The Difference Between One-Way ANOVA and Kruskal-Wallis Test — When to Use and How They Differ

In quantitative research, when researchers need to compare the mean differences among more than two groups, the most commonly used statistical methods are One-Way ANOVA and Kruskal-Wallis Test.

While both tests are used to examine differences across multiple groups, the key question is: “Which one should I use?”

The answer depends on the nature of your data and whether it meets the statistical assumptions required for each test.

The Difference Between One-Way ANOVA and Kruskal-Wallis Test

What Is One-Way ANOVA?

The One-Way ANOVA (Analysis of Variance) is a parametric test used to compare the means of three or more independent groups to determine whether their average scores differ significantly.

Assumptions of One-Way ANOVA

1. The data in each group are normally distributed.

2. The variances across groups are equal or approximately equal (homogeneity of variance).

3. The groups are independent of one another.

Example:

Research Topic: “Customer Satisfaction across Different Hotel Types”

• Independent Variable: Type of hotel (3-star, 4-star, 5-star)

• Dependent Variable: Customer satisfaction score (1–5 Likert scale)

If the data are normally distributed and the group variances are equal, the One-Way ANOVA can be used to compare the mean satisfaction scores among the three hotel types.

What Is the Kruskal-Wallis Test?

The Kruskal-Wallis Test is a non-parametric alternative to One-Way ANOVA.It is used to test for differences among three or more independent groups when the assumptions for ANOVA are not met.

This method is appropriate when the data are non-normally distributed or contain outliers that distort the mean.Instead of comparing means, the Kruskal-Wallis test compares the ranks of the data to determine whether the distributions differ significantly across groups.

Example:

Research Topic: “Stress Levels Among Employees by Job Position”

• Independent Variable: Job position (staff / supervisor / manager)

• Dependent Variable: Stress level (measured on a 1–5 Likert scale)

If the data are skewed or contain outliers, the Kruskal-Wallis Test is more suitable than ANOVA, as it uses data ranks rather than raw scores.

How to Choose Between One-Way ANOVA and Kruskal-Wallis Test

The choice between the two depends on your data distribution and measurement level:

• Use One-Way ANOVA if your data are normally distributed and group variances are homogeneous.

• Use Kruskal-Wallis Test if your data are non-normal, contain outliers, or are ordinal in nature.

• For interval or ratio-scale variables (e.g., income, scores, time), ANOVA is more appropriate.

• For ordinal variables (e.g., satisfaction level, rating, ranking), Kruskal-Wallis is recommended.

In summary:

Use One-Way ANOVA when your data meet parametric assumptions.Use Kruskal-Wallis Test when your data violate those assumptions or are not continuous.

Why You Should Use Data Investigator

Selecting the correct statistical test is not just about applying formulas — it requires an in-depth understanding of data characteristics, assumptions, and appropriate interpretation.A small error in statistical selection can lead to misinterpretation of results and invalid conclusions.

With over 15 years of experience in SPSS-based data analysis, Data Investigator provides expert support in academic, business, and medical research.Our team ensures every analysis is conducted correctly, with clear, detailed explanations you can confidently include in your report.

Our Services Include

• Conducting data analysis using SPSS with professional accuracy

• Checking statistical assumptions (e.g., Normality, Homogeneity of Variance)

• Recommending the appropriate test — One-Way ANOVA or Kruskal-Wallis Test

• Providing detailed explanations and interpretations of results

• Issuing an official Certificate of Statistical Analysis

Whether you are a thesis student, medical researcher, or government organization,Data Investigator ensures your statistical analysis is accurate, valid, and clearly explained.

For more information:

E-mail: info@datainvestigatorth.com

Line: @datainvestigator