# Two-way ANOVA

What is the Two-way ANOVA?

The two-way ANOVA is a variance analysis which can test more than one independent (related) variable on their means, next to the testing of groups already discussed. This way it can test interaction effects between independent variables next to the main effects.

When do you use the Two-way ANOVA?

You'll have to use the Two-way ANOVA if you would like to compare two or more groups next to one ore more independent variable based on their means.

Example of a Two-way ANOVA

You want to test whether intelligent people score higher on a exam than less intelligent people based on hours of study. Because this is a two-way ANOVA you want to use groups, in this case: intelligence (high/low) and hours of study (much/little). It can by divided into more groups, but for this example we'll use 2 groups per independent variable. The two-way ANOVA enables us to examine whether the group 'intelligence high' scores higher on the exam in comparison to the group 'intelligence low'. Furthermore we can examine whether the score of the group 'hours of study high' is higher than the score of 'hours of study low' and if there's an interaction effect between the two independent variables.

Next to that it will be tested for an interaction effect between intelligence and hours of study. In our example it can be possible that next to the main effects a student with higher intelligence can have more advantage with more hours of study.
The group with lower intelligence will improve their exam after many hours of study with an average of 1 point. The group with higher intelligence will improve their exam after many hours of study with 2 points, so 1 point higher than the low intelligence group. This 1 point higher in this example is the interaction effect. The main effect of hours of study is different for the two groups; this is called the interaction-effect.
*the main effects become more pure. If you would only look at intelligence (ANOVA or t-test) there would be a lot of noise of the fact whether a student did or didn't study for the exam. A less intelligent student who did study hard is easily able to score a point higher compared to the more intelligent student who hardly studied. When you would only look at intelligence you could say in this case there's no difference between the students, because you didn't have look at the independent variable 'hours of study'. This way the data become more pure.

What's important when considering the Two-way ANOVA?

The Two-way ANOVA is a strong statistical test which easily can be used to draw conclusions. The output of this test includes more tables which you first have to become acquainted with, which makes the interpretation a little hard at first. Bear in mind you're going to compare more than two 'cells' of group means, so you'll need sufficient respondents. Approximately 30 respondents per 'cell' will be sufficient in most cases (in our example that would be 4x30=120 respondents). A thesis based on Two-way ANOVA's will be statistically well built in general.

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