Non-Parametric Tests in Research

  

Definition:
Non-parametric tests are statistical tests that do not assume a specific distribution (like normality) for the data. They are also known as distribution-free tests, and are especially useful for ordinal data, nominal data, or small sample sizes.

 When to Use Non-Parametric Tests

Use non-parametric tests when:

• Data does not meet assumptions of parametric tests (e.g., normality, equal variances).
• The sample size is small.
• The data is ordinal or nominal.
• There are outliers or skewed distributions.
• The measurement scale is not interval or ratio.

 Common Non-Parametric Tests

Test Name	Purpose	Parametric Equivalent	Example
Chi-Square Test (χ²)	Tests association between categorical variables	None	Gender vs. Voting Preference
Mann–Whitney U Test	Compares two independent groups (ordinal/continuous)	Independent t-test	Comparing satisfaction levels of two customer groups
Wilcoxon Signed-Rank Test	Compares two related samples or matched pairs	Paired t-test	Pre- and post-test scores of same participants
Kruskal–Wallis Test	Compares more than two independent groups	One-way ANOVA	Comparing ranks of test scores across 3 teaching methods
Friedman Test	Compares more than two related groups	Repeated-measures ANOVA	Measuring improvement in performance across 3 time points
Spearman’s Rank Correlation	Measures strength/direction of ordinal/monotonic relationships	Pearson correlation	Ranking income vs. happiness levels
Kolmogorov–Smirnov Test	Tests the distribution of a sample against a reference distribution	Normality test	Testing if a sample follows normal distribution
Run Test	Tests randomness in a sequence	—	Checking randomness in a sequence of stock price changes

 Advantages of Non-Parametric Tests

• Do not require assumptions about population parameters.
• Can be used with ordinal, nominal, or non-normally distributed interval data.
• Robust to outliers and skewed data.
• Ideal for qualitative and ranked data.

 Disadvantages

• Generally less powerful than parametric tests (higher chance of Type II error).
• Do not provide parameter estimates (e.g., means, standard deviations).
• May require larger sample sizes for detecting small effects.

 Summary Table: Parametric vs. Non-Parametric

Feature	Parametric Test	Non-Parametric Test
Data Type	Interval/Ratio (Quantitative)	Ordinal/Nominal/Non-Normal
Assumption of Normality	Required	Not required
Example Tests	t-test, ANOVA, Regression	Chi-square, Mann–Whitney, Kruskal–Wallis
Efficiency	More powerful if assumptions met	Less powerful but more flexible
Use with Small Samples	Not recommended	Recommended