Question

When we are discussing Two-Way ANOVAs, what do we mean when we talk about a mixed-model design?

There is an advantage to doing a Two-Way ANOVA rather than two One-Way ANOVAs. What is it?

Answer 1

In a mixed-design model, the dependent variable is measured more than once per subject for each level of the within-subjects factor but there are different sets of subjects for between-subjects factor levels. Hence, there is a combination of within-subjects and between-subjects factor in a mixed model design. An example of the within-subjects factor could be different times, the DV is measured before and after a particular event, and this is done for all the subjects. A between subject factor could be anything like brand for example. There will be different subjects for each group of brand.
How is it different to a two-way ANOVA is that in this case, we have two between-subjects factor. Each Dependent variable is measured exactly once for a single subject.

If you conduct two one-way ANOVAs, the risk of type 1 error will be 5% (If alpha = 0.05) for each test and hence the total risk for a type 1 error will increase to 10% approximately. If we conduct a two-way ANOVA instead, the total risk remain at 5% and we can be more confident about our results being statistically significant. This is the same as conducting one-way ANOVA rather than multiple t-tests.