What is parametric and non-parametric test?

As this lesson you’ll able to know Detail of parametric and non-parametric test or distribution free tests with advantage and disadvantage continue…

What is parametric test and non-parametric test in statistics?

All the parametric test (like t – test, Z – test, F – test) are based upon the assumption that the random samples are drawn from a normal population. These tests are concerned with statistical hypothesis about the parameters of the population (distribution of the random variables) from which the samples are drawn. But in practice, there are many situations in which the samples are selected from the non-normal population.

In such cases, the hypothesis tests are not concerned about the parameters of the population. These tests are called non parametric tests and also called distribution free tests.
Generally, non parametric tests are performed when the assumptions about the underlying population parameters are in a weak state, data are not normally distributed, data are measured in nominal and ordinal scale, and the hypothesis is concerned about the qualitative characteristics.

When to apply non parametric test?

• When data are not normally distributed.
• When assumptions of parametric procedure are not satisfied.
• When data are measured in nominal and ordinal.
• When data size is small.
• When basic question of interest is distribution free in nature.

Assumptions of non parametric test

• The sample observations are independent.
• The variable under study is continuous.
• Sample probability density function is continuous.
• Lower order moments exists.

Advantages and disadvantage of non parametric test

Advantages

• it is simple and easy to apply and do not require complicated theory.
• It is less time consuming.
• It needs no assumptions about the population parameters form which the samples are drawn.
• It can be applied to qualitative as well as qualitative data.
• There is no restriction for the minimum size of sample for valid and reliable results.➢

Disadvantages

• All Non parametric tests are not simple and easy to apply.
• Non parametric tests can not be used to estimate the unknown parameters of the population.
• These tests are less reliable and less powerful than parametric tests.
• Lot of tables are needed for tests.
• These tests are not suitable for the data measured in interval and ratio.

Non-parametric vs parametric test

S.N	 Parametric test:	 Non parametric test:
1.	Parametric test is concerned with the hypothesis about the parameters of the population from which the samples are drawn.	Non parametric test is not concerned with the hypothesis about the parameters of the population from which the samples are drawn.
2.	It is used in testing of hypothesis and estimation of parameters of the population.	It is used in testing of hypothesis only.
3.	This test is used if data are measured in interval and ratio scale.	This test is used if data are measured in nominal and ordinal scale.
4.	It is more powerful test as compared to non parametric test.	It is less powerful test as compared to parametric test.
5.	It requires complicated sampling techniques.	It does not require complicated sampling techniques.
6.	The commonly used parametric tests are t test, Z test, F test.	The commonly used Non parametric tests are Run test, Binomial test, Mann Whitney test, Chi-square test, Kolmogorov – Smirnov test etc.

Which are the type non parametric test?

The commonly used of distribution free test are:

❑ One sample test:

1. Run test.
2. Binomial test.
3. Kolmogorov – Smirnov test. ❑ Two independent samples test:
4. Median test.
5. Kolmogorov – Smirnov test.
6. Mann Whitney test.
7. Chi-square test
   Paired-sample test:
8. Wilcoxon signed rank test
   K samples test:
9. Cochran Q test.
10. Kruskal Wallish H test.
11. Friedman F test.

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