# Nonparametric Statistical Tests

• Charan Singh Rayat
Chapter

## Abstract

Standard methods of statistical analyses are based on the normal distribution or binomial distribution of random variables. These standard procedures fail to provide required inference after statistical analysis whenever there is non-normal distribution of variables. The term “nonparametric” was introduced by Wolfowitz for defining the population beyond finite number of parameters. We apply nonparametric tests for statistical inference where we find non-normal distribution.

The term “parametric” is used when random variables are based on the assumption of “normal distribution” or “binomial distribution,” whereas in case of “non-normal distribution,” the term “nonparametric is used.” The “parametric tests” are Z-test, t-test (student’s t-test and t-paired test), F-test, and analysis of variance (ANOVA). A nonparametric test would be concerned with the “form of population” rather than with any parametric value. The term “nonparametric” does not mean “distribution-free,” but it is concerned beyond “normal distribution” as well as “binomial distribution.” There are wider applications of nonparametric statistical tests.