2-Way ANOVA

Two-way ANOVA is a statistical technique used to examine the effects of two independent categorical variables (factors) on a continuous dependent variable. It allows us to determine if there are significant interactions between the two factors and the dependent variable.

Two-way ANOVA can answer three main questions:

1. Main Effect of Factor A: Does factor A affect the outcome?
2. Main Effect of Factor B: Does factor B affect the outcome?
3. Interaction Effect: Does the combination of factors A and B influence the outcome in a way that the individual factors don’t?

Assumptions of Two-Way ANOVA

Before running a two-way ANOVA, the following assumptions must be met:

1. Independence: Observations should be independent of each other.
2. Normality: The dependent variable should be approximately normally distributed for each combination of factors.
3. Homogeneity of variances: The variance of the dependent variable should be equal across groups.

Hypotheses in Two-Way ANOVA

For each factor and the interaction, we test the following hypotheses. A two-way analysis of variance (ANOVA) test tests three null hypotheses:

Factor A (e.g., Drug Type):

• Null hypothesis (H₀​): The means are equal across the levels of factor A.
• Alternative hypothesis (H₁​): The means are not equal across the levels of factor A.

Factor B (e.g., Dosage):

• Null hypothesis (H₀​): The means are equal across the levels of factor B.
• Alternative hypothesis (H₁​​): The means are not equal across the levels of factor B.

Interaction (A * B):

• Null hypothesis (H₀​): There is no interaction between the two factors.
• Alternative hypothesis (H₁​​): There is an interaction between the two factors.