Mann-Whitney U Test in STATA

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Introduction

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This blog post focuses on one such statistical test—the Mann-Whitney U Test in STATA. This non-parametric test is a powerful tool for comparing differences between two independent groups, making it essential for various research fields. We will guide you through understanding, performing, and interpreting the Mann-Whitney U Test in STATA.

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PS: Need Mann-Whitney U Test in STATA in SPSS or R? Check out our guides for SPSS and R here.

2. What is the Mann-Whitney U Test and their assumptions and hypotheses?

The Mann-Whitney U Test in STATA is a non-parametric test used to determine whether there is a significant difference between the distributions of two independent groups. Unlike the t-test, it does not assume normal distribution, making it suitable for ordinal data or when your sample size is small. This test ranks all the values from both groups together and then evaluates the ranks to see if the two groups differ significantly.

Key assumptions for the Mann-Whitney U Test include independent samples, an ordinal scale, and similar shapes of the distributions for the two groups. The null hypothesis states that the distributions of the two groups are identical, while the alternative hypothesis suggests a difference in distributions. Researchers use this test when the assumptions of parametric tests are not met.

3. Example for Mann-Whitney U Test using STATA

Let’s illustrate the Mann-Whitney U Test in STATA with an example. Suppose you are comparing the self-confidence scores of students who passed a Math exam versus those who did not. Self-confidence scores are not normally distributed, so the Mann-Whitney U Test is appropriate. Here, the two independent groups are “students who passed” and “students who did not pass.”

In this scenario, you would collect self-confidence scores from both groups. The Mann-Whitney U Test would then assess whether the median self-confidence scores differ between the two groups. If STATA shows a significant result, it would suggest that passing the Math exam correlates with higher or lower self-confidence.

4. How to Perform the Mann-Whitney U Test in STATA?

Performing the Mann-Whitney U Test in STATA is straightforward. Follow these steps to ensure accurate results:

Load your data: Begin by importing your dataset into STATA. Make sure your data is organized correctly, with separate variables for the groups being compared.
Run the test: Use the ranksum command in STATA. For example, type ranksum self_confidence, by(pass_status) in the command window. This command tells STATA to compare self-confidence scores between students who passed and those who didn’t.
Review output: After executing the command, STATA will provide you with several output tables. These tables will contain the U statistic, z-value, and p-value, which are crucial for interpreting the results.

1. Step in STATA
2. Step in STATA

1. Step in STATA

2. Step in STATA

5. STATA Output for Mann-Whitney U Test

When you run the Mann-Whitney U Test in STATA, you will receive several output tables. Here’s what they show:

Ranks Table: Displays the sum of ranks for each group, which is the basis for calculating the U statistic.
U Statistic: Indicates the test statistic used to assess whether the distributions differ between the groups.
Z-value: Standardized value that shows how far the U statistic deviates from the null hypothesis.
P-value: Determines whether the observed difference is statistically significant. A p-value below 0.05 typically indicates a significant difference.

Each of these outputs helps in understanding whether the difference between groups is due to chance or a real effect.

1. STATA Output

1. STATA Output

6. Interpret the key results for the Mann-Whitney U Test

Interpreting the results of the Mann-Whitney U Test in STATA is crucial for drawing conclusions. If the p-value is less than 0.05, you reject the null hypothesis. This suggests a significant difference between the self-confidence scores of students who passed and those who did not pass the Math exam.

On the other hand, if the p-value is greater than 0.05, you fail to reject the null hypothesis, indicating no significant difference between the two groups. Additionally, consider the Z-value; a high absolute value strengthens the evidence against the null hypothesis. Finally, look at the sum of ranks; the group with the higher sum typically has higher scores, which helps in understanding the direction of the effect.

7. Final Thoughts and Further Support

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