Parametric vs. Non-Parametric Tests in Clinical Research: When, Why, and How

📘 Introduction

In clinical epidemiology and biostatistics, choosing the right statistical test hinges not only on the study design and data type but also on the distributional characteristics of your data. Two major families of statistical tests—parametric and non-parametric—are used to analyze quantitative outcomes. The choice between them isn’t merely technical—it directly affects the robustness and interpretability of your clinical findings.

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🔍 Definitions and Conceptual Foundations

Parametric Tests assume the data come from a specific distribution—usually the normal (Gaussian) distribution. These tests estimate population parameters (means, variances) and use these estimates to make inferences.

Non-Parametric Tests make no assumptions about the shape of the data distribution. They operate on ranks or signs, offering a distribution-free alternative that is more robust to outliers and skewed data.

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📊 When to Use Each: Decision Logic Table

Criterion	Parametric	Non-Parametric
Assumes Normality	✅ Yes	❌ No
Scale of Data	Interval/Ratio	Ordinal/Non-normal Interval
Example Tests	t-test, ANOVA, Linear Regression	Mann-Whitney, Wilcoxon, Kruskal-Wallis
Output	Mean, SD, Coefficients	Median, Rank Differences
Sample Size Needed	Smaller samples work if normality holds	Better for small or skewed samples
Power	Higher if assumptions met	Lower, but safer under violations

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🧪 Common Normality Checks Before Parametric Use

• Visual: Q-Q Plot, Histogram

• Statistical: Shapiro-Wilk test (n < 50), Kolmogorov-Smirnov (historical)

• Descriptive: Skewness, Kurtosis values

Clinical Best Practice: Focus on residuals in regression—not raw data. For group comparisons (especially in RCTs with n > 30), the Central Limit Theorem often neutralizes skewness concerns.

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🎓 Examples from Clinical Trials

Task	Best Practice
Baseline comparison in RCT	Use means or medians descriptively; no hypothesis testing needed
Small n comparison (<20)	Check normality visually; use Shapiro-Wilk; consider Wilcoxon if severely skewed
Regression modeling	Always assess residuals; parametric valid if residuals ≈ normal
Ordinal scales (e.g., pain scores)	Prefer non-parametric tests

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⚠️ Pitfalls to Avoid

• Mechanical Normality Testing: Especially with large n, minor deviations yield p < 0.05 but don’t invalidate t-tests.

• Overusing Non-Parametric Tests: You lose power and interpretability (e.g., mean differences).

• Confusing Raw Data vs. Residual Normality: In regression, residuals should be checked, not the original variables.
  

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✅ Summary

• Use parametric tests when assumptions (especially normality) are reasonably met.

• Use non-parametric tests for skewed data, ordinal variables, or small samples where normality is uncertain.

• Focus less on raw data distribution and more on model residuals, especially in regression contexts.

• Visual inspection trumps mechanical testing when it comes to real-world data interpretation.