1150 LearnersLast updated on June 18th, 2025
Non-Parametric Test
The non-parametric test is a statistical approach we use as it does not assume a specific probability distribution for the population. It is used in comparing two quantities, such as the test results of students in two different schools. In this topic, we will explore more about Non-parametric tests in detail.
What is a Non-Parametric Test in Statistics?
In statistics, hypothesis testing is classified into parametric and non-parametric tests. Non-parametric tests are often called the distribution-free test, as they do not rely on assumptions to analyze the population distribution. They can be used as an alternative tool to parametric tests. We usually apply this test when the sample size of the data is small.
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Difference Between Parametric and Non-Parametric
Parametric and Non-parametric are the two types of hypothesis testing. Here, we will discuss the key differences between the two methods:
| Parametric Method | Non-Parametric Method |
| Assumes a certain probability distribution | Makes no assumptions about the population distribution. |
| Often tests numerical or normally distributed data. | Suitable for ordinal, ranked, or skewed data. |
| Analyzes data using key parameters such as mean and standard deviation. | Does not rely on pre-determined parameters. |
| Due to the rigid assumptions it is limited to specific datasets. | More flexible and are applied to real-world data. |
| Examples: ANOVA, t-test, linear regression. | Examples: Mann-Whitney U test, Kruskal-Wallis test, signed - rank test. |
What are the different types of Non-Parametric Tests?
There are different types of Non-parametric tests. Let’s now learn the key features of each of them:
Statistical Tests:
- Kendall’s Tau: It measures the correlation between two variables, useful for small datasets with tied ranks.
- Friedman Test: It compares three or more related paired samples, often used for repeated measures data.
- F-test: A test that compares the variances of two groups to analyze if they are the same or not.
- Chi-square test: Tests to analyze the relationships between categorical variables.
Machine Learning Models:
Decision Trees:
Decision trees is a hierarchical model that splits based on feature conditions, where each node represents a decision rule, leading to predictions at leaves.
Random Forests:
It is an ensemble of multiple decision trees that improve accuracy and reduce overfitting by averaging predictions from randomly selected data subsets.
K-Nearest Neighbors:
Also known as KNN, it is a kind of lazy learning algorithm that classifies a data point on the majority label of its closest k neighbors in the feature space.
Support Vector Machines:
Also known as SVM is a model that maps data into higher-dimensional space using kernel functions.
Common Mistakes and How to Avoid Them in Non-Parametric Test
Students tend to make mistakes while understanding the concept of non-parametric tests. Let us see some of the common mistakes and how to avoid them in non-parametric tests:
Mistake 1
Confusion between Non-Parametric Tests and Parametric Tests
Some students might apply non-parametric tests even when the data requires parametric tests.
Students need to know that it is important to check the assumptions like distribution and variances to determine which test needs to be used.
Mistake 2
Applying Without Checking for Adequacy
Students sometimes have a misconception that non-parametric tests apply to all small sample sets without checking for adequacy.
Always check that the sample size meets the adequacy of the test. If the sample size is too low, it has a higher chance of resulting in inaccurate results.
Mistake 3
Overlooking Assumptions of Non-Parametric Tests
One common mistake is that non-parametric tests ignore all the assumptions.
Non-parametric tests often do not follow fixed assumptions, but it is always important to check for independent observations and correct measuring scales before applying the test.
Mistake 4
Incorrect Selection of Parametric Test for the Data
They mistakenly use a non-parametric test that is not appropriate for the given data.
For example: Students sometimes consider a test for independent groups when comparing multiple types of groups.
Always, verify the type of test selected is correct by considering the type of data and the population size.
Mistake 5
Confusion between Independent and Dependent Sample Tests
Some students may mistakenly apply an independent sample test in cases where a dependent sample test is required.
Double-check if the samples are paired or independent before applying the test.
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Solved Examples of Non-Parametric Tests
Problem 1
Angel wants to check if a new cooking method has improved her business. Four customers’ were recorded before and after the method was introduced.
|
Customer |
Sales Before |
Sales After |
Difference (After- Before) |
|
1 |
60 |
90 |
+30 |
|
2 |
52 |
85 |
+33 |
|
3 |
43 |
95 |
+52 |
|
4 |
40 |
82 |
+42 |
The introduction of the new cooking method has positively impacted business performance.
Explanation
|
Customer |
Sales Before |
Sales After |
Difference (After- Before) |
Absolute Difference |
Rank |
|
1 |
60 |
90 |
+30 |
30 |
3 |
|
2 |
52 |
85 |
+33 |
33 |
4 |
|
3 |
43 |
95 |
+52 |
52 |
2 |
|
4 |
40 |
82 |
+42 |
42 |
1 |
Here, every rank is given a positive value as each difference is positive.
Calculating Test Statistic:
Sum of positive ranks (W⁺) = 1 + 2 + 3 + 4 = 10
Sum of negative ranks (W⁻) = 0 (no negative differences)
The test statistic W is the smaller of W⁺ and W⁻, so W = 0
Comparing with Critical Value
For n = 4 at α = 0.05 (one-tailed test), the critical value from the Wilcoxon table is 0.
Since W (0) ≤ Critical Value (0), we reject the null hypothesis (H₀).
Hence, we can conclude that:
There has been a significant increase in sales because of the application of the new cooking method. This tells us that the technique has positively impacted business performance.
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FAQs on Non-Parametric Test
1.What is a non-parametric test?
2.What are the common non-parametric tests?
3.When should non-parametric tests be used?
4.Is ANOVA a non-parametric test?
5.What is a parametric test?
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Jaipreet Kour Wazir
About the Author
Jaipreet Kour Wazir is a data wizard with over 5 years of expertise in simplifying complex data concepts. From crunching numbers to crafting insightful visualizations, she turns raw data into compelling stories. Her journey from analytics to education ref
Fun Fact
: She compares datasets to puzzle games—the more you play with them, the clearer the picture becomes!
