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In a factorial experiment with two independent variables, researchers often graph the results by plotting one independent variable along the $$x$$-axis and the second independent variable using differently colored bars or distinct line formats. The $$y$$-axis is always used to plot the dependent variable.

Graphing Factorial Experiments

When graphing the results of a factorial experiment with two independent variables, there is no strict rule determining which variable goes on the $$x$$-axis and which is represented by formatting features like bar color or line style. Researchers should select the visual arrangement that most effectively and clearly communicates the study's findings to their audience.

Assigning Variables in Factorial Graphs

Researchers use line graphs to plot factorial experiment results when the independent variable assigned to the $$x$$-axis is quantitative and consists of a few distinct levels. Additionally, line graphs are the standard choice for displaying time series data, where the $$x$$-axis represents measurements recorded over a continuous time interval.

Line Graphs in Factorial Designs

Graphical representations of factorial experiments vary based on the nature of the variables involved. For instance, in a $$2 	imes 2$$ design, researchers might use a bar graph with a categorical variable like 'time of day' on the $$x$$-axis and 'cell phone use' indicated by different colored bars. Conversely, for a $$4 	imes 2$$ design that includes a quantitative variable, a line graph is typically used; here, the quantitative variable, such as 'psychotherapy length', is placed on the $$x$$-axis, while the categorical variable, like 'psychotherapy type', is represented by distinct line formats.

Example of Graphing Factorial Experiments

Interaction effects in factorial experiments can be visually interpreted and analyzed using either bar graphs or line graphs. In these visualizations, spreading interactions are identifiable when there is a large difference in the dependent variable at one level but little to no difference at the other. Cross-over interactions are characterized by a distinct reversal in the pattern of bar heights or by line graphs where the plotted lines literally intersect and cross over one another.

Graphing Interactions

Match each variable in a factorial experiment with two independent variables to its standard graphical representation.

A psychology student is creating a graph for a factorial experiment investigating the effects of room temperature and background noise on reading comprehension scores. Based on standard graphing conventions for factorial designs, how should the student assign the variables to the graph's visual elements?

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