Non Parametric Test – Formula and Types

What Is A Non Parametric Test?

Non parametric tests are mathematical methods that are used in statistical hypothesis testing. This method is used when the data are skewed and the assumptions for the underlying population is not required therefore it is also referred to as distribution-free tests. In other words, if the given population is uncertain or when the data are not distributed normally, non parametric tests are used. The word non parametric method does not indicate that there are absolutely no parameters but it tells us that the characteristic and number of parameters are not predefined but flexible. Usually we use a non parametric test when we have a non continuous data which has a large sample size. 

Parametric Test And Non Parametric Test

The only difference between parametric test and non parametric test is that parametric test assumes the underlying statistical distributions in the data whereas non parametric tests do not rely on any distribution. In a parametric test, there are several conditions of validity that must be met to make the result reliable whereas non parametric tests can be applied even if parametric conditions of validity are not met.

Non Parametric Test Formula

In Kruskal-Wallis H-Test, we use a formula to calculate the results. The formula can be written as: 


H = \[\frac{12}{n(n+1)}\] \[\left (\sum_{i-l}^{m} \frac{R_{i}}{N_{i}} \right )\] - 3(n + 1)


For more information on the formula download non parametric test pdf or non parametric test ppt

Types of Non Parametric Test

When we talk about parametric in stats, we usually mean tests like ANOVA or a t test as both of the tests assume the population data to be a normal distribution. But this is not the same with non parametric tests. Non parametric tests do not take the data to be normally distributed. The only non parametric test in the elementary stats is the chi-square test. However, there are different types of non parametric tests such as the Kruskal Willis test which is a non parametric alternative to the One way ANOVA and the Mann Whitney which is also a non parametric alternative to the two sample t test. We have listed below a few main types of non parametric test.

  1. 1-sample Sign Test: This test is used to estimate the median of a population followed by comparing it to a reference value or target value.

  2. 1-sample Wilcoxon Signed Rank Test: This test is the same as the previous test except that the data is assumed to come from a symmetric distribution. 

  3. Friedman Test: Friedman tests examines the difference between groups with ordinal and dependent variables.

  4. Kruskal-Wallis Test: this test finds out if two or more medians are different. The ranks of the data points are utilized for the calculations, rather than the data points themselves.

  5. The Mann-Kendall Trend Test: This test checks the trends in time-series data.

  6.  Mann-Whitney Test: This test judges the differences between two independent groups on a condition that the dependent variables will either be ordinal or continuous.

  7. Mood’s Median Test: This test is used instead of the sign test when we have two independent samples.

  8. Spearman Rank Correlation: We use this test to find the correlation between two sets of data. 

Non Parametric Test Advantages And Disadvantages

There are few non parametric test advantages and disadvantages.

Some of the advantages of non parametric test which are listed below: 


  1. The basic advantages of non parametric tests is that they will have more statistical power if the assumptions for the parametric tests have been violated. 

  2. There are very assumptions in the non parametric tests as compared to parametric tests. 

  3. Non parametric tests include short calculations which are easily understandable. 

  4. It is applicable to all types of data such as nominal variables, interval variables etc irrespective of small sample sizes or large sample sizes. 


The Disadvantages of Non Parametric Test are as follows: 


  1. The basic disadvantages of non parametric test inon parametric tests are less powerful than parametric tests if the assumptions haven’t been violated.

  2. In non parametric tests, calculation by hand becomes tough. 

  3. Computer software packages do not include critical value tables for many non parametric tests. 

  4. The results of non parametric tests may or may not come true as it is based on distribution free datas. 

FAQ (Frequently Asked Questions)

1. What are the applications of non parametric tests?

Non parametric tests are used when the data fails to satisfy the conditions that are needed to be met by parametric statistical tests. Non parametric tests are also very useful for a  variety of hydrogeological problems. The non parametric tests such as Kruskal‐Wallis and Mann‐Whitney are the two tests that are used to judge the difference between two medians or two independent groups on a condition that the dependent variables will either be ordinal or continuous. Apart from this, non parametric tests are also used for quick data analysis, for testing hypotheses when there is no distribution available. It is also used when we have unscaled data.

2. is a chi square test? List the basic assumptions of the chi square test?

In statistics, Chi Square tests are usually used for testing relationships between categorical variables. In a Chi Square test, a null hypothesis results in no relationship on the categorical variables in the population; they are alway independent. The basic Chi square assumptions are: 

  1. The data in the Chi Square cell must be a frequency instead of percentages.

  2. The categories or the variables must be mutually exclusive. 

  3. The subject must contribute the data to only one cell in the x2

  4. For two different groups that are related, we need to use two different tests. Therefore, the study groups must be independent.