Module 10: Factorial design

What is a Factorial Design?

• A factorial design = study with MORE than one independent variable (IV)

• Each IV is called a factor

• Each factor has levels (conditions)

• Example:

  • IV 1: Pick-up line (cute vs direct)

  • IV 2: Scent (present vs absent)

  👉 A 2 × 2 design =

  • 2 variables

  • Each has 2 levels

  • Total conditions = 4

🔢 How to Count Conditions

• Multiply levels of each variable

Examples:

• 2 × 2 = 4 conditions

• 2 × 3 = 6 conditions

• 2 × 4 × 3 = 24 conditions

• 🧠 Key Terms

  • Factor = Independent Variable

  • Level/Condition = version of the IV

  • Condition = combination of all IV levels

Example:

Training Type	Modality	Condition
Training	Online	Training + Online
Training + Coaching	In-person	Training + Coaching + In-person

Types of Factorial Designs

True Experimental

• All IVs are manipulated

• Can determine cause-and-effect

Types of Factorial Designs

Hybrid Design

• At least one IV is measured (not manipulated)

  • Example: gender, age

• ❌ Cannot claim causation for that variable

Cell Mean:

• Mean for a specific condition

• Example: Doll + Humorous

Marginal Mean:

• Mean for one variable overall

• Used to test main effects

Main Effects:

• Effect of one IV on the DV

• Looks at variables independently

👉 Uses marginal means

Example:

• Does mood affect tipping? → main effect of mood

Interaction Effects:

• When the effect of one IV depends on another IV

• Key idea: “It depends…”

👉 Uses cell means

Example:

• Best condiment depends on the food:

  • Chocolate sauce good for ice cream

  • Mustard good for hot dogs

  • ❌ Mustard on ice cream = bad

 Important:

• You can have:

  • Interaction WITHOUT main effects

  • Main effects WITHOUT interaction

Types of Interactions (know concept, not names)

• Variables can combine in different ways:

  • Strengthen effect

  • Weaken effect

  • Reverse effect

👉 You don’t need to memorize specific names (like crossover)

ANOVA in Factorial Designs

• Used instead of multiple t-tests

Why ANOVA?

• Tests:

  • Main effect of IV #1

  • Main effect of IV #2

  • Interaction effect

👉 All in one test

What to Look For:

• F-value

• p-value (< .05 = significant)

• Eta² (effect size)

  • How much variance is explained

 Follow-Up After ANOVA:

• If main effect is significant → may need post-hoc tests

• If interaction is significant:

  • Must interpret interaction first

  • Often best to graph results

Research Example (Pick-Up Line Study):

Findings:

• Cute-direct lines > direct lines (main effect)

• Scent improved effectiveness

• Interaction: best results =
  👉 Cute-direct + scent

Important Design Considerations:

• Random assignment

• Ethics

• Control of variables

• Use of confederates

• Clear procedures (protocol)

Reliability:

• Needed when multiple observers

👉 Type:

• Inter-rater reliability

  • Are observers consistent?

Manipulation Check:

• Confirms IV worked as intended

Example:

• Ask participants:

  • Was the pick-up line “cute” or “direct”?

  • Did you notice scent?

Data Analysis Steps:

1. Descriptive stats

   • Who was in study?

   • Means per condition

2. Inferential stats (ANOVA)

   • Test significance