What is the difference between parametric and nonparametric statistical tests?

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Parametric statistics assume a normal distribution.

Parametric and nonparametric statistical tests are two different approaches used in hypothesis testing. The main difference lies in the assumptions made about the underlying population distribution.

Parametric tests assume that the data follows a specific distribution, usually Gaussian (Normal). These tests require the estimation of unknown parameters, such as the mean or standard deviation. Some common parametric tests include t-tests, ANOVA, and linear regression. Parametric tests are generally more powerful when the assumptions are met, meaning they can detect smaller effects with a smaller sample size.

Nonparametric tests, on the other hand, do not make any assumptions about the underlying distribution. They are known as distribution-free tests because they do not rely on estimating parameters. Instead, nonparametric tests use ranks or other non-numerical data to evaluate differences between groups. Examples of nonparametric tests include the Mann-Whitney U test, Wilcoxon signed-rank test, and Kruskal-Wallis test. Nonparametric tests are more robust to violations of assumptions, so they can be used when the data deviate from normality or when sample sizes are small.

To determine whether to use a parametric or nonparametric test, you should consider the nature of your data and the assumptions of the test. If your data meets the assumptions of a parametric test (e.g., normal distribution), then a parametric test may be appropriate. However, if the assumptions are not met or the data is non-numerical, a nonparametric test would be a better choice.

To use these tests, you can find statistical software or programming languages such as R or Python. These languages have built-in functions to perform both parametric and nonparametric tests. It is important to consult the documentation or seek guidance to understand the specific steps to implement each test correctly.