PSY200
ProblemSet5
1.
Thefollowingdatarepresenttheresultsfromanindependent-measures(i.e.,betweensubjects)
experimentcomparingthreetreatmentconditions.
TreatmentI
0
0
2
1
2
M=1
SS=4
DataSet#1
TreatmentII
2
4
0
1
3
M=2
SS=10
TreatmentIII
5
6
4
7
8
M=6
SS=10
N=15
G=45
2
ΣX =229
Intheabovedata(DataSet#1),thetreatmentsweresignificantlydifferentprimarilybecausethemean
fortreatmentIIIisnoticeablydifferentfromtheothertwosamples(M1=1,M2=2,M3=6).Feelfreeto
conducttheANOVAwithDataSet#1aboveifyouwantextrapractice,butyoudon’thaveto;thisdatawill
beusedforthesakeofcomparisonwiththecalculationsyouwilldoonDataSet#2.Herearetheresultsof
theANOVAfromDataSet#1:
Source SS
df
MS
Betweentreatments
70
2
35
Withintreatments
24
12
2
F(2,12)=17.50
Total 94
14
Forthefollowingdata(DataSet#2below)wehavetakenthescoresfromDataSet#1andreducedthe
differencesbetweentreatmentsbymovingthetreatmentIIImeanclosertotheothertwogroups.
Specifically,wehavesubtracted3pointsfromeachscoreinthethirdgrouptoproducesamplemeansof
M1=1,M2=2,M3=3.
TreatmentI
0
0
2
1
2
M=1
SS=4
a.
b.
DataSet#2
TreatmentII
2
4
0
1
3
M=2
SS=10
TreatmentIII
2
3
1
4
5
M=3
SS=10
N=15
G=30
2
ΣX =94
Beforeyoubeginanycalculations,predicthowthechangesinthedatashouldinfluencethe
outcomeoftheanalysis.Thatis,howwilltheF-ratioforDataSet#2comparewiththeF-ratio
fromDataSet#1?
Useananalysisofvariancewithα=.05todeterminewhetherthereareanysignificant
differencesamongthethreetreatmentsinDataSet#2.Doesyouransweragreewithyour
predictioninpart(a)?
2.
Considerthefollowingdata:
TreatmentI
2
6
2
6
M=4
SS=16
DataSet#3
TreatmentII
3
7
6
4
M=5
SS=10
TreatmentIII
7
5
4
8
M=6
SS=10
N=12
G=60
2
ΣX =344
InDataSet#3,thethreesamplemeansareclosetogetherandtherearenosignificantmeandifferences.
FeelfreetoconducttheANOVAwithDataSet#3aboveifyouwantextrapractice,butyoudon’thaveto;
thisdatawillbeusedforthesakeofcomparisonwiththecalculationsyouwilldoonDataSet#4.Hereare
theresultsoftheANOVAfromDataSet#3:
Source SS
df
MS
Betweentreatments
8
2
4
Withintreatments
36
9
4
F(2,9)=1.0
2
Total 44
11
η =8/44=.18=18%
Toconstructthefollowingdata(DataSet#4,below),westartedwiththescoresinDataSet#3andthen
increasedthesizeofthemeandifferences.Specifically,weloweredthesmallestmeanbysubtracting2
pointsfromeachscoreintreatmentI,andweincreasedthelargestmeanbyadding2pointstoeachscore
intreatmentIII.Asaresult,thethreesamplemeansinDataSet#4arenowmuchmorespreadout.
TreatmentI
0
4
0
4
M=2
SS=16
a.
b.
DataSet#4
TreatmentII
3
7
6
4
M=5
SS=10
TreatmentIII
9
7
6
10
M=8
SS=10
N=12
G=60
2
ΣX =408
UseanANOVAwithα=.05todeterminewhetherthereareanysignificantdifferencesamongthe
threetreatmentsinDataSet#4.ComparetheoutcomewiththeresultsfromDataSet#3.
2
Computeη forDataSet#4.ComparetheoutcomewiththeresultfromDataSet#3.
3.
4.
Theresultsfromanindependent-measures(i.e.,betweensubjects)researchstudyindicatethatthereare
significantdifferencesbetweentreatments,F(3,36)=3.28,p<.05.
a. Howmanytreatmentconditionswerecomparedinthestudy?
b. Howmanyindividualsparticipatedintheentirestudy?
ThefollowingsummarytablepresentstheresultsfromanANOVAcomparingthreetreatmentconditions
withn=8participantsineachtreatment.Completeallmissingvalues.
Source
BetweenTreatments
WithinTreatments
Total
SS
?
?
124
df
?
?
?
MS
20
?
F=?
5.
6.
Acommonscience-fairprojectinvolvestestingtheeffectsofmusiconthegrowthofplants.Foroneof
theseprojects,asampleof40newlysproutedbeanplantsisobtained.Theseplantsarerandomly
assignedtofourtreatments,withn=10ineachgroup.Thefourconditionsarerock,heavymetal,
country,andclassicalmusic.Thedependentvariableistheheightofeachplantafter2weeks.Thedata
fromthisexperimentwereexaminedusinganANOVA,andtheresultsaresummarizedinthefollowing
table.Fillinallmissingvalues.
Source
SS
df
MS
BetweenTreatments
72
?
?
F=?
WithinTreatments
?
?
3
Total
?
?
Thefollowingdatawereobtainedfromarepeated-measures(i.e.,withinsubjects)studycomparingthree
treatmentconditions.
Subject
A
B
C
D
TreatmentI
6
5
1
0
T=12
SS=26
TreatmentII
8
5
2
1
T=16
SS=30
TreatmentIII
10
5
3
2
T=20
SS=38
P
24
15
6
3
G=48
2
ΣX =294
UsearepeatedmeasuresANOVAwithα=.05todeterminewhetherthesedataaresufficientto
demonstratesignificantdifferencesbetweenthetreatments.
7.
Thefollowingmatrixpresentstheresultsofatwo-factorexperimentwithtwolevelsoffactorA,two
levelsoffactorB,andn=10subjectsineachtreatmentcondition.Eachvalueinthematrixisthemean
scoreforthesubjectsinthattreatmentcondition.Noticethatoneofthemeanvaluesismissing.
A1
FactorA
a.
b.
8.
A2
FactorB
fB1
B2
10
50
40
??
Whatvalueshouldbeassignedtothemissingmeansothattheresultingdatawouldshowno
maineffectforfactorA?Hint:startbycalculatingthemarginalmeansforthetableabove.
Whatvalueshouldbeassignedtothemissingmeansothatthedatawouldshownointeraction?
Hint:startbyplottingthevalueslistedinthetableabove.
Thefollowingdatashowtheresultsofatwo-factorexperimentwithn=10ineachtreatmentcondition
(cell):
A1
FactorA
A2
FactorB
B1
B2
M=4
M=2
SS=40
SS=50
M=3
SS=50
2
ΣX =480
M=1
SS=40
a.
b.
c.
Sketchagraphshowingtheresultsofthisexperiment.
Lookatyourgraph:doesthereappeartobeanAXBinteraction?DoesfactorAappeartohave
anyeffect?DoesfactorBappeartohaveanyeffect?
EvaluatethesedatausinganANOVAwithα=.05.Note:becarefulnottoswitchtheeffectsfor
FactorAandFactorB.