Non parametric test

Parametric statistics are based on assumptions about the population distribution that the sample was drawn from. Nonparametric statistics are not based on assumptions, which means that data can be acquired from a sample that does not fit into a certain distribution.The three hypothesis testing modules covered a variety of hypothesis tests for continuous, dichotomous, and discrete outcomes. Continuous outcome tests concentrated on comparing means, whereas dichotomous and discrete outcome tests concentrated on comparing proportions. The tests offered in the hypothesis testing modules are all parametric tests that are based on certain assumptions.

As an example,All parametric tests assume that the outcome is essentially normally distributed in the population when running hypothesis tests for means of continuous outcomes. This does not imply that the data in the seen sample follows a normal distribution, but rather that the outcome in the entire population, which is not observed, follows a normal distribution. The normalcy assumption is accepted by investigators for many outcomes. Many statistical tests also turn out to be resilient, which implies they keep their statistical qualities even when assumptions aren’t met completely. 

Based on the Central Limit Theorem, tests are robust in the presence of violations of the normality assumption when the sample size is large.Alternative tests known as nonparametric tests are appropriate when the sample size is limited and the outcome distribution is unknown and cannot be assumed to be approximately normally distributed.

Definition of Non Parametric Test

Nonparametric statistics is the  branch of statistics that isn’t fully based on parameterized probability distribution. Nonparametric test is predicated on being either distribution-free or having a given distribution with unspecified parameters. Both descriptive statistics and statistical inference are included in nonparametric statistics. When the assumptions of parametric tests are violated, nonparametric tests are frequently used.

Purpose and applications

The purpose and Application of Non parametric Test are in the follow:

• For investigating populations that take on a ranked order, non-parametric approaches are commonly used (such as movie reviews receiving one to four stars). When the given data has a ranking but not obvious numerical interpretation, such as when analyzing preferences, non-parametric approaches can be used. Non-parametric approaches produce ordinal data in terms of measurement levels.
• Non-parametric approaches have a considerably broader applicability than parametric methods since they require fewer assumptions. They can be used in cases where little is known about the application in issue, for example. Non-parametric approaches are also more robust because they rely on fewer assumptions.
• Another reason for using non-parametric approaches is their simplicity. Non-parametric approaches may be easier to employ in some instances, even when parametric methods are acceptable. Non-parametric approaches are considered by some statisticians as having less possibility for misuse and misinterpretation because of their simplicity and better resilience.
• Non-parametric tests’ broader applicability and higher resilience come at a cost: non-parametric tests have less power in circumstances where a parametric test would be more suited. To put it another way, a greater sample size may be necessary to reach the same level of confidence in results.

There are a number of advantages to using nonparametric testing. Nonparametric tests may be the only technique to examine data with outcomes like those outlined above. Ordinal, ranked, outlier-prone, or imprecisely measured outcomes are difficult to assess using parametric methods without making large assumptions about their distributions, as well as coding judgments for some values (e.g., “not detected”). Nonparametric tests, as discussed above, can also be relatively straightforward to perform.

Use Non-Parametric Tests with Caution:

1. When measurements are taken on interval and ratio scales, converting them to nominal or ordinal scales will result in a significant loss of information. As a result, parametric testing should be used in such cases as much as possible. We are wasting dollars in order to save pennies by utilizing a non-parametric approach as a shortcut.

2. When the assumptions underpinning a parametric test are met and both parametric and non-parametric tests are available, the parametric test should be chosen because most parametric tests have more power in these instances.

3. Non-parametric tests, without a doubt, allow for the avoidance of the distribution’s normality assumption. However, these solutions do little to eliminate the assumption of homoscedasticity independence in all cases.

4. Before collecting data, behavioral scientists should identify the null hypothesis, alternative hypothesis, statistical test, sampling distribution, and threshold of significance. After the data has been collected, looking for a statistical test tends to magnify the effects of any chance differences that favor one test over another.

Most non-parametric statistical tests are predicated on the following assumptions:

• 1. That the observations are unrelated to one another;
• 2. There is underlying continuity in the variable under investigation;
• 3. Unlike parametric tests, non-parametric tests can be applied to data measured on an ordinal scale and others to data measured on a nominal or categorical scale; 
• 4. Unlike parametric tests, non-parametric tests can be applied to data measured on an ordinal scale and others to data measured on a nominal or categorical scale.

Some of the Non-Parametric Tests are given below:

• 1. Sign Test: The sign test is the most basic of all distribution-free statistics, with a wide range of applications. It can be employed in cases where the critical ratio, t, test for correlated samples can’t be used because the normality and homoscedasticity requirements aren’t met.
• 2. Median Test:

When comparing the performance of two independent groups, such as an experimental group and a control group, the median test is utilized. To begin, the two groups are combined and a common median is determined.

Non-Parametric Tests Have the Following Drawbacks: 

1. If all of the assumptions of a parametric statistical method are met in the data and the research hypothesis can be verified with a parametric test, then non-parametric statistical tests are pointless.
2. The power-efficiency of the non-parametric test expresses the degree of wastefulness.

Point to Remember:

• “Distribution-free” tests are non-parametric tests. They don’t presuppose that the scores under consideration are selected from a population with a certain distribution, such as a regularly distributed population.
• Non-parametric techniques can be applied to scores that aren’t accurate in any numerical sense but are, in effect, ranks.