Assessing the Effect of Finite Sample Properties on Hypothesis Testing Power and Error Rate Control

Posted: Jun 26, 2013

• Austin Rivera
• Benjamin Cox
• Blake Henderson

Abstract

Statistical hypothesis testing represents a cornerstone of scientific inference across numerous disciplines, from biomedical research to social sciences and engineering. The theoretical foundations of hypothesis testing, as developed by Neyman, Pearson, and Fisher, rely heavily on asymptotic properties that assume infinite sample sizes or sufficiently large samples to approximate these ideal conditions. However, in practical research settings, investigators frequently operate with finite samples that may not satisfy these asymptotic assumptions. This fundamental disconnect between theoretical expectations and practical realities raises critical questions about the validity and reliability of statistical conclusions drawn from finite samples. The conventional approach to hypothesis testing typically employs procedures whose properties are derived under asymptotic conditions, with the implicit assumption that these properties will hold approximately for finite samples. This assumption, while convenient, often lacks rigorous justification and may lead to substantial errors in statistical inference. The divergence between nominal and actual error rates, the miscalibration of power calculations, and the inappropriate interpretation of p-values all represent potential consequences of neglecting finite sample properties. This research addresses a significant gap in the statistical literature by systematically investigating how finite sample characteristics influence the performance of common hypothesis testing procedures. We move beyond traditional asymptotic analysis to develop a comprehensive framework that captures the complex interplay between sample size, effect size, distributional assumptions, and test performance. Our work challenges several conventional practices in statistical testing and provides novel insights into the conditions under which standard procedures may fail to deliver their promised properties. The primary contributions of this paper are threefold. First, we develop an integrated methodological approach that combines computational simulations with analytical derivations to quantify finite sample effects across diverse testing scenarios. Second, we identify specific patterns of test performance degradation that emerge under finite sample conditions, revealing unexpected interactions