Describe the difference between parametric and non-parametric tests.

Parametric tests make assumptions about population parameters, while non-parametric tests do not make such assumptions.

Parametric tests are statistical procedures that assume the data come from a type of probability distribution and make inferences about the parameters of this distribution. They are based on the assumption that the data are normally distributed, that the samples are dependent, and that the variances are equal - these are known as the assumptions of homogeneity of variance and independence. Examples of parametric tests include the t-test, Analysis of Variance (ANOVA), and regression analysis.

On the other hand, non-parametric tests do not make assumptions about the population parameters and the distribution of the data. They are often used when the data are not normally distributed, which makes them more flexible. Non-parametric tests are also less powerful than parametric tests, meaning they are less likely to reject a null hypothesis when it is false. Examples of non-parametric tests include the Mann-Whitney U test, the Wilcoxon signed-rank test, and the Kruskal-Wallis test.

The choice between using a parametric or non-parametric test depends on the nature of your data. If your data meet the assumptions of a parametric test, then these tests can provide more accurate and precise estimates. However, if your data do not meet these assumptions, then a non-parametric test may be more appropriate.

In summary, parametric tests are based on assumptions about the population and require the data to be normally distributed, while non-parametric tests do not make such assumptions and can be used with data that are not normally distributed. Both types of tests have their advantages and disadvantages, and the choice between them should be based on the characteristics of your data.