Hypothesis Testing with Small Sample Size Without Restricting Covariance Structure

• Activity Number: 253
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): David Jarjoura*+ and Xueliang Pan and Xiaobai Li
• Companies: The Ohio State University and The Ohio State University and The Ohio State University
• Keywords: type I error control ; laboratory experiments ; mixed models

Abstract

In leukemia research much progress has been made by ex-vivo experimentation with human leukemic cells. Typically a critical experiment defines a single very clear hypothesis test about a pathway, and involves a contrast across multiple conditions. Mixed models are generally used for these studies. Due to the small sample size, simple structures are often assumed unnecessarily, and this can lead to inflated type I error. Inflation of type I error can be attributed to 1) underestimation of residual variance or 2) overestimation of degrees of freedom of the test statistics. We compared the type I error control of different approaches to address the covariance structure estimation problem with small sample sizes. We show that over simplified structures tend to ignore important condition-by-subject interaction effect variance components. We also propose approaches to avoid an assumption of simplified structures. We found that all approaches except those that agree completely with a saturated covariance structure approach do not adequately control type I error.