Chapter 8. Experimental Design II: Factorial

Designs

Chapter 8. Experimental Design II: Factorial Designs

Chapter Objectives

• Describe factorial designs using a standardized notation system (2x2, 3x5, etc.) and place data accurately into a factorial matrix to calculate row and column means

• Understand what is meant by a main, interaction effect and know how to determine if one exists

Identify the varieties of factorials that correspond to the single-factor designs of Chapter 7

Chapter Objectives

• Identify a mixed factorial design and a PxE factorial

Calculate the number of participants needed to complete each type of factorial design

Construct an ANOVA source table for an independent groups factorial design

Factorial Essentials

• Factorial design = more than one IV• IVs referred to as “factors”• Identifying factorial designs• Notation system• Digits represent IVs• Numerical values of digits represent the # of levels of each

IV• 2x3 factorial (say: “two by three”)• 2 IVs, one with 2 levels, one with 3 = 6 total conditions

• 2x4x4 factorial• 3 IVs, with 2, 4, and 4 levels = 32 total conditions

Factorial Essentials

• Identifying factorial designs• Factorial matrix• 2x2 (two levels each of type of training and

presentation rate)

Outcomes—Main Effects and Interactions• Main Effects• Overall effect of IV “type of training”• Main effect compares data in both light-shaded cells

(imagery) with data in both dark-shaded cells (rote)• Main effect compares row means (imagery vs. rote)

Outcomes—Main Effects and Interactions

• Main Effects • Overall effect of IV “presentation rate”• Main effect of compares data in both light-shaded cells

(2-sec rate) with data in both dark-shaded cells (4-sec rate)

• Main effect compares column means (2-sec vs. 4-sec)

Outcomes—Main Effects and Interactions • Main Effects • Calculations row and

column means• For hypothetical data:• Row mean #1 (imagery)

= 20• Row mean #2

(rote) = 15• Column mean #1

(2-sec) = 14.5• Column mean #2

(4-sec) = 20.5

Outcomes—Main Effects and Interactions

• Main Effects • For hypothetical data:• Main effect for type of training• Imagery (M = 20) produces better recall than rote (M = 15)

• Main effect for presentation rate• 4-sec rate produces better recall (M = 20.5) than 2-sec rate

(M = 14.5)

Outcomes—Main Effects and Interactions

• Interactions• effect of one factor depends on the level of the

other factor, can be described two ways IVs course emphasis and student major

• No main effects (row and column means all equal 75)

Outcomes—Main Effects and Interactions

• Interactions • Whether lab or lecture emphasis is better depends on

which major is being evaluated• Lab emphasis science majors do better (80>70)• Lecture emphasis humanities majors do better (80>70)

Outcomes—Main Effects and Interactions

• Interactions • Whether science or humanities majors do better

depends on what type of course emphasis there is• Science majors better with lab emphasis (80>70)• Humanities majors better with lecture emphasis (80>70)

Outcomes—Main Effects and Interactions • Interactions • Research example 18: Studying in noise or silence• IVs study conditions (silent or noisy) and test

conditions (silent or noisy)• No main effects, but an interaction• Best memory when study and test conditions match

Outcomes—Main Effects and Interactions

• Interactions can trump main effects• Caffeine, aging, and memory study• Two main effects – neither relevant

Outcomes—Main Effects and Interactions

• Combinations of main effects and interactions• Main effect for imagery instructions (22>14), no

main effect for presentation rate, no interaction

Outcomes—Main Effects and Interactions

• Combinations of main effects and interactions• No main effect for imagery instructions, a main

effect for presentation rate (22>14), no interaction

Outcomes—Main Effects and Interactions

• Combinations of main effects and interactions• Main effect for imagery instructions (20>16) and

presentation rate (20>16), no interaction

Outcomes—Main Effects and Interactions

• Combinations of main effects and interactions• Interaction and two main effects

Outcomes—Main Effects and Interactions

• Combinations of main effects and interactions• Interaction and two main effects

Outcomes—Main Effects and Interactions

• Combinations of main effects and interactions• Line graphs occasionally used to highlight

interactions (nonparallel lines indicate interaction)

Varieties of Factorial Designs

Varieties of Factorial Designs

• Mixed factorial designs• At least one IV is a between-subjects factor• At least one IV is a within-subjects factor

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Pre-Proactiv Post-ProactivNewOld

Varieties of Factorial Designs

• Factorials with subject and manipulated variables : P x E designs• P = person factor (a subject variable)• E = environmental factor (a manipulated variable)• If E is a repeated measure mixed P x E factorial

• Main effect for P factor

• Introverts outperform extroverts, regardless of room size

Varieties of Factorial Designs

• Factorials with subject and manipulated variables : P x E designs

• Main effect for P factor• Introverts outperform extroverts, regardless of room

size

Varieties of Factorial Designs

• Factorials with subject and manipulated variables : P x E designs

• Main effect for E factor• Performance worse in small room, regardless of

personality

Varieties of Factorial Designs

• Factorials with subject and manipulated variables : P x E designs • P x E interaction• Introverts do better in large room, while extroverts do

better in small room

Summary• Factorial designs allow us to evaluate the effects of

multiple IVs on the DV or DVs.

• There are different types of factorial designs, depending on how you manipulate your IVs.• Between-subjects, repeated measures, mixed, PxE

• Main effects of each IV and interactions among IVs are the results from factorial designs.

• Factorial ANOVAs are the statistical tests used.

• With the experimental design tools at your disposal, remember to be an ethical researcher.