Sample Size Estimation          

John Eng, M.D.
The Russell H. Morgan Department of Radiology and Radiological Science
Johns Hopkins University, Baltimore, Maryland, USA

Web browser requirements for this page:  For Windows, Netscape Navigator 4.0 or Microsoft Internet Explorer 4.0 (later versions are preferred). For Macintosh, Netscape Navigator 4.0.x to 4.7.x. This page may not work with Microsoft Internet Explorer for the Macintosh or later versions of Netscape Navigator for the Macintosh, due to incomplete browser support for Internet standards. Please send any bugs, questions, comments, or suggestions to All electronic mail will be answered.

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:  The lavender box at the top of this page contains StatSupport, a program that supplies basic numerical functions for performing statistical calculations on the Web. StatSupport is written in the Java programming language to enable its use over the Web. Ref. 2 documents the algorithm for StatSupport's inverse normal distribution routine, which was 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.


(Page last modified: 5/1/2003)