A Structured Guide to Univariate Test Selection Based on Normality, Variance Homogeneity, and Graphical Data Exploration

Abstract

Introduction

The credibility of surgical research depends on appropriate statistical methodology. However, univariate statistical tests are frequently applied inconsistently, and key assumptions—particularly normality and variance homogeneity—are often misunderstood or inadequately assessed. These methodological shortcomings can distort inference, undermine internal validity, and compromise the clinical interpretability of research findings.

Methods

This article presents a structured, assumption-based framework to guide univariate statistical test selection in surgical research. The approach integrates visual data exploration (histograms, Q–Q plots, violin plots) with formal assumption testing, including the Shapiro-Wilk test for normality and Levene’s test for variance homogeneity, explicitly addressing the sample-size dependence of normality tests, which may lack power in small samples and overdetect trivial deviations in large datasets. The framework addresses common pitfalls related to distributional shape (including bimodality), outliers, data transformation, and the treatment of ordinal variables. When standard assumptions are violated, the framework discusses robust alternatives—such as Welch’s tests, nonparametric approaches, and modern robust estimators—to preserve valid and interpretable statistical inference.

Results

The proposed framework yields a practical decision algorithm, supported by summary tables and illustrative figures, that links data characteristics to appropriate univariate tests and summary measures. By emphasizing combined visual and statistical assessment, the framework clarifies when parametric, robust parametric, or nonparametric methods are most suitable and highlights frequent sources of misinterpretation in the surgical literature.

Conclusions

An assumption-driven approach to univariate test selection enhances statistical rigor, transparency, and reproducibility in surgical research. By aligning test choice and data summarization with underlying distributional properties, this framework supports more reliable statistical inference and clinically meaningful interpretation of univariate analyses.