Experimental Design and Analysis for Psychology

192 Pages·2.09 MB·English

by  Williams L.J., Krishnan A., Abdi H

oxford
[R] Companion for
Experimental
Design and Analysis
for Psychology
Lynne J. Williams,
Anjali Krishnan & Hervé Abdi
OXFORDUNIVERSITY
PRESS
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⃝c
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Preface
You have successfully designed your first experiment, run the subjects,
andyouarefacedwithamountainofdata. What’snext?1 Doescomputing
an analysis of variance by hand suddenly appear mysteriously attractive?
Granted,writingan[R]programandactuallygettingittorunmayappear
to be quite an intimidating task for the novice, but fear not! There is no
time like the present to overcome your phobias. Welcome to the wonder-
fulworldof[R]
The purpose of this book is to introduce you to relatively simple [R]
programs. Each of the experimental designs introduced in Experimental
DesignandAnalysisforPsychologybyAbdi,etal. arereprintedherein,fol-
lowed by their [R] code and output. The first chapter covers correlation,
followed by regression, multiple regression, and various analysis of vari-
ance designs. We urge you to familiarize yourself with the [R] codes and
[R]output,astheyintheirrelativesimplicityshouldalleviatemanyofyour
anxieties.
We would like to emphasize that this book is not written as the tuto-
rial in the [R] programming language. For that there are several excellent
books on the market. Rather, use this manual as your own cook book of
basic recipies. As you become more comfortable with [R], you may want
toaddsomeadditionalflavorstoenhanceyourprogramsbeyondwhatwe
havesuggestedherein.
1Panicisnottheanswer!
ii 0.0
⃝c 2009Williams,Krishnan&Abdi
Contents
Preface i
1 Correlation 1
1.1 Example: WordLengthandNumberofMeanings . . . . . . . 1
1.1.1 [R]code . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.2 [R]output . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 SimpleRegressionAnalysis 7
2.1 Example: MemorySetandReactionTime . . . . . . . . . . . 7
2.1.1 [R]code . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.2 [R]output . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3 MultipleRegressionAnalysis: OrthogonalIndependentVariables 13
3.1 Example: RetroactiveInterference . . . . . . . . . . . . . . . . 13
3.1.1 [R]code . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.1.2 [R]output . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4 MultipleRegressionAnalysis:Non-orthogonalIndependentVari-
ables 21
4.1 Example: Age,SpeechRateandMemorySpan . . . . . . . . . 21
4.1.1 [R]code . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.1.2 [R]output . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5 ANOVAOneFactorBetween-Subjects,𝒮(𝒜) 27
5.1 Example: ImageryandMemory . . . . . . . . . . . . . . . . . 27
5.1.1 [R]code . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.1.2 [R]output . . . . . . . . . . . . . . . . . . . . . . . . . . 28
5.1.3 ANOVAtable . . . . . . . . . . . . . . . . . . . . . . . 30
5.2 Example: RomeoandJuliet . . . . . . . . . . . . . . . . . . . . 30
5.2.1 [R]code . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
5.2.2 [R]output . . . . . . . . . . . . . . . . . . . . . . . . . . 32
5.3 Example: FacePerception,𝒮(𝒜)with𝒜random . . . . . . . . 34
5.3.1 [R]code . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
5.3.2 [R]output . . . . . . . . . . . . . . . . . . . . . . . . . . 35
5.3.3 ANOVAtable . . . . . . . . . . . . . . . . . . . . . . . 37
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5.4 Example: Images... . . . . . . . . . . . . . . . . . . . . . . . . 38
5.4.1 [R]code . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.4.2 [R]output . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5.4.3 ANOVAtable . . . . . . . . . . . . . . . . . . . . . . . 40
6 ANOVAOneFactorBetween-Subjects: RegressionApproach 41
6.1 Example: ImageryandMemoryrevisited . . . . . . . . . . . . 42
6.1.1 [R]code . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
6.1.2 [R]output . . . . . . . . . . . . . . . . . . . . . . . . . . 43
6.2 Example: RestagingRomeoandJuliet . . . . . . . . . . . . . . 45
6.2.1 [R]code . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
6.2.2 [R]output . . . . . . . . . . . . . . . . . . . . . . . . . . 47
7 PlannedOrthogonalComparisons 51
7.1 ContextandMemory . . . . . . . . . . . . . . . . . . . . . . . 51
7.1.1 [R]code . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
7.1.2 [R]output . . . . . . . . . . . . . . . . . . . . . . . . . . 55
7.1.3 ANOVAtable . . . . . . . . . . . . . . . . . . . . . . . 59
8 PlannedNon-orthogonalComparisons 61
8.1 Classicalapproach: Testsfornon-orthogonalcomparisons . 61
8.2 RomeoandJuliet,non-orthogonalcontrasts . . . . . . . . . . 62
8.2.1 [R]code . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
8.2.2 [R]output . . . . . . . . . . . . . . . . . . . . . . . . . . 65
8.3 MultipleRegressionandOrthogonalContrasts . . . . . . . . 70
8.3.1 [R]code . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
8.3.2 [R]output . . . . . . . . . . . . . . . . . . . . . . . . . . 73
8.4 MultipleRegressionandNon-orthogonalContrasts . . . . . 78
8.4.1 [R]code . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
8.4.2 [R]output . . . . . . . . . . . . . . . . . . . . . . . . . . 82
9 Posthocora-posteriorianalyses 87
9.1 Scheffe´’stest . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
9.1.1 RomeoandJuliet . . . . . . . . . . . . . . . . . . . . 88
9.1.2 [R]code . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
9.1.3 [R]output . . . . . . . . . . . . . . . . . . . . . . . . . . 91
9.2 Tukey’stest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
9.2.1 ThereturnofRomeoandJuliet . . . . . . . . . . . . 96
9.2.1.1 [R]code . . . . . . . . . . . . . . . . . . . . . 97
9.2.1.2 [R]output . . . . . . . . . . . . . . . . . . . . 100
9.3 Newman-Keuls’test . . . . . . . . . . . . . . . . . . . . . . . . 106
9.3.1 TakingoffwithLoftus... . . . . . . . . . . . . . . . . 106
9.3.1.1 [R]code . . . . . . . . . . . . . . . . . . . . . 107
9.3.1.2 [R]output . . . . . . . . . . . . . . . . . . . . 112
9.3.2 Guesswho? . . . . . . . . . . . . . . . . . . . . . . . 119
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9.3.2.1 [R]code . . . . . . . . . . . . . . . . . . . . . 119
9.3.2.2 [R]output . . . . . . . . . . . . . . . . . . . . 122
10 ANOVATwoFactors;𝑆(𝒜×ℬ) 129
10.1 CuteCuedRecall . . . . . . . . . . . . . . . . . . . . . . . . . . 129
10.1.1 [R]code . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
10.1.2 [R]output . . . . . . . . . . . . . . . . . . . . . . . . . . 133
10.1.3 ANOVAtable . . . . . . . . . . . . . . . . . . . . . . . 139
10.2 ProjectiveTestsandTestAdministrators . . . . . . . . . . . . 139
10.2.1 [R]code . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
10.2.2 [R]output . . . . . . . . . . . . . . . . . . . . . . . . . . 140
10.2.3 ANOVAtable . . . . . . . . . . . . . . . . . . . . . . . 143
11 ANOVAOneFactorRepeatedMeasures,𝒮 ×𝒜 145
11.1 𝒮 ×𝒜design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
11.1.1 [R]code . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
11.1.2 [R]output . . . . . . . . . . . . . . . . . . . . . . . . . . 146
11.2 Drugsandreactiontime . . . . . . . . . . . . . . . . . . . . . 148
11.2.1 [R]code . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
11.2.2 [R]output . . . . . . . . . . . . . . . . . . . . . . . . . . 150
11.2.3 ANOVAtable . . . . . . . . . . . . . . . . . . . . . . . 152
11.3 ProactiveInterference . . . . . . . . . . . . . . . . . . . . . . . 152
11.3.1 [R]code . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
11.3.2 [R]output . . . . . . . . . . . . . . . . . . . . . . . . . . 154
11.3.3 ANOVAtable . . . . . . . . . . . . . . . . . . . . . . . 156
12 TwoFactorsRepeatedMeasures,𝒮 ×𝒜×ℬ 157
12.1 Plungin’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
12.1.1 [R]code . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
12.1.2 [R]output . . . . . . . . . . . . . . . . . . . . . . . . . . 160
12.1.3 ANOVAtable . . . . . . . . . . . . . . . . . . . . . . . 164
13 FactorialDesign,PartiallyRepeatedMeasures: 𝒮(𝒜)×ℬ 165
13.1 BatandHat.... . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
13.1.1 [R]code . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
13.1.2 [R]output . . . . . . . . . . . . . . . . . . . . . . . . . . 167
13.1.3 ANOVAtable . . . . . . . . . . . . . . . . . . . . . . . 171
14 NestedFactorialDesign: 𝒮 ×𝒜(ℬ) 173
14.1 FacesinSpace . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
14.1.1 [R]code . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
14.1.2 [R]output . . . . . . . . . . . . . . . . . . . . . . . . . . 175
14.1.3 F andQuasi-F ratios . . . . . . . . . . . . . . . . . . . . 178
14.1.4 ANOVAtable . . . . . . . . . . . . . . . . . . . . . . . 179
Index 183
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⃝c 2009Williams,Krishnan&Abdi
1
Correlation
1.1 Example:
Word Length and Number of Meanings
Ifyouareinthehabitofperusingdictionariesasawayofleisurelypassing
time, you may have come to the conclusion that longer words apparently
have fewer meanings attributed to them. Now, finally, through the mira-
cleofstatistics,ormoreprecisely,thePearsonCorrelationCoefficient,you
neednolongerponderthisquestion.
We decided to run a small experiment. The data come from a sample
of20wordstakenrandomlyfromtheOxfordEnglishDictionary. Table1.1
onthefollowingpagegivestheresultsofthissurvey.
AquicklookatTable1.1onthenextpagedoesindeedgivetheimpres-
sion that longer words tend to have fewer meanings than shorter words
(e.g., compare“by”with“tarantula”.) Correlation, ormorespecificallythe
Pearson coefficient of correlation, is a tool used to evaluate the similar-
ityoftwosetsofmeasurements(ordependentvariables)obtainedonthe
same observations. In this example, the goal of the coefficient of corre-
lation is to express in a quantitative way the relationship between length
andnumberofmeaningsofwords.
For a more detailed description, please refer to Chapter 2 on Correla-
tioninthetextbook.
1.1.1 [R] code
# Correlation Example: Word Length and Number of Meanings
# We first enter the data under two different variables names
Length=c(3,6,2,6,2,9,6,5,9,4,7,11,5,4,3,9,10,5,4,10)
Meanings=c(8,4,10,1,11,1,4,3,1,6,2,1,9,3,4,1,3,3,3,2)
data=data.frame(Length,Meanings)
Mean=mean(data)
Std_Dev=sd(data)
# We now plot the points and SAVE it as a PDF
# Make sure to add the PATH to the location where the plot is
2 1.1 Example: WordLengthandNumberofMeanings
Numberof
Word Length Meanings
bag 3 8
buckle 6 4
on 2 10
insane 6 1
by 2 11
monastery 9 1
relief 6 4
slope 5 3
scoundrel 9 1
loss 4 6
holiday 7 2
pretentious 11 1
solid 5 9
time 4 3
gut 3 4
tarantula 9 1
generality 10 3
arise 5 3
blot 4 3
infectious 10 2
TABLE1.1Length(i.e.,numberofletters)andnumberofmeaningsofarandomsampleof20wordstakenfrom
theOxfordEnglishDictionary.
# to be saved
pdf(’/home/anjali/Desktop/R_scripts/01_Correlation/corr_plot.pdf’)
plot(Length,Meanings,main="Plot of Length vs Meanings")
dev.off()
# We now perform a correlation and a test on the data which gives
# confidence intervals
cor1=cor.test(Length, Meanings,method = c("pearson"))
# We now perform a regression analysis on the data
reg1=lm(Length˜Meanings)
# We now perform an ANOVA on the data
aov1=aov(Length˜Meanings)
# We now print the data and all the results
print(data)
print(Mean)
print(Std_Dev)
print(cor1)
summary(reg1)
summary(aov1)
⃝c 2009Williams,Krishnan&Abdi