​Example -Inspect Spray and Tooth Growth

There are multiple types of ANOVA. The two commonly used ones are:

• One-way ANOVA
• Two-way ANOVA

One-way ANOVA compares variance of group  means considering only one independent variable. For instance, in the insect spray example, only the type of spray was considered as an independent variable.
In two-way ANOVA, groups are split on two independent variables. This is to study whether there is an interaction between the two independent variables on the response variable. For example, we can study whether the spray type and spray dosage will affect the count of insects through two-way ANOVA.
Assumptions of a Two-way ANOVA:

• Observations are independent
• Dependent variable is continuous
• Dependent variable follows normal distribution for every combination of the groups of the two independent variables.
• Each of the two independent variables consists of two or more categorical groups
• Variance of every combination of the groups of the two independent variables are homogenous
• There are no significant outliers.