Statistical tests are at the heart of data analysis. Whether you’re working in finance, healthcare, psychology, or business research, you need the right test to validate your findings. One of the most common questions is: Should I use a parametric test or a nonparametric test?
This article explains both approaches in detail, compares them side by side, and provides simple real-world examples so you can confidently decide which test to apply.
What Are Parametric Tests?
Parametric tests are statistical tests that rely on assumptions about the population distribution. Most often, they assume data are drawn from a normal distribution. They are designed to evaluate hypotheses about population parameters such as the mean, variance, or correlation.
Key Features of Parametric Tests
- Require assumptions about the population distribution (e.g., normality).
- Depend on parameters such as mean and standard deviation.
- Generally more powerful than nonparametric tests when assumptions are met.
- Require interval or ratio data (true numerical values).
Common Examples
- Z-test: Tests whether the sample mean differs from a known population mean when variance is known or sample size is large.
- T-test: Compares means between one or more groups when variance is unknown.
- ANOVA (Analysis of Variance): Compares means across three or more groups.
- Pearson correlation: Measures the strength of a linear relationship between two variables.
Example in Practice
A researcher wants to test if the average exam score of students in a class is significantly higher than 70. Assuming the data is normally distributed, a one-sample t-test can be used.
What Are Nonparametric Tests?
Nonparametric tests do not require a specific distribution assumption. They are sometimes called distribution-free tests. Instead of relying on population parameters like means and variances, they often work by ranking or categorizing the data.
Key Features of Nonparametric Tests
- Do not require normality assumptions.
- Work with ordinal data (ranks, Likert scales) or when the assumptions for parametric tests are not met.
- More flexible and robust, but can be less powerful than parametric tests.
- Can test hypotheses unrelated to population parameters (e.g., randomness).
Common Examples
- Mann–Whitney U test: Alternative to the independent samples t-test, compares medians between two groups.
- Wilcoxon signed-rank test: Alternative to paired t-test.
- Kruskal–Wallis test: Alternative to one-way ANOVA.
- Spearman’s rank correlation: An Alternative to Pearson correlation, used for ordinal data.
- Runs test: Tests whether a sequence of data points is random.
Example in Practice
A company surveys customers with satisfaction ratings from 1 (very dissatisfied) to 5 (very satisfied). Since the data is ordinal, a Mann–Whitney U test is better than a t-test when comparing satisfaction levels between two branches.
When to Use Parametric vs. Nonparametric Tests
Here’s a simple decision framework:
Use Parametric Tests When:
- Data is normally distributed (or the sample size is large enough for the Central Limit Theorem).
- You’re testing means, variances, or correlations (parameters).
- Data type is interval or ratio.
Use Nonparametric Tests When:
- Assumptions are violated: e.g., data is skewed, non-normal, and the sample size is small.
- Example: Testing the median daily return of a stock with only 12 skewed observations.
- Data is ordinal or ranked.
- Example: Analyzing customer satisfaction ratings or product rankings.
- The hypothesis does not involve parameters.
- Example: Using a runs test to check if a stock’s daily up/down sequence is random.
Practical Scenarios
- Finance: Testing if the average return differs from zero → t-test (parametric).
- Healthcare: Comparing patient pain scores on a 1–10 ordinal scale → Mann–Whitney U (nonparametric).
- Psychology: Analyzing survey Likert scales (strongly agree → strongly disagree) → nonparametric tests.
- Data Science: Checking if click-through rates follow a random pattern → runs test.
Conclusion
Choosing between parametric and nonparametric tests depends on your data type, sample size, and assumptions.
- Use parametric tests when data is numeric and distribution assumptions hold—they give stronger, more precise results.
- Use nonparametric tests when data is ordinal, assumptions fail, or randomness/distribution-free analysis is needed.
By understanding these two categories and their applications, you can make smarter, more reliable decisions in your statistical analysis.