Inferential statistics is a branch of statistics that involves making inferences or drawing conclusions about a population based on sample data. Parametric and non-parametric tests are two types of statistical tests used in inferential statistics.
1. Parametric tests: Parametric tests assume that the data follows a specific distribution, usually the normal distribution. These tests make certain assumptions about the population parameters, such as the mean and variance. Some common parametric tests include t-tests, analysis of variance (ANOVA), and regression analysis. Parametric tests are more powerful and efficient when the assumptions are met, but they can be sensitive to violations of these assumptions.
2. Non-parametric tests: Non-parametric tests, also known as distribution-free tests, do not make any assumptions about the underlying distribution of the data. These tests are based on ranks or medians rather than the actual values of the data. Non-parametric tests are often used when the data is not normally distributed or when the assumptions of parametric tests are violated. Examples of non-parametric tests include the Mann-Whitney U test, Kruskal-Wallis test, and Wilcoxon signed-rank test. Non-parametric tests are generally less powerful than parametric tests but are more robust to violations of assumptions.
The choice between parametric and non-parametric tests depends on the nature of the data and the assumptions that can be reasonably made. Parametric tests are preferred when the data is normally distributed and the assumptions are met, while non-parametric tests are used when the data is not normally distributed or when the assumptions of parametric tests are violated.