# The basis of non-parametric tests

## Non-parametric Tests: An Overview

• Non-parametric tests are statistical methods used when data are not assumed to come from specific distributions. They are also known as distribution-free tests.
• Unlike parametric tests, they do not require assumptions about the parameters of the population distribution from which the samples are drawn.
• Non-parametric tests are used when the data is nominal or ordinal, rather than interval or ratio.

• Non-parametric tests can be used with data that is not normally distributed. This provides greater flexibility compared to parametric tests.
• These tests are less sensitive to outliers and can therefore provide robust results when outliers are present.
• They often require fewer assumptions about the data, making them more applicable in many situations.
• Non-parametric tests can be utilised with small sample sizes which is not possible with some parametric tests.

## Common Non-parametric Tests

• Wilcoxon Rank Sum Test or Mann-Whitney U Test: This is used to compare the distributions of two independent samples.
• Wilcoxon Signed Rank Test: This is used to compare the distributions of two related samples.
• Kruskal-Wallis Test: This is an extension of the Mann-Whitney U Test to more than two samples. It’s used to compare the distributions of independent samples.

## Applying Non-parametric Tests

• All non-parametric tests use the same basic approach: they rank the data and then analyse the ranks.
• Calculation often involves looking at rank sums, rather than the raw data.
• The null and alternative hypotheses are still in play, but usually relate to the median, not the mean.
• Critical test statistics and p-values can be calculated exactly for small sample sizes, or approximated for larger ones.

## Limitations of Non-parametric Tests

• Non-parametric tests tend to have less power to detect an effect, if it exists, compared to parametric tests. Therefore, larger sample sizes might be needed to reach conclusions with the same degree of confidence.
• They generally only allow for more simplistic hypotheses, often relating to median values rather than specifics about parameters.
• Non-parametric tests may not provide as much information about the data as parametric tests do. Specifically, they provide less detailed estimates of effect sizes and their confidence intervals.

## Non-parametric Tests and Further Mathematics

• Understanding the fundamentals of non-parametric tests can both condense and extend a knowledge of statistics.
• It’s crucial to discern when to apply non-parametric tests and to appreciate their limitations as well as their strengths.
• Mastery of this topic integrates skills of data analysis, hypothesis testing, and statistical inference.