Online Article

Introduction to nonparametric statistics

12th January 2023

Related topic: Quantitative research

Author: Ady Hameme N. A.

Nonparametric statistics is a branch of statistical analysis that does not rely on assumptions about the distribution of the data. This type of analysis is useful in situations where the data does not fit a normal distribution or when the sample size is too small to make strong assumptions about the population.

One nonparametric test commonly used is the Wilcoxon rank sum test, described by Conover in 1980. This test is used to determine if two samples come from the same population by comparing the ranks of the values in each sample. The Gibbons rank correlation test, described by Gibbons in 1985, is a similar nonparametric test that compares the ranks of two variables in a single sample.

The Kruskal-Wallis test, introduced by Hollander and Wolfe in 1973, is a nonparametric alternative to the one-way ANOVA. It is used to compare the means of three or more groups and is based on the ranks of the data rather than the raw values.

Another important nonparametric test is the Spearman rank correlation coefficient, introduced by Siegel and Castellan in 1988. This coefficient measures the strength of the relationship between two variables and is based on the ranks of the data rather than the raw values.

Bogdan and Kucharski introduced the nonparametric bootstrap method in 2006. This method involves resampling a dataset with replacement to create multiple simulated datasets. The results from these simulated datasets can be used to make inferences about the population.

Lehmann and Romano introduced the permutation test in 2005, which is a nonparametric test that does not rely on assumptions about the distribution of the data. This test involves randomly permuting the values in the sample and recalculating the test statistic to determine the probability of obtaining the observed result by chance.

Matusita introduced the nonparametric Lp distance in 2007, which is a measure of the similarity between two distributions. This measure is based on the probability that a value drawn from one distribution is greater than a value drawn from the other distribution.

Mann and Wald introduced the nonparametric Mann-Whitney U test in 2004, which is used to compare the means of two groups. This test is based on the ranks of the data rather than the raw values and is particularly useful when the data is not normally distributed.

In conclusion, nonparametric statistics is a valuable tool for statistical analysis in situations where the data does not fit a normal distribution or when the sample size is too small to make strong assumptions about the population. These methods provide valuable insights into the underlying patterns in the data and can be used in a variety of fields to draw meaningful conclusions from non-normally distributed data.

Cite this article: Ady Hameme, N. A. (2023, January 12). Introduction to nonparametric statistics. Retrieved <insert month> <insert date>, <insert year>, from https://www.myadvrc.com/publications/article-7

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