When graphing the results of a factorial experiment that includes one quantitative independent variable (e.g., length of psychotherapy) and one categorical independent variable (e.g., type of psychotherapy), which type of graph is typically used?

In psychology research, the way factorial experiments are graphed depends on the nature of the variables. Match each graphical element with the specific variable type and role it represents in the examples described.

A researcher is graphing the results of a factorial experiment studying the effects of 'Medication Dosage' (0mg, 50mg, 100mg) and 'Patient Age' (Young vs. Old) on recovery time. To correctly apply the standard research conventions shown in the provided examples, the researcher should place 'Medication Dosage' on the x-axis of a line graph.

A researcher is visualizing the results of a factorial study examining 'Medication Dosage' (0, 10, 20, or 30mg) and 'Patient Age' (Young vs. Old) on 'Recovery Time.' Sequence the steps of the analytical process to correctly organize these variables into a line graph according to standard psychology research conventions.

In a bar graph used to represent a $2 imes 2$factorial experiment with a categorical variable on the$x$$-axis, how are the levels of the second independent variable typically distinguished?

According to standard conventions in psychology research, a bar graph is typically preferred over a line graph to represent factorial designs that include a quantitative independent variable.

A peer reviewer evaluates a researcher's decision to use a bar graph for a $5 \times 2$ factorial design where 'Time Elapsed' (10, 20, 30, 40, or 50 minutes) is the independent variable on the $x$-axis. The reviewer concludes that a line graph is more appropriate because 'Time Elapsed' is a _____ variable, and conventions suggest using lines to better represent functional relationships between such numerical levels.

A research team must choose how to graph results from several factorial experiments. Match each study description or graph element on the left to the correct graphing decision or representational role on the right.

A student examines two published factorial-experiment graphs. Graph A depicts a $2 \times 2$ study with 'feedback type' (positive vs. negative) on the x-axis and 'study method' (active vs. passive) shown as differently colored bars. Graph B depicts a $4 \times 2$ study with 'practice duration' (1, 2, 3, or 4 weeks) on the x-axis and 'instruction style' (lecture vs. discussion) shown as differently formatted lines. After comparing the two graphs, the student identifies that the structural reason Graph B uses lines rather than bars is that the variable placed on its x-axis — 'practice duration' — is _____, whereas the x-axis variable in Graph A is categorical.

A researcher receives peer-review feedback that their graph for a $4 \times 2$ factorial study is incorrectly formatted: the categorical IV ('therapy type': CBT vs. DBT) was placed on the x-axis, and the quantitative IV ('session count': 4, 8, 12, or 16 sessions) was represented by differently colored bars. Sequence the steps the researcher should follow to evaluate and correct this graphing error.

Based on the graphing conventions for factorial experiments, describe how the choice of graph type differs when using categorical versus quantitative variables. In your response, describe the specific graphical setup for a $2 \times 2$ design with categorical variables and a $4 \times 2$ design that includes a quantitative variable, specifying what is placed on the $x$-axis and how the second variable is represented.

Explain why the student's proposed bar graph setup is inappropriate for presenting the results of this factorial design based on standard graphing conventions. Describe what type of graph should be used instead and how the variables should be correctly arranged on it.

A psychology researcher conducts a $3 \times 2$ factorial experiment examining the effects of a quantitative independent variable, 'Dosage of Drug' (with levels: 5mg, 10mg, 15mg), and a categorical independent variable, 'Patient Gender' (with levels: Male, Female). Applying standard psychology graphing conventions, state the type of graph that should be used and explain how these two independent variables must be represented on it.