Aug 29, 2003

Documentation for

Sample Size for a Proportion

Kevin M. Sullivan, PhD, MPH, MHA

cdckms@sph.emory.edu

This module calculates a sample size for a proportion. The data input screen is as follows:

The four values requested are:

· Population size – what is the size of the population to be surveyed? The default value is one million. In general, when sampling from a “large” population, whether there are 100,000 in the population or 100 million, this will not affect the sample size calculation. However, when the population size is small, then this could reduce the sample size.

· Anticipated % frequency (p) – provide an educated guess of the percent of the population with the outcome of interest. Of course, if you knew this with any accuracy, you would not need to perform the survey. If you are unsure of the percentage, use of 50% will result in the largest sample size (holding the other three pieces of information being requested the same).

· Confidence limits as +/- percent of 100 – this question is asking exactly how wide (in absolute terms) you would like the confidence interval to be around your point estimate. Using the default values, with an anticipated frequency of 50% and confidence limits as +5%, for the calculated sample size the confidence interval would be 50% +5%, i.e., (45%, 55%). With an anticipated frequency of 85% with confidence limits of +10%, for the calculated sample size the confidence interval would be (75%, 95%).

· Design Effect – if simple random sampling is to be used to select individuals (or whatever the element of analysis), then the design effect (DEFF) should be left as one. If a cluster-type survey is being used in the sampling methodology, the DEFF is frequently larger than one, perhaps in the range of 2 to 10 depending on the outcome being studied. An estimate of the DEFF can usually be found in the literature.

The results of the calculation, using the default values, is shown next:

At the top of the output are the values supplied by the user. In the middle section are sample sizes for various confidence levels, from 80% to 99.99%. In most situations the 95% confidence level is used, therefore in this example, the sample size is 384.

The sample size formula used is as follows:

where

# References

Schaeffer RL, Mendenhall W, Ott L. Elementary Survey Sampling, Fourth Edition. Duxbury Press, Belmont, California 1990.