Before diving into different types of ANOVA, it's important to understand some key terminology:

Factor: A factor (also called an independent variable) is a categorical variable that defines the groups you're comparing. Examples include:

•Treatment (placebo vs. drug A vs. drug B)

•Species (mouse vs. rat vs. hamster)

•Gender (male vs. female)

•Time point (0 hours, 24 hours, 48 hours)

Levels: The levels of a factor are the specific groups or categories within that factor. In the example of the treatment factor above, there are three levels: placebo, drug A, and drug B. Similarly for the time point factor example, there are three levels: 0 hours, 24 hours, and 48 hours (though you may design your experiment to have more or less depending on your experimental design).

The number of factors determines the type of ANOVA

One factor → One-way ANOVA (e.g. comparing three drugs)

Two factors → Two-way ANOVA (e.g. comparing three drugs in both males and females)

Three factors → Three-way ANOVA (e.g. three drugs × two genders × four time points)

Four or more factors → Generally simply referred to as "multifactor ANOVA" (e.g. adding genotype as a fourth factor)

An example to illustrate factors and levels

Suppose you're studying the effect of diet and exercise on weight loss. You have:

•Factor 1 - Diet type: Mediterranean, Low-carb, Low-fat (3 levels)

•Factor 2 - Exercise regimen: None, Moderate, Intense (3 levels)

This is a two-way ANOVA design with 3 × 3 = 9 total groups (combinations of diet and exercise). Performing this ANOVA would allow you to investigate the effect of diet on weight loss, the effect of exercise on weight loss, or to investigate the combination of diet and weight loss together (called an interaction) on weight loss.