To make the generalisation about the population from the sample, statistical tests are used. A statistical test is a formal technique that relies on the probability distribution, for reaching the conclusion concerning the reasonableness of the hypothesis. These hypothetical testing related to differences are classified as parametric and nonparametric tests.The** parametric test** is one which has information about the population parameter.

On the other hand, the** nonparametric test**Β is one where the researcher has no idea regarding the population parameter. So, take a full read of this article, to know the significant differences between parametric and nonparametric test.

## Content: Parametric Test Vs Nonparametric Test

### Comparison Chart

Basis for Comparison | Parametric Test | Nonparametric Test |
---|---|---|

Meaning | A statistical test, in which specific assumptions are made about the population parameter is known as parametric test. | A statistical test used in the case of non-metric independent variables, is called non-parametric test. |

Basis of test statistic | Distribution | Arbitrary |

Measurement level | Interval or ratio | Nominal or ordinal |

Measure of central tendency | Mean | Median |

Information about population | Completely known | Unavailable |

Applicability | Variables | Variables and Attributes |

Correlation test | Pearson | Spearman |

### Definition of Parametric Test

The parametric test is the hypothesis test which provides generalisations for making statements about the mean of the parent population. A t-test based on Student’s t-statistic, which is often used in this regard.

The t-statistic rests on the underlying assumption that there is the normal distribution of variable and the mean in known or assumed to be known. The population variance is calculated for the sample. It is assumed that the variables of interest, in the population are measured on an interval scale.

### Definition of Nonparametric Test

The nonparametric test is defined as the hypothesis test which is not based on underlying assumptions, i.e. it does not require population’s distribution to be denoted by specific parameters.

The test is mainly based on differences in medians. Hence, it is alternately known as the distribution-free test. The test assumes that the variables are measured on a nominal or ordinal level. It is used when the independent variables are non-metric.

## Key Differences Between Parametric and Nonparametric Tests

The fundamental differences between parametric and nonparametric test are discussed in the following points:

- A statistical test, in which specific assumptions are made about the population parameter is known as the parametric test. A statistical test used in the case of non-metric independent variables is called nonparametric test.
- In the parametric test, the test statistic is based on distribution. On the other hand, the test statistic is arbitrary in the case of the nonparametric test.
- In the parametric test, it is assumed that the measurement of variables of interest is done on interval or ratio level. As opposed to the nonparametric test, wherein the variable of interest are measured on nominal or ordinal scale.
- In general, the measure of central tendency in the parametric test is mean, while in the case of the nonparametric test is median.
- In the parametric test, there is complete information about the population. Conversely, in the nonparametric test, there is no information about the population.
- The applicability of parametric test is for variables only, whereas nonparametric test applies to both variables and attributes.
- For measuring the degree of association between two quantitative variables, Pearson’s coefficient of correlation is used in the parametric test, while spearman’s rank correlation is used in the nonparametric test.

### Hypothesis Tests Hierarchy

### Equivalent Tests

Parametric Test | Non-Parametric Test |
---|---|

Independent Sample t Test | Mann-Whitney test |

Paired samples t test | Wilcoxon signed Rank test |

One way Analysis of Variance (ANOVA) | Kruskal Wallis Test |

One way repeated measures Analysis of Variance | Friedman's ANOVA |

### Conclusion

To make a choice between parametric and the nonparametric test is not easy for a researcher conducting statistical analysis. For performing hypothesis, if the information about the population is completely known, by way of parameters, then the test is said to be parametric test whereas, if there is no knowledge about population and it is needed to test the hypothesis on population, then the test conducted is considered as the nonparametric test.

Poorvi says

December 1, 2016 at 3:49 pmVery nice article. students can clearly understand the actual concept.

Osoba Adunola says

December 5, 2016 at 3:11 pmThe information is very detailed and easy to grab. Thanks

Sue Smith says

December 15, 2016 at 11:37 amThis is excellent. The flowchart was really helpful. Thank you.

Surbhi S says

December 15, 2016 at 11:52 amWe are really contented with your views, this means a lot, keep sharing.

Nyadenga wellington says

April 10, 2017 at 6:30 pmGreat!. This clears off subject anxiety. keep sharing

tariro says

May 29, 2017 at 2:23 amThank u guys for simplifying this for us…. then u wonder why lecturers make it sound so hectic when things can be explained in such an easy to grasp way saving us the anxiety n pressure

Madan says

July 11, 2017 at 8:13 amthank you

MD. MEHEDI HASAN says

July 25, 2017 at 6:08 pmThese informations are very helpful to understand the concepts.

Thanks

Suparna says

October 20, 2017 at 10:40 amThank you very much for the information and the explanation you’ve given… It helped me to understand the topic much better.

Morrel says

November 28, 2017 at 1:38 pmThank you!

Super Ball says

November 29, 2017 at 9:05 pmInformation is clear to understand, very helpful. Thank you π

Kimnna says

December 13, 2017 at 12:05 amThis is super helpful!

It is well detailed and easy to understand.

kakai brian says

February 6, 2018 at 1:31 pmam liking this site

it is great

Lillian Ramos says

February 11, 2018 at 9:12 amThis was extremely helpful on a very technical and difficult subject such as statistics.

Keith says

March 13, 2018 at 2:08 pmPlease help me ….. I fail to understand what is meant if the question reads as follows:

State the parametric and non-parametric equivalent of the Wilcoxon Signed Rank Test

ABAH Augustine says

March 24, 2018 at 8:05 pmvery informative and educating. nice one

Surbhi S says

May 11, 2018 at 3:36 pmMillions of thanks to all the readers of the page, for liking and sharing your valuable opinions with us, keep reading. π

Sean says

June 30, 2018 at 5:18 pmThis article is really helpful…

Cheers to Surbhi S for creating this article and pls do continue on creating articles like this…

Prakash Mistri says

July 23, 2018 at 8:25 pmvery much effective documents. This material provides very good clarity on the parametric and non-parametric difference.

NORA says

August 24, 2018 at 9:24 pmthank you so much for making this more simplified

hanadi says

September 13, 2018 at 1:47 amthank you for the simple yet detailed elaboration. million thanks you saved me.

Valsamma Cherian says

September 18, 2018 at 1:12 pmThank you . For this is very simple and apt information

kinza batool malik says

January 8, 2019 at 6:42 pmits quite helpful and easy to understand..

Sally Morton says

February 28, 2019 at 10:17 pmThank you so much for this article, especially the Hypothesis Test Hierarchy chart. I am reviewing statistics, and this chart serves as a roadmap.

Shahzad rauf says

April 1, 2019 at 1:27 pmVery helpful, I wll say awsome

Vishnu says

May 24, 2019 at 11:29 pmVery good content and clear explanation

Aqib says

June 17, 2019 at 3:42 amThanks for a wonderfully easy explanation….

DPN says

June 20, 2019 at 8:00 amawesome