#### Non-Parametric Tests in Statistics

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

### 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.

### Advantages

There are some advatages 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.

### Disadvantages

- 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 Paramettric and Non-parametric test

Parametric Test |
Non- Parametric Test |

Normality of the distribution |
Non- normality of the distribution |

Homogeneity of variance |
Homogeneity of variance |

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. |