Mann-Whitney U Test Using SPSS Statistics
What is the Mann-Whitney U Test?
The Mann-Whitney U test is used to compare differences between two independent groups when the outcome (dependent) variable is either ordinal or continuous. It is commonly applied when the data is not normally distributed, thus violating the normality assumption required for a t-test. In such cases, the Mann-Whitney U test serves as a non-parametric alternative to the Independent Samples t-test, as it does not assume a specific data distribution. This test is particularly useful for small sample sizes where the t-test may be unreliable.
The dependent variable must be either ordinal or continuous. Below, we discuss these types of variables with examples.
Ordinal Variable
An ordinal variable represents data with a meaningful order or ranking, but the intervals between categories are not equal and cannot be quantified.
Examples of Ordinal Variables
- Likert scale responses (e.g., “strongly agree,” “agree,” “neutral,” “disagree,” “strongly disagree”)
- Education levels (e.g., “High school,” “Bachelor’s,” “Master’s,” “PhD”)
These examples show a clear ranking, but the differences between the levels are not quantifiable.
Continuous Variable
A continuous variable, on the other hand, can take any value within a given range, and the difference between values can be measured or quantified. Continuous variables are measured on a scale and may include decimal values.
Examples of Continuous Variable
- Height (e.g., 4.3 feet, 6.1 feet)
- Weight (e.g., 60.5 kg, 90.3 kg)
- Temperature (e.g., 97.7°F, 100.4°F)
In summary, continuous variables are measured on a continuous scale, whereas ordinal variables represent ranked categories without equal intervals between them.
Examples Where the Mann-Whitney U Test Can be Used
The Mann-Whitney U test can be used in the following examples to compare two independent groups. In the first three examples, the dependent variable is ordinal, while in the fourth, the dependent variable is continuous.
Example 1: Comparing Pain Levels After Two Types of Surgery
- Scenario: A researcher wants to compare post-operative pain levels between patients who underwent two different types of surgery: minimally invasive surgery vs. traditional open surgery.
- Dependent Variable: Pain levels measured on an ordinal scale (e.g., 1 = “No pain,” 2 = “Mild pain,” 3 = “Moderate pain,” 4 = “Severe pain”).
- Independent Variable: Type of surgery, with two independent groups: minimally invasive surgery and traditional open surgery.
Example 2: Customer Satisfaction Based on Payment Methods
- Scenario: A business wants to know whether customer satisfaction varies depending on the payment method.
- Dependent Variable: Customer satisfaction, measured on an ordinal scale (e.g., 1 = “Very dissatisfied,” 2 = “Dissatisfied,” 3 = “Neutral,” 4 = “Satisfied,” 5 = “Very satisfied”).
- Independent Variable: Payment method, with two independent groups: online payment and cash payment.
Example 3: Stress Levels of Employees in Different Work Settings
- Scenario: A company investigates whether employee stress levels differ between remote workers and office workers.
- Dependent Variable: Stress levels, measured on an ordinal scale (e.g., 1 = “Low stress,” 2 = “Moderate stress,” 3 = “High stress”).
- Independent Variable: Work setting, with two independent groups: remote work and office work.
Example 4: Comparing Blood Pressure Between Smokers and Non-Smokers
- Scenario: A researcher wants to determine whether systolic blood pressure differs between smokers and non-smokers.
- Dependent Variable: Systolic blood pressure, a continuous variable measured in mmHg (e.g., 120 mmHg, 135 mmHg).
- Independent Variable: Smoking status, with two independent groups: smokers and non-smokers.
Assumptions for Mann Whitney U Test
- The two groups being compared must be independent of each other.
- The dependent (outcome) variable must be ordinal or continuous.
- Each group’s data must be independent (i.e., no participant can appear in both groups).
- The shape of the distribution for the dependent variable should be similar for each group.
Example Scenario for Performing the Mann-Whitney U Test in SPSS
In this example, a researcher examines whether male and female movie ratings differ. Data was collected from 20 males and 20 females, along with their respective ratings. The dependent variable is the movie rating, while the independent variable is gender, with two independent groups (male and female).
- Null Hypothesis: There is no difference in movie ratings between males and females.
- Alternative Hypothesis: There is a difference in movie ratings between males and females.
Check out how to perform the Mann-Whitney U test using R for the example. Interestingly, we got the same results using two different software.
Movie Ratings Sample Data
Running the Mann-Whitney U Test in SPSS: Step-by-Step Explanation
STEP 1: For us to perform the test in SPSS, we need to import and organize the data in SPSS. Therefore, we will group male and female data into a gender variable and allocate value 1 for males and value 2 for females. The figures below show both the data view and variable view of our imported and organized data.
Data View
Variable View
STEP 2: Select Analyze → Nonparametric Tests → Legacy Dialogs → 2 Independent Samples as shown below
STEP 3: In the new window, move the dependent variable (movie rating) to the Test Variable List and the independent variable (gender) to the Grouping Variable box. Then click on Define Groups to specify group codes (1 for males, 2 for females).
STEP 4: Define the groups in the new window by entering the corresponding codes (1 for males, 2 for females), then click Continue.
STEP 5: Click the Options tab, check Descriptives and Quartiles, then click Continue. After this, click OK to run the test and generate the output.
STEP 6: The output will appear in the SPSS output window as shown below.
Reporting the Mann-Whitney U Test Results
Reporting Descriptive Statistics
The table below presents the descriptive statistics for gender and movie ratings, showing values for the number of observations (N), mean, standard deviation, minimum, maximum, and percentiles.
| Descriptive Statistics | ||||||||
| N | Mean | Std. Deviation | Minimum | Maximum | Percentiles | |||
| 25th | 50th (Median) | 75th | ||||||
| Movie Ratings | 40 | 5.8937 | .80238 | 4.68 | 8.21 | 5.4200 | 5.7150 | 5.9650 |
| Gender | 40 | 1.5000 | .50637 | 1.00 | 2.00 | 1.0000 | 1.5000 | 2.0000 |
Reporting Ranks Table
The table below shows the ranks, including the number of observations (N), mean rank, and sum of ranks for the two independent groups (male and female).
| Ranks | ||||
| Gender | N | Mean Rank | Sum of Ranks | |
| Movie Ratings | Male | 20 | 20.75 | 415.00 |
| Female | 20 | 20.25 | 405.00 | |
| Total | 40 | |||
Reporting Mann Whitney U Test Statistics
The Mann-Whitney U test produced a U value of 195.000 and a p-value of 0.892. Since p > 0.05, we fail to reject the null hypothesis and conclude that there is no significant difference in movie ratings between males and females.
es.
| Test Statistics | |
| Movie Ratings | |
| Mann-Whitney U | 195.000 |
| Wilcoxon W | 405.000 |
| Z | -.135 |
| Asymp. Sig. (2-tailed) | .892 |
| Exact Sig. [2*(1-tailed Sig.)] | .904b |
H2: Interpreting Mann Whitney U Test SPSS Results in APA Format
A Mann-Whitney U test was conducted to assess the difference in movie ratings between males and females. The test indicated no significant difference between the two groups (U = 195, p = 0.892). Thus, we fail to reject the null hypothesis, concluding that there is no significant difference in movie ratings between males and females.
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