Nonparametric Tests
Tests without distribution assumptions.
Key idea
Tests without distribution assumptions.
In depth
Tests like the sign test, Wilcoxon and Mann–Whitney use ranks rather than values, so they need fewer assumptions about the distribution. They work for ordinal data and small, skewed samples, at some cost to power.
Worked example
Mann–Whitney compares whether one group tends to have higher ranks than another.
Real-world uses
- Analysing ranked customer ratings or small skewed datasets without assuming normality
Common mistake
Using them when assumptions of parametric tests are fine, losing power.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Nonparametric Tests?
Tests without distribution assumptions. It is a topic at the expert level in Probability & Statistics.
Where is Nonparametric Tests used in real life?
Real-world examples: Analysing ranked customer ratings or small skewed datasets without assuming normality.
What should I learn before Nonparametric Tests?
Make sure you are comfortable with ANOVA, the previous topic in Probability & Statistics.
What is a common mistake with Nonparametric Tests?
Using them when assumptions of parametric tests are fine, losing power.
How can I practise Nonparametric Tests?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Nonparametric Tests?
Move on to Multiple Regression next.
Related expert topics in Probability & Statistics
- Skewness and Kurtosis – Measures of asymmetry and tail heaviness.
- Residuals and R² – Error of a fit and proportion of variance explained.
- Simpson’s Paradox – A trend reverses when groups are combined.
- Law of Total Probability – Split an event over a partition.
- Bayes’ Theorem – Update beliefs with evidence.
- Medical Tests and Base Rates – Why positive results can still be probably false.