Nonparametric Tests
So far, you have learned several statistical tests such as t-tests and ANOVA.
These tests are called parametric tests because they rely on assumptions about the data distribution.
When these assumptions are violated, nonparametric tests provide a reliable alternative.
Why Nonparametric Tests Are Needed
Parametric tests require conditions such as:
- Normal distribution of data
- Equal variances
- Interval or ratio scale measurement
In real-world data, these conditions are often not satisfied.
Nonparametric tests:
- Do not assume normality
- Work well with ordinal data
- Are robust to outliers
When to Use Nonparametric Tests
Nonparametric tests are recommended when:
- Sample size is very small
- Data is skewed or contains outliers
- Data is ordinal (ranks, ratings)
- Normality assumption is violated
They trade some statistical power for greater flexibility.
Parametric vs Nonparametric Tests
| Scenario | Parametric Test | Nonparametric Alternative |
|---|---|---|
| One group vs value | One Sample t-test | Wilcoxon Signed-Rank Test |
| Two independent groups | Independent t-test | Mann–Whitney U Test |
| Two related samples | Paired t-test | Wilcoxon Signed-Rank Test |
| Three or more groups | One-Way ANOVA | Kruskal–Wallis Test |
Example Scenario
A company collects customer satisfaction ratings on a scale from 1 to 5.
Because these ratings are ordinal and not normally distributed, a nonparametric test is more appropriate than a t-test.
For comparing two independent groups, the Mann–Whitney U Test would be used.
Running Nonparametric Tests in SPSS (Menu)
SPSS provides a dedicated menu for nonparametric tests:
- Go to Analyze → Nonparametric Tests
- Select the appropriate test based on design
- Define groups or test values
- Click OK
SPSS automatically handles ranking and test statistics.
Using SPSS Syntax (Example)
Below is an example of the Mann–Whitney U test:
NPAR TESTS
/MANN-WHITNEY=Rating BY Group(1 2)
/MISSING ANALYSIS.
This syntax compares satisfaction ratings between two independent groups.
Interpreting Nonparametric Output
When interpreting results:
- Focus on the test statistic (U, Z, or H)
- Check the p-value
- Interpret results using ranks, not means
Decision rule:
- p < 0.05 → significant difference
- p ≥ 0.05 → no significant difference
Common Mistakes
Common errors include:
- Using parametric tests when assumptions fail
- Misinterpreting ranks as means
- Ignoring data measurement level
Test selection must always match the data characteristics.
Quiz 1
Why are nonparametric tests used?
When parametric assumptions are violated.
Quiz 2
Which data type suits nonparametric tests?
Ordinal or non-normal data.
Quiz 3
What is the nonparametric alternative to ANOVA?
Kruskal–Wallis Test.
Quiz 4
Do nonparametric tests use means?
No, they use ranks.
Quiz 5
What does p < 0.05 indicate?
A statistically significant difference.
Mini Practice
Collect customer satisfaction ratings (1–5) for two service centers.
Use a nonparametric test to determine whether satisfaction differs between the centers.
Use Mann–Whitney U Test via Analyze → Nonparametric Tests.
What’s Next
In the next lesson, you will enter Linear Regression, where prediction and modeling begin.