Parametric vs Non-Parametric Statistics: Understanding the Differences

In statistics, a parameter is a value that describes a characteristic of a population, such as the mean or proportion of individuals with a certain trait. Parametric methods use mathematical models to analyze data and make inferences about the population based on the parameters. These methods are often more powerful and precise than non-parametric methods, but they require that the data meet certain assumptions about the distribution of the data, such as normality or equal variances.

In contrast, non-parametric methods do not rely on specific assumptions about the distribution of the data, and can be used with any type of data. These methods are often less powerful and less precise than parametric methods, but they are more flexible and can be used in a wider range of situations.

Some common examples of parametric tests include:

* T-tests to compare the means of two groups
* ANOVA to compare the means of three or more groups
* Regression analysis to model the relationship between a dependent variable and one or more independent variables
* Chi-square tests to compare the distributions of categorical data

Some common examples of non-parametric tests include:

* Wilcoxon rank-sum test to compare the medians of two groups
* Kruskal-Wallis H-test to compare the medians of three or more groups
* Mann-Whitney U test to compare the distributions of categorical data
* Spearman rank correlation coefficient to measure the strength and direction of the relationship between two continuous variables.