Table POT0x. Exact test for single proportion

Power is computed using the cumulative binomial distribution. The cut-point for rejection is computed as the largest k for which the probability of observing k or fewer successes is less than or equal to the significance level, α, when π = π0 , for a one-sided test in which πA < π0.  For a one-sided test in which πA > π0, we choose the smallest k for which the probability of observing k or more successes is less than or equal to α. For a two-sided test we require both probabilities to be less than or equal to α /2. Power is computed for the rejection regions for π = πA .

See Dixon, W.J., Massey, F.J. (1983) Introduction to Statistical Analysis. 4th Edition. McGraw-Hill. Pages 281-284 and Chernick, M.R., Liu, C. Y. “The saw-toothed behavior of power versus sample size and software solutions: single binomial proportion using exact methods.” The American Statistician 56(2002) pp 149-155. Figure POT0x shows computations for one example. Additional values tested: significance level .001, .20 one and two-sided for proportions between .001 and .999 and sample sizes  10 to 10,000. Checked against tables in Dixon, W.J., Massey, F.J. (1983) Introduction to Statistical Analysis. 4th Edition. McGraw-Hill, Hintze J (2008)  PASS 2008.  NCSS LCC, Kaysville Utah, and Ralph O’Brien tutorial 1999.

Figure POT0x. In these four columns, nQuery Advisor® 7.0 computed power for five sample sizes.