Tests for One Proportion

Introduction The One-Sample Proportion Test is used to assess whether a population proportion (P1) is significantly different from a hypothesized value (P0). This is called the hypothesis of inequality. The hypotheses may be stated in terms of the proportions, their difference, their ratio, or their odds ratio, but all four hypotheses result in the same test statistics. For example, suppose that the current treatment for a disease cures 62% of all cases. A new treatment method has been proposed and studied. In a sample of 80 subjects with the disease that were treated with the new method, 63 were cured. Do the results of this study support the claim that the new method has a higher response rate than the existing method? This procedure calculates sample size and statistical power for testing a single proportion using either the exact test or other approximate z-tests. Exact test results are based on calculations using the binomial (and hypergeometric) distributions. Because the analysis of several different test statistics is available, their statistical power may be compared to find the most appropriate test for a given situation. This procedure has the capability for computing power using both the normal approximation and binomial enumeration for all tests. Some sample size programs use only the normal approximation to the binomial distribution for power and sample size estimates. The normal approximation is accurate for large sample sizes and for proportions between 0.2 and 0.8, roughly. When the sample sizes are small or the proportions are extreme (i.e. less than 0.2 or greater than 0.8) the binomial calculations are much more accurate.