Factorial Designs

FACTORIAL E

XPERIMENTS

R E S E A R C H ME T H O D S 3

AIM: TO INTRODUCE THE PRINCIPLES OF A FACTORIAL EXPERIMENT

F A C T O R I A L E X P E R I M E N T S 2

Factorial Experime

nts

Example 1 Overview Example 2 Other designs

F A C T O R I A L E X P E R I M E N T S

EXAMPLEBushman et al (1971): Do adults feel more violent after seeing violence?Do males generally feel more violent then females?Are males affected more by seeing violence than females?

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EXAMPLEIndependent variables.(1) Violence of video with two levels:

Violent video & Neutral video.(2) Gender with two levels:

Male & Female.Dependent variable:Feelings of aggressionMeasured by the number of aggressive associates to ambiguous words e.g. cuff - “shirt” or “punch”.

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EXAMPLEThis is a factorial experiment Each level of each independent variable occurs with each level of the other factor:

male subjects see the violent videomale subjects see the neutral videofemale subjects see the violent videofemale subjects see the neutral video

It is also an independent groups experimentDifferent subjects in each condition

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SUMMARY OF EXPERIMENTViolence of Video

(IV1)

Neutral(level 1)

Violent(level 2)

Gender of Subject (IV2)

Male (level 1) Group 1 Group 2

Female (level 2) Group 3 Group 4

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Experiment referred to as a: 2 x 2 unrelated (between subjects) experiment


EXAMPLEDesign permits three hypotheses:1 Main effect

The effect of type of video on aggression Seeing a violent video will produce more feelings of aggression than seeing a neutral video

2 Main effectThe effect of gender on aggression Males will generally feel more aggressive then females, regardless of video

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EXAMPLE

3 Interaction effect

The interaction of type of video and gender

Relative to the neutral video, violent video affects males more than females.

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EXAMPLEType of Video

neutral video

violent video

Condition Means (gender)

Gender

Male 6.2 7.7 6.95Female 5.1 6.5 5.80Condition Means (video)

5.65 7.10

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EXAMPLE Result 1 – Main effectThe effect of type of video on aggression • 5.65 (neutral) vs 7.1

(violent) • The violent video produces

a higher aggression score than the neutral video

• This result needs to be confirmed with a statistical test Series1

0123456789

10

5.65

7.10

Neutral

Violent

Video type

Aggr

essi

on s

core

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EXAMPLE Result 2 – Main effect• The effect of gender on

aggression • 6.95 (male) vs 5.80

(female)• Males produce higher

aggression scores than females

• This result needs to be confirmed with a statistical test Series1

0123456789

10

6.955.8

malefemale

Gender

Aggr

essi

on s

core

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EXAMPLE Result 3 – InteractionThe interaction of type of video and genderThere seems to be no interaction effect (if lines are parallel usually the case)i.e. The violent video doesn’t seem to have a greater effect on males than females

Neutral Violent012345678

Figure 1. Effect of video type and gender on ag-

gression scores

MaleFe-male

Video Type

Agg

ress

ion

Scor

e

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PROGRESSION POINT

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Factorial Experiments

Example 1

Overview

Example 2

Other designs


FACTORIAL DESIGNSSingle factor experiments deal with one independent variableMost psychological phenomena are governed by several independent variablesOften these variables have combined or interactive effectsThus need to look at several factors in the same experimentUse Factorial Designs

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FACTORIAL DESIGNSFactorial design: each level of each variable is combined with each level of every other variable Factorial designs provide information about:The effect of each IV on its own, called the main effectsThe effect of each combination of IVs, called the interaction effect

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FACTORIAL DESIGNSComplexity can vary in (1) number of independent variables and (2) number of levels of each independent variable Describing a factorial design:m x n – two Independent variables, one with m levels, the other with n levels l x m x n – three independent variables, one with l levels, one with m levels and one with n levelsSee over for examples

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FACTORIAL DESIGNS

Video type (IV1)

neutral violent

Gender(IV2)

male

female

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NOTE: If there is no interaction the results of the simplest design (2 x 2) can be interpreted directly without further post hoc comparisons

Example: A 2 x 2 factorial design


FACTORIAL DESIGNS

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Video type (IV1)

caring neutral violent

Gender (IV2)

male

female

Example: A 2 x 3 factorial design

When there are three or more levels of an independent variable post hoc tests will be required if the main effect involves that variable, or if there is an interaction


FACTORIAL DESIGNSAdvantages of Factorial DesignsEconomical - looks at more than one variable at a time.Interactive - can look at the combined effects of variablesCaution with factorial designsInterpretation of results becomes problematic as:

the number of levels of each variable increasesE.g. 2 x 2 ; 3 x 3; 4 x 4; etc

the number of factors increasesE.g. 2 x 2; 2 x 2 x 2; 2 x 2 x 2 x 2

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PROGRESSION POINT

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Example 1

Overview

Example 2

Other designs


EXAMPLE 2 (WITH SIGNIFICANT INTERACTION)

Hypothetical experiment:Effects of alcohol and sleep deprivation on driving performance

Independent variables1. Amount of alcohol: 0 mls. vs 50 mls.2. Amount of sleep deprivation: 4 hrs vs 12 hrs

Dependent variableNumber of mistakes on simulator

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EXAMPLESleep deprivation4 hrs 12 hrs Condition

Means (alcohol)

Amount ofAlcohol

zero millilitres 10.67 12.67 11.6750 millilitres 15.00 26.00 20.50

Condition Means (sleep deprivation)

12.84 19.34

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EXAMPLEThee results have to be tested: two main effects and one interaction1. Main effect of alcohol2. Main effect of sleep deprivation3. Interaction between alcohol and sleep deprivation

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EXAMPLE 2: MAIN EFFECT OF ALCOHOL

0 mls 50 mls05

10152025

11.67

20.5

Amount of alcohol

Number of errors

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Figure 1: Effect of amount of alcohol on number of errors


EXAMPLE 2 MAIN EFFECT OF SLEEP DEPRIVATION

4 hrs 12 hrs05

10152025

12.84

19.3

Amount of sleep deprivation

Number of errors

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Figure 2: Effect of amount of sleep deprivation on number of errors


EXAMPLE 2 INTERACTION

4 hrs 24 hrs05

1015202530

10.67 12.6715

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0 mls50 mls

Amount of sleep deprivation

Number of errors

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Figure 3: Effect of the interaction of amount of alcohol and amount of sleep deprivation on number of errors


PROGRESSION POINT

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Example 1

Overview

Example 2

Other designs


OTHER FACTORIAL DESIGNS: MORE LEVELSSleep deprivation

4 hrs 12 hrs 24 hrsAmount of alcohol

0 mls Group 1 Group 2 Group 3



RM3 - Topic 4

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This is a 3 x 3 unrelated (between subjects) designYields: Two main effects and one interaction effect . Post hoc comparisons are needed to see where the differences lie because one variable has three levels


OTHER FACTORIAL DESIGNS: MORE INDEPENDENT VARIABLES

4 hrs sleep deprivation

12 hrs sleep deprivation

caffeine no caffeine

caffeine no caffeine

0 mls alcohol Group 1 Group 2 Group 3 Group 4

50 mls alcohol Group 5 Group 6 Group 7 Group 8

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This is a 2 x 2 x 2 unrelated design: variables are (1) sleep deprivation, (2) amount of alcohol and (3) amount of caffeine

Yields: three main effects and four interaction effects. Post hoc comparisons may be needed


OTHER FACTORIAL DESIGNS: MIXED

Sleep deprivation4 hrs 24 hrs

Amount ofAlcohol

0 millilitres Group 1 Group1

50 millilitres Group 2 Group 2

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This is a 2 x 2 mixed design: same subjects for one variable; different subjects for the other variable

Yields two main effects and one interaction effect but analysis is different


LEARNING OUTCOMESExplain why factorial designs are importantIdentify the information that comes from a factorial designExplain the terms “Main Effects” and “Interaction Effect”Identify the advantages and cautions of factorial designsOutline the nature of more complex designs

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READINGHowitt, D & Cramer, D (1997) An Introduction to Statistics in Psychology. Chapter 22 (two-way analysis of variance for unrelated scores) and chapter 24 (More complex designs).Howitt, D & Cramer, D (1999) Introduction to SPSS in Psychology. Chapter 22 (two-way analysis of variance for unrelated) and (optional) chapter 24 (analysis of covariance and two-way mixed designs).

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Factorial Designs