Mann Whitney Test
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Mann–Whitney U test is the nonparametric alternative to the independent-samples t test for two independent groups, especially under non-normality or ordinal measurement.
Briefing
Mann–Whitney U test offers a practical way to compare two independent groups when the usual independent-samples t test assumptions don’t hold—especially when the dependent variable isn’t normally distributed or is ordinal. Instead of comparing group means, the test converts all observations into ranks and then checks whether the rank distributions of the two groups differ enough to indicate a real difference in central tendency (often interpreted through medians). Because it relies on ranks rather than the original score distribution, it remains useful when normality is questionable.
The transcript lays out when to use this nonparametric approach. One set of scenarios involves non-normal continuous data: a quality manager comparing supplier versus customer service quality, a market researcher comparing attention to social media between men and women, or an HR manager comparing compensation across departments such as finance and HR. Another key trigger is measurement level: when the dependent variable is ordinal, independent-samples t tests are not appropriate, and Mann–Whitney U becomes the go-to option.
A worked example focuses on social media advertising preference between male and female respondents. The analysis is run in SPSS via Nonparametric Tests → Legacy Dialogs → Two Independent Samples. The dependent variable is set to “social preference,” while the grouping variable is “gender” (coded 1 for male and 2 for female). After running the test, the output emphasizes ranks and medians rather than means. With 79 male and 73 female respondents (152 total), the results indicate no statistically significant difference in social preference between the two genders.
Reporting is handled in two layers: first, the significance conclusion (the test revealed insignificant differences), and second, the median values for each group. The transcript shows how to obtain medians in SPSS by using Compare Means and selecting the median option. In this example, the median social preference is 2 for both males and females, reinforcing the conclusion drawn from the rank-based test.
Finally, the transcript addresses effect size, noting that SPSS doesn’t directly provide an effect size for Mann–Whitney U. Instead, the Z statistic from the output can be used to approximate an effect size R. Using the reported Z value (about −0.439) and the relevant sample size term (N = 132 in the calculation described), the effect size comes out around 0.3, which is characterized as negligible/small. The overall takeaway is that even if a difference were detected, the magnitude would need to be assessed separately; here, both the significance test and the effect-size estimate point to no meaningful gender difference in social media ad preference.
Cornell Notes
Mann–Whitney U test is a nonparametric alternative to the independent-samples t test for comparing two independent groups when the dependent variable is not normally distributed or is ordinal. It ranks all observations and tests whether the rank distributions differ, which corresponds to differences in central tendency (commonly interpreted via medians). In the example, male (n=79) and female (n=73) respondents are compared on social media ad preference using SPSS’s Two Independent Samples (Nonparametric). The test result indicates no significant difference in social preference between genders, and both groups share the same median value (2). The transcript also shows how to approximate effect size from the Z statistic to judge whether any difference is practically meaningful.
Why use Mann–Whitney U test instead of an independent-samples t test?
How does Mann–Whitney U interpret group differences?
What SPSS settings are used in the example to run the test?
What were the sample sizes and the conclusion in the social preference example?
How are medians and effect size handled for reporting?
Review Questions
- In what two situations is Mann–Whitney U preferred over an independent-samples t test?
- What does the Mann–Whitney U test compare after converting data to ranks, and how does that change interpretation versus a t test?
- How would you report both statistical significance and practical importance (effect size) for a Mann–Whitney U result?
Key Points
- 1
Mann–Whitney U test is the nonparametric alternative to the independent-samples t test for two independent groups, especially under non-normality or ordinal measurement.
- 2
The test ranks all observations and evaluates whether the two groups’ rank distributions differ, rather than comparing means directly.
- 3
For reporting, focus on rank-based significance plus group medians (not means) when using Mann–Whitney U.
- 4
In the example, male (n=79) and female (n=73) respondents showed no significant difference in social media ad preference, with both medians equal to 2.
- 5
SPSS output for Mann–Whitney U emphasizes ranks and provides statistics like U, Z, and P that drive the significance conclusion.
- 6
Effect size isn’t directly provided by SPSS for this test in the transcript’s workflow; an approximate effect size R can be computed from the Z statistic to judge practical impact.