Parametric and non-parametric statistical tests are two broad categories of statistical methods used for hypothesis testing and data analysis. Here's a description of the key differences between them:
Parametric Statistical Tests :
* Parametric tests assume that the data follows a specific probability distribution, usually a normal distribution. Common parametric tests include t-tests, analysis of variance (ANOVA), linear regression, and chi-square tests.
* Parametric tests typically make assumptions about the population parameters, such as the mean, variance, or shape of the distribution.
* These tests often require that the data meet certain assumptions, such as normality and homogeneity of variances.
* Parametric tests are generally more powerful (i.e., have higher statistical power) than non-parametric tests when the assumptions are met.
* Examples of parametric tests include:
* Student's t-test for comparing means of two groups.
* One-way ANOVA for comparing means of more than two groups.
* Pearson correlation coefficient for assessing linear relationships between variables.
* Linear regression for modeling the relationship between a dependent variable and one or more independent variables.
Non-parametric Statistical Tests :
* Non-parametric tests do not assume any specific probability distribution for the data. Instead, they are based on fewer or weaker assumptions about the underlying population.
* Non-parametric tests are often used when the data do not meet the assumptions required for parametric tests, such as when the data are skewed, have outliers, or come from non-normal distributions.
* Non-parametric tests are generally less powerful than parametric tests, especially with larger sample sizes, but they are more robust to violations of assumptions.
* These tests are sometimes referred to as distribution-free tests because they do not rely on distributional assumptions.
* Examples of non-parametric tests include:
* Mann-Whitney U test (Wilcoxon rank-sum test) for comparing medians of two independent groups.
* Kruskal-Wallis test for comparing medians of more than two independent groups.
* Spearman's rank correlation coefficient for assessing monotonic relationships between variables.
* Chi-square test for independence for comparing categorical variables.
