chapter 8. experimental design ii: factorial designs

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

12 4

14 11

Pre-Proactiv Post-Proactiv

NewOld

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.