Real-world examples of Mann-Whitney U test for beginners

Everyday examples of Mann-Whitney U test examples for beginners

Instead of starting with formulas, let’s start with real life. The Mann-Whitney U test is a non-parametric alternative to the independent samples t-test. In plain English: it compares two independent groups without assuming the data follow a normal (bell-shaped) distribution.

If you’re looking for examples of Mann-Whitney U test examples for beginners, a helpful rule of thumb is:

• You have two groups (like Treatment vs Placebo, App A vs App B, Method 1 vs Method 2).
• Your outcome is numeric or ordered (like pain scores 0–10, satisfaction 1–5 stars, ranks, or skewed test scores).
• The data are not normal, heavily skewed, or measured on an ordinal scale.

Now let’s walk through several real examples, step by step.

Health and medicine: examples include pain scores and recovery time

Health research is packed with great examples of Mann-Whitney U test examples for beginners, because many medical variables are skewed or measured on rating scales.

Example 1: Comparing pain scores after two treatments

Imagine a hospital testing two types of physical therapy after knee surgery:

• Group A: Traditional therapy
• Group B: New virtual-reality–assisted therapy

After one week, each patient rates their pain on a 0–10 scale. Pain scores are usually not normally distributed. Many people report low pain, a few report very high pain, and the distribution gets lopsided.

The researcher wants to know: Are pain scores lower in the VR group than in the traditional group?

Because pain scores are ordinal-ish (0–10 scale) and skewed, this is a classic example of Mann-Whitney U test use. The test compares the ranks of pain scores between the two groups instead of relying on means and standard deviations.

If the Mann-Whitney U test shows a statistically significant difference, the hospital can say, with some confidence, that the new VR therapy tends to lead to lower pain scores than traditional therapy.

For context, you can see how pain scales are often used in clinical research on sites like the National Institutes of Health (NIH).

Example 2: Recovery time with and without a new discharge protocol

A hospital introduces a new discharge planning protocol for heart failure patients. They compare:

• Group A: Patients discharged before the new protocol
• Group B: Patients discharged after the new protocol

They measure the number of days until readmission within 30 days. Recovery and readmission times are often heavily skewed: many patients are never readmitted, a few come back very quickly, and some come back much later.

The variable “days until readmission” is non-normal, so a t-test isn’t a great fit. This is another simple example of Mann-Whitney U test application: compare the distribution of days between the two groups.

If the test suggests Group B has significantly longer times to readmission, that supports the idea that the new protocol may be helping patients stay out of the hospital longer.

For real-world background on readmission research, the Centers for Medicare & Medicaid Services (CMS) and CDC publish related data and methods.

Education: best examples from test scores and teaching methods

Education research often produces perfect examples of Mann-Whitney U test examples for beginners, because test scores and ratings are frequently skewed or ordinal.

Example 3: Traditional lectures vs online interactive modules

A college wants to compare two teaching approaches for an introductory statistics course:

• Group A: Traditional in-person lectures
• Group B: Online interactive modules with quizzes and videos

At the end of the semester, students take the same final exam. But the exam scores are strange: most students do pretty well, with a big cluster near the top and a long tail of low scores. The distribution is right-skewed.

The department suspects the online modules might lead to higher performance. However, because the exam scores are skewed and the class sizes are modest, they choose the Mann-Whitney U test instead of an independent t-test.

The test compares the ranked exam scores between the two groups. If the online group tends to have higher ranks (higher scores), and the result is statistically significant, the department has evidence that the online method is outperforming traditional lectures.

You can see similar educational research designs discussed on sites like Harvard’s Graduate School of Education.

Example 4: Comparing student satisfaction with two grading policies

Suppose a high school experiments with grading policies:

• Group A: Traditional letter grades (A–F)
• Group B: Standards-based grading with detailed feedback

At the end of the term, students rate their satisfaction with the grading system on a 1–5 Likert scale (1 = very dissatisfied, 5 = very satisfied).

Likert-scale ratings are ordinal: a 4 is more than a 3, but the difference between 3 and 4 may not be exactly the same as the difference between 4 and 5. This makes them a good candidate for non-parametric methods.

Here, the Mann-Whitney U test compares the distribution of satisfaction ranks between the two groups. This is one of the best examples of Mann-Whitney U test usage for beginners, because it shows how the test handles ordered categories rather than assuming equal intervals.

If the test indicates that Group B has significantly higher satisfaction ratings, the school has data to support expanding standards-based grading.

Business and UX: real examples from customer ratings and app performance

Modern product and UX teams often work with rating scales and weirdly shaped data. That gives us more real examples of Mann-Whitney U test examples for beginners.

Example 5: Comparing customer satisfaction between two apps

A company offers two versions of a mobile banking app:

• Version A: Existing design
• Version B: New design with simplified navigation

After using the app for a week, customers rate their overall experience on a 1–7 satisfaction scale. Ratings are often clustered at the high end (lots of 6s and 7s) with a sprinkling of low scores.

The UX team wants to know whether Version B produces higher satisfaction than Version A. Because the outcome is on an ordinal scale and the data are skewed, this is a clean example of Mann-Whitney U test use in UX research.

The test compares whether users in Version B tend to give higher-ranked ratings than users in Version A. If the result is significant, the team has statistical backing to roll out the new design.

Example 6: Comparing completion times for a checkout flow

Now imagine an e-commerce site testing two checkout flows:

• Flow A: Traditional multi-page checkout
• Flow B: Streamlined single-page checkout

They measure time to complete checkout in seconds. Time data are almost always skewed: many users finish quickly, some get distracted or have issues and take much longer.

Because of this skewness and possible outliers (someone leaves the tab open for 20 minutes), the team is wary of using a standard t-test. This is another example of Mann-Whitney U test examples for beginners, because the test is more resistant to outliers when comparing two independent groups.

If the Mann-Whitney U test shows that Flow B users have significantly shorter completion times (lower ranks), the business has evidence that the new checkout is genuinely faster from the user’s perspective.

Social science: attitudes, scales, and non-normal data

Social and behavioral research routinely uses rating scales, questionnaires, and scores that don’t fit the tidy normal curve. That makes it a goldmine of examples of Mann-Whitney U test applications.

Example 7: Comparing anxiety levels before and after a policy change (independent groups)

A researcher studies workplace anxiety in two different offices of the same company:

• Office A: Before a major policy change
• Office B: After the policy change is implemented in a different location

Employees fill out a standardized anxiety questionnaire, producing a score from 0 to 40. These scores are often skewed and may not meet normality assumptions, especially with small samples.

Because the two offices have different people (independent groups), the researcher uses the Mann-Whitney U test to compare anxiety score distributions.

If scores in Office B are significantly lower, the researcher can argue that the policy change might be associated with reduced anxiety.

For more on standardized scales and non-parametric methods, organizations like the American Psychological Association (APA) often discuss these tools in applied research.

Example 8: Comparing trust in institutions between two age groups

Suppose a survey asks respondents to rate their trust in public health agencies on a 1–10 scale. The researcher wants to compare:

• Group A: Adults aged 18–34
• Group B: Adults aged 65 and older

Trust scores tend to be bumpy and irregular, especially in the wake of events like the COVID-19 pandemic and shifting public opinion in 2024–2025.

Because the variable is ordinal-like and the distributions differ between age groups, the researcher uses the Mann-Whitney U test to see whether one age group generally reports higher trust than the other.

This is another example of Mann-Whitney U test examples for beginners that connects directly to current trends and public data often reported by agencies like the CDC and NIH.

How to recognize a good example of Mann-Whitney U test in your own work

By now, you’ve seen several real examples of Mann-Whitney U test examples for beginners across health, education, business, and social science. Let’s translate that into a quick mental checklist you can use.

You’re probably looking at a good example of Mann-Whitney U test use when:

• You have two independent groups (no repeated measures on the same people for this test).
• Your outcome is ordinal (ratings, ranks) or continuous but non-normal (skewed times, weirdly shaped scores, outliers).
• You care about whether one group tends to have higher or lower values than the other.

Some everyday scenarios that often fit:

• Comparing hospital stay lengths between two treatment protocols.
• Comparing user ratings of two different product designs.
• Comparing teacher evaluation scores between two schools.
• Comparing income or spending between two demographic groups when the data are skewed.

In all these, you’re not just chasing a mean difference; you’re asking whether one group’s values are generally higher or lower in rank than the other’s. That’s exactly what the Mann-Whitney U test is built to do.

If you ever run a normality test (or eyeball a histogram) and think, “Yikes, that’s not bell-shaped,” keep these examples of Mann-Whitney U test examples for beginners in mind.

Quick comparison: When not to use the Mann-Whitney U test

To keep this practical, it helps to know when your situation is not an example of Mann-Whitney U test usage.

You probably should not use it when:

• You have paired data on the same people (before/after on one group). Then you’d usually consider the Wilcoxon signed-rank test instead.
• You have more than two groups. Then you’d think about the Kruskal–Wallis test as a non-parametric alternative to one-way ANOVA.
• Your data are approximately normal and meet t-test assumptions. In that case, a standard independent t-test might be more common.

But when your scenario looks like the real examples we walked through—two independent groups, skewed or ordinal data—there’s a good chance you’re looking at a solid example of Mann-Whitney U test use.

FAQ: Common beginner questions about Mann-Whitney U test examples

What is a simple real-life example of Mann-Whitney U test use?

A very simple example of Mann-Whitney U test use is comparing pain scores between two groups of patients given different medications. Each patient rates their pain from 0 to 10, the scores are skewed, and you want to know whether one medication leads to generally lower pain ratings than the other.

Are Likert-scale questions (1–5, 1–7) good examples of Mann-Whitney U test situations?

Yes, Likert-scale ratings are some of the best examples of Mann-Whitney U test applications. Because the responses are ordered categories, not precise measurements, the test’s rank-based approach works well. Comparing satisfaction with two apps, two teaching methods, or two policies using 1–5 or 1–7 scales is a classic example of non-parametric testing.

Can I use the Mann-Whitney U test for more than two groups?

No. The Mann-Whitney U test is specifically for two independent groups. If you have three or more groups (for example, comparing satisfaction across three different apps), you’d typically use the Kruskal–Wallis test instead, which extends the same rank-based idea.

Do I need large samples for these examples of Mann-Whitney U test use?

Not necessarily. One advantage of the Mann-Whitney U test is that it can be used with small to moderate sample sizes, especially when normality is questionable. That said, larger samples always help with more stable estimates and better power.

Is the Mann-Whitney U test comparing means or medians?

Technically, the test compares the distributions of the two groups using ranks. In practice, many people interpret a significant result as evidence that one group tends to have higher or lower median values than the other, especially when the shapes of the distributions are similar.

Where can I learn more about non-parametric tests like this?

You can find accessible explanations and examples on:

• University statistics pages, such as UCLA’s Institute for Digital Research and Education.
• Public health and medical research methods sections on NIH or CDC.
• Introductory biostatistics resources from medical schools and public health programs.

By focusing on real examples of Mann-Whitney U test examples for beginners—pain scores, satisfaction ratings, test scores, and skewed times—you can start to recognize when this test fits naturally into your own work. You don’t have to be a statistician to use it wisely; you just need to know your data, your groups, and whether your outcome behaves more like a neat bell curve or a messy real-world distribution.