Some experiments are designed so that two or more treatments (independent variables) are explored simultaneously. Such experimental designs are referred to as factorial designs. In factorial designs, every level of each treatment is studied under the conditions of every level of all other treatments. Factorial designs can be arranged such that three, four, or n treatments or independent variables are studied simultaneously in the same experiment. If two independent variables are analyzed by using a completely randomized design, the effects of each variable are explored separately (one per design).
Thus, it takes two completely randomized designs to analyze the effects of the two independent variables. By using a factorial design, the business researcher can analyze both variables at the same time in one design, saving the time and effort of doing two different analyses and minimizing the experiment-wise error rate. Some business researchers use the factorial design as a way to control confounding or concomitant variables in a study. By building variables into the design, the researcher attempts to control for the effects of multiple variables in the experiment.
With the completely randomized design, the variables are studied in isolation. With the factorial design, there is potential for increased power over the completely randomized design because the additional effects of the second variable are removed from the error sum of squares. The researcher can explore the possibility of interaction between the two treatments variables in a two-factor factorial design if multiple measurements are taken under every combination of levels of the two treatments.
Factorial designs with two treatments are similar to randomized block designs.
However, whereas randomized block designs focus on one treatment variable and control for a blocking effect, a two-treatment factorial design focuses on the effects of both variables. Because the randomized block design contains only one measure for each (treatment-block) combination, interaction cannot be analyzed in randomized block designs. Many applications of the factorial design are possible in business research. For example, the natural gas industry can design an experiment to study usage rates and how they are affected by temperature and precipitation.
Theorizing that the outside temperature and type of precipitation make a difference in natural gas usage, industry researchers can gather usage measurements for a given community over a variety of temperature and precipitation conditions. At the same time, they can make an effort to determine whether certain types of precipitation, combined with certain temperature levels, affect usage rates differently than other combinations of temperature and precipitation (interaction effects).
Stock market analysts can select a company from an industry such as the construction industry and observe the behavior of its stock under different conditions. A factorial design can be set up by using volume of the stock market and prime interest rate as two independent variables. For volume of the market, business researchers can select some days when the volume is up from the day before, some days when the volume is down from the day before, and some other days when the volume is essentially the same as on the preceding day.