Non Parametric Test – Formula and Types

# Non Parametric Test – Formula and Types

## What is a Non Parametric Test?

A nonparametric test is a statistical test that does not rely on the assumption of a normal distribution. This type of test is used when the data does not meet the requirements of a parametric test. Nonparametric tests are usually less powerful than parametric tests, but they are also less sensitive to violations of the normality assumption.

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## Parametric Test and Nonparametric Test

Parametric testing is a type of statistical hypothesis testing in which the test statistic is assumed to be drawn from a certain family of distributions. Nonparametric testing is a type of statistical hypothesis testing in which the test statistic is not assumed to be drawn from any particular family of distributions.

## Non Parametric Test Formula

A nonparametric test is a statistical test that does not require the assumption of a normal distribution. Nonparametric tests are typically used when the data are not normally distributed or when the sample size is small.

There are many different types of nonparametric tests, but the most common is the Wilcoxon rank-sum test. The Wilcoxon rank-sum test is used to compare two groups of data. The test determines whether the two groups are statistically different from each other.

The Wilcoxon rank-sum test is a two-tailed test, which means that it can detect differences in either direction. The test is also non-directional, which means that it is not specific about the direction of the difference.

The Wilcoxon rank-sum test is a hypothesis test. The test compares the two groups of data and determines whether the difference between the groups is statistically significant. To perform the Wilcoxon rank-sum test, you first need to calculate the rank of each data point in each group. The ranks are then summed for each group. The group with the higher sum is considered to have the larger sample size.

The Wilcoxon rank-sum test statistic is then calculated. The statistic is a measure of the difference between the two groups. The statistic is compared to a chi-squared distribution to determine whether the difference is statistically significant.

## Types of Non Parametric Test

There are five types of non parametric tests:

1. Chi-square test
2. Mann-Whitney U test
3. Kruskal-Wallis H test
4. Wilcoxon signed-rank test
5. Friedman test

Non parametric tests are advantageous because they are less likely to be influenced by the distribution of the data. They are also easier to use than parametric tests.

Non parametric tests are disadvantageous because they are less powerful than parametric tests.

## The Disadvantages of Non Parametric Test are as follows:

1. Non parametric tests are less powerful than parametric tests.

2. Non parametric tests are not as widely accepted as parametric tests.

3. Non parametric tests are less versatile than parametric tests.

4. Non parametric tests are more difficult to use than parametric tests.

## Hypothesis Significance

The null hypothesis is that there is no significant difference between the two treatments.

The significance of the difference between the two treatments is 0.023.

## Hypothesis Testing

Null Hypothesis: The average height of all males is the same.

Alternative Hypothesis: The average height of all males is not the same.

1. Introduction
2. Theoretical Framework
2.1. Game Theory
2.2. Nash Equilibrium
3. Empirical Analysis
3.1. Data and Methodology
3.2. Results
4. Conclusion

1. Introduction

The purpose of this paper is to empirically investigate the impact of trade liberalization on regional trade blocs. In particular, the paper seeks to answer the following question: do trade blocs become more or less active following a trade liberalization event?

To answer this question, the paper employs a game theoretic approach, specifically the Nash equilibrium. The Nash equilibrium is a concept from game theory that describes a situation in which each player in a game has chosen a best strategy given the strategies of the other players. The Nash equilibrium is important in the context of trade blocs because it allows us to understand how blocs will behave in the presence of liberalization.

The paper finds that trade blocs become more active following a trade liberalization event. This finding is significant because it suggests that trade blocs are an important tool for countries looking to increase trade.

2. Theoretical Framework

In order to understand the impact of trade liberalization on trade blocs, it is necessary to first understand the theoretical framework underlying trade blocs. This section will discuss two key concepts from game theory that are relevant to this topic: the

## Parametric Tests

The chi-squared statistic is used in a number of different parametric tests.

The chi-squared statistic can be used to test the null hypothesis that two or more independent samples are drawn from the same population.

The chi-squared statistic can be used to test the null hypothesis that a population is binomial.

The chi-squared statistic can be used to test the null hypothesis that a population is Poisson.

The chi-squared statistic can be used to test the null hypothesis that a population is normal.

## Non-Parametric tests in Statistics

Non-parametric tests are tests that don’t rely on any assumptions about the population distribution. This makes them less sensitive to departures from the norm, and they can be used even when the population is not normal.

There are a number of different non-parametric tests, but the most common are the chi-square test, the Mann-Whitney U test, and the Kruskal-Wallis H test.

## Applications of Non-Parametric Test

1. To compare the means of two groups

2. To compare the proportions of two groups

3. To compare the median of two groups

4. To compare the variability of two groups

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