Statistical analysis plays a crucial role in data interpretation across various fields. While parametric tests are widely used, non-parametric tests provide a robust alternative when data assumptions are not met.
In statistics, Non-parametric tests test which does not make any assumption as to the form of distribution in the population from which the sample is drawn i.e. to say that the functional form of the distributions is not known. The test is called a non-parametric test or distribution-free test. In this guide, we will explore non-parametric tests, their advantages, types, and when to use them.
What Are Non-Parametric Tests?
Non-parametric tests are statistical tests that do not assume a specific distribution for the data. Unlike parametric tests, which require normal distribution and homogeneity of variance, non-parametric tests can be applied to ordinal, nominal, or non-normally distributed data.
Assumptions of Non-Parametric Tests
Non-parametric tests follow some assumptions. They are,
- Sample observations are independent
- The variable under study is continuous.
- The pdf is continuous.
- Lower order moment exists.
Common Non-Parametric Tests and Their Applications
1. Mann-Whitney U Test
- Purpose: Compares two independent groups.
- Use Case: Evaluating median differences in customer satisfaction scores.
2. Wilcoxon Signed-Rank Test
- Purpose: Compares paired samples.
- Use Case: Analyzing before-and-after effects of a treatment.
3. Kruskal-Wallis Test
- Purpose: Compares three or more independent groups.
- Use Case: Comparing performance scores across multiple teams.
4. Friedman Test
- Purpose: Compares repeated measures in related samples.
- Use Case: Measuring user experience before and after software updates.
5. Chi-Square Test
- Purpose: Examines the association between categorical variables.
- Use Case: Analyzing the relationship between customer demographics and purchase behavior.
Most used non-parametric Tests
There are some other tests which are generally used widely.
Advantages
There are some advantages of non-parametric test,
- Non-parametric methods are readily comprehensive very simple and easy to apply and do not require complicated sample theory.
- No assumption is made when the sample is drawn from the population.
- Non-parametric tests are available to deal with the data which are given in rank.
Disadvantages
- It can be used only if the measurements are nominal and ordinal even in that case if a parametric test exists it is more powerful than a non-parametric test.
- Non-parametric tests are designed to test statistical hypothesis only and not to estimate the parameter.
- A large number of different types of tables is required.
The steps for the testing procedure of Non-parametric test
Step 1 : Hypothesis test: State the null hypothesis (Ho) and its alternative hypothesis (H1)
2: Statistical test: Among several tests that might be given research design, choose the test that most closely approximates the conditional research in terms of the assumptions the test is based.
3: Significance level: Specify a level of significance (α) and size (n )
4: Sampling distribution: finding the sampling distribution statistic test under the assumption that Ho.
5: Critical Region: Based on steps 2,3 and 4 above the region of rejection for the statistic form
6: Decision: If the value of the test statistic is one of rejection, the decision is to reject wise accept.
Difference between Parametric and Non-parametric test
Parametric Test | Non- Parametric Test |
Normality of the distribution | Non-normality of the distribution |
Scales of measurement are intervals. | Scales of measurement are ordinal and nominal. |
It depends upon on parameter of the population. | It does not depend on the parameter of the population. |
It is not always easy to apply. | Easy to apply and does not need complicated sample theory. |
It makes assumptions as to the form of distribution to the population. | It does not make assumptions as to the form of the distribution to the population. |
Here assumptions are too strict. | Here assumptions are less strict. Such: as continuity, discreteness, symmetry, etc. |
Here, Outlier exists. | Here, Outlier does not exist. |
The homogeneity of variance for the parametric test is,
![\[ \sigma _{1}^{2}=\sigma _{2}^{2}=...=\sigma _{n}^{2} \]](https://www.statisticalaid.com/wp-content/ql-cache/quicklatex.com-a78c622878802f6d7c3a21c3c753e0d6_l3.png "Rendered by QuickLaTeX.com")
The homogeneity of variance for non-parametric tests is,
![\[ \sigma _{1}^{2}\neq \sigma _{2}^{2}\neq ...\neq \sigma _{n}^{2} \]](https://www.statisticalaid.com/wp-content/ql-cache/quicklatex.com-5515d1bbb11fa92cc74908e0b2fe868f_l3.png "Rendered by QuickLaTeX.com")
When to Use Non-Parametric Tests
- When data does not follow a normal distribution.
- When dealing with small sample sizes.
- When using ordinal or categorical data.
- When variance assumptions of parametric tests are violated.
Limitations
- Less statistical power compared to parametric tests.
- May not provide precise estimates of population parameters.
- More challenging to interpret results.
Conclusion
Non-parametric tests are essential tools for statistical analysis, especially when data does not meet parametric assumptions. Understanding their applications and limitations allows researchers to make informed decisions when analyzing data. Whether working with small sample sizes, ordinal data, or non-normally distributed variables, non-parametric tests provide a reliable alternative for drawing meaningful conclusions.
For more insights on statistical analysis, stay updated with our latest content! Data Science Blog