# Two-Way ANOVA Calculator

*Load ANOVA data set*

To calculate a two-way ANOVA online, simply select one metric variable and two nominal variables! A two-way ANOVA will then be calculated automatically.

The results of the 2-way ANOVA are then clearly presented. First you can read the hypotheses, then the descriptive statistics, followed by the Levene's test and the 2-way ANOVA table. Finally, the post hoc test is displayed.

# Two-Way ANOVA

A Two-Way ANOVA (Analysis of Variance) is a statistical test used to determine the effects of two independent variables (or factors) on a dependent variable. The Two-Way ANOVA is an extension of the one-way ANOVA calculator for situations where there are two independent factors. This method can also assess the interaction between the two factors. A basic outline of a Two-Way ANOVA is as follows:

#### Factors and Levels:

- The two independent variables are known as factors.
- Each factor can have two or more levels. For example, a Two-Way ANOVA could examine the effects of gender (male vs. female) and treatment type (treatment A vs. treatment B vs. treatment C) on some outcome.

#### Hypotheses:

There are three sets of null hypotheses in a Two-Way ANOVA:

- The means of the dependent variable are the same across levels of the first factor.
- The means of the dependent variable are the same across levels of the second factor.
- There is no interaction between the two factors.

#### Assumptions:

Several assumptions must be met for the results of a Two-Way ANOVA to be valid:

- Normality: The dependent variable is approximately normally distributed within each combination of the groups of the two factors.
- Homogeneity of variance: The variances of the dependent variable are equal across all groups.
- Independence: The observations are independent of each other.

#### Results:

If the results of the ANOVA indicate significant effects, it means that the dependent variable differs across the levels of at least one of the factors or that there's an interaction effect between the factors. Significant main effects for each factor can be further explored using post-hoc tests. If there's a significant interaction, it means the effect of one factor depends on the level of the other factor.

#### Visual Representation:

The results of a Two-Way ANOVA can often be depicted graphically using line graphs or bar graphs. This visualization can help in understanding main effects and interactions.