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# 3-Way ANOVA calculator

If you want to calculate a 3-way analysis of variance online, simply select three nominal variables and one metric variable. The results of a three-way ANOVA will then be calculated.

You will then see the results of the calculated 3-way ANOVA. First the hypotheses are displayed and then the table with the calculated main effects and the interaction effects.

## 3-Way ANOVA

A 3-way ANOVA, also known as a three-factor ANOVA, is a statistical test used to determine the effects of three independent categorical variables (or factors) on a continuous dependent variable. It also assesses the interactions between these three factors. In other words, a 3-way ANOVA is an extension of the one-way and two-way ANOVA calculator for situations where there are three independent factors.

### Possible Outcomes:

1. Main effects for each of the three factors:
• Effect of factor A on the dependent variable, ignoring factors B and C.
• Effect of factor B on the dependent variable, ignoring factors A and C.
• Effect of factor C on the dependent variable, ignoring factors A and B.
2. Two-way interaction effects between pairs of factors:
• Interaction effect between factors A and B, ignoring factor C.
• Interaction effect between factors A and C, ignoring factor B.
• Interaction effect between factors B and C, ignoring factor A.
3. Three-way interaction effect among all three factors:
• Interaction effect between factors A, B, and C. This tests whether the two-way interactions are consistent across levels of the third factor.

The idea behind these tests is to assess not only how each factor independently affects the dependent variable but also how combinations of factors do. For instance, a two-way interaction indicates that the effect of one factor depends on the level of another factor.

The results of a 3-way ANOVA can be complex and require careful interpretation. If significant interactions are detected, it is common to conduct post-hoc tests or plot interaction graphs to better understand the nature of these interactions.

Cite DATAtab: DATAtab Team (2024). DATAtab: Online Statistics Calculator. DATAtab e.U. Graz, Austria. URL https://datatab.net