Non-Parametric Tests in Statistics

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In statistics, Non parametric tests test which does not make any assumption as to the form of distribution in the population from which the sample is drawn i.e. to say that the functional form of the distributions is not known. The test is called non parametric tests or distribution free test.

non parametric test

Assumptions of Non parametric test

Non-parametric tests follow some assumptions. They are,

  • Sample observations are independent
  • The variable under study is continuous.
  • The pdf is continuous.  
  • Lower order moment exists.

Most used non-parametric Tests

There are some test which are generally used widely.


There are some advantages of non parametric test,

  • Non parametric methods are readily comprehensive very simple and easy to apply and do not require complicated sample theory.
  • No assumption is made when the sample is drawn from population.
  • Non- parametric tests are available in deal with the data which are given in rank.


  • It can be used only if the measurements are nominal and ordinal even in that case if a parametric test exists it is more powerful than non-parametric test.
  • Non Parametric tests are designed to test statistical hypothesis only and not for estimated the parameter.
  • A large number of different type of table is required.

The steps for testing procedure of Non-parametric test

Step 1 : Hypothesis test

State the null hypothesis  (Ho) and it’s alternative hypothesis (H1)

Step 2 : Statistical test 

Among several test which might be given research design, choose that test the which most closely approximates the conditional research in terms of the assumptions the test based.

Step-3 : Significance level 

Specify a level of significance (α)  and size (n )

Step-4: Sampling distribution 

finding the sampling distribution statistic test under the assumption that Ho.

Step 5 : Critical Region 

In the basis of step 2,3 and 4 above the region of rejection for the statistic form

Step 6 : Decision 

If the value of the test statistic is on of rejection, the decision is to reject wise accept.

Difference between Parametric and Non-parametric test

Parametric Test

Non- Parametric Test

     Normality of the distribution

  Non- normality of the distribution


     Scale of measurement is interval.

 Scale of measurement is ordinal and nominal. 

     It depends upon on parameter of population.

 It does not depends upon or parameter of population.

     It is not always easy to apply.

 Easy to apply and does not need complicated sample theory. 

     It makes assumptions as to the form of distribution to population.

 It does not make assumptions as to the form of the distribution to population.

     Here assumptions are too strictly.

Here assumptions are less strict. Such : continuity, discreteness, symmetry etc. 

     Here, Outlier exists.

Here, Outlier does not exists.

Homogeneity of variance for parametric test is,

    \[ \sigma _{1}^{2}=\sigma _{2}^{2}=...=\sigma _{n}^{2} \]

Homogeneity of variance for non-parametric test is,

    \[ \sigma _{1}^{2}\neq \sigma _{2}^{2}\neq ...\neq \sigma _{n}^{2} \]


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