How is the total number of simple effects calculated for a factorial experiment?

A team of psychologists is designing several factorial experiments to investigate human behavior. Match each study's description of independent variables with the total number of simple effects that can be analyzed in that specific design.

If a psychologist knows that their factorial experiment consists of exactly 12 unique experimental conditions, they have sufficient information to conclude that the study will yield exactly 7 simple effect analyses.

An instructional designer is evaluating several proposed research studies to determine the amount of statistical follow-up required for significant interactions. Rank the following factorial designs from the one requiring the fewest total simple effect analyses to the one requiring the most.

A researcher is developing a factorial study to investigate the effects of different teaching methods and study environments on student performance. The project budget allows for exactly $12$ unique experimental conditions (cells). To ensure the most detailed follow-up analysis of a potential interaction, the researcher aims to construct a design that maximizes the total number of simple effect analyses. Which of the following design frameworks should the researcher create to achieve this goal?

In a factorial experiment, a researcher determines the total number of simple effects by multiplying the number of levels of each independent variable.

A cognitive psychologist designs a factorial experiment to study memory retention, utilizing a 3 × 5 design. Based on the levels of these independent variables, the total number of simple effects analyses they can conduct is _____.

A research methods instructor presents four factorial designs and asks students to match each design notation to the correct description of how simple effects analyses are distributed across its two independent variables. Note that two designs yield the same total number of simple effects but differ in how those analyses are distributed. Match each design to its correct description.

A researcher initially designs a $2 \times 3$ factorial study to examine the effects of feedback type and practice schedule on skill acquisition. After a literature review reveals that a key moderating variable has more granularity than expected, the researcher adds one additional level to each independent variable, converting the study to a $3 \times 4$ factorial design. Compared to the original design, the revised design will require _____ additional simple effect analyses to fully interpret a significant interaction.

A researcher obtains a statistically significant interaction in a $2 \times 4$ factorial ANOVA and must now conduct simple effects analyses to fully interpret it. Rank the following steps from FIRST (1) to LAST (5) in the logically correct order for determining, conducting, and interpreting simple effects for this design. Consider which steps must be completed before others are even possible.

Describe the rule used to calculate the total number of simple effects analyses in a factorial experiment. In your response, explain why the number of simple effects depends on the levels of the independent variables, and provide the examples of designs and their corresponding number of simple effects as mentioned in the text.

Based on this scenario, identify the design notation, state the total number of simple effects analyses that can be conducted, and explain how the levels of the independent variables determine this total number.

Apply the rule for calculating simple effects to a study investigating the effects of room lighting (dim, medium, bright) and background noise (silent, moderate, loud) on task performance. Calculate the exact number of simple effects analyses that can be conducted and show your calculation.