Kruskal Wallis Test In A Report

Reporting the Kruskal-Wallis Test: A Comprehensive Guide

The Kruskal-Wallis test is a non-parametric method used to compare the medians of three or more independent groups. It's a powerful alternative to the one-way ANOVA when your data violates the assumptions of normality or homogeneity of variances. This guide will walk you through how to effectively report the results of a Kruskal-Wallis test in your research report or dissertation. Understanding how to properly present your findings is crucial for clear communication and accurate interpretation.

What to Include in Your Report

A well-written report on a Kruskal-Wallis test should include the following key elements:

1. Research Question and Hypothesis

Begin by clearly stating the research question your analysis aims to address. This provides context for your statistical analysis. For example: "Does the type of fertilizer used significantly affect the median yield of tomatoes?" Then, state your null and alternative hypotheses. The null hypothesis (H0) typically states that there's no difference between the group medians, while the alternative hypothesis (H1) suggests at least one group median differs significantly from the others.

2. Descriptive Statistics

Before presenting the Kruskal-Wallis results, provide descriptive statistics for each group. This includes the sample size (N), median, and interquartile range (IQR) or other measures of variability appropriate for your data. This allows readers to understand the distribution of data within each group before diving into the inferential statistics. Present this in a clear and concise table.

3. Kruskal-Wallis Test Results

This section presents the core findings of your analysis. Report the following:

• Test Statistic (H): This is the calculated value from the Kruskal-Wallis test. Report this value to at least two decimal places.
• Degrees of Freedom (df): This is calculated as k - 1, where k is the number of groups being compared.
• P-value: This is the probability of observing the obtained results (or more extreme results) if the null hypothesis were true. Report the exact p-value.
• Software Used: Mention the statistical software package you used (e.g., SPSS, R, SAS). This adds transparency and allows others to replicate your analysis.

4. Interpretation of Results

This is a crucial section where you explain the meaning of your findings in the context of your research question. Interpret the p-value:

• If p ≤ α (typically 0.05): Reject the null hypothesis. Conclude that there is a statistically significant difference between the group medians. Specify which groups differ significantly based on post-hoc tests (see below).
• If p > α: Fail to reject the null hypothesis. Conclude that there is not enough evidence to suggest a statistically significant difference between the group medians.

5. Post-Hoc Tests (If Significant)

If the Kruskal-Wallis test reveals a significant difference (p ≤ α), you need to conduct post-hoc tests to determine which specific groups differ significantly from each other. Common post-hoc tests for the Kruskal-Wallis include the Dunn's test or pairwise Mann-Whitney U tests with a Bonferroni correction for multiple comparisons. Report the results of these post-hoc tests, including p-values and any significant differences identified.

6. Limitations

Acknowledge any limitations of your study, such as a small sample size or potential confounding variables. These limitations can affect the generalizability of your findings.

7. Conclusion

Summarize your key findings and their implications. Relate your findings back to the research question and highlight the contribution of your study.

Example Report Snippet:

"A Kruskal-Wallis test was conducted to compare the median tomato yields across three fertilizer types (A, B, C). Descriptive statistics are presented in Table 1. The Kruskal-Wallis test revealed a statistically significant difference between the groups (H(2) = 10.54, p = 0.005). Post-hoc Dunn's tests with a Bonferroni correction indicated that the median yield of tomatoes treated with fertilizer A was significantly higher than that of tomatoes treated with fertilizer B (p = 0.012) and fertilizer C (p = 0.008). There was no significant difference between the yields of fertilizer B and C (p = 0.92)."

Table Example (Table 1):

By following these guidelines, you can ensure that your report on the Kruskal-Wallis test is clear, accurate, and effectively communicates your findings to your audience. Remember to always present your data and analysis in a transparent and understandable manner.