randomized factorial design

Definition
Randomized factorial design: A true experimental research design that incorporates two or more factors (e.g., an independent variable and an attribute variable), permitting testing of the main effect and interaction effects.

Notes

The term factorial in research describes designs that combine two or more independent variables (or attribute variables) within a single experiment to determine their joint effect, in addition to the overall effect of each variable singly. (Suter 2012, pg. 13)

(The general term factor, then, usually refers to either an independent variable or an attribute variable, or both.) The joint effect of two variables is referred to as an interaction, an important but difficult concept.

You may be familiar with the concept of interaction already, possibly in the form of warnings about drug interactions. This occurs if two drugs—each separately having a small effect—when combined have an amplifying effect. For example, some medications may make you slightly sleepy; so might a glass of wine. The combination of medication and wine, however, may make you very sleepy (more than the slight effects merely added together)—an interaction effect. (pg. 14)

Factorial designs in educational research are commonly used, in part because of their ability to uncover interactive relationships.

Factorial designs in education involve two or more factors ( independent or attribute variables ), thus permitting the evaluation of main effects and interaction effects.

Main effects and interaction effects exist independently in research outcomes. In other words, whether or not variables interact tells us nothing about whether or not there are main effects. And one variable's main effect tells us nothing about the other variable's main effect or whether or not there is an interaction between variables. (pg. 20)

Factorial designs become very complex with the addition of a third factor (e.g., A, B, and C). There are now three main effects and four interaction effects possible: the main effects for A, B, and C; and the interactions for AB, AC, BC, and ABC. Two-way interactions are more easily interpreted than three-way interactions. With the addition of a fourth factor, the potential interactions are exceedingly complex. (pg. 21)