Nonparametric Tests Overview
So far, many of the statistical tests we studied (t tests, ANOVA, regression) rely on certain assumptions.
But real-world data is often messy:
- Not normally distributed
- Contains outliers
- Measured on an ordinal scale
Nonparametric tests provide reliable alternatives when these assumptions are violated.
What Are Nonparametric Tests?
Nonparametric tests are statistical methods that:
- Do not assume a specific distribution
- Often use ranks instead of raw values
- Work well with ordinal or skewed data
They are sometimes called distribution-free tests.
When Should You Use Nonparametric Tests?
Nonparametric tests are appropriate when:
- Normality assumption is violated
- Sample size is very small
- Data contains strong outliers
- Data is ordinal rather than numerical
Parametric vs Nonparametric (Big Picture)
| Aspect | Parametric Tests | Nonparametric Tests |
|---|---|---|
| Distribution assumption | Required | Not required |
| Data type | Numerical | Ordinal / Numerical |
| Sensitivity to outliers | High | Low |
| Statistical power | Higher (when assumptions hold) | Lower (but safer) |
Common Nonparametric Tests
Each nonparametric test corresponds to a familiar parametric test.
| Parametric Test | Nonparametric Alternative | Used When |
|---|---|---|
| One-sample t test | Sign test / Wilcoxon signed-rank | Non-normal data |
| Independent t test | Mann–Whitney U test | Skewed distributions |
| Paired t test | Wilcoxon signed-rank | Ordinal or outliers |
| One-way ANOVA | Kruskal–Wallis test | Non-normal groups |
Key Idea: Ranking Instead of Raw Values
Most nonparametric tests work by:
- Ranking all observations
- Comparing rank sums between groups
This reduces the influence of extreme values and skewed distributions.
Real-World Example
A company collects customer satisfaction ratings on a scale of 1 to 5.
Because these ratings are ordinal and often skewed, a nonparametric test is more appropriate than a t test.
Advantages of Nonparametric Tests
- Fewer assumptions
- Robust to outliers
- Works with small samples
- Applicable to ordinal data
Limitations
- Less powerful when parametric assumptions hold
- Results may be harder to interpret
- Often test medians rather than means
Common Mistakes to Avoid
- Using nonparametric tests unnecessarily
- Ignoring data type and scale
- Assuming nonparametric means “inferior”
- Forgetting what parameter is being tested
Quick Check
Why are nonparametric tests more robust to outliers?
Practice Quiz
Question 1:
What is the main advantage of nonparametric tests?
Question 2:
Which nonparametric test replaces one-way ANOVA?
Question 3:
Are nonparametric tests always better?
Mini Practice
You are comparing customer satisfaction scores (1–5) across three stores.
- Which type of test is appropriate?
- Why?
What’s Next
In the next lesson, we will apply statistics in practice using Excel, bringing theory into real-world tools.