What is a two-way ANOVA?

A two-way ANOVA (“analysis of variance”) is used to investigate whether or not there is a statistically significant difference between the means of 3 or more independent (unrelated) groups that have been split on two variables or factors. 

A two-way ANOVA is typically used to determine how two factors affect a response variable. Researchers use this test to investigate if there is a relation between the independent factors and the dependent factor and whether or not there is an interaction effect between the two factors on the response variable. For example, botanists use two-way ANOVA to investigate how exposure to sunlight and watering frequency may affect plant growth. In this case sunlight exposure and watering frequency are the two factors and plant growth is the response variable. If the study aimed to investigate the effect of only one factor ( either sunlight exposure or watering frequency) on plant growth, a one-way ANOVA would be the preferred statistical test.