## What Is the Three-Way ANOVA?

The three-way ANOVA is used by statisticians to determine whether there is a three-way relationship among variables on an outcome. It determines what effect, if any, three factors had on an outcome. Three-way ANOVAs are useful for gaining an understanding of complex interactions where more than one variable may influence the result and have many applications in finance, social science, and medical research, among a host of other fields.

A three-way ANOVA is also known as three-factor ANOVA. By using ANOVA, a researcher is able to determine whether the variability of the outcomes is due to chance or to the factors in the analysis.

### Key Takeaways

• A three-way ANOVA tests which of three separate variables have an effect on an outcome, and the relationship between the three variables.
• It is also called a three-factor ANOVA, with ANOVA standing for "analysis of variance."
• The test is useful to get a gauge of complex interactions, and whether they are due to chance or factors in the analysis.
• Three-way ANOVAs have many applications in finance, social science, and other fields.
• For example, a pharmaceutical company may do a three-way ANOVA to test a drug, given the different genders or ethnicities of their subjects.

## Understanding a Three-Way ANOVA

A pharmaceutical company, for example, may do a three-way ANOVA to determine the effect of a drug on a medical condition. One factor would be the drug, another may be the gender of the subject, and another may be the ethnicity of the subject.

These three factors may each have a distinguishable effect on the outcome. They may also interact with each other. The drug may have a positive effect on male subjects, for example, but it may not work on males of a certain ethnicity. Three-way ANOVA allows the scientist to quantify the effects of each and whether the factors interact.