Question

1. What is another name for a two-way ANOVA?

2. What is a main effect?

3. What is an interaction?

Answer 1

Introduction

The two-way ANOVA compares the mean differences between groups that have been split on two independent variables (called factors). The primary purpose of a two-way ANOVA is to understand if there is an interaction between the two independent variables on the dependent variable. For example, you could use a two-way ANOVA to understand whether there is an interaction between gender and educational level on test anxiety amongst university students, where gender (males/females) and education level (undergraduate/postgraduate) are your independent variables, and test anxiety is your dependent variable. Alternately, you may want to determine whether there is an interaction between physical activity level and gender on blood cholesterol concentration in children, where physical activity (low/moderate/high) and gender (male/female) are your independent variables, and cholesterol concentration is your dependent variable.

The interaction term in a two-way ANOVA informs you whether the effect of one of your independent variables on the dependent variable is the same for all values of your other independent variable (and vice versa). For example, is the effect of gender (male/female) on test anxiety influenced by educational level (undergraduate/postgraduate)? Additionally, if a statistically significant interaction is found, you need to determine whether there are any "simple main effects", and if there are, what these effects are (we discuss this later in our guide).

In statistics, a main effect is the effect of just one of the independent variables on the dependent variable. The first step in determining if the main effect results in statistically significant differences in the dependent variable is calculating the marginal mean of each group. To find the marginal mean, average the means of the individual groups. For example, in the table below, the marginal mean for the 250 mg/kg treatment group is found by adding all the means in that column (88%, 92%, and 105%) and dividing by three to get 95%.

The main effect for each factor is determined by comparing marginal means.

Just calculating the marginal means, however, isn't enough to determine if the different concentrations of drug result in statistically significant differences in tumor reduction. ANOVA is a statistical test that's used to determine if there are differences between groups when there are more than two treatment groups.