Non-Parametric Statistics

Non-parametric statistics is a branch of statistics that focuses on the analysis of data without making rigid assumptions about their distribution. This makes it extremely versatile and suitable for many situations in which parametric methods, which instead require specific hypotheses on the data, would not be applicable.

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Non-Parametric Statistics

One of the main characteristics of non-parametric statistics is its absence of assumptions about the distribution of the data. While parametric methods, such as the Student’s t test, require the data to follow a normal distribution, nonparametric methods can be used even if the data is not normally distributed. This is especially useful when analyzing ordinal or nominal data, that is, data that cannot be easily described by a continuous distribution.

Another important feature is robustness. Nonparametric tests are often more robust than parametric ones, especially in the presence of outliers or non-normal distributions. This robustness makes them reliable tools for analyzing real data that may present anomalies or not meet ideal conditions.

Main Non-Parametric Techniques

Single Sample Test

  • Sign Test: This test is used to evaluate whether the median of a population differs from a specific value. It is especially useful when the data is ordinal and cannot be treated with parametric tests.


The Sign Test

  • Wilcoxon Sign-Rank Test: Similar to the sign test, but also considers the ranks of the data, providing greater sensitivity in analyses.

Two Sample Test

  • Mann-Whitney U test: This test compares two independent samples to see if they come from the same population. It is a nonparametric alternative to the independent samples t test.
  • Wilcoxon Signed Rank Test: Used to compare two paired or dependent samples. It is the nonparametric alternative to the paired-samples t test.

Test for More Than Two Samples

  • Kruskal-Wallis test: An extension of the Mann-Whitney U test that allows you to compare more than two groups. It is the nonparametric equivalent of one-way ANOVA.
  • Friedman Test: Used for nonparametric analysis of variance for repeated measures. It is the nonparametric alternative to repeated measures ANOVA.

Correlation Analysis

  • Spearman Correlation Coefficient: Measures the strength and direction of the association between two ordinal variables. It is the nonparametric alternative to the Pearson correlation coefficient.
  • Kendall’s Correlation Coefficient: Similar to Spearman, but more suitable for small samples or for dealing with links in the data.

Advantages and disadvantages

The advantages of nonparametric methods include their flexibility and robustness. They can be applied to a wide range of data types and are less affected by outliers and violations of distribution assumptions. However, they also have some disadvantages. In general, they have less statistical power than parametric tests when the latter’s assumptions are met, and the results can be less intuitive and more difficult to interpret.

Applications of Non-Parametric Statistics

Nonparametric statistics finds application in many fields. In biology and medicine, it is used to analyze data that does not follow a normal distribution, such as disease severity scores. In the social sciences, it is used to test hypotheses on ordinal or categorical data. In economics and finance, it is useful for analyzing non-normal data or for robustness testing.


In summary, nonparametric statistics is a valuable tool for analyzing real data that does not meet the rigid assumptions of parametric techniques. It offers versatile and robust methods for a variety of analytical situations, making it indispensable in many areas of scientific research and data analysis.

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