Copyright © Allyn & Bacon (2007) Factorial Designs Graziano and Raulin Research Methods: Chapter 12...

Copyright © Allyn & Bacon (2007)Copyright © Allyn & Bacon (2007)

Factorial DesignsFactorial Designs

Graziano and RaulinGraziano and RaulinResearch Methods: Chapter 12Research Methods: Chapter 12This multimedia product and its contents are protected under copyright law. The following are This multimedia product and its contents are protected under copyright law. The following are prohibited by law: (1) Any public performance or display, including transmission of any image prohibited by law: (1) Any public performance or display, including transmission of any image over a network; (2) Preparation of any derivative work, including the extraction, in whole or in over a network; (2) Preparation of any derivative work, including the extraction, in whole or in part, of any images; (3) Any rental, lease, or lending of the program.part, of any images; (3) Any rental, lease, or lending of the program.


Factorial DesignsFactorial Designs

Includes two or more independent Includes two or more independent variablesvariables

Essentially two (or more) studies in oneEssentially two (or more) studies in one By testing more than one independent By testing more than one independent

variable at a time, we can look at the variable at a time, we can look at the interactive effectsinteractive effects of independent of independent variablesvariables

Most independent variables in psychology Most independent variables in psychology interact with other independent variablesinteract with other independent variables


Main Effects and Main Effects and InteractionsInteractions The effect of each of the The effect of each of the

independent variables on the independent variables on the dependent variable is the dependent variable is the main main effecteffect of that variable of that variable

The combined effect of two or more The combined effect of two or more independent variables on the independent variables on the dependent variable (i.e., more than dependent variable (i.e., more than just a sum of the main effects) is an just a sum of the main effects) is an interactioninteraction


Graphing Factorial Graphing Factorial DesignsDesigns For two independent variables (IV)For two independent variables (IV)

– Select one independent variable, and label Select one independent variable, and label the the XX-axis with the levels of that variable-axis with the levels of that variable

– Label the Label the YY-axis with enough range to -axis with enough range to graph the mean scores of each cellgraph the mean scores of each cell

– Graph and label the means from the first Graph and label the means from the first level of the second independent variable level of the second independent variable and label that lineand label that line

– Repeat that process for each level of the Repeat that process for each level of the other independent variables, labeling each other independent variables, labeling each lineline


Sample Data to GraphSample Data to Graph

A1 A2

B1 10 20

B2 20 40

B3 50 40


Graph of Previous Graph of Previous SlideSlide

05101520253035404550

B1 B2 B3

A1

A2


Possible OutcomesPossible Outcomes


Factorial ANOVAFactorial ANOVA

ANOVA can analyze any factorial designANOVA can analyze any factorial design The number of effects will depend on The number of effects will depend on

the number of independent variables the number of independent variables (IVs)(IVs)– 2 IVs: A & B main effects; AB interaction2 IVs: A & B main effects; AB interaction– 3 IVs: A, B, & C main effects; AB, AC, BC, & 3 IVs: A, B, & C main effects; AB, AC, BC, &

ABC interactionsABC interactions– 4 IVs: A, B, C, & D main effects; AB, AC, 4 IVs: A, B, C, & D main effects; AB, AC,

AD, BC, BD, CD, ABC, ABD, BCD, & ABCD AD, BC, BD, CD, ABC, ABD, BCD, & ABCD interactionsinteractions

– 5 IVs: You DON’T want to know!5 IVs: You DON’T want to know!


Example: Children’sExample: Children’sDark Fears StudyDark Fears Study Two factorsTwo factors

– Level of illumination (lighted or dark)Level of illumination (lighted or dark)– Images (frightening or neutral)Images (frightening or neutral)

Test hypothesis that fear of the Test hypothesis that fear of the dark in children is really a fear of dark in children is really a fear of darkness and frightening darkness and frightening thoughts or imagesthoughts or images


Factorial Design LogicFactorial Design Logic


Study DesignStudy Design

Factor AFactor A(Illumination)(Illumination)

Factor BFactor B(images)(images)

Level ALevel A11

(lighted)(lighted)Level ALevel A22

(dark)(dark)

Level BLevel B11

(feared)(feared)

Level BLevel B22

(neutral)(neutral)


Mean ScoresMean Scores

Factor AFactor A(Illumination)(Illumination)

Factor BFactor B(images)(images)

Level ALevel A11

(lighted)(lighted)Level ALevel A22

(dark)(dark)

Level BLevel B11

(feared)(feared) 98.398.3 114.1114.1

Level BLevel B22

(neutral)(neutral) 98.198.1 99.999.9


ANOVA Summary TableANOVA Summary Table

SourceSource dfdf SSSS MSMS FF pp

Factor AFactor A

(illumination)(illumination)11 765.62765.62 765.62765.62 7.887.88 .008.008

Factor BFactor B

(images)(images)11 525.62525.62 525.62525.62 5.415.41 .026.026

AB InteractionAB Interaction 11 497.02497.02 497.02497.02 5.125.12 .030.030

ErrorError 3636 3497.503497.50 97.1597.15

TotalTotal 3939 5285.785285.78


Evaluating Main Evaluating Main EffectsEffects

Evaluating main Evaluating main effects involveseffects involves– Looking at all the Looking at all the

people tested people tested under each level a under each level a Factor A Factor A regardless of the regardless of the level of Factor Blevel of Factor B

– Doing the same Doing the same for Factor B, as for Factor B, as shown hereshown here


Evaluating InteractionsEvaluating Interactions

The interaction is The interaction is best seen by best seen by graphing the graphing the resultsresults

The fact that the The fact that the lines are not lines are not parallel suggests parallel suggests an interaction, an interaction, which is confirmed which is confirmed by the ANOVAby the ANOVA


Repeated-Measures Repeated-Measures FactorialsFactorials Within-subjects design (also called Within-subjects design (also called

repeated measures design) repeated measures design) As with all within-subjects designs, As with all within-subjects designs,

sequence effects must be controlledsequence effects must be controlled The ANOVA will have to take into The ANOVA will have to take into

account that the same participants account that the same participants appear in all of the conditionsappear in all of the conditions


Mixed DesignsMixed Designs

The IVs do not have to be the The IVs do not have to be the same (e.g., all within-subjects or all same (e.g., all within-subjects or all between-subjects)between-subjects)– Mixed (within-subjects & between-Mixed (within-subjects & between-

subjects): the ANOVA must take this subjects): the ANOVA must take this into accountinto account

– Mixed (manipulated & Mixed (manipulated & nonmanipulated): will affect the nonmanipulated): will affect the interpretation interpretation

– Mixed in both senses is also possibleMixed in both senses is also possible


Between and WithinBetween and Within

Level of DistractionLevel of Distraction

(within-subjects factor)(within-subjects factor)

LowLow MediumMedium HighHigh

Amount of RewardAmount of Reward

(between-subjects(between-subjectsfactor)factor)

SmallSmall

LargeLarge


Manipulated and Manipulated and NonmanipulatedNonmanipulated

Level of CrowdingLevel of Crowding

(manipulated factor)(manipulated factor)

NoneNone SlightSlight VeryVery

Sex of ParticipantSex of Participant

(nonmanipulated(nonmanipulatedfactor)factor)

MaleMale

FemaleFemale


Mixed in Both WayMixed in Both Way

Type of WordsType of Words(within-subjects factor)(within-subjects factor)

(manipulated factor)(manipulated factor)

NeutralNeutral EmotionalEmotional

DiagnosisDiagnosis(between-subjects (between-subjects

factor)factor)

(nonmanipulated(nonmanipulatedfactor)factor)

SchizophreniSchizophrenicc

NormalNormal


Another Look at the Another Look at the Solomon Four-Group Solomon Four-Group DesignDesign Introduced in Chapter 10Introduced in Chapter 10 CombinesCombines

– Pretest-posttest control-group designPretest-posttest control-group design– Posttest-only control-group designPosttest-only control-group design

Allows us to look at whether the Allows us to look at whether the treatment interacts with the pretesttreatment interacts with the pretest– The word “interact” should suggest The word “interact” should suggest

that this is really a factorial designthat this is really a factorial design


Solomon’sSolomon’sFour-Group DesignFour-Group Design


Solomon Four-Group Solomon Four-Group Design as a FactorialDesign as a Factorial

TreatmentTreatment No No TreatmentTreatment

PretestPretest Group AGroup A Group BGroup B

No PretestNo Pretest Group CGroup C Group DGroup D


Variations on ANOVAVariations on ANOVA

ANOVA is a flexible analysis approachANOVA is a flexible analysis approach– Handles any number of IVs and any Handles any number of IVs and any

combination of within-subjects and combination of within-subjects and between-subjects factorsbetween-subjects factors

Variations of ANOVAVariations of ANOVA– ANCOVA (Analysis of Covariance)ANCOVA (Analysis of Covariance)– MANOVA (Multivariate Analysis of Variance)MANOVA (Multivariate Analysis of Variance)

Easy to do with statistical analyses Easy to do with statistical analyses programsprograms


SummarySummary

Factorial designs are like running two or Factorial designs are like running two or more studies at oncemore studies at once

Factorial studies are the only way to Factorial studies are the only way to study the interaction of independent study the interaction of independent variablesvariables

ANOVA will analyze factorial studiesANOVA will analyze factorial studies Factors may be mixedFactors may be mixed

– within-subjects and between-subjects factorswithin-subjects and between-subjects factors– manipulated and nonmanipulated factorsmanipulated and nonmanipulated factors– mixed in both sensesmixed in both senses

Copyright © Allyn & Bacon (2007) Factorial Designs Graziano and Raulin Research Methods: Chapter 12...

Documents

Transcript of Copyright © Allyn & Bacon (2007) Factorial Designs Graziano and Raulin Research Methods: Chapter 12...