Nonparametric Statistics: An Overview

Nonparametric statistics, also known as distribution-free or non-parametric methods, is a set of statistical procedures that do not make any assumptions about the underlying distribution of the data in question. This makes them ideal for use with data sets that are small or otherwise difficult to work with, or when the underlying distribution of the data is unknown. Nonparametric statistics are also commonly used in areas where there is limited external data to draw upon, such as surveys and polls.

Nonparametric statistics are relatively simple to use, making them popular among novice researchers. They are also inexpensive and easy to compute, and they can be used to analyze any data set. However, the precision of nonparametric statistics is not as precise as other statistical models.

Rather than focus on the numerical values, nonparametric statistics consider the order of the data when making comparisons. This means, even if the numerical data changes slightly, the same patterns and relationships between the variables can still be observed. This is particularly helpful when dealing with data sets that are small and highly volatile, as it can give hints that can guide further investigations without having to invest time in further data analysis.

The most popular nonparametric procedures include the Wilcoxon-Mann-Whitney test and the Kruskal-Wallis test. The Wilcoxon-Mann-Whitney test assesses whether there is a difference between two data sets, rather than any linear correlation. The Kruskal-Wallis test assesses whether there is a correlation between two variables and whether it is significant. Other tests include the Friedman test, which tests if there is a difference in the means of two or more samples, and the Spearman Rank Correlation, which is used to measure the strength of the relationship between two variables.

When deciding whether to use nonparametric statistics, it is important to consider the project's goals and the data set being used. Nonparametric statistics can be very useful in certain cases, but they are limited in scope and accuracy. Therefore, if the project is looking for precision, it might be best to use another type of statistical analysis. On the other hand, if the goal is to identify patterns and relationships given limited data, nonparametric statistics can offer an informative, cost-efficient solution.