# Kruskal-Wallis Test

The Kruskal-Wallis test is a nonparametric (distribution free) test, and is used when the assumptions of one-way ANOVA are not met.  Both the Kruskal-Wallis test and one-way ANOVA assess for significant differences on a continuous dependent variable by a categorical independent variable (with two or more groups).  In the ANOVA, we assume that the dependent variable is normally distributed and there is approximately equal variance on the scores across groups.  However, when using the Kruskal-Wallis Test, we do not have to make any of these assumptions.  Therefore, the Kruskal-Wallis test can be used for both continuous and ordinal-level dependent variables.  However, like most non-parametric tests, the Kruskal-Wallis Test is not as powerful as the ANOVA.

Null hypothesis: Null hypothesis assumes that the samples (groups) are from identical populations.

Alternative hypothesis: Alternative hypothesis assumes that at least one of the samples (groups) comes from a different population than the others.

How do test scores differ between the different grade levels in elementary school?

Do job satisfaction scores differ by race?

### Discover How We Assist to Edit Your Dissertation Chapters

Aligning theoretical framework, gathering articles, synthesizing gaps, articulating a clear methodology and data plan, and writing about the theoretical and practical implications of your research are part of our comprehensive dissertation editing services.

• Bring dissertation editing expertise to chapters 1-5 in timely manner.
• Track all changes, then work with you to bring about scholarly writing.
• Ongoing support to address committee feedback, reducing revisions.

The distribution of the Kruskal-Wallis test statistic approximates a chi-square distribution, with k-1 degrees of freedom, if the number of observations in each group is 5 or more.  If the calculated value of the Kruskal-Wallis test is less than the critical chi-square value, then the null hypothesis cannot be rejected.  If the calculated value of Kruskal-Wallis test is greater than the critical chi-square value, then we can reject the null hypothesis and say that at least one of the samples comes from a different population.

Assumptions

1. We assume that the samples drawn from the population are random.
2. We also assume that the observations are independent of each other.
3. The measurement scale for the dependent variable should be at least ordinal.

Related Pages:

Statistics Solutions can assist with your quantitative analysis by assisting you to develop your methodology and results chapters. The services that we offer include:

Data Analysis Plan

Edit your research questions and null/alternative hypotheses

Write your data analysis plan; specify specific statistics to address the research questions, the assumptions of the statistics, and justify why they are the appropriate statistics; provide references

Justify your sample size/power analysis, provide references

Explain your data analysis plan to you so you are comfortable and confident

Quantitative Results Section (Descriptive Statistics, Bivariate and Multivariate Analyses, Structural Equation Modeling, Path analysis, HLM, Cluster Analysis)

Clean and code dataset

Conduct descriptive statistics (i.e., mean, standard deviation, frequency and percent, as appropriate)

Conduct analyses to examine each of your research questions

Write-up results

Provide APA 6th edition tables and figures

Explain chapter 4 findings

Ongoing support for entire results chapter statistics

Please call 727-442-4290 to request a quote based on the specifics of your research, schedule using the calendar on this page, or email [email protected]