What are the different types of ANOVA tests?

There are several different types of Analysis of Variance (ANOVA) tests, each with its own specific use and application. Here are the four most commonly used types of ANOVA tests:

1. One-way ANOVA: This test is used to compare the means of two or more groups that are defined by a single categorical independent variable. For example, a one-way ANOVA could be used to compare the heights of individuals across three different age groups (child, adult, and senior).
2. Two-way ANOVA: This test is used to compare the means of two or more groups that are defined by two categorical independent variables. For example, a two-way ANOVA could be used to compare the effects of two different treatments (A and B) on two different populations (male and female).
3. Repeated-measures ANOVA: This test is used when measurements are taken on the same group of individuals over time or under different conditions. For example, a repeated-measures ANOVA could be used to compare the performance of a group of athletes before and after a training program.
4. Multivariate ANOVA (MANOVA): This test is used to compare the means of two or more groups that have multiple dependent variables. For example, a MANOVA could be used to compare the performance of two groups of students across multiple subjects (math, science, and reading).

These ANOVA tests are all used to test for significant differences between groups based on different independent variables or different combinations of independent variables. Choosing the appropriate ANOVA test depends on the specific research question and design of the study.