Chapter 12 – Factorial Designs (Morling, Research Methods in Psychology)

Question–answer flashcards covering key definitions, calculations, and concepts related to factorial experimental designs, main effects, interactions, ANOVA interpretation, graphing, and design variations.

What is a factorial design in experimental psychology?

A study that manipulates two or more independent variables (factors), each with at least two levels, to observe their separate and combined effects on a dependent variable.

In factorial notation (e.g., 3 × 2 × 4), what does the quantity of numbers tell you?

How many independent variables are included in the design (three IVs in a 3 × 2 × 4).

In factorial notation, what do the numbers themselves indicate?

The number of levels or conditions for each independent variable.

How many experimental conditions exist in a 2 × 3 design?

Six conditions (2 × 3 = 6).

How many experimental conditions exist in a 2 × 3 × 2 design?

Twelve conditions (2 × 3 × 2 = 12).

Define a ‘subject variable’ in the context of factorial designs.

An independent variable on which participants already differ (e.g., sex, age, political affiliation) and that cannot be manipulated by the researcher.

Give two reasons researchers use factorial designs instead of single-IV studies.

(1) Efficiency: multiple main effects can be tested in one study, saving time and participants. (2) Informativeness: allows detection of interaction effects showing how variables combine to influence the DV.

What is a main effect?

The overall effect of one independent variable on the dependent variable, averaging across all levels of the other independent variable(s).

In a 4 × 2 × 3 design, how many potential main effects are there?

Three; one for each independent variable.

What is an interaction effect?

A result in which the effect of one independent variable on the dependent variable depends on the level of another independent variable.

For a 2 × 2 design, how many possible two-way interactions exist?

One interaction (IV1 × IV2).

For a 2 × 2 × 2 design, how many possible interactions are there in total?

Four: three two-way interactions (IV1×IV2, IV1×IV3, IV2×IV3) and one three-way interaction (IV1×IV2×IV3).

Why are interactions usually emphasized more than main effects when both are present?

Because interactions reveal that ‘it depends’—they show that the influence of one IV changes across levels of another, providing a fuller explanation than main effects alone.

Describe a crossover interaction.

An interaction where the lines in a line graph cross, indicating that the effect of one IV reverses across levels of the other IV (e.g., liking hot vs. cold depends on food type).

Describe a spreading interaction.

An interaction where the effect of one IV appears only at certain levels of the second IV (lines are non-parallel but do not cross; e.g., a dog sits only when you both give a command and have a treat).

What are marginal means and what are they used for?

Arithmetic means for each level of an IV, averaged over the other IV(s); they are examined to evaluate main effects.

In a means table for a 2 × 2 design, how do you test for an interaction using ‘differences of differences’?

Calculate the difference between the two means in each row (or column) and compare those two differences; if they are unequal, an interaction is suggested.

Which three F-values are reported in a 2 × 2 factorial ANOVA?

F for IV1 (FRows), F for IV2 (FColumns), and F for the IV1 × IV2 interaction (FInteraction).

How many participants are required for a 2 × 2 independent-groups design with 50 participants per cell?

200 participants (4 cells × 50 each).

How many participants are required for a 2 × 2 within-groups design with 50 participants per condition?

50 participants total, because each participant completes all four conditions.

What is a mixed factorial design?

A design where at least one IV is manipulated between-subjects and another IV is manipulated within-subjects.

If researchers add a third level (hands-free) to the cell-phone IV in a 2 × 2 study, what is the new design notation?

2 × 3 design (e.g., age: young/old × phone condition: handheld, hands-free, none).

In factorial graphs, where should the dependent variable always appear?

On the y-axis.

What graphical pattern indicates ‘no interaction’ in a line graph of a 2-IV study?

Parallel lines.

What is the primary advantage of using line graphs over bar graphs in factorial studies?

Line graphs make it easier to visually detect interactions (non-parallel or crossing lines).

Provide an example of a subject variable and a manipulated variable that could be combined in a factorial design.

Subject variable: Age group (young vs. old). Manipulated variable: Cell phone use (on phone vs. not on phone).

When examining an ANOVA table, what conclusion is drawn if the interaction term is statistically significant but neither main effect is?

The combined influence of the IVs matters (‘it depends’); you interpret the interaction and typically downplay the non-significant main effects.

How can factorial designs improve external validity?

By showing that an effect generalizes—or fails to—across levels of another variable, revealing boundary conditions of a phenomenon.

What is the minimum number of levels each independent variable must have in a factorial design?

Two levels.

If a study reports a ‘significant main effect of reward’ and a ‘significant interaction of reward × distraction’, how should the results be interpreted first?

Focus on the interaction (reward × distraction) to explain how the effect of reward changes with distraction, then discuss any remaining main effects in context.

How many total cells are in a 3 × 3 factorial design?

Nine cells.

What does the term ‘between-subjects factorial design’ mean?

A factorial design where all independent variables are implemented as independent-groups factors (different participants in each cell).

When lines in a factorial line graph cross, what specific type of interaction is suggested?

A crossover interaction, indicating that the direction of one IV’s effect reverses across levels of the other IV.

Why are factorial designs considered ‘efficient’?

Because they allow researchers to test multiple hypotheses about main effects and interactions in a single experiment, using fewer overall resources than separate single-IV studies.