Join our Community Groups and get customized solutions Join Now! Watch Tutorials Youtube

Non-Parametric Test: Types, and Examples

Discover the power of non-parametric tests in statistical analysis. Explore real-world examples and unleash the potential of data insights

Key Points:

  • Non-parametric tests are statistical processes that do not rely on specific data distribution assumptions, making them more versatile and resilient than parametric tests.
  • They may analyze variables measured on an ordinal, interval, or nominal scale. They are especially effective when data contradicts assumptions such as normality or equal variances.
  • Non-parametric tests, such as the Mann-Whitney U Test, Kruskal-Wallis Test, Spearman's Rank-Order Correlation, and the Chi-Square Test, serve distinct objectives and analyze different data types.
  • Non-parametric tests provide advantages such as applying to any data, being resistant to violations of distributional assumptions, and being trustworthy with small sample sizes.
  • While non-parametric tests have less power than parametric tests when assumptions are satisfied, they give valuable insights into connections, group comparisons, and hypothesis testing without jeopardizing the analysis's integrity.
Non Parametric Tests


Introduction to Non-Parametric Tests

Parametric tests in statistical analysis frequently rely on presumptions about the data, including normality or equal variances. These presumptions could, however, only seldom be true in practical situations this situation Non-parametric testing is useful. Non-parametric tests provide alternative statistical techniques without particular population distribution assumptions. These tests are adaptable and reliable, making them appropriate for various data types and research contexts.

Definition

Non-parametric tests, often distribution-free, are statistical techniques that need fewer data assumptions than parametric tests. These tests use rank or categorical data. They may do ordinal, interval, or nominal scale analysis on variables. Unlike parametric tests, non-parametric tests do not presuppose a specific distribution in the data, such as normal distribution or equal variances.

The phrase "non-parametric test" has recognized relevance in statistics. It refers to a group of statistical approaches that make no assumptions about the population distribution's characteristics. The dictionary definition of a non-parametric test is consistent with the prior discussion, emphasizing the absence of particular assumptions about the form or features of the population distribution.

Statistics

Non-parametric tests are essential in statistical analysis, especially when the data violates the assumptions of parametric tests, such as normality or variance homogeneity. These tests include the Mann-Whitney U test, the Wilcoxon signed-rank test, the Kruskal-Wallis test, and Spearman's rank correlation coefficient. Non-parametric tests using ranks or distribution-free procedures give alternatives to their parametric equivalents, such as the independent t-test, paired t-test, analysis of variance (ANOVA), and Pearson's correlation coefficient.

Psychology

Non-parametric tests are commonly used in psychology, particularly when analyzing data from experiments or surveys. They are beneficial when dealing with data measured on ordinal scales or not regularly distributed data. Psychologists frequently use non-parametric tests to compare medians, test for differences across groups, examine correlations between variables, or analyze ranked data.

Non-Parametric Tests

Understanding the Purpose of Non-Parametric Tests

Non-parametric tests are used for a variety of applications in statistical analysis. They are frequently used in the following contexts:

  • Data violates parametric test assumptions, such as normality or variance homogeneity.
  • Data is ordinal or nominal scale.
  • Small Sample size.
  • The data contains outliers.

In these cases, non-parametric tests provide a viable alternative, allowing researchers to make legitimate results without jeopardizing the correctness of their investigation.

Types of Non-Parametric Tests

Non-parametric tests encompass various techniques, each designed for specific research scenarios. Here is a list of commonly used non-parametric tests:

  1. Mann-Whitney U test
  2. Wilcoxon signed-rank test
  3. Kruskal-Wallis test
  4. Friedman test
  5. Spearman's rank correlation coefficient
  6. Kendall's rank correlation coefficient
  7. Runs test
  8. McNemar's Test
  9. Kolmogorov-Smirnov test
  10. Chi-square test for independence
  11. McNemar's test
  12. Median test

1. Mann-Whitney U Test

The Mann-Whitney U test, or the Wilcoxon rank-sum test, compares two independent groups. It assesses whether the distributions of the two groups differ significantly. The test uses the ranks of the observations to make the comparison.

Consider comparing the efficacy of two different weight loss programs. Participants can be assigned to either Programme A or Programme B at random. You gather weight loss data from both groups at the end of the trial. The Mann-Whitney U test can examine whether the two programs have a statistically significant difference in weight reduction.

2. Wilcoxon Signed-Rank Test

The Wilcoxon signed-rank test is used when analyzing paired data. It determines whether the medians of two related groups are significantly different. The test compares the differences between the paired observations using their ranks.

Assume you're looking at the effect of a new teaching approach on pupils' test results. You give the same set of pupils a pre-test and a post-test. The Wilcoxon signed-rank test can assess whether there is a significant change in the students' results before and after implementing the new teaching approach.

3. Kruskal-Wallis Test

The Kruskal-Wallis test is a non-parametric alternative to one-way analysis of variance (ANOVA). It compares three or more independent groups to determine if there are significant differences among the medians.

Assume you wish to compare the degrees of pain experienced by patients who got one of three different pain management treatments: drug A, medication B, and a placebo. You assess the pain levels of each group of patients and apply the Kruskal-Wallis test to see if there are any significant variations in pain reduction between the three therapies.

4. Friedman Test

The Friedman test is a non-parametric alternative to repeated measures ANOVA. It compares three or more related groups to determine if there are significant differences in the distributions.

Consider the following scenario: you wish to assess participants' preferences for three distinct flavors of ice cream: chocolate, vanilla, and strawberry. You invite each participant to rate their favorite flavors in order of importance. The Friedman test can assess whether there is a statistically significant difference in preference rankings between the three flavors.

5. Spearman's Rank-Order Correlation

Spearman's rank-order correlation measures the degree and direction of a monotonic link between two variables. It is employed when the data is ordinal, or Pearson's correlation assumptions are unsatisfied.

Assume you're researching the association between students' study hours and exam grades. You gather information on the number of study hours and exam grades for a set of pupils. Regardless of the detailed quantitative data, Spearman's rank correlation coefficient may assess if there is a significant association between study hours and exam grades.

6. Kendall's Rank Correlation

Kendall's rank correlation is another way to determine the relationship between two variables. When the data contains ties, it determines the strength and direction of the rank-order connection.

Consider analyzing consumer preference rankings for three smartphone brands: Brand X, Brand Y, and Brand Z. Every consumer ranks their favorite brand. Kendall's rank correlation coefficient may determine the degree of agreement or relationship between customer ranks and smartphone brands.

7. Chi-Square Test

The chi-square test is used to determine the independence of two categorical variables. It examines the observed and predicted frequencies to see if there is a meaningful link.

Assume you want to see if there is a link between smoking status (smoker/nonsmoker) and the occurrence of lung cancer. You collect data from a sample of people and apply the chi-square test for independence to see if there is a link between smoking status and the prevalence of lung cancer.

8. McNemar's Test

McNemar's test evaluates the proportional difference in paired nominal data. It is frequently used when comparing data before and after an intervention or therapy.

Consider the following scenario: you want to evaluate the success of a new advertising campaign. You poll a group of customers before and after the drive to see if they are familiar with the brand. McNemar's test can assess whether there is a statistically significant difference in brand awareness before and after the promotion.

9. Sign test

The sign test is a basic non-parametric test that compares the medians of two related samples. It is useful when the data is ordinal or highly skewed.

Assume you wish to assess the new medicine's effectiveness in lowering pain symptoms. You gather a group of patients and consider their pain levels before and after they take the drug. The Sign Test can detect whether there is a substantial improvement in pain levels following drug administration. When the data is paired and non-parametric, this test is ideal for circumstances when the data does not fit the assumptions of parametric tests.

10. Runs test

The run test determines if data values are random or independent. It controls whether the observations alternate or cluster non-randomly.

Assume you're looking at the incidence of "hot streaks" in a basketball player's performance. During a series of games, you note whether the player makes a successful shot or misses a shot. The run test can identify if the player's performance has a strong pattern or streak.

11. Median Test

The median test compares two or more independent groups' medians. It assesses whether or not there are substantial differences in medians without making any assumptions about the underlying distribution.

Consider comparing the median wages of two separate cities, City A and City B. You collect income information from a random sample of people in each town. The Median Test may be used to see if there is a statistically significant difference in median income between the two cities. This test is especially beneficial when the data is skewed or does not follow a normal distribution.

12. Kolmogorov-Smirnov test

The Kolmogorov-Smirnov test is a non-parametric statistical test that compares a sample's distribution to a known distribution or two independent models. It is based on the most significant difference under the null hypothesis between the empirical cumulative distribution function (ECDF) of the sample(s) and the theoretical cumulative distribution function (CDF).

Assume you are a researcher looking into the heights of adult males in a specific population. You may want to know if the height distribution is normally distributed. You collect heights from a random sample of people and want to see how well they fit a normal distribution.

Example of Non-Parametric Test

Consider the following scenario: a researcher wants to compare the effects of two different teaching methods on student performance. Instead of assuming normally distributed data and equal variances, the researcher can apply the non-parametric Mann-Whitney U test to determine whether there is a significant difference in median scores between the two groups.

Examples of Parametric Tests

While non-parametric tests provide greater flexibility in statistical analysis, parametric tests must also be understood. Metric tests assume the distributional features of the data. Parametric testing includes the following:

  • The t-test for students
  • ANOVA (Analysis of Variance)
  • Pearson's coefficient of correlation
  • Regression linear
  • The paired t-test

When the assumptions are satisfied, the Chi-square test for independence is used. Parametric tests are frequently employed, although they are sensitive to changes in underlying assumptions. Non-parametric tests give a credible alternative when the data violates these assumptions. 

Difference between Parametric and Non-Parametric Tests

The primary distinction between parametric and non-parametric tests is in their data assumptions. Specific distributions, such as the normal distribution and equal variances, are assumed by parametric tests. Non-parametric tests, on the other hand, depend on rankings or categorical data and make fewer assumptions. When the premises are satisfied, non-parametric tests are frequently regarded as more robust. However, they may have lower power than parametric tests.

Advantages and Limitations of Non-Parametric Tests

In statistical analysis, non-parametric tests have various advantages:

  • Any kind of data, including ordinal and nominal scales.
  • Normal distributional assumptions are being violated.
  • Small sample numbers produce accurate findings.
  • Adaptable and may be used in a variety of study domains.

Non-parametric tests, on the other hand, have limitations:

  • Have less power than parametric tests when the latter's assumptions are satisfied.
  • They may not give particular parameters or extensive information about the underlying distribution.
  • They need higher sample numbers to get the same degree of power as parametric tests.

Non-Parametric Test for ANOVA

The Kruskal-Wallis test is a non-parametric version of one-way ANOVA that allows researchers to determine if there are significant differences between groups based on rankings rather than averages.

Softwares

Several software programs are regularly used for parametric testing and statistical analysis. Here's a rundown of some prominent software solutions, along with their benefits and drawbacks:

SPSS (Statistical Package for the Social Sciences)

SPSS is a popular statistical software program noted for its user-friendly interface and broad statistical features. It includes a variety of parametric tests and data analysis processes, making it appropriate for fundamental and sophisticated statistical analysis. SPSS also includes data visualization and reporting tools.

Limitations: SPSS can be costly, particularly for individual users. The learning curve may be longer for users new to statistical software. Furthermore, specific complex statistical approaches may necessitate extra modules or programming abilities.

R or Rstudio, R Langauge

R is a statistical programming language and software environment that is free and open source. It includes many tools and libraries for performing parametric tests and sophisticated statistical analysis. R is adaptable, allowing users to customize and increase its features. It has a large and active user base and is frequently utilized in academics and research.

Limitations: R needs some programming skills, which may be difficult for people who have never coded. Compared to other software programs, it may have a higher learning curve. Furthermore, its graphical user interface (GUI) may need to be more user-friendly than other specialist statistical tools.

Stata

Stata is a sophisticated statistical software program noted for its simplicity and user-friendly interface. It offers a diverse set of parametric tests and statistical models. Stata facilitates repeatable research and has high-quality graphical capabilities. It is frequently utilized in various domains, such as social sciences, epidemiology, and economics.

Limitations: Stata can be costly, especially for individual users or small research projects. Some complex statistical approaches may necessitate the purchase of extra modules or licenses. Stata's programming language may have a significantly higher learning curve when compared to similar tools.

Conclusion

Non-parametric tests are valuable tools in statistical analysis because they give researchers flexibility and resilience when data violates parametric assumptions. Understanding the purpose, kinds, and differences between parametric and non-parametric tests allows researchers to select the best statistical strategy depending on their data characteristics and research aims. Using non-parametric tests broadens the statistical analysis toolbox, enabling accurate findings and valuable insights even when stringent assumptions are not used.

Frequently Asked Questions (FAQs)

Can non-parametric tests be used with continuous data?

Yes, non-parametric tests can be used with continuous data. They rely on ranks or transformations of the data and are not limited to specific types of variables.

Are non-parametric tests less potent than parametric tests?

Non-parametric tests may have lower power when the latter's assumptions are met. However, they offer robustness in situations where the premises are violated.

How do I choose between a parametric and a non-parametric test?

The choice between parametric and non-parametric tests depends on the data's nature and the tests' assumptions. Suppose the data violate the assumptions of parametric tests or are measured on ordinal/nominal scales. In that case, non-parametric tests are a suitable choice.

Can non-parametric tests be used for hypothesis testing?

Yes, non-parametric tests can be used for hypothesis testing. They provide p-values and test statistics, allowing researchers to draw inferences.

What are the 4 non-parametric tests?

The four common non-parametric tests are:

1.     Mann-Whitney U test

2.     Wilcoxon signed-rank test

3.     Kruskal-Wallis test

4.     Friedman test

What is an example of a non-parametric t-test?

A non-parametric equivalent of the t-test is the Wilcoxon signed-rank test. It is used when comparing two related groups or paired observations.

Is chi-square a non-parametric test?

The chi-square test is a non-parametric test commonly used to assess the association between categorical variables.

Is ANOVA a non-parametric test?

No, ANOVA (Analysis of Variance) is a parametric test that compares the means of three or more groups.

Is Kruskal-Wallis a non-parametric test?

The Kruskal-Wallis test is a non-parametric test used to compare three or more independent groups.

Is ANOVA a parametric test?

Yes, ANOVA is a parametric test used to compare the means of three or more groups based on the assumption of normality and equal variances.

How do you know if a test is non-parametric?

A test is considered non-parametric if it does not assume a specific probability distribution for the population or if it makes fewer distributional assumptions.

Is an independent t-test a non-parametric test?

The independent t-test is a parametric test used to compare means between two separate groups.

What makes a test non-parametric?

A test is considered non-parametric if it does not assume a specific probability distribution or makes fewer distributional assumptions than parametric tests.

What is the most common non-parametric test?

The Mann-Whitney U test, or the Wilcoxon rank-sum test, is one of the most common non-parametric tests used to compare two independent groups.

What is the most commonly used non-parametric test?

The chi-square test is one of the most commonly used non-parametric tests to analyze categorical data.

What is an example of non-parametric data?

Non-parametric data refers to data that do not have a specific distributional assumption. Examples include rankings, categorical data, or data measured on an ordinal scale.

Is ANOVA a parametric or non-parametric test?

ANOVA is a parametric test that compares the means of three or more groups, making assumptions about normality and equal variances.

Is regression a non-parametric test?

Regression analysis is a parametric method used to model the relationship between a dependent variable and one or more independent variables.

Is the Mann-Whitney test non-parametric?

Yes, the Mann-Whitney U test is a non-parametric test used to compare two independent groups when the assumptions of parametric tests are not met.

What is the simplest non-parametric test?

The sign test is considered one of the simplest non-parametric tests. It is used to assess whether the median of a single sample differs from a hypothesized value.

What data type is a non-parametric test?

Non-parametric tests can be applied to both continuous and categorical data types. However, they are more commonly used with ordinal or categorical data.

What is a one-sample non-parametric test?

One-sample non-parametric tests compare a sample distribution against a known or hypothesized distribution without assuming a specific underlying population distribution.

What are the two kinds of non-parametric tests?

The two main non-parametric tests are tests for independent samples and tests for related or paired samples.

Why not use the chi-square test?

The chi-square test is unsuitable for specific situations, such as small sample sizes or low expected cell counts. In such cases, alternative non-parametric tests may be more appropriate.

What is the difference between parametric and non-parametric tests?

Parametric tests assume specific population distributions and make assumptions about parameters, such as means and variances. Non-parametric tests do not rely on these assumptions. They are more flexible in analyzing data that do not meet parametric assumptions.

Is Spearman's test non-parametric?

Yes, Spearman's rank correlation coefficient is a non-parametric test used to assess the strength and direction of the monotonic relationship between two variables.

Is Pearson's test non-parametric?

No, Pearson's correlation coefficient is a parametric test used to measure the linear relationship between two continuous variables.

Can I use ANOVA for non-parametric data?

No, ANOVA assumes normality and equal variances, so it is inappropriate for non-parametric data. Non-parametric alternatives like the Kruskal-Wallis test can be used instead.

What is a non-parametric substitute for the t-test?

The non-parametric substitute for the t-test is the Wilcoxon rank-sum test (Mann-Whitney U test) for independent samples and the Wilcoxon signed-rank test for related samples.

 

When should you use a non-parametric test?

Non-parametric tests should be used when the data do not meet the assumptions of parametric tests, such as normality or equal variances, or when dealing with categorical or ordinal data.

Why are non-parametric tests less powerful?

Non-parametric tests are less potent because they make fewer population and data distribution assumptions. However, they are more robust and can be used in a broader range of scenarios.

Non-parametric vs. parametric

The distinction between non-parametric and parametric tests lies in the assumptions about the underlying population and the data distribution. Parametric tests assume specific distributions and parameters, while non-parametric tests are distribution-free or have fewer assumptions.

Non-parametric statistics

Non-parametric statistics refer to statistical methods and tests that do not rely on specific population assumptions or parameters, making them more flexible and robust in various situations.

Parametric and non-parametric test examples

Examples of parametric tests include t-tests, ANOVA, and regression analysis. Non-parametric tests include the Mann-Whitney U test, the Kruskal-Wallis test, and the chi-square test.

Non-parametric data

Non-parametric data refers to data that do not adhere to a specific distributional assumption or do not have fixed parameters. Examples include rankings, categorical data, and data measured on an ordinal scale.

Where can I learn more about non-parametric tests?

In our upcoming blog post, we will in detail explore this topic. Follow us and stay updated.


Related Posts


About the Author

Ph.D. Scholar | Certified Data Analyst | Blogger | Completed 5000+ data projects | Passionate about unravelling insights through data.

Post a Comment

RStudiodataLab Chatbot
Have A Question?We will reply within minutes
Hello, how can we help you?
Start chat...
Cookie Consent
We serve cookies on this site to analyze traffic, remember your preferences, and optimize your experience.
Oops!
It seems there is something wrong with your internet connection. Please connect to the internet and start browsing again.