Empirical Evaluation of Paired Differences for Small Sample Sizes

• Activity Number: 336
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Consulting
• Author(s): Jonathan D. Mahnken*+
• Companies: University of Kansas Medical Center
• Keywords: Normal mixture distribution ; One-sample t-test ; Simulation

Abstract

Small sample sizes are frequently encountered in collaborative research. In early phase research, questions as to the shape of the true, unknown underlying distribution often preclude the use of parametric approaches, and nonparametric approaches may lose power when the operating characteristics of the parametric apply also to this underlying distribution. Using randomly selected normal mixture distributions, the operating characteristics of the one-sample t-test are evaluated empirically. Power and type I error were determined for these randomly selected underlying distributions for two-sided tests with a theoretical type I error rate of 0.05. Results are presented under various sample sizes to empirically examine the points at which the asymptotic properties of this test apply. Among the preliminary findings, very small sample sizes provide reasonable protection against type I errors, though power for such sample sizes low.