# Difference Between Parametric and Nonparametric

Edited by Diffzy | Updated on: September 22, 2023

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## Introduction

It is known that in statistics, two types of variables are used, namely independent and dependent, and there are many other different tools along with these that are used in the field of statistics for analyzing accurate information in the research arena. In statistics, data management and analysis are done. So, concerning this, there are two types of tests, namely Parametric tests and Nonparametric tests, that are used by statisticians. The major area of difference between them is that statistical data distribution is used in parametric tests, and they rely upon it, whereas nonparametric tests are flexible, and any continuous data can be used for it.

## Parametric vs Nonparametric

A person needs to choose the statistical method he wants to follow while conducting a hypothesis test that he finds suitable according to the data and the research question. There are two types of statistical methods followed for this hypothesis test, which are parametric tests and nonparametric tests. Parametric tests are based on assumptions and are not flexible. In parametric tests, it is already assumed that the provided data has certain specific characteristics and follows a certain distribution. The idea behind parametric tests is that it is already being assumed that the data is received from a population and its distribution is either known or hypothesized. Hypothesized distribution can be binomial, exponential, and normal. Nonparametric tests of statistics, on the other hand, are different from parametric statistics as they are not based on assumptions and are flexible for all types of data, including ordinal as well as nominal. Contrary to parametric tests, they do not assume that the data being received from a population has a known or hypothesized distribution.

## What is Parametric?

Statisticians do data analysis and research with the help of two kinds of test, of which, one of them is Parametric test. Parametric test is a hypothesis test through which the elements of a sample are analysed. The sample amount for a parametric test is usually large. In this kind of test, assumptions are made on a population’s distribution of data. Quantitative data having continuous variables is required for this kind of test. Since, parametric tests are conducted on normal data distribution, inferential statistics and mathematical formulas can be used to estimate various parameters of data distribution such as standard deviation, proportion, and mean. The hypothesis of the test is tested in the final stage.

Numeric variables can be only used for parametric tests. Moreover, a large population sample should always be taken for parametric tests because this provides more accuracy while calculating. Parametric tests have a higher statistical power, and the chance of making mistakes in this kind of test is also low, but it is to be remembered that parametric tests cannot be used in every situation, which means it is not versatile. The probability distribution to be followed in a parametric test is normal or Gaussian probability distribution for random selection of samples. The mean value is considered as the central tendency value of Parametric tests. The famous parametric tests that are used worldwide are the Z-test, t-test, Pearson's rank Correlation, ANOVA, and linear regression. There are several merits and demerits of Parametric tests.

The merits of Parametric tests are: -

• The most significant fact to remember while conducting parametric tests is that much data is not required for this type of test, and one does not need to convert the required data into rank formats or orders.
• In Parametric tests, everything can be calculated very easily, and accurate and precise information can be obtained. This is the reason why a true effect or difference can be detected by parametric tests more if it even exists.

In terms of the data parameters as well as confidence intervals, parametric tests have been found to provide real information about the concerned population. Generalizations can be made based on the sample data about a population.

The demerits of Parametric tests are: -

• A small sample of data cannot be used for parametric tests because they do not provide valid results.
• Parametric tests become difficult due to the large size of sample collections. This issue is not there in Nonparametric tests, which makes it a little difficult to carry out Parametric tests.
• Parametric tests are highly sensitive when their assumptions are violated. The assumptions of a parametric test should be always checked and corrected if they are wrong, after which the test should be conducted. This is because the data must match these assumptions as only after that one can understand that the results are correct.

### Types of Parametric Tests

There are various types of Parametric tests, and some of them are: -

• T-test
• ANOVA
• Pearson’s rank Correlation

### T-Test

When the difference in means is compared between two groups, then a student's T-test is used. The data can be paired or unpaired by us, which is being obtained from the two groups. When the difference is to be found between two variables that belong to the same object, then, in that case, a paired T-test is being used. When the difference is to be compared in means between two independent groups then an unpaired T-test is being used.

### ANOVA

The full form of ANOVA is Analysis Of Variance. When there are more than two groups, then ANOVA is needed to find out the difference among them, if there is at all a difference. There are various sample groups present in this test, and the variance from among all of them is used to find out if all of them are collected from the same population. It can be called an extension of the T-test.

### Pearson’s Rank Correlation

The strength of association and direction between two variables is measured through this method. The range of the coefficient is 0 to 1, and if the value is nearer to 1, then that means there is a higher correlation because nearer to 1 means higher is the correlation.

## What is Nonparametric?

Nonparametric tests are the opposite of parametric tests. They do not depend on any assumptions of the distribution of data or any parameters for research and analysis purposes. They are also sometimes called distribution-free tests because they do not require any data distribution for analysis. Whenever the data is skewed, Nonparametric tests are used. The fact that it is nonparametric does not indicate that it is free of parameters. There are parameters here also, and the data still has to be organized as it is organized. In this test, there is no rigidness in regard to the parameters.

Nonparametric tests are used in several cases when assumptions of the parametric test don’t match the given data distribution, when there is skewed data, when the sample size is small, and lastly, when the data to be analyzed is nominal or ordinal data. They do not require any particular kind of data distribution, and any type of data distribution can be used for this test. However, nonparametric tests have lower statistical power, and the chance of errors happening here is very high. For real-life applications, nonparametric tests are preferable because in real-life life data cannot be found distributed normally and is maximum times found non-linear. The median value is the central tendency value of nonparametric tests. Every parametric tests have a nonparametric test such as the nonparametric equivalent of the T-test is The Mann-Whitney U Test.

Just like parametric tests, nonparametric tests also have several merits and demerits.

Some of the merits of nonparametric tests are

• Nonparametric tests can turn out to be more suitable for a particular situation since, in this kind of test there are very few assumptions made on the data that is provided. Moreover, for research purposes, the hypothesis that is provided here may turn out to be more accurate and precise.
• Data that can be measured in a nominal scale only, such as categorical or classificatory data, can also be treated by nonparametric methods because no parametric methods are available for such kind of data.
• It is much easier to understand nonparametric tests and apply them in practical life rather than parametric tests, which are a little bit hard to learn in comparison. Moreover, interpreting them is also direct and simple.

Some of the demerits of nonparametric tests are

• Nonparametric tests become a waste when the assumptions match with the data distribution because only then the results of parametric tests are valid. Moreover, through parametric tests, the option of testing research hypotheses is also available. So, if all of these requirements are fulfilled in parametric tests, then there is no need to conduct nonparametric tests.
• It is also to be remembered that nonparametric tests are not systematic in nature.
• Convenience is not an option for nonparametric tests when it comes to the use of tables. Nonparametric tests can be implemented in tables only, and they are very necessary for conducting the tests, but there are different formats of tables, and they are widely scattered.

## Types of Nonparametric Tests

There are several types of Nonparametric tests, and some of them are

• Mann-Whitney U Test
• The Kruskal-Wallis Test
• Wilcoxon Signed Rank Test

### Mann-Whitney U Test

The T-test with independent samples has the nonparametric equivalent Mann-Whitney U Test. Two independent samples having ordinal data are required for this test. The continuous outcomes that lie within the independent samples are compared here.

### The Kruskal-Wallis Test

The alternative to the parametric test ANOVA is the nonparametric test named The Kruskal-Wallis Test. The ordinal data is compared here like the Mann-Whitney U Test, but the number of independent groups or samples should be more than two.

### Wilcoxon Signed Rank Test

The alternative to the paired samples T-test is the nonparametric Wilcoxon Signed Rank Test. Here, two dependent or paired sample groups with ordinal data types are compared.

## Main Difference Between Parametric and Nonparametric (In Points)

• Parametric Tests depend on assumption, whereas Nonparametric tests do not depend on making assumptions. The main idea behind parametric tests is that it depends on the use of certain parameters for testing, and along with the parameters, the data distribution type of the population is also assumed to bring out the results of the test. However, the type of data distribution that can be used for parametric tests is only normal data distribution. Nonparametric tests do not depend on making assumptions about the data distribution and instead use other methods that include signs, data frequencies, and ranks for statistical analysis and research. They can be used on any particular data type such as data having different units or scales, data having outliers, or skewed data, unlike parametric tests.
• Parametric tests are not flexible like nonparametric tests as they can be used on a particular data distribution only, which is normal, and the parameters are also rigid here for the test, but in nonparametric tests, the parameters are still there, but they are not so rigid as parametric tests which is why Parametric tests cannot be applied in every situation whereas, nonparametric tests can be applied in any situation due to their flexibility. They are a more useful basis for statistical analysis and excellent for practical application in real life because data in real life cannot be always normally distributed and happens to be non-linear at times.
• To conduct Parametric tests, large samples of data are required for accuracy, unlike nonparametric tests where small samples of data are required. Large samples of data are required for parametric tests as they help to provide accuracy. The test assumptions should match the data distribution, so if they are wrong, they should be corrected, after which the test should be conducted, and the results can be valid only then. This problem is not there in nonparametric tests as the small samples are used there, which makes it difficult to conduct parametric tests.
• The chance of making errors is less in parametric tests because of the large samples of data that are needed to conduct the test. Large samples assure more accuracy. However, nonparametric tests have a higher chance of making errors, which is why they are conducted in very small amounts only when the results are not valid or are wrong in parametric tests. They are the second option in statistical analysis. Parametric tests have a higher statistical power, whereas nonparametric tests have a lower statistical power.

## Conclusion

Hence, Parametric tests include assuming the data distribution type of the population sample to find out the results, whereas Nonparametric tests are free of making any assumptions and rely on other methods of analysis to find out the results. Parametric tests have a lower chance of making mistakes than nonparametric tests, which makes them have higher statistical power than nonparametric tests. However, Parametric tests are rigid and follow fixed parameters, but nonparametric tests are not rigid and are flexible, which makes them useful for practical daily use because data in real life is non-linear.

## References

• https://corporatefinanceinstitute.com/resources/data-science/nonparametric-tests/
• https://simplyeducate.me/2020/09/19/parametric-tests/?expand_article=1&_gl=1*jb6ykx*_up*MQ..*_ga*MzE5NzA1MzcwLjE2OTQ3OTcyODc.*_ga_TWKB5R2G2M*MTY5NDc5NzI5NC4xLjAuMTY5NDc5NzI5NC4wLjAuMA
• https://www.shiksha.com/online-courses/articles/difference-between-parametric-and-nonparametric-test/

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