# difference between parametric and non parametric test

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## Difference Between Parametric and Non

The difference between parametric and nonparametric test is that former rely on statistical distribution whereas the latter does not depend on population knowledge. Learn more differences based on distinct properties at BYJU'S.

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## Difference Between Parametric And Non-Parametric Test

The key **difference between parametric and nonparametric test** is that the parametric test relies on statistical distributions in data whereas nonparametric do not depend on any distribution. Non-parametric does not make any assumptions and measures the central tendency with the median value. Some examples of Non-parametric tests includes Mann-Whitney, Kruskal-Wallis, etc.

Parametric is a statistical test which assumes parameters and the distributions about the population is known. It uses a mean value to measure the central tendency. These tests are common, and therefore the process of performing research is simple.

## Definition of Parametric and Nonparametric Test

**Parametric Test Definition**

In Statistics, a parametric test is a kind of the hypothesis test which gives generalizations for generating records regarding the mean of the primary/original population. The t-test is carried out based on the students t-statistic, which is often used in that value.

The t-statistic test holds on the underlying hypothesis which includes the normal distribution of a variable. In this case, the mean is known, or it is considered to be known. For finding the sample from the population, population variance is identified. It is hypothesized that the variables of concern in the population are estimated on an interval scale.

**Non-Parametric Test Definition**

The non-parametric test does not require any population distribution, which is meant by distinct parameters. It is also a kind of hypothesis test, which is not based on the underlying hypothesis. In the case of the non-parametric test, the test is based on the differences in the median. So, this kind of test is also called a distribution-free test. The test variables are determined on the nominal or ordinal level. If the independent variables are non-metric, the non-parametric test is usually performed.

## What is the Difference Between Parametric And Non-parametric?

The key differences between nonparametric and parametric tests are listed below based on certain parameters or properties.

**Properties**

**Parametric**

**Non-parametric**

Assumptions Yes No

central tendency Value Mean value Median value

Correlation Pearson Spearman

Probabilistic distribution Normal Arbitrary

Population knowledge Requires Does not require

Used for Interval data Nominal data

Applicability Variables Attributes & Variables

Examples z-test, t-test, etc. Kruskal-Wallis, Mann-Whitney

Population and Sample

Mean, Median, and Mode

Null Hypothesis Statistics Z-Score Table

These were the Difference Between Parametric And Non-parametric. To know more about each of them separately register with BYJU’S – The Learning App!

## Frequently Asked Questions – FAQs

### What is the benefit of using nonparametric test?

Nonparametric test do not depend on any distribution, hence it is a kind of robust test and have broader range of situations.

### What is the benefit of using parametric test?

Parametric test is completely dependent on statistical data and have more chances of accuracy.

### What central tendency value we consider for parametric and nonparametric test?

For parametric mean value is taken and for non-parametric test median value is taken into consideration.

### What are the examples of parametric test?

T-test and Z-test are the examples of parametric test, in statistics

### What are the examples of non-parametric test?

Kruskal-Wallis and Mann-Whitney

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## Difference Between Parametric and Non

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## Difference Between Parametric and Non-Parametric Test

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## Parametric vs Non-parametric Tests

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Parametric is a test in which parameters are assumed and the population distribution is always known. To calculate the central tendency, a mean value is used. These tests are common, and this makes performing research pretty straightforward without consuming much time. No assumptions are made in the Non-parametric test and it measures with the help of the median value. A few instances of Non-parametric tests are Kruskal-Wallis, Mann-Whitney, and so forth. In this article, you will be learning what is parametric and non-parametric tests, the advantages and disadvantages of parametric and nan-parametric tests, parametric and non-parametric statistics and the difference between parametric and non-parametric tests.

### What is a Parametric Test?

In Statistics, the generalizations for creating records about the mean of the original population is given by the parametric test. This test is also a kind of hypothesis test. A t-test is performed and this depends on the t-test of students, which is regularly used in this value. This is known as a parametric test.

The t-measurement test hangs on the underlying statement that there is the ordinary distribution of a variable. Here, the value of mean is known, or it is assumed or taken to be known. The population variance is determined in order to find the sample from the population. The population is estimated with the help of an interval scale and the variables of concern are hypothesized.

### What is a Non-Parametric Test?

There is no requirement for any distribution of the population in the non-parametric test. Also, the non-parametric test is a type hypothesis test that is not dependent on any underlying hypothesis. In the non-parametric test, the test depends on the value of the median. This method of testing is also known as distribution-free testing. Test values are found based on the ordinal or the nominal level. The parametric test is usually performed when the independent variables are non-metric. This is known as a non-parametric test.

### Differences Between The Parametric Test and The Non-Parametric Test

Properties Parametric Test Non-Parametric Test Assumptions

Yes, assumptions are made

No, assumptions are not made

Value for central tendency

The mean value is the central tendency

The median value is the central tendency

Correlation Pearson Correlation

Spearman Correlation

Probabilistic Distribution

Normal probabilistic distribution

Arbitrary probabilistic distribution

Population Knowledge

Population knowledge is required

Population knowledge is not required

Used for

Used for finding interval data

Used for finding nominal data

Application

Applicable to variables

Applicable to variables and attributes

Examples T-test, z-test

Mann-Whitney, Kruskal-Wallis

### Advantages and Disadvantages of Parametric and Nonparametric Tests

A lot of individuals accept that the choice between using parametric or nonparametric tests relies upon whether your information is normally distributed. The distribution can act as a deciding factor in case the data set is relatively small. Although, in a lot of cases, this issue isn't a critical issue because of the following reasons:

Parametric tests help in analyzing non normal appropriations for a lot of datasets.

Nonparametric tests when analyzed have other firm conclusions that are harder to achieve.

The appropriate response is usually dependent upon whether the mean or median is chosen to be a better measure of central tendency for the distribution of the data.

A parametric test is considered when you have the mean value as your central value and the size of your data set is comparatively large. This test helps in making powerful and effective decisions.

A non-parametric test is considered regardless of the size of the data set if the median value is better when compared to the mean value.

Ultimately, if your sample size is small, you may be compelled to use a nonparametric test. As the table shows, the example size prerequisites aren't excessively huge. On the off chance that you have a little example and need to utilize a less powerful nonparametric analysis, it doubly brings down the chances of recognizing an impact.

The non-parametric test acts as the shadow world of the parametric test. In the table that is given below, you will understand the linked pairs involved in the statistical hypothesis tests.

### Related Pairs of Parametric Test and Non-Parametric Tests

Parametric Tests for Means

Non-Parametric Test for Medians

1 - sample t - test

1 - sample Wilcoxon, 1 - sample sign

2 - sample t - test Mann - Whitney Test One - way ANOVA

Kruskal- Wallis, Mood’s median test

With a factor and a blocking variable - Factorial DOE

Friedman Test

### Classification Of Parametric Test and Non-Parametric Test

There are different kinds of parametric tests and non-parametric tests to check the data. Let us discuss them one by one.

## Difference Between Parametric and Nonparametric Test (with Comparison Chart)

Knowing the difference between parametric and nonparametric test will help you chose the best test for your research. 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 nonparametric test.

## Difference Between Parametric and Nonparametric Test

Last updated on September 1, 2017 by Surbhi S

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** 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 Definition Key Differences

Hypothesis Tests Hierarchy

Equivalent Tests Conclusion

### 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.

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