# Chapter 8. Experimental Design II: Factorial Designs

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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
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
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
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
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
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
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
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
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 Pre-Proactiv Post-Proactiv New 12 4 14 11 Old

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.