[Maths Class Notes] on Difference Between Parametric and Non-Parametric Test Pdf for Exam

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


Parametric Test

Non-Parametric Test


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


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


Applicable to variables

Applicable to variables and attributes


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:

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 the
m one by one.

Types Of Parametric Test

  • Student’s T-Test:- This test is used when the samples are small and population variances are unknown. The test is used to do a comparison between two means and proportions of small independent samples and between the population mean and sample mean.

  • 1 Sample T-Test:- Through this test, the comparison between the specified value and meaning of a single group of observations is done. 

  • Unpaired 2 Sample T-Test:- The test is performed to compare the two means of two independent samples. These samples came from the normal populations having the same or unknown variances.

  • Paired 2 Sample T-Test:- In the case of paired data of observations from a single sample, the paired 2 sample t-test is used.

  • ANOVA:- Analysis of variance is used when the difference in the mean values of more than two groups is given.

  • One Way ANOVA:- This test is useful when different testing groups differ by only one factor.

  • Two Way ANOVA:- When various testing groups differ by two or more factors, then a two way ANOVA test is used.

  • Pearson’s Correlation Coefficient:- This coefficient is the estimation of the strength between two variables. The test is used in finding the relationship between two continuous and quantitative variables.

  • Z – Test:- The test helps measure the difference between two means. 

  • Z – Proportionality Test:- It is used in calculating the difference between two proportions.

Types Of Non-Parametric Test

  • 1 Sample Sign Test:- In this test, the median of a population is calculated and is compared to the target value or reference value. 

  • 1 Sample Wilcoxon Signed Rank Test:- Through this test also, the population median is calculated and compared with the target value but the data used is extracted from the symmetric distribution.

  • Friedman Test:- The difference of the groups having ordinal dependent variables is calculated. This test is used for continuous data.

  • Goodman Kruska’s Gamma:- It is a group test used for ranked variables.

  • Kruskal-Wallis Test:- This test is used when two or more medians are different. For the calculations in this test, ranks of the data points are used.

  • The Mann-Kendall Trend Test:- The test helps in finding the trends in time-series data.

  • Mann-Whitney Test:- To compare differences between two independent groups, this test is used. The condition used in this test is that the dependent values must be continuous or ordinal.

  • Mood’s Median Test:- This test is used when there are two independent samples.

  • Spearman Rank Correlation:- This technique is used to estimate the relation between two sets of data. 

Applications Of Parametric Tests

  • This test is used when the given data is quantitative and continuous. 

  • When the data is of normal distribution then this test is used. 

  • The parametric tests are helpful when the data is estimated on the approximate ratio or interval scales of measurement. 

Applications Of Non-Parametric Tests

  • These tests are used in the case of solid mixing to study the sampling results.

  • The tests are helpful when the data is estimated with different kinds of measurement scales. 

  • The non-parametric tests are used when the distribution of the population is unknown.

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