An important type of experimental research design, is the factorial design. In a factorial design, several independent variables, also called factors, are investigated, simultaneously. For example, we could investigate, the effectiveness, of an experimental drug, aiming to reduce migraine attacks. Suppose we create three conditions, that differ in the administered dosage, low, medium, and high. We can now investigate the effect of the factor dosage, on the number of migraine attacks. Is a higher dosage more effect, in reducing attacks? We can extend the simple design and make it factorial, by adding a second factor. For example, gender. If we make sure there are enough, preferably equal numbers of men and women, assigned to each of the dosages, then we end up with six conditions. Men who receive a low, medium or high dosage, and women, who receive a low, medium, or high dosage. Besides the effect of dosage, we can now also investigate the effect of the second factor, gender. Do women suffer more migraine attacks, than men? We can also investigate the combined effect, of dosage and gender. We can see, whether a higher dosage, is more effective in reducing the number of migraine attacks, for women as compared to men. The effects of the factors separately, are called, main effects. The combined effect, is called the interaction effect. In this case, we're dealing with a two-way interaction, because the effect combines two factors. Of course we can add more factors, making it possible to investigate higher order interactions. But as the number of factors increases, the design becomes very complicated, very quickly. Suppose we add diet as a factor, with two conditions, a normal diet and a diet eliminating all chocolate and red wine. Let's call this, the No Fun diet. This would require that each of the six groups, is split in two, with half of the participants being assigned to the normal diet, and half, to the No Fun diet. We can now look at the main affect of diet. Is a No Fun diet effective at reducing migraine attacks? We could also look at the two-way interaction between diet and gender. Maybe, the No Fun diet, is effective for men but not for women. We can also look at the two way interaction between diet and dosage. Is a higher dosage more effective, when a no-fun diet is being followed, as compared, to a normal diet? Finally, we can look at the three-way interaction. Maybe, a higher dosage is effective for women, regardless of diet. But maybe for men, a higher dosage is effective only if they follow a No fun diet, and not if they follow a normal diet. Like I said, it can get pretty complicated, pretty quickly. There are even more complicated factorial designs, called incomplete designs. Where not all combinations of levels of the factors, or cells, are actually present in the design. Now we won't go into those designs right now. What's important here, is that you understand, the basics of factorial designs. You need to know, that factorial design consists of two or more independent variables. And for now, one dependent variable. The independent variables are crossed, to ensure that all cells are represented in the study and that each cell, contains enough participants. Factorial designs are very useful. Because they allow us to investigate, not the only the main effects of several factors, but also, the combined effects or interaction effects.
