5Assumptions in Nonparametric Tests
5.1 Introduction
Statistical inference is used for generalizing results from the sample to the population. Most of the statistical tests depend on two main assumptions: randomness and normality. However, in some situations, these assumptions are violated and using the parametric tests will not be appropriate. Therefore, statisticians introduced the nonparametric techniques to deal with such cases, where the above assumptions aren't met. The nonparametric statistics is known to be distribution free.
The nonparametric statistics is appropriate when the population's parameters do not satisfy certain criteria, i.e. not measurable, such as in the categorical data, where the mean and variance are not defined. In other words, if there is a small sample size and non‐normal distribution, the nonparametric techniques have to be utilized for making an inference about the population's parameters. The readers should know that the nonparametric tests are less precise when compared with the parametric tests because there is less known information about the population.
In this chapter, the readers will get familiar with the required nonparametric assumptions, different nonparametric tests, how to perform those using IBM SPSS®1 Statistics software (SPSS), and what should be done if there is any violation for these assumptions.
5.2 Common Assumptions in Nonparametric Tests
The nonparametric tests rely on fewer assumptions about the sample data used for drawing ...