Introduction

In biomedical and clinical research, comparing three or more independent groups is common. When data are normally distributed, researchers typically use One-Way ANOVA. However, when the normality assumption is violated or sample sizes are small, a nonparametric alternative becomes necessary.

The Kruskal–Wallis test is a nonparametric method used to compare medians across multiple independent groups. It does not assume normal distribution and is based on ranking data rather than raw values.

In this article, we demonstrate a complete Kruskal–Wallis test in MedCalc using cholesterol level data (mg/dL) across three independent groups:

• Group A
• Group B
• Group C

We will cover:

• Descriptive statistics
• Test statistic interpretation
• Dunn post hoc analysis
• Box plot visualization
• Practical clinical interpretation

This tutorial is designed for researchers, medical students, PhD scholars, and biostatistics learners.

Study Design and Data Description

Dependent Variable:

Cholesterol (mg/dL)

Independent Factor:

Group (A, B, C)

Sample Size:

Total n = 15 result
Each group contains 5 observations.

📥 Download Cholesterol Dataset (Excel File)

Descriptive Statistics

From your MedCalc output result:

Observations

• Group A shows the highest median cholesterol (182 mg/dL).
• Group B has intermediate values (median = 169 mg/dL).
• Group C has the lowest median (155 mg/dL).
• The groups appear clearly separated.

The box plot visually confirms this decreasing trend:
A > B > C

Box plot showing cholesterol distribution across Groups A, B, and C.

Why Use the Kruskal–Wallis Test?

Kruskal–Wallis is used when:

• Comparing ≥ 3 independent groups
• Data are not normally distributed
• Sample sizes are small
• Outliers may be present

It is the nonparametric alternative to One-Way ANOVA.

Instead of comparing means, it compares rank sums across groups.

Kruskal–Wallis Test Results

From MedCalc result:

Interpretation of Kruskal–Wallis Test

Since P = 0.00193 < 0.05, we reject the null hypothesis.

Statistical Conclusion:

There is a statistically significant difference in cholesterol levels among at least one of the three groups.

However, the Kruskal–Wallis test does not indicate which groups differ. Therefore, post hoc testing is required.

Post Hoc Analysis: Dunn Test

MedCalc performed Dunn’s multiple comparison test result.

Average Ranks

Significant Differences (P < 0.05)

• Group A differs significantly from Group C
• Group C differs significantly from Group A
• Group B does not significantly differ from A or C at the 0.05 level

Post Hoc Interpretation

1. Group A vs Group C
   Significant difference (largest separation)
2. Group B vs Group A
   Not statistically significant
3. Group B vs Group C
   Not statistically significant

What Does This Mean?

The strongest evidence of difference exists between Group A and Group C.

Group B appears intermediate and does not significantly differ from either group.

Clinical Interpretation

From a biomedical perspective:

• Group A has highest cholesterol values
• Group C has lowest cholesterol values
• Group B shows moderate levels

If these groups represent:

• Different treatments
• Different diets
• Different drug doses

Then the data suggest a clear reduction in cholesterol from Group A to Group C.

Clinically, a reduction from 182 mg/dL to 155 mg/dL is meaningful and may significantly reduce cardiovascular risk.

Comparison with One-Way ANOVA

If the data were normally distributed, One-Way ANOVA could be used. However:

• Kruskal–Wallis is more robust
• Less sensitive to outliers
• Appropriate for small samples

In your case (n = 5 per group), the nonparametric approach is justified.

Advantages of Kruskal–Wallis Test

• No normality assumption
• Works with ordinal data
• Suitable for skewed distributions
• Simple interpretation

Limitations

• Tests medians, not means
• Less powerful than ANOVA if normality holds
• Does not directly measure effect size

How to Report in Research Paper

Example:

A Kruskal–Wallis test showed a statistically significant difference in cholesterol levels among groups (H(2) = 12.50, p = 0.0019). Dunn post hoc analysis indicated that Group A differed significantly from Group C.

Conclusion

This Kruskal–Wallis analysis in MedCalc demonstrated a statistically significant difference in cholesterol levels across three independent groups.

Key findings:

• Overall significant difference (P = 0.00193)
• Strongest difference between Group A and Group C
• Group B shows intermediate values
• Box plot visually confirms ranking pattern

The Kruskal–Wallis test is a powerful and reliable nonparametric alternative to ANOVA and is particularly useful in small biomedical datasets.

MedCalc provides a clear and structured output, making interpretation straightforward for researchers and students.