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# 1.9: Factorial Design

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Factorial Design

### 1.9: Factorial Design

Factorial Analysis is an experimental design that applies Analysis of Variance (ANOVA) statistical procedures to examine a change in a dependent variable due to more than one independent variable, also known as factors. Changes in worker productivity can be reasoned, for example, to be influenced by salary and other conditions, such as skill level. One way to test this hypothesis is by categorizing salary into three levels (low, moderate, and high) and skills sets into two levels (entry level vs. experienced).

Naming

This scientific approach is designated a label that either underscores the number of factors or the number of conditions tested for each independent variable. The example experiment above would be described as a two-way factorial ANOVA, because it involves two independent variables. In respect to the number of levels considered for salary (low, moderate, and high) and skill sets (entry level and experienced), this same experiment is also designated as a 3 by 2 design, formally written as a 3 x 2 Factorial ANOVA. Of note, computing the product of 3 and 2 signifies that there is a total of 6 combinations of experimental conditions observed.

Observing the effects of at least two independent variables is a more practical and economical approach. This averts the need to expend time and resources for separate experiments. Furthermore, collecting data for different combinations of conditions enables researchers to make a variety of assessments, including main and interaction effects.

Certain research questions may require understanding know how each factor may independently impact a dependent variable. For example, observed changes in worker productivity scores due to salary are separated from those due to skill level, to help determine the main effects for each. Results could potentially reveal that high productivity found in entry level employees may or may not apply to those who are more experienced. Likewise, low productivity that may be found in low salaried employees may or may not be evident with increased wages. The ability to recognize if results can be generalized to different circumstances or group features thus serves as another advantage for this type of design.

An interaction effect occurs when the influence of an independent variable on a given dependent variable depends on the level of other factors being examined. It might be found, for instance, that the impact of salary on worker productivity may be more pronounced for entry level as opposed to experienced employees. This type of analysis allows researchers to gain a deeper view of patterns that may emerge in the data set.

Implications of Factorial Analysis

Due to its flexibility and practicality, factorial analysis continues to be one of the most common experimental designs used across all disciplines. A recent study, for instance, investigated whether consumer behavior may depend on whether the product is utilitarian or hedonic. In addition to product type, researchers also included product image (close-up vs. wide shot) as a potential factor that influenced purchase decisions. These researchers further examined if type of persuasive technique, such as rational or emotional appeal would have an impact (Kim, Lee, & Choi, 2019). Hedonic products tended to gain more favorable attitudes when a wide shot image was accompanied by emotion inducing advertisements. Inverse findings were observed for utilitarian products in this 2 x 2 x 2 Factorial ANOVA, otherwise known as a three-way ANOVA.