The Impact of Data Skewness on Parameter Estimation and Hypothesis Testing Reliability Across Research Designs

Posted: Nov 16, 2023

• Jack Smith
• Mason Anderson
• Samuel Smith

Abstract

Statistical analysis forms the backbone of empirical research across scientific disciplines, with parameter estimation and hypothesis testing serving as fundamental tools for drawing inferences from data. The reliability of these statistical procedures, however, hinges critically on the underlying assumptions about data distribution. While classical statistical theory predominantly assumes normality, real-world data frequently violate this assumption through various forms of non-normality, with skewness representing one of the most prevalent and impactful deviations. Data skewness, defined as the asymmetry in probability distribution, manifests across diverse research contexts—from income distributions in economics to reaction times in psychology and gene expression levels in biology. Despite its ubiquity, the comprehensive impact of skewness on statistical inference across different research designs remains inadequately characterized, with most existing studies focusing on isolated conditions or specific statistical tests. The consequences of ignoring skewness extend beyond theoretical concerns to practical implications for research validity. When data exhibit substantial skewness, conventional estimators such as sample means and ordinary least squares regression coefficients may become inefficient or biased, while standard errors and confidence intervals may misrepresent true uncertainty. Similarly, hypothesis tests assuming normality may demonstrate inflated Type I error rates or reduced power, potentially leading to false discoveries or missed effects.