# Non-parametric tests

## Non-parametric Tests

• Non-parametric tests are a class of statistical techniques that do not require data to follow a specific distribution.
• These tests are also known as distribution-free tests, because their validity does not depend on the assumption of any underlying probability distribution of data.
• Non-parametric tests are used when data is ordinal (ranked but not necessarily equally spaced) or nominal (categorical) in nature.
• They are more robust to outliers and skewed data than parametric tests.

## Types of Non-parametric Tests

• Some common non-parametric tests include the Mann-Whitney U test, the Wilcoxon signed-rank test, the Kruskal-Wallis test and the Chi-squared test.
• The Mann-Whitney U test compares the distributions of two independent samples.
• The Wilcoxon signed-rank test compares the distributions of two paired or matched samples.
• The Kruskal-Wallis test compares the distributions of three or more independent samples.
• The Chi-squared test examines the association between two categorical variables.

## Assumptions and Applications

• Non-parametric tests do not require the assumptions of normality, linearity, or homoscedasticity (equal variances), which are needed for parametric tests.
• However, they often require the assumption of symmetry or independence.
• Non-parametric tests have wide applications in fields where data may not follow standard or normal distribution. These include medicine, psychology, and environmental and ecological research.

## Power and Efficiency

• Non-parametric tests are usually less statistically powerful than their parametric counterparts when data is normal. This means they are more prone to Type II errors, failing to detect an effect that is present.
• The efficiency of a non-parametric test could be less than a parametric one, in the sense that a higher sample size may be needed to achieve the same level of precision or power.

## Limitations

• Non-parametric tests may not provide as much information about the nature or magnitude of differences or effects as parametric tests.
• They are often based on ranks rather than original data values, hence may result in a loss of information.