how to conduct wilcoxon test in stata

Daniel Parker

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17-03-2025

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The Wilcoxon signed-rank test is a non-parametric statistical test used to compare two related samples or repeated measurements on a single sample. It's a powerful alternative to the paired t-test when your data violates the assumptions of normality or when your data is ordinal. This article will guide you through performing a Wilcoxon signed-rank test in Stata, step-by-step.

Understanding the Wilcoxon Signed-Rank Test

Before diving into the Stata commands, let's briefly review the test's purpose. The Wilcoxon signed-rank test assesses whether there's a significant difference between paired observations. Unlike the paired t-test, it doesn't assume that the data is normally distributed. Instead, it ranks the absolute differences between paired observations and examines the sum of ranks for positive and negative differences.

When to Use the Wilcoxon Signed-Rank Test:

• Non-normal data: When your data significantly deviates from a normal distribution.
• Ordinal data: When your data is measured on an ordinal scale (e.g., rankings).
• Small sample sizes: While applicable to larger samples, it's particularly useful when dealing with small datasets where the assumption of normality might be questionable.

Performing the Wilcoxon Signed-Rank Test in Stata

Let's assume you have two variables, pre_score (pre-treatment score) and post_score (post-treatment score), representing paired observations. Here's how to perform the test in Stata:

Step 1: Input your data. Ensure your data is correctly entered into Stata. Each observation should represent a single subject or unit with pre_score and post_score values.

Step 2: Run the signrank command. The core command for the Wilcoxon signed-rank test in Stata is signrank. The basic syntax is:

signrank post_score == pre_score

This command compares post_score to pre_score to see if there's a significant difference. The == operator specifies a paired test.

Step 3: Interpret the Output. Stata will provide output including:

• Wilcoxon signed-rank statistic: This is the test statistic itself.
• Z-statistic: A standardized version of the test statistic, used for determining the p-value.
• P-value: The probability of observing the obtained results (or more extreme results) if there's no true difference between the paired observations. This is crucial for making inferences. A p-value below your chosen significance level (typically 0.05) indicates a statistically significant difference.

Example:

Let's say you have data on student test scores before and after a new teaching method. The following code demonstrates the analysis:

// Sample Data (replace with your actual data)
clear
input pre_score post_score
20 25
15 18
22 28
18 20
25 27
end

// Perform Wilcoxon signed-rank test
signrank post_score == pre_score

The output will provide the Wilcoxon statistic, Z-statistic and the p-value.

Handling Missing Data

Stata's signrank command automatically handles missing values by excluding observations with missing data in either pre_score or post_score. You don't need to explicitly handle missing data within the command.

One-Sided vs. Two-Sided Tests

By default, signrank performs a two-sided test. This checks for a difference in either direction (i.e., whether post_score is significantly greater or less than pre_score). For a one-sided test (e.g., testing if post_score is significantly greater than pre_score), you would need to specify the direction using additional options, which are beyond the scope of this basic tutorial, but easily searchable in Stata's help documentation.

Conclusion

The Wilcoxon signed-rank test is a valuable tool for comparing paired data when the assumptions of the paired t-test are violated. Stata's signrank command provides a straightforward way to perform this analysis. Remember to always carefully interpret the p-value within the context of your research question and consider the limitations of non-parametric tests. Always consult a statistician if you have complex research designs or require more advanced statistical analysis.