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**Chapter 8. Experimental Design II: Factorial Designs**

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**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

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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

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**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

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**Factorial Essentials Identifying factorial designs Factorial matrix**

2x2 (two levels each of type of training and presentation rate)

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**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)

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**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)

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**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

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**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)

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**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)

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**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)

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**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)

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**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

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**Outcomes—Main Effects and Interactions**

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

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**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

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**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

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**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

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**Outcomes—Main Effects and Interactions**

Combinations of main effects and interactions Interaction and two main effects

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**Outcomes—Main Effects and Interactions**

Combinations of main effects and interactions Interaction and two main effects

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**Outcomes—Main Effects and Interactions**

Combinations of main effects and interactions Line graphs occasionally used to highlight interactions (nonparallel lines indicate interaction)

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**Varieties of Factorial Designs**

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**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

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**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

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**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

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**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

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**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

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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.

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