# Applied Statistics Lesson of the Day – The Full Factorial Design

March 4, 2014 1 Comment

An experimenter may seek to determine the causal relationships between **factors** and the **response**, where . On first instinct, you may be tempted to conduct separate experiments, each using the completely randomized design with 1 factor. Often, however, it is possible to conduct 1 experiment with factors at the same time. This is better than the first approach because

- it is
**faster** - it uses
**less resources**to answer the same questions - the
**interactions**between the factors can be examined

Such an experiment requires the **full factorial design**; in this design, the treatments are all possible combinations of all levels of all factors. After controlling for confounding variables and choosing the appropriate range and number of levels of the factor, the different **treatments** are applied to the different groups, and data on the resulting responses are collected.

The simplest full factorial experiment consists of 2 factors, each with 2 levels. Such an experiment would result in treatments, each being a combination of 1 level from the first factor and 1 level from the second factor. Since this is a *full* factorial design, experimental units are independently assigned to *all* treatments. The **2-factor ANOVA** model is commonly used to analyze data from such designs.

In later lessons, I will discuss interactions and 2-factor ANOVA in more detail.

I try to include a discussion about power in these types of discussions. We know that you can get better results faster with less effort by using factorial based designs. I think showing how powerful these designs are compared to t-tests gives factorial based designs a little extra umph.