Background of parametric and nonparametric statistics
In parametric statistics, the information about the distribution of the population is known and is based on a fixed set of parameters. In nonparametric statistics, the information about the distribution of a population is unknown, and the parameters are not fixed, which makes is necessary to test the hypothesis for the population.
Parametric statistics assume that the sample data follows a probability distribution that is based on a set of parameters. The most common assumption is that data is distributed normally. Most of the common statistical methods are parametric. Although parametric statistics are considered more powerful than nonparametric statistics, they are not always applicable for the analysis of the significance of differences. The reason is that the assumptions on which they are based are not always met.
In nonparametric statistics, the sample data does not have to follow a normal distribution. The sample data is not based on numbers but on other criteria, such as ranking or commonness.
The following table gives an overview of the main differences between parametric and nonparametric statistics:
| Parametric | Nonparametric |
|---|---|
| Population is well-known | No information about the population available |
| Assumptions made about the population | No assumptions made about the population |
| Sample data based on distribution | Arbitrary sample data |
| Applicable for continuous variables | Applicable for continuous and discrete variables |
| More powerful | Less powerful |