# *Geek Box: 2 x 2 Factorial Design

#### *Geek Box: 2 x 2 Factorial Design

A 2 x 2 factorial design is a specific trial design which tests two interventions in the one study sample. In a 2 x 2 design, there are two [or more] independent variables, and a dependent variable. The ‘factor’ is the independent variable. Each factor may have different levels. Therefore, in a “2 x 2” design, there are two independent variables [factors] and two levels of each factor, e.g., two separate time points.

For example, you could want to test two different drugs which target a similar outcome, e.g., test a statin [independent factor No.1] vs. placebo and a PCSK9-inhibitor [independent factor No.2] vs. placebo for their effects on lowering LDL-cholesterol [dependent variable], and also test the effect of Dose A [level No.1] or Dose B [level No.2] for each drug. Thus, we have 2 factors [each drug] and 2 levels [different doses of each drug].

So you would have participants randomised to Statin-Dose A, Statin-Dose B, PCSK9-inhibitor-Dose A, PCSK9-inhibitor-Dose B: 2 x 2. There are a number of results you can get from this type of design. You could main effects and/or interaction effects. The ‘main effect’ is an outcome related to the levels of the factor. In our hypothetical example, there could be a main effect of the dose if the drug had an effect at each level of the dose. There could also be a main effect of drug if we found a difference between drugs that was independent of dose. You could also have an ‘interaction effect’, e.g., it could be that the combination of the PCSK9-inhibitor drug plus Dose B improves the outcome better than the other combinations.

To bring this back around to the present study, we can see that each participant consumed both the standard test meal [factor No.1] and high protein test meal [factor No.2] at 8am [level No.1] in the morning and 8pm [level No.2] in the evening, for a total of four test meals. The present study also utilised a cross-over design, meaning that each subject served as their own control and consumed each of the four test meals.

Cross-over designs are useful for nutrition interventions, given that there may be distinct inter-individual differences in metabolism and responses to a particular exposure [either diet or supplement]. Factorial designs – whether 2 x 2, 2 x 4, etc. – are helpful trial designs which allow for different independent variables [the factors] to be included in a single study, so they are an efficient way of doing research. They also allow for interaction effects to be examined, which is important in determining whether differences in treatment may be explained by variations between the factors and levels examined.