StatTools : Sample Size for Comparing Two Proportions Explained and Tables

Links : Home Index (Subjects) Contact StatTools

Related link :
Sample Size Introduction and Explanation Page
Pilot Studies Explained Page
Sample Size for Comparison of Two Proportions Program Page
Unpaired Comparison of Two Proportions Program Page
Unpaired Proportions Explanations Page

Introduction Sample Size Tables References
This page presents tables of sample size (per group) comparing two unpaired proportions, for the following combinations.
  • Powers of 0.8, 0.9, and 0.99
  • Probability of Type I Error (α) of 0.1, 0.05, 0.01, and 0.001
  • One and two tail models
Sample size calculated to be less than 1/proportion (ssiz<1/p1 or ssiz<1/p2) are not included in the table, as a single positive case in the group will then exceed the proportion being compared.

Sample size for two proportions are used mostly in the Risk Difference model, although it is also used for Risk Ratio comparisons.

The sample size from this page can be used for Odds Ratio comparison, if Odds Ratio is used in a similar manner as Risk Differences or Risk Ratio to compare two proportions. However, Odds Ratio is often used in matched pair controlled studies, and in that case the sample size is calculated as number of matched units, and a different algorithm is used. Sample size for matched paired controlled studies are available in the Sample Size for Matched Paired Controlled Studies Program Page

if a researcher wishes to use a smaller sample size than those published in these tables or calculated using the Sample Size for Comparison of Two Proportions Program Page , he/she should use either the Chi Squares Test for the 2x2 contingency table or the Fisher's Exact probability, as these do not assume a normal transformation of the difference between proportions.

The Chi Squares Test requires a minimum of 30 cases overall, and each cell in the 2x2 table should have a minimum of 5 cases.

The Fisher's Exact Probability is based on the Poisson distribution, and has no minimal sample size requirement. However, a statistically significant result (p<0.05) is unlikely whatever the data, if less than 6 cases overall are included.

In the tables

  • Power= 1-β, where β is the Probability of Type II Error
  • α is the Probability of Type I Error
  • p1 and p2 are the proportions in the two groups to be detected
  • 1 tail and 2 tail are the statistical models.