Unbiased Small Sample Size Determination for Major Statistical Parameters

• Activity Number: 684
• Type: Contributed
• Date/Time: Thursday, August 8, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Eugene Demidenko*+
• Companies: Dartmouth Medical School
• Keywords: Power function ; Hypothesis testing ; Unbiased test ; Poisson rate ; Correlation coefficient ; Binomial proportion

Abstract

The existing practice of the sample size determination is self-contradictory. On one hand, a finite sample size (as small as possible) is sought to achieve the specified power of detection. On the other hand, an asymptotic approximation to the power function is used that assumes that the sample size is large. Consequently, the equal-tail test for the double-sided hypothesis is usually used even when the exact power can be computed. Although it is known that the equal-tail test is biased it is widely popular in statistical practice. We derive unbiased tests, the power functions and the respective unbiased sample sizes for major statistical parameters: normal variance and standard deviation, binomial proportion, Poisson rate, and Pearson correlation coefficient. The difference between the unbiased sample size and the standard sample size determination with equal tails is especially considerable when the sample size is small and the regular normal approximation is poor. We present algorithms and report simulations that support our power calculation and the required sample size.