for four simple study designs. The equations are discussed more fully in Ref. 1, and this web page is intended to accompany that article. To estimate a sample size, identify the equation appropropriate to your study design. Enter values for the parameters under "Input Values" and click the corresponding "Calculate" button. See below for program development details, acknowledgments, and a list of references.

Equation 1 Sample size for a comparison of two means. Input Values Calculated Results Minimum expected difference: Sample size (N): (total, 2 groups) Estimated standard deviation: Zcrit: Desired power: Zpwr: Significance criterion (2-tailed):

Equation 2 Sample size for a comparison of two proportions. Input Values Calculated Results Estimate of 1st proportion (p1): Sample size (N): (total, 2 groups) Estimate of 2nd proportion (p2): Zcrit: Desired power: Zpwr: Significance criterion (2-tailed):

Equation 3 Sample size for a confidence interval around a mean. Input Values Calculated Results Width of confidence interval: Sample size (N): Estimated standard deviation: Zcrit: Significance criterion (2-tailed):

Equation 4 Sample size for a confidence interval around a proportion. Input Values Calculated Results Width of confidence interval: Sample size (N): Estimated proportion (p): Zcrit: Significance criterion (2-tailed):

Program Development Details and Acknowledgments:  This page uses normsdist.js, a small library that supplies numerical functions for performing statistical calculations on the web related to the normal distribution. The normsdist.js library is written in the JavaScript programming language to enable its use over the web. Ref. 2 documents the algorithm for normsdist.js's inverse normal distribution routine, which is used to calculate Eqs. 1 and 2.

References:
1. Eng J. Sample size estimation: how many individuals should be studied? Radiology 2003; 227: 309-313.
2. Acklam PJ. An algorithm for computing the inverse normal cumulative distribution function. Available at home.online.no/~pjacklam/notes/invnorm. Accessed 28 August 2002.

(Content updated 4/20/2017, page modified 3/17/2020.)