# Non parametric hypthesis test

Spearman Definition of Parametric Test The parametric test is the hypothesis test which provides generalisations for making statements about the mean of the parent population. The t-statistic rests on the underlying assumption that there is the normal distribution of variable and the mean in known or assumed to be known. How are Non-Parametric tests different from Parametric tests? Parametric tests are used when the information about the population parameters is completely known whereas non-parametric tests are used when there is no or few information available about the population parameters. In simple words, parametric test assumes that the data is normally distributed.

However, non-parametric tests make no assumptions about the distribution of data. But what are parameters? A teacher calculated average marks scored by the students of her class by using the formula shown below: Look at the formula given above, the teacher has considered the marks of all the students while calculating total marks.

Assuming that the marking of students is done accurately and there are no missing scores, can you change the total marks scored by the students? Therefore, average marks is called a parameter of the population since it cannot be changed.

When can I apply non-parametric tests? A winner of the race is decided by the rank and rank is allotted on the basis of crossing the finish line. Now, the first person to cross the finish line is ranked 1, the second person to cross the finish line is ranked 2 and so on.

A sample of 20 people followed a course of treatment and their symptoms were noted by conducting a survey. The patient was asked to choose among the 5 categories after following the course of treatment.

Also, the ranks are allocated and not calculated. In such cases, parametric tests become invalid.

## What is a Parametric Test?

For a nominal data, there does not exist any parametric test. Limit of detection is the lowest quantity of a substance that can be detected with a given analytical method but not necessarily quantitated as an exact value.

For instance, a viral load is the amount of HIV in your blood. A viral load can either be beyond the limit of detection or it can a higher value. What is an outlier?

The income of Shahrukh lies at an abnormal distance from the income of other economics graduates.

## When to Use a Nonparametric Test

So the income of Shahrukh here becomes an outlier because it lies at an abnormal distance from other values in the data. To summarize, non-parametric tests can be applied to situations when: The data does not follow any probability distribution The data constitutes of ordinal values or ranks There are outliers in the data The data has a limit of detection The point to be noted here is that if there exists a parametric test for a problem then using nonparametric tests will yield highly inaccurate answers.

Pros The pros of using non-parametric tests over parametric tests are 1. Non-parametric tests deliver accurate results even when the sample size is small. Non-parametric tests are more powerful than parametric tests when the assumptions of normality have been violated.Hypothesis testing with non-parametric tests Now you know that non-parametric tests are indifferent to the population parameters so it does not make any assumptions about the mean, standard deviation etc of the parent population.

## Parametric and Non-Parametric Hypothesis Tests

Most of the MCQs on this page are covered from Estimate and Estimation, Testing of Hypothesis, Parametric and Non-Parametric tests etc. Question 1: The sign test is A) Less Powerful than that of the Wilcoxon signed rank test.

In statistics, parametric and nonparametric methodologies refer to those in which a set of data has a normal vs. a non-normal distribution, respectively. Parametric tests make certain assumptions about a data set; namely, that the data are drawn from a population with a specific (normal) distribution. 