Exploring the Relationship Between Statistical Power and Effect Size in Inferential Decision-Making Scenarios

Posted: Nov 05, 2016

• Alexander Wilson
• Amelia Green
• Aria Clark

Abstract

The conventional framework of statistical inference has long emphasized the importance of statistical power and effect size as fundamental concepts in research design and interpretation. Statistical power, defined as the probability of correctly rejecting a false null hypothesis, and effect size, representing the magnitude of a phenomenon of interest, are typically treated as distinct considerations in experimental planning. However, this separation belies the complex, dynamic relationship between these concepts in practical decision-making contexts. The traditional approach to power analysis, which involves specifying an expected effect size and desired power level to determine necessary sample sizes, assumes a static relationship that may not reflect the realities of inferential decision-making across diverse domains. This research challenges the conventional separation of power and effect size considerations by examining their interdependence in real-world decision scenarios. We propose that the relationship between these statistical concepts is not merely mathematical but fundamentally contextual, influenced by the practical consequences of inference errors and the decision-making environment. Our investigation addresses a critical gap in the statistical literature: while extensive research exists on power analysis methodologies and effect size interpretation separately, few studies have systematically examined how these concepts interact in applied decision-making contexts where statistical inferences inform consequential choices. Our research questions focus on three primary areas of inquiry. First, how does the relationship between statistical power and effect size vary across different decision-making domains with varying consequences for Type I and Type II errors? Second, to what extent do conventional power analysis methods