# Non-Parametric Test

## Non Parametric test

The test which does not make any assumption as to the form of distribution in the population from 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 test or distribution free test.

### Assumptions of Non-parametric test

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

### 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 test are available in deal with the data which are given in rank.

### Disadvantages of non- parametric test

• Non- Parametric test 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 test 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.

 Parametric Test Non- Parametric Test 1    Normality of the distribution Non- normality of the distribution 2    Homogeneity of variance  $\sigma_{1}^{2}=\sigma&space;_{2}^{2}=...=\sigma&space;_{n}^{2}$ Homogeneity of variance $\sigma_{1}^{2}\neq&space;\sigma&space;_{2}^{2}\neq&space;...\neq&space;\sigma&space;_{n}^{2}$ 3    Scale of measurement is interval. Scale of measurement is ordinal and nominal. 4    It depends upon on parameter of population. It does not depends upon or parameter of population. 5    It is not always easy to apply. Easy to apply and does not need complicated sample theory. 6     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. 7     Here assumptions are too strictly. Here assumptions are less strict. Such : continuity, discreteness, symmetry etc. 8     Here, Outlier exists. Here Outlier does not exists.