age R2 for age when it was considered value was reduced

advertisement
Copyright
1993by theAmericanPsycholosicallAssmrldllijlb
DevelopmentalPsychology
1993.vol. 29. No. 4. 722-73E
in Cognition
SpeedMediationof Adult AgeDifferences
Timothy A. Salthouse
Previous researchhas establishedthat a large proportion of the adult age-relatedvariance in
various measuresoffluid or processcognition is reducedwhen statisticalcontrol proceduressuch
as hierarchical regressionare used to eliminate variation in measuresofperceptual speed.This
finding was confirmed in the presentstudy and was extendedto include paired-associateand
free-recallmeasuresof memory in addition to measuresof reasoningand spatialabilities. Most of
the speedmediation was associatedwith speedmeasuresrequiring cognitive operationssuch as
comparisonor substitution insteadof merelymotor responsessuchascopyingsymbolsor drawing
lines.Theseresultssuggestthat the rateof performing elementarycognitiveoperationsis an important proximal mediator ofthe adult agedifferencesin severaltypes ofcognitive tasks.
Inspiredlargelyby ideasof Birren (e.g.,1955,1965,1974),
Salthouse0985a) proposed that the adult age differencesin
certain measuresof cognitive functioning might be partially
mediated by age-relatedreductionsin the speedofexecuting
relevantmental operations.The evidenceavailableat that time
wasratherweak,becauseno publishedstudieshad beenexplicitly designedto investigatethis hypothesis.Most of the data
relevantto the hypothesiswereobtainedby locating published
articlesreportingcorrelationsamongage,a measureof processing speed,and a measureof cognition (or studiesby Salthouse
containing the relevant data), and then computing partial
correlationsbetweenageand the cognitivemeasureafter partialing out the measureof speed.Only a few data setswith the
necessaryinformation could be identified, and the samples
wereoften small and usually involvedtwo extremeagegroups
rather than a continuous range of ages.Furthermore, in all
with a singlemeacasesthe relevantconstructswere assessed
sureratherthan with potentially more reliableand valid multiple measures.Despite these limitations, the hypothesis receivedsomesupport becausestatisticalcontrol of the measure
ofspeed frequentlyresultedin an appreciablereduction in the
magnitudeof the relation betweenageand the measureof cognition.
In the last 5 years,severalmore extensivestudieshavebeen
conductedin which data relevantto the hypothesishavebeen
reported.The major onesinvolving at least 200 adultswith an
agerangeofat least35 yearsand including severalmeasuresof
both speedand cognition are summarized in Table 1. In all
cases,the availablespeed measureshave been combined to
form a more reliablecompositeindex. (This requireda reanalysisofthe data from Salthouse,Kausler,& Saults,I 988) It can be
seenthat resultsfrom thesemore recentstudiesareclearlyconsistentwith the speed-mediationhypothesis.That is, the aver-
This researchwas supportedby National Institute on Aging Grant
in superR37 AC06826.I thank JenniferShawfor valuableassistance
vising the testingof participants and the initial analysesof the data.
concerningthis article shouldbe addressedto TimCorrespondence
othy A. Salthouse,SchoolofPsychology,GeorgiaInstitute ofTechnology,Atlanta,Georgia30332-0170.
ageR2 for agewhen it wasconsideredalonewas.158,but the
valuewasreducedto only.035afterthe variationin a composite measureof perceptualspeedwas controlled. Theseresults
thereforesuggestthat almost807o(i.e.,[.I 58 - .035]l I 58 = .778)
variancein certain measuresoffluid cogniofthe age-related
tion is associatedwith variationsin perceptualspeed.
The researchreported in this article was designedwith two
major goalsin mind. One goalwasto examinethe generalityof
the speed-mediationphenomenon by including measuresof
memory in addition to measuresof fluid or processaspectsof
cognition.Extendingthe researchin this direction is ofinterest, becauselessconvincingsupport for a mediationaleffectof
speedwasfound with m€asuresreflectingmemory functioning
in the partial correlation analyses reported in Salthouse
(l 985a).That is, partialinga measureofprocessingspeedhad a
smaller effecton the correlationsbetweenageand measuresof
memory than it did on the correlationsbetweenageand measuresof other types of cognitivefunctioning. Moreover,additional analyseson the data from the Salthouseet al. (1988)
project similar to those summarized in Table I also revealed
weakerattenuationofthe agerelationsficrmeasuresrepresenting memory functioning than for measuresrepresentingother
types of cognitive functioning. For example,the attenuation
was only 63.8Vofor a measureof the accuracyof reproducing
the identitiesof items in a matrix, only 4'l .59ofor a measureof
the accuracyof reproducingthe positionsof items in a matrix,
memory.
and only l6.7vofor a measureof paired-associate
memory
differthe
age-related
The smaller attenuation of
encesafter control of measuresof speedraisesthe possibility
that quicknessof mental operationsmay be a less important
factor in the agedifferencesin traditional memory teststhan in
reasoningor spatialabilities. Although
cognitivetestsassessing
this speculationis plausibleon the basisofthe availableresults,
strongerevidenceofthe differential influenceofspeed on cognitive and memory measuresis desirablebeforeone can conclude that speedfactors have a minimal role in the relations
betweenageand memory.One type of evidencethat would be
relevant in this regard would be a discovery that substantial
age-relatedeffectsremained after statistical control of a measure of perceptual speed, or equivalently,a finding that the
722
SPEED MEDIATION
relations between age and measuresof memory were attenuatedonly slightlyafter oneremovedthe variancein the perceptual speedmeasuresthat waslinearly relatedto the measuresof
memory.Severalmemory measureswerethereforeincluded in
the presentstudy to allow this implication to be investigated.
The secondmajor goal of the presentstudy wasto examinea
variety of different speedmeasuresto identify the aspectsof
speedmost responsiblefor mediating age-cognitionrelations.
Two issueswereof particularinterestin this connection.One
wasthe extentto which sensoryor motor factorswereinvolved
in the influenceofperceptualspeedon age-cognitionrelations.
Becausemost testsofperceptual speedinvolvevisual presentation of materialsand requirea written responseto communicatedecisions,sensoryand motor aspectsmay be contributing
to many measuresof perceptualspeed.In an attemptto remove
the influenceofperipheral input and output speedwhen analyzing the influenceofperceptualspeed,participantsin the present researchproject, in addition to performing more conventional perceptualspeedtests,also performed severalspeeded
taskswith minimal cognitiverequirements.
Anotherissuerelatedto the measurement
of speedconcerns
the significanceof the systematicrelationsoften reported betweenthe averagetimes ofyoung and old adultsacrossdifferent
combinationsof speededtasks.Many researchershave found
that thereis frequentlyan orderlyrelationbetweenthe response
timesof youngadultsacrossa rangeofexperimentalconditions
or tasksand the responsetimes of older adultsin thosesame
conditionsor tasks(e.g.,Brinley,1965;Cerella,1985,l99l;
Lima, Hale,& Myerson,199l; Myerson,Hale,Wagstaff,poon,
& Smith,1990;Salthouse,
1985a,I 985b).Ir is possibleto disringuishbetweenstrongandweakpositionsregardingthetheoretical significance
of thesesystematicrelations.The strongposition emphasizes
the quantitativeform of the relationbetween
the times of youngand old adultsbecauseof the assumption
that the relationis informativeabout both the magnitudeand
the natureof the age-related
slowingevidentacrossmany measuresof speededperformance.A weakerposition maintains
that the existenceofsystematicrelationssuggests
that the agerelatedinfluenceson the variousmeasuresare not independent, but this perspectivedoes not necessarilyconsiderthe
lorm of the relationinformativeabout either the rate or the
precisenatureofage-related
slowing.That is, lack ofindependencecan be inferredifknowledgeofthe agedifferences
in one
measureprovidesinformation about the age differencesin
other measures,
but no specialsignificanceis attachedto the
parametersof the functionsrelatingthe times of youngadults
to the timesof olderadults.
The distinction betweenstrongand weak positionsregarding the systematicrelationsbetweenthe timesof adultsof diflerentagescan be elaboratedafter one first considershow these
relationsweredeterminedin the presentstudy.The initial step
involvedthe administrationof a batteryof speedtests-involving a rangeof operationsand completiontimes-to 100college
studentswho servedas the referencegroup.Scoreson eachof
thesetestswerethen convertedinto unitsof secondsper item,
with the averages
rangingfrom 0.4 s to almost2 s per item.The
nextstepin the procedureconsistedof administeringthe same
batteryof speedteststo a sampleof over300 adultsfrom a wide
rangeofages.Eachoftheseparticipants'scores
werethen con-
723
verted into the seconds-per-itemmetric and wasanalyzedin a
linear regressionequation relating those times to the average
times of the referencegroup on the sametasks.It is important
to emphasizethat unlike most previousreports of systematic
relations(but seeCharness& Campbell,1988,for an exception), these analysesare conducted at the level of individual
subjects.That is, a regressionequationwascomputed for each
subjectrelating his or her times (asthe dependentor criterion
variables)to the mean times of the studentreferencegroup (as
the independentor predictor variables).
Linear regressionequationscan be characterizedin terms of
three parameterscorrespondingto the correlation, the intercept, and the slope.The correlation is informative about the
degreeto which there is a systematic(linear)relationamongthe
variables.The intercept indicates the magnitude of an influencethat is constant acrossall variables,and the slope representsthe amount by which the individual'stime increasesfor
everyunit increasein the time of the reference
group.Of these
parameters,
the slopeis often consideredthe most interesting,
becauseit hasbeeninterpretedasa reflectionofthe magnitude
of age-related
slowing(e.g.,
Cerella,I 985,199I ; Cerella,poon.&
Williams, 1980;Lima et al.,199I ; Myersonet al., I 990).
A strong interpretationof the systematicrelationsamong
speedmeasuresis that the slopeis a direct index ofa general
speedfactor. The slope is not measuredin absoluteunits becauseit is alwaysrelativeto somereferencegroup,but it can still
be meaningfulin across-individual
comparisonsif everyoneis
evaluatedagainstthe samereference
group.A weakerposition
regardingthe systematicrelationsamong speedmeasuresis
that the slopeis merelyan indexof the relationamongvariables
that areeachdeterminedby otherinfluencesin additionto the
hypothesizedspeedfactor. Becausethe contribution of the
other influencescan be expectedto differ acrossvariables.the
weak positionviewsthe slopeas a lessdirect index of the hypothesizedspeedfactorthan manyofthe observedspeedmeasures.(SeeSalthouse,1992a.for further discussionof this distinction)
In summary,in both the strongand weak interpretations,
a
high correlationbetweenthe times of the individual and the
groupimpliesthat the measures
timesof the reference
areassociatedand not independent,but the meaningofthe slopeparameteris quite diffbrentin the two perspectives.
The strong
position maintainsthat the slopeis an important index of a
centralspeedconstructbecauseit has a specialstatusas the
mostdirect indicatorofthe hypothesized
speedfactol whereas
the weak positionviewsthe slopeas much lessinterestingbecauseit is assumedonly indirectly to reflectthe operationof
any relativelygeneralage-relatedspeedfactorsthat might exist.
Onemannerin whichthe validityof thesealternative
conceptualizationsof the systematicrelationsamongspeedmeasures
might be investigated
involvesexaminingthe strengthof linkagesbetweenvariousmeasures
ofspeedand both ageand cognition.The reasoningis asfollows.If, asthe resultssummarized
in TableI suggest,speedof processing
is an importantmediating factorin the agedifferences
in somemeasures
of cognition,
then comparisonsof the degreeto which age-cognitionrelations are attenuatedafter control ofalternative speedmeasures
may be informativeaboutthe statusof thosespeedmeasures
as
reflectionsof a common or generalspeedfactor.Specifically,
724
TIMOTHY A. SALTHOUSE
TableI
Resultsof Studies Examining the Relations Betwem Age and Cognition Beforeand After
Statistical Control of PerceptualComparison Speed
Age
range
(in years)
R2 for age
Speed
r(age - speed)
Cognition
Before
After
70attenuation
Schaie(1989)
6ll
22-84
FindA's, IDPict
-.53
628
22-84
FindA's, IDPict
-.65
Space
Reason
Space
Reason
.1 6 8
.281
.22r
.360
.036
.058
.032
.058
78.6
79.4
85.5
83.9
PMA Space
PMA Reason
Spatial Relations
SpatialVisualization
Induction
.124
.237
.209
.128
.202
.01l
.02'l
.032
.029
.02r
9r . l
88.6
84.7
't7.3
89.6
.221
.322
.097
.227
.1 8 6
.203
.1 7 8
.083
.104
.208
.024
.056
.o2l
.ol2
.050
.007
.002
.001
.022
.006
.003
.ol2
.015
.014
.029
.033
.0t2
.020
.065
.070
.009
.03'l
.012
89.l
82.6
82.r
90.7
82.9
8l.l
89.5
99.5
86.7
91 . 3
94.6
90.2
87.6
94.5
78.2
66.0
94.'l
89.2
68.0
60.7
89.2
64.4
94.2
.2tl
.006
9't.2
.328
.100
.1 8 4
.o'14
.100
.019
.092
.033
69.5
81.0
50.0
55.4
.l'12
.179
.lt2
.t37
.128
.046
.049
.082
.025
.001
.008
20.3
28.5
58.9
54.6
29.1
46.8
92.9
55.6
PMA
PMA
PMA
PMA
Hertzog ( 1989)
592
43-78
FindA's, IDPict
Number Compar.
AnswerSpeed
?
Letter Compar.
PatternCompar.
-.61
(l99la)
Salthouse
221
20-80
228
20-82
Letter Compar.
PatternCompar.
-.7|
223
20-84
ktter Compar.
PatternCompar.
-.60
Shipley# Cor.
Raven # Cor.
Shipley7oCor.
Raven 7oCor.
Working Memory
PapFld # Cor.
CubAsm # Cor.
Analog # Cor.
Reason# Cor.
PapFld 7oCor.
CubAsm 7oCor.
Analog 7oCor.
Reason7oCor.
Working Memory
PapFld # Cor.
CubAsm # Cor.
Analog # Cor.
Reason# Cor.
PapFld 7oCor.
CubAsm 7oCor.
Analog 7oCor.
Reason7oCor.
Working Memory
.l l'7
.t29
.292
.037
.019
.1 8 9
. 165
.069
.056
.t23
.t2l
.254
.IJJ
Salthouseand Babcock ( I 99 I )
233
l 8-82
Letter Compar.
PatternCompar.
-.65
Working Memory
Salthouse,Kausler,and Saults( 1988)
ZJJ
20-78
Digit Symbol
Number Compar,
.46
Analog Time
SeriesCompl.Time
Analog 7oCor.
SeriesCompl.7oCor.
Salthouse
and Mirchell(1990)
383
r 8-84
FindA's
Number Compar.
-.28
PapFld # Cor.
SurDev # Cor.
lrtSet # Cor.
Shipley# Cor.
PapFld 7oCor.
SurDev 7oCor.
LetSet7oCor.
Shipley7oCor.
. r08
.l16
.04'7
.014
.018
Note. FindAs=FindingAsTestfromEkstrom,French,Harman,andDermen(1976);IDPict=IdenticalPicturesTestfromEkstrometal.(1976);
PMA Space= SpaceTest from Primary Mental Abilities Battery (Schaie,1985);PMA Reason= ReasoningTest from Primary Mental Abilities
SPEED MEDIATION
725
Tablel bontinued\
Battery(Schaie,1985);NumberCompar.: NumbercomparisonTestfrom Ekstromet al. (1976);shipley#
cor. = numberof correctresponses
in
ShipleyAbstractionTest;Shipley%Cor..=
percentageofresponsescorrect
in ShipleyAbstractionTestjRaven#Cor.: numberofcorrectresponses
R3y"n: AdvancedProgressiveMatrices Test; Riven 7oCbr. = percentageof rlsponsescorrect in Raven's
progressive
Advanced
iL
Matrices Test;
Working Memory = compositeof ListeningSpanand Computation Spanicores;PapFld # Cor. : number
of correct responsesin a paper lolding
test; PapFld% Cor' = percentageofcorrect responsesin a paperlolding test;CubAsm# Cor. : number
ofcorrect responsisin a.uU. urr'",oUtv,.rt;
CubAsm.ToCor. : percentageof correct responsesin a cube assembly-test;
Analog # Cor. = number of correct responsesin a geometricanalogres
test; Analog 7oCor. - percentageofcorrect responsesin a geometricanalogiestest; Reason# Cor. = number
ofcoirect respon-ses
in an integrative
reasoningtest;Reason% Cor.= percentage
ofcorrectresponses
in an integfativereasoningtestgAnalojiime : mediantime percorrectresponse
in a geometricanalogies
:
test;seriescompl.Time mediin tim. p.. "or..!t ,.rponsein a si.ier "o-pt.iion t.it; ieriescompl.vo
Cor.-percentage
of correctresponses
in a seriescompletiontest;SurDev# Cor. = numberof correctresponses
in tire SurfacebevelopmentTest(Ekstromet al.,
I 976);SurDev7ocor. = percentage
ofcorrect responses
in the SurlaceDevelopmentTesi(Eksrromet al..I 976);Letset# cor. - numberofcorrect
responses
in the LetterSetsTest(Ekstromet al.,I 976);LetSet7oCor.= percentage
ofcorrectresponses
in the LetterSetsTest(Ekstromet al.,| 976).
the attenuationproducedby statisticalcontrolofthe slopeparametershouldbe greaterthan that producedby statisticalcon_
trol ofthe observedmeasures
ifthe slopeis a directreflectionof
the speedfactor,but it should be lessthan that producedby at
leastsomeof the observedmeasures
if the slopeonly indirectly
representsthe influenceof a common speedfactor. The pro_
posedmethodfocuseson relationswith cognitionto discrimi_
nateamongthe alternativeinterpretations
ofspeedbecauseof
the assumptionthat speedis interestingprimarily becauseof
the implicationsit hasfor other aspectsof cognitivefunctioning.
The presentresearchprojectinvolveda batteryoflT tests,
yielding l9 separatemeasures,that was administeredto two
samplesof researchparticipants.One sampleconsistedof 100
collegestudentswho servedas the referencegroup for certain
analyses,
and the othersampleconsistedof 305 adultsranging
from l9 to 84 yearsofage.Elevenofthe testswereintendedto
measurespeed,with 8 of them speciallydesignedto vary sys_
tematicallywith respect1othe amountof requiredprocessing.
These8 new taskswere composedof four pairs, with each
memberof the pair requiringsimilar activitiesbut involving
slightlydifferentmaterials.The four pairsinvolvedthe following operations:Marking (i.e.,crossingvertical or horizontal
linesto makeplussigns);Copying(i.e.,copyinglettersor numbers);Completing(i.e.,comparingtwo stringsof lettersor digits
and then writing the item missingfrom onestring);and Trans_
forming(i.e.,incrementingan initial valueby one or two in the
alphabeticor numeric sequenceand then writing the new
value).Threeotherspeedmeasures
werealsoincludedto facilitate comparisonswith earlierresearchusing thosemeasures:
the WechsIer I d uIt I nteIIigence ScaIe- Revrserl(WAIS-R) Digit
SymbolSubstitutionTest(Wechsler,
198I ) and the LetterComparisonand PatternComparisonmeasures
describedby Salt_
house(l 99I a) and Salthouse
and Babcock0 99 I ).
The criterion,or to-be-explained,
variableswerelour cognitive measures
and four memorymeasures.
The cognitivemeasureswerederivedfrom testssimilar to thoseusedin earlier
studies.Thesewerethe Primary MentalAbilities(pMA) Space
and PMA Reasoningtestsusedby Hertzog(1989)and Schaie
(1989)and the integrativereasoningand geometricanalogies
testsusedby Salthouse(l99la). The four memory measures
werederivedfrom a paired-associates
test and a free-recalltest
yielding measuresof recall accuracyfor the primacy,asymptote,and recencysegments
of the serialpositionfunction.
Method
Subjects
Demographiccharacteristics
of the individualswho participatedin
this project are summarizedin Table 2. Collegestudentsreceived
credit toward a course requirementfor their participation, and
membersof the adult sample,who were recruitedlrom newspaper
advertisements,
received$10 lor their participation.Becauseof the
relativelyhighmeanlevelsofeducation,
theadultsamplecanbeconsid_
eredto be a positivelybiasedsamplecomposedlargelyof peoplefrom
middleand high socioeconomic
levels.Healthstatuswasevaluatedby
responsesto three questions:(a) How would you rate your overall
healthon ascalefrom l: excellent165= poorwith3 = average?,
(b)
How many prescriptionmedicationsdo you take eachweek?;and (c)
How many times in the past 5 yearshaveyou been hospitalizedor
receivedother treatmentfor cardiovascular
or neurologicalproblems
(e.g.,heart attack,stroke,or high blood pressure)?
As can be seenin
Table 2, the number of medicationsand medical trearmentswas
greaterwith increasedage,but the overall health ratingsremained
relativelyconstant.(SeeSalthouse,
Kausler,& Saults,I 990,for similar
lindings)
Procedure
All testingwas conductedin small groups,and everyparticipant
receivedthe testsin the samefixedorder.Materialsfor the testswere
assembled
in folders,whichalsocontainedthe informed-consent
form
and a brief questionnairerequestinginformationabout age,gender,
health,and yearsofeducationcompleted.The orderofthe testswasas
follows:Digit Symbol,Line Marking(in theordervertical.horizontal.
vertical,and horizontal),Copying(in the ordernumbers,letters,numbers,and letters).Completion(in the ordernumbers,letters,numbers,
and letters),Transformation(in the order numbers,letters,numbers,
and letters).PatternComparison(in the order three-itempairs, sixitem pairs, and nine-item pairs), Letter Comparison(in the order
three-itempairs,six-itempairs,and nine-itempairs),pMA Reasoning
(Schaie,1985),PMA Space(Schaie,1985),integrativereasonrng,
geometricanalogies,
paired-associate
memory,and free-recallmemory.In
all but the memorytests,the participantswereencouraged
to perlorm
asrapidlyand asaccuratelyas possible.Instructionsin the two memory testsemphasizedtrying to rememberas many wordsas possible.
with guessingencouraged
when in doubt abouta response.
The Digit Symbol,PMA Reasoning,
and pMA Spacetestswereadministeredaccordingto the publishedinstructionsexceptthat answers
wereto bewrittendirectlyon the testlorm in the two pMA testsrather
than on separate
answersheetsasspecifiedin the standardadministrationsofthesetests.This modificationwasintroducedto avoidpossible
726
TIMOTHY A. SALTHOUSE
Table 2
Means and Standard Deviations of DemographicChamcteristics
of the ResearchSamplesby Age Decade
Age
Age
decade
M
Education
^sD
M
Health
.tD
Medication
Medical
treatment
M
SD
t.7
2.3
2.0
2.7
2.5
2.6
2.4
0.8
1.4
r.3
1.6
t.2
1.3
t.4
0.27
0.20
0.r l
0.53
0.62
1.52
l .00
0.78
0.52
0.32
1.23
l.16
t.82
t.4l
0.08
0.00
0.00
0 .l 8
0.10
0.52
0.93
0.53
0.00
0.00
0.53
0.30
1.06
2.64
r.0
1.3
t.4
1.3
1.3
1.2
|.2
0.29
0.55
0.32
0.50
1.22
1.44
1.63
0.5|
0.86
0.78
l.l3
t.2t
2.t2
1.27
0.00
0.18
0.86
0.17
0.09
0 .1 3
0.97
0.00
0.39
3.23
0.56
0.39
0.41
2.'t7
M
,SD
M
SD
Men
Students
20s
30s
40s
50s
60s
70s
59
20
l9
t t
2l
JJ
l4
20.9
23.9
34.4
43.9
54.2
65.0
74.2
1.3
3.0
2.9
2.9
3.5
2.2
3.7
13.3
l4.t
1 5l.
1 5l.
15.8
16.4
16.1
1.3
t.9
2.9
2.5
3.4
l.9
2.9
Women
Students
20s
30s
40s
50s
60s
70s
4l
22
22
36
J/
39
30
20.8
24.2
34.5
44.9
53.9
64.6
74.0
t;l
2.6
3.0
2.8
3.0
2.7
3.7
t3.7
15.0
t5.7
15.4
15.8
14.7
14.0
1.5
t.4
t.7
2.4
2.6
2.7
2.3
2.0
2.3
2.5
2.3
2.1
2.3
2.4
Note. Education refersto yearsof formal educationcompleted,and health representsa self-assessment
on a 5-point scaleranging from | = excellentto 5 = poor. Medication refersto number ofprescription
medicationstaken eachweek,and medical treatmentrefersto numberof treatmentsfor cardiovascularor
neurologicalproblemsin the past 5 years.
confusionor delaysassociatedwith the useofa separateform for recording one'sanswers,which may be greaterwith increasedage(e.g.,
Bellucci & Hoyer,1975;Hertzog, 1989;Hoyer,Hoyer,Treat, & Baltes,
l 978-l 979).
Two versionsof the Line Marking test wereadministered,one with
28 rowsofl6 horizontallinesand the otherwith 23 rowsof20 vertical
lines. Researchparticipantswereinstructed to work from left to right
placing short vertical lines through eachhorizontal line and to work
from top to bottom placingshort horizontal lines through eachvertical line. The pageswerearrangedsuchthat vertical marks weremade
first, then horizonlal marks, then vertical marks, and finally horizontal marks. The time allowed to work on eachpagewas30 s.
The Copying test wasadministeredin two versions,one containing
numbersand the other letters.In both cases,the test pagescontained
l0 rowsofl 5 pairs ofboxes, with a letter or number in the top box and
nothing in the bottom box. The participant'stask wasto copy the ilem
in the top box in the empty box immediatelybelow it. There werefour
separatelytimed sectionsin the task, involving numbers,letters,numbers.and letters.with 30 s allowed for eachsection.
The Completiontestswerealsoadministeredwith both numberand
letter versions.The materials in these tests consistedof pagesof 50
pairs of numbers or letters, with one element missing from one
memberof the pair. The completememberof the pair containednine
elementsand appearedrandomly on either the left or the right. The
participant'stask wasto examinethe completememberof the pair to
determine the identity of the missing elementand then to write that
elementin a box correspondingto the number or letter missing from
the other member of the pair. There were four separatelytimed sections in the task, involving numbers,letters,numbers,and letters,with
30 s allowed for eachsection.
The Transformationtest wassimilar to the Copying test exceptthat
eachitem consistedofthree boxes,with a letter or a number in the top
box, nothing in the bottom box, and either one or two +'s (pluses)in
the middle box. The plus signs in the middle box indicated how the
letter or number in the top box wasto be transformed;one plus meant
that the value should be incrementedby one in the alphabeticor numeric sequence,and two plusesmeant that the valueshould be incrementedby two. For example,an F with two pluseswould yield H, and a
5 with I plus would yield 6. After carrying out the transformation
specifiedin the middle box, the participant must write the identity of
the new letter or number in the bottom box. Each page contained
sevenrows ofl5 setsofboxes, and the separatelytimed (30 s) pages
were presentedin the order numbers,lett€rs,numbers,and letters.
The Pattern Comparison and Letter Comparison tests were very
similar to the earlier versionsofthese testsdescribedby Salthouseand
Babcock (1991).The patterns were constructed by connecting dots
within an imaginary 4 X 4 matrix, and the letter sequenceswereconstructed by random selection (without replacement)of consonants.
Within eachtest, there werethreeseparatelyiimed (30s)sections,with
sectionscontaining pairs ofitems with three, six, and nine
successive
elementsper item. The task for the participant wasto examinethe two
"S" on the line betweenthem if
membersof the pair and to write an
"D"
on the line if they were different. One
they were the sameand a
half of the pairs on eachpagewere the same,and the other half were
different becauseofan alteration in the identity or the position ofone
of the elements.Each sectionof the test consistedof 32 pairs of line
patternsor 64 pairs of letter strings.'
I Analyseswere also conductedon the Letter Comparisonand Pattern Comparison scoresaccording to the number of items (letters or
line segments)beingcompared.Correlationsbetweenageand the average of the Letter Comparison and Pattern Comparison scoreswere
-.58 for three items,-.54 for six items,and -.52 for nine items.The
percentageattenuationoftheage-cognition relations,analogousto the
SPEED MEDIATION
727
The integrativereasoningtest consistedof72 problems,eachcon_
ity ofthe averagevalue.Becausethere wasonly oneadministration for
taining premisesdescribingthe relationbetweentwo terms(e.g.,R and
sometestsin this study,reliability could not be computedfor all mea_
S, do the OPPOSITE),and a questionabout the consequences
on one
sures.However,reliabilities ofstandardized testshavebeen reported
term of a specifiedchangein another term (e.g.,If R DECREASES,
in other sources,with valuesof .82 lor the Digit Symboltest (Wechsler,
will S INCREASE?).(SeeSalthouse,
Mitchell,Skovronek,& Babcock,
I 98I ), .72to.8 I for the PMA Spacetest(Schaie,
I 9g5),and.g2 to.g6 firr
I 989;and Salthouse,Legg,palmon,& Mitchell, 1990,lor further de_
the PMA Reasoningtest (Schaie,1985).
scription of this task) One problem within eachsetof three problems
Most ofthe valuesin Table3 appearsatislactorybecausethe reliabil_
had a singlepremisebelore the question,one problem had two premity estimatesare generally in the moderate to high range of .g0 or
ises,and one problem had three premisespresentedbeforethe ques_
greater.The three measuresfrom the free-recalltaskare notableexcep_
tion. The correct answ€rfor half of the problemswasyes and that for
tions,perhapsbecausethesecomponentsoffree-recall
memoryperfor_
the remaining problemswas ro. In all cases,the task for the research
mance are not very stable when assessedwith only two trials. Esti_
participantwasto placea mark eitherin a column labeledyesor in a
mated reliability of a measureof totar recail acrossalr serial positions
column labeledno. Participantswereallowed4 min to completeas
was somewhatgreater (i.e., .68), but the component measureswere
many problemsas possible.
retainedbecausetheyareofgreatertheoreticalinterestthan the undif_
Thegeometricanalogies
testwasarrangedin a fashionsimilarto the
ferentiatedmeasureof total recall.
integrativereasoningtest in that therewere72 problems,with I ofeach
The completecorrelationmatrix with all measures,
includingage,is
of 3 problemtypes in everyset of 3 problems.problemsin this test
presentedin Table4. All of the correlationsinvolvingagein the main
consistedof four boxes,with eachbox containingbetweenone and
sampleof adults (abovethe diagonal)are negative,and most of the
three lettersin variousconfigurations.For example,one problem con_
remainingcorrelationsin this sampleare moderatein magnitude.
sistedof the followingarrangement
of letters:first box_a solidletterC
Correlationsin the sampleof students(belowthe diagonal)aresome_
in the upperleft corneranda solidletterA rotatedclockwise9ff in the
what smallerand, as expected,becauseof the restrictedage range,
bottom right corner;secondbox-an outline letterC in the upperleft
noneofthose involvingageweresignificantlydifferentfrom zero.
cornerand a solid letter A rotatedclockwise9f in the bottom right
corner;third box-a solid letterD in the upperleft cornerand a solid
letterC rotatedclockwise9f in the bottom right corner;lourth box_
MeasurementModel
a solid letter D in the upper left corner and a solid letterC rotated
clockwise9f in the bottom corner.The participant'staskwasto deter_
Relationsamongthe variableslor the main sampleof adultsin Table
mine if the patternof relationships
4 wereexaminedby meansof a confirmatoryfactoranalysisspecifying
betweenthe lettersin the first two
boxeswasidenticalto that in the secondtwo boxes.The answerto the
four factorsof motorspeed,perceptualspeed,memory,andcognition.
problemjust describedwould thereforebe no, becausethe shift of
The hypothesizedfactor structure, with the estimatedcoefficients,is
solid to outline form for the letter in the upper left corner was nor
portrayedin FigureI . Notice that a correlationwaspostulatedbetween
represented
in the secondpair ofboxes.An equalnumberofproblems
the residualsofeach ofthe measures
derivedfrom parallelmethods,
had one,two,or threelettersin eachbox in the problem,and one half
with the exceptionofthe two copy measures.
Becausethe initial estiof the problemshad correspondingrelationships,
mate of the correlation betweenthe residualsof the letter copy and
and the other half
did not. As in the integrativereasoningtest,decisionswerecommuni_
number copy measureswas negative,no relation was specified becatedby placinga mark eitherin a columnlabeledyES or in a column
tweenthe residualsof thosemeasures.
The chi-squarefor the model
labeledNO. Participantswerealloweda time limit of 4 min to com_
illustrated
in FigureI was121142,
N: 305)= 3 19.25,
p < .0t, indicating
pleteas manyproblemsas possible.
that there wasa significantdiscrepancybetweenthe model and the
The words used in the two memory testswere four-letternouns
data. However,other measuressuggestedthat the model provided at
selectedfrom the most frequent1,000wordslisted in the Thorndike
leastan adequatefit to the data. Accordingto Steiger(19g9,p. 9l),
and Lorge(1944)word count. The rateofpresentationin both tasks
valuesabove.90of the adjustedpopulationgammaindex,which is a
wasapproximatelyI word every 2 s. Two separatetrials with different
coefficient of model determination adjusted for model complexity,
wordswerepresented
in eachtask.Trialsin the paired_associates
and valuesbelow .10 of the adjustedroot-mean-square,
task
which is a
consistedof the oral presentationof 6 word pairs.followedimmedi_
root-mean-square
standardizedresidualadjustedfor model complex_
atelyby instructionsto turn to a pagecontainingthe first membersof
ity,can beconsidered
asrepresenting
a goodfit. Valueswith this model
eachpair. Participantswereinstructedto write the secondmemberof
were .928 firr the adjustedpopulation gamma index and .062 lor the
eachpair adjacentto the first term, and they wereencouraged
adjusted root-mean-square.
The Joreskog-Sorbom
to guess
goodness-of-fitin_
evenifthey werenot sureofthe correctresponse.
dexwas.905.
Approximately60 s
wasallowedfor the response
phaseofthe trial. Trialsin the free_recall
A surprisingfeatureofthe coefficients
in FigureI is the high correla_
taskinvolvedtheoral presentation
tion (.88I ) betweenthe latentvariablesofperceptualspeedand cogni_
of a list of l2 wordslollowedimme_
diatelyby the wordRECALL, at whichtime the participantturnedthe
tion. As a meansof testingwhetherthis correlationwassignificantly
pageand wrote as many wordsas he or shecould remember.Approxidifferentfrom 1.0,the path betweenthesetwo variableswas fixedat
mately60 s wasallowedfor the responsephaseofeach trial.
1.0and the fit of the model redetermined.The chi-squarefor the ad_
justed model wasx2(143,N: 305) : 362.22,p < .01, which yields
a
significantdifferencechi-squareof 42.9j (d.f: I, p < .01), indicating
MeasurementReliability
that the altered model fit the data significantlyworsethan the original
model.Because
the modelconstrainingthe correlationto 1.0provides
Estimatesof the reliabilitiesfor the dependentmeasures
in the two
a significantly poorer {it to the data than the model with the correla_
samplesare reported in Table 3. All estimateswere derived by using
tion asa freelyestimatedparameter,it can be inlerred that, given the
the Spearman-Brownlormula to adjust the correlation betweenthe
assumptions
represented
by the structureofthe model,the true correvaluesfrom the two administrationsofeach test to predict the reliabil_
lation betweenthe perceptualspeedand cognition constructsin these
data is not equalto | .0. In other words,although the two consrructsare
highly related,they are not completelyidentical.
valuesreported in Table 8, were94.6Vofor three items. gg.67olor six
The correlationbetweenthe motorspeedand perceptualspeedconitems,and 85-l7ofor nine items.
structswas.8 I 2. The nestedmodel procedurewasusedto test whether
728
TIMOTHY A. SALTHOUSE
Table 3
Reliabilities of the PerformanceMeasures
Estimatedreliability
Measure
Students
Horizontal mark: No. of horizontal marks made on vertical lines (30 s)
Vertical mark: No. of vertical marks made on horizontal lines (30 s)
Copying,letters:No. ofletters correctlycopied (30 s)
Copying, numbers:No. of digits conectly copied(30 s)
Letter completion:No. of correct completionsof letter strings(30 s)
Number completion:No. of correctcompletionsof number strings(30 s)
Letter transformation:No. of correcttransformationsof letters(30 s)
Number transformation:No. of correct transformationsof numbers(30 s)
ktter comparison:No. of correct same/differentjudgments about letter
strings(30 s)
Pattern comparison:No. of correct same/differentjudgments about line
patterns(30 s)
Digit symbol: No. of items correct in WAIS-R Digit Symbol Substitution
Test (90 s)
PMA Reasoning:No. of items correct in PMA SeriesCompletion
ReasoningTest (6 min)
PMA Space:No. of items correct in PMA Figure Rotation Test (5 min)
Integrativereasoning:No. of items correct in integrativereasoningtest (4
min)
Analogy: No. of items correct in geometricanalogiestest (4 min)
Pairedasociates:No. ofwords correct in paired associates
Primacy: No. of words recalledfrom serialpositions I to 4
Asymptote:No. of words recalledfrom serialpositions5 to 8
Recency:No. of words recalledfrom serialpositions9 to 12
.82
.89
.88
.88
.88
.'7|
.89
.92
.88
.92
.97
.83
.83
.85
.90
.9)
.86
.92
.92
.91
(.82r
(.84)o
(.'7't)'
30
.39
.44
.)t
n
.5v
.50
.46
Note. WAIS-R = WechslerAdult IntelligenceScale-Revised; PMA = Primary Mental Abilities.
b Averagevaluesfrom Schaie(l 985).
' Valuefrom Wechsler(198I
).
this correlationwassignificantlydifferent from 1.0by constrainingthe
correlationto 1.0and examiningthe chi-squaredifferencebetweenthe
original and alteredmodels.The differencechi-squarewas199.75(df=
I , p < .01), implying that the correlationwassignificantlylessthan I .0.
All standard errors for the coefficientsillustrated in Figure I were
lessthan .06, and those for the coefficientsbetweenperceptualspeed
and cognition and betweenmotor speedand perceptualspeedwere
both .024.Becausethesevaluesindicatethat the relationsbetweenthe
observedvariablesand the latent constructsare significantly greater
than zero and that the correlationsbetweenconstructsare all significantly less than 1.0, the constructs can be consideredto have both
convergentand discriminant validity, respectively(cf. Anderson &
Gerbing,1988).
Results
Composite Variables
Compositevariableswere createdfior eachof the forrr constructsby averagingthe unit-weightedz scoresfor the measures
hypothesizedto representeachconstruct(accordingto the relations portrayedin FigureI ). Correlationsamongthesecompositesand estimatesof their reliabilitiesare presentedin Table5.
Notice that the correlations among the composite variables
havethe samepattern but are generallysmaller in magnitude
than thoseamong the latent constructsportrayedin Figure 1.
Mean compositescoresat eachdecade,expressedin standard
deviationsof the scoresof the referencestudent sample,are
illustrated in Figure 2. There are two particularly salient featuresofthese data.The first is the very pronouncedagetrends
evidentin eachmeasure:The averageperformanceof adultsin
their 60s and 70s is betweenone and two standarddeviations
belowthat ofadults in their 20sand 30sfor eachofthe composite variables.
The secondnoteworthyfeatureofthe data in Figure2 is that
even the performanceof the adults in their 20s is appreciably
lower than that ofthe referencegroup ofstudents, particularly
for the cognition compositevariable.This differencemay be
attributableto the fact that the studentswere recruited from a
relatively select university and consequentlymay have had
higher levelsofcognitive ability than the averageyoung adult
to participatein projrecruitedfrom newspaperadvertisements
ectsof this type. Somesupport for this interpretation is available in the observation that the students in this study performed between 0.6 and 0.9 standard deviations above the
meansof the 22- to28-year-oldsin the normativesamplefor the
1985venion of the PMA Spaceand Reasoningtests(Schaie,
1985).The fact that the nonstudentresearchparticipantsin
their 20shad a slightly lower averagenumberofyears ofeducation than adults in subsequentdecades(seeTable 2) could also
be interpretedasindicating that the 20- to 30-year-oldadultsin
this sample were not as positively biased as the adults from
other ageranges.
Whether it is becausethe samplein the decadeof the 20s is
lessselectthan the samplesfrom other agegroupsor because
there are little age-relatedeffectsin thesemeasuresuntil middle age,the data in Figure 2 suggestthat performancein some
testsmay remain relativelystableuntil the 30sor 40s.The nature of the agerelationsin the compositevariableswasinvesti-
SPEED MEDIAIION
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730
TIMOTHY A. SALTHOUSE
.7Gr (
.586
I
I
(
3 4 (
.313
(
MEMORY
COGNITION
Figure l. Hypothesizedmeasurementmodel and coefficientsobtained from confirmatory factor analysis.(MSPD : motor speed;PSPD= perceptualspeed.Variablesin the boxesare asfollows:HMark : no.
of horizontalmarks madeon vertical lines;VMark: no. of vertical marks madeon horizontallines;
LCopy = no. of letterscorrectly copied; NCopy = no. ofdigits correctly copied; LComp = no. ofcorrect
letter-stringscompletion; NComp = no. of correct number-stringscompletion; LTran = no. of correct
transformationof letters;NTran = no. of correct transformationof numbers;PatCom = no. of correct
same/differentpattern comparison judgments; LetCom = no. of correct same/differentletter comparisons;Digsym = digit symbol;PairAsoc= paired associates;
PMAReas= Primary Mental Abilities Inductive ReasoningTest; IntReas= integrativereasoning)
gatedmoresystematicallyby examiningthe significanceofquadratic (age-squared)
terms in the regressionequation.The quadratic term was associatedwith a significant increment in R2
for the motor speedand memory variables,but in both casesit
was relativelysmall (i.e.,.029 and.037, respectively).Because
the variance associatedwith the linear age trend was much
larger(i.e.,R2valuesrangingfrom . 184to .297),only the linear
relationswereconsideredin all subsequentanalyses.
Main effectsand interactionsof gender,self-assessed
health
status,numberof medications,numberof medical treatments,
and yearsofeducation werealsoexaminedin regressionequations on the four compositevariables.The only significantef-
fect other than age was the main effect of education on the
memorycompositevariable,,F0, 301): 10.79,p < .01,M,S =
0.367, indicating that people with more educationp€rformed
better on the memory tests than people with lesseducation.
The absenceofany interactionsinvolvingagesuggeststhat the
age trends in the compositevariableswere not moderatedby
gender,availableindexesof health, or education,and consequently thesefactorswere ignored in all remaining analyses.
Hierarchical Regression Analyses
Resultsof the hierarchicalmultiple regressionanalysesconducted on the compositevariablesare summarizedin Table6.
\
I
SPEEDMEDIATION
731
Table 5
CorrelationsAmong Composite Scores
.I
,l
sociatedvariancein the cognition measurefrom.202when age
wasthe only variablein the equationto.003 when the variance
associatedwith perceptualspeedwascontrolledby enteringage
Variable
in the regressionequationafter perceptualspeed.
-.46
t . Age
-.55
-.43
-.45
Second,the earlier resultsare extendedby the finding that
2. Motor speed
.04
(.e5)
.70
.38
.43
the
relationsbetweenageand perceptualspeedarestill statisti_
3 . Perceptualspeed
.08
.59
(.97)
.51
.74
cally
significantafter controlling the influenceof motor speed
4. Memory
.05
.16
.23
(.77)
.52
-.01
(i.e.,
5 . Cognition
R2
of.062) and by the finding that therewasa largerattenu_
)\
st
(.86)
,J I
ation ofthe age-relatedeffectsin cognition after control ofper_
Note. Values
abovethediagonalofnumbersin parentheses
arecorre_ ceptualspeedthan after control of motor speed(i.e.,reductions
lationsfromtheadultsample(r: 305),andthoie belowthediagonal
r1 R2 to .003 for perceptualspeedvs. .0g0 for'motor speed).
arecorrelations
lromthestudentsample(z= I 00).Values
in pare-nthe_
This
combination of resultssuggeststhat only a portion of the
sesarereliabilitiesof the composite
scoresfor the adultsampleestimatedbytheformuladescribed
age-relatedslowingthat afects cognitivefunctioning is motoric
by Kenney
(1979,p.132):.ef
iaUifity:
n(average
r)/lt + (n- t)(average
rjl.
in nature.
Third, anothernew finding is that the age-relatedvariancein
measuresof memory is also substantiallyattenuatedafter sta_
Entriesin the first column of this table indicate the cumulative
tistical control of perceptualspeed.The percentageattenua_
R2 in the prediction of the criterion variableafter the variable
tion,82.6Vo,is not as largeasthe 98.52oevidentin the cognitive
on that row and the variableson immediately precedingrows
measure,but it is still quite substantial.
had been enteredinto the regressionequation.Entries in the
And fourth, agewasassociatedwith a very small proportion
secondcolumn indicatethe incrementin R2associatedwith the
of the total variance in the cognitivemeasureafter the influ_
addition ofthe variableon that row into the regressionequa_ encesof motor
speed, perceptual speed, and memory were
tion. Finally, valuesin the third column indicate the F values
taken into consideration.Furthermore, the direction of the
fo-rthe significanceeitherof the initial R2or of the incrementin
standardizedregressioncoefficientfor agein the completere_
R2.
gressionanalysiswasactually positiverather than negative,in_
Severalpointsshouldbe noted regardingthe resultssumma_ dicating that if anything,
increasedage was associatedwith
rized in Table6. First, it is clearthat earlier findings wererepli_
higher levelsof cognitiveperformancewhen the contributions
catedconcerningthe attenuationofthe relationsbetweenage
of motor speed, perceptual speed, and memory were con_
and cognitionafter statisticalcontrol ofa compositemeasureof
trolled.
perceptualspeed.This is evidentin the reductionofthe age_as_
The resultsjust describedare relevantto both of the maior
0.5
Memory
--c"MSpd
-aPSpd
U'
E
c
0
f
c
o -0.5
\
o
o
---l---
l
\
(U
'5
Cognition
-1
o
(u - 1 . 5
o
c(u
\
U) -2
c
o
o -2.5
I
U)
f
F
-3
20
30
40
50
60
70
Chronological
Age
Figure 2' Mean performanceat each decadefor the four composite
variablesexpressedin standard
deviationsofthe t00 collegestudentsserving as the referencegroup. (Bars
aboveor below the symbols
representone standarderror. MSpd = motor speed;pSpd = perceptual
speed)
732
TIMOTHY A. SALTHOUSE
Table6
Hierarchical RegressionResultsBasedon
CompositeScoresin Aduh Sample
Criterion/predictor
Motor speed
Age
R2
Incr. R2
.2t4
82.45*
Perceptualspeed
Age
.297
t28.t2*
Motor speed
Age
.495
.557
337.30*
41.80*
.r84
68.I 2*
Memory
Age
Motor speed
Age
.t47
.22'7
.080
57.58*
3 l . 3 l*
Perceptualspeed
Age
.261
.293
.032
tt2.24r
13.70*
Motor speed
Perceptualspeed
Age
.t47
.262
.293
Cognition
Age
.ll5
.031
62.69+
48.7l*
13.20*
.202
76.68i
Motor speed
Age
.1 8 5
.265
.080
75.98*
32."18*
Perceptualspeed
Age
.546
.549
.003
365.20+
2.08
Memory
Age
.275
.337
.o62
I 25.35+
2 8 .I 5 +
Motor speed
Perceptualspeed
Age
.1 8 5
.562
.567
.377
.00s
t28.5"1*
26l .80+
3 . 7|
Motor speed
Perceptualspeed
Memory
Age
.185
.562
.593
.594
.3-17
.031
.001
I 36.78+
2 7 8 . 5I *
23.1t*
1.05
ceptual speedand cognition, respectively.Coefficientsin the
top panel of Figure 3 are basedon the standardizedregression
coefficientsfrom multiple regressionanalyseson the composite
scores.Coefficientsin the bottom panel werederivedfrom the
EZPNIII (Steiger,1989)structural equationprogram with the
latentconstructsdefinedin the measurementmodel illustrated
in Figure l. (That is, this figure illustratesthe structural coefficientsfrom a structural equation model superimposedon the
measurementmodel representedin Figure l) The chi-square
for this modelwasy21l6S,N: 305): 414.92,p < .01,but the
goodness-of-fitmeasuresindicated an adequate fit of the
model to the data (i.e.,adjusted population gamma index :
: .069,and Joreskog-Sorbom
.907,adjustedroot-mean-square
goodness-of-fit
index = .883).Explorationofseveralvariations
ofthe model portrayedin Figure3 revealedthat the fit could be
improved by minor alterationsof the structure representedin
FiguresI and 3 (e.g.,specifyingdirect as well as indirect paths
betweenageand the letter transformation,numbertransformation, and recencyvariables),
but noneofthe modificationsresultedin an appreciablechangein the structuralparameters
depictedin the bottom ofFigure 3.
(A)
Note. Incr.R2: incrementin R2association
with additionofsecond.
third. or fourth variable.
* p <.01.
goals ofthe project. They addressthe issueofspeed mediation
of age differencesin memory, becausestatistical control of the
composite measure ofperceptual speed greatly attenuatesthe
age-relatedvariance in the composite measureof memory. The
resultsare also relevantto the issueofthe type ofspeed involved
in the mediation, because the attenuation of the age-related
variance was greater after control of measures of perceptual
speed than after control of measuresof motor speed.
Structural Model
A structural model illustratingthe hypothesizedrelations
amongthe primary constructsis represented
in Figure3. The
causallinkagesare hypothesizedto be from motor speedto
perceptualspeedand from memory to cognition rather than
vice versa,becausemotor speedand memory areassumedto be
more elementarythan, and perhapsevenconstituentsof, per-
Figure 3. Hypothesized structural relations and path coefficients
basedon the compositevariables(A) and on the latent variables(B).
(MSPD: motor speed;PSPD: perceptualspeed)
733
SPEED MEDIAIION
It is apparentin Figure3 is that althoughthe relationbetween
perceptualspeedand cognition is highly positive, there is a
negativerelationbetweenmotor speedand cognition.This was
unexpected,becauseit indicatesthat when perceptualspeedis
controlled, fastermotor speedis associatedwith lower levelsof
cognitive performance.Interpretation of this finding should
probably be deferred until it has been confirmed in another
sample,but it may reflectthe operationof sometype of impulsiveness.In most other respects,however,the relations portrayed in Figure 3 are similar to the conclusionsinferred from
the regressionanalyses.Specifically,thereare negativerelations
betweenageand motor speed,perceptualspeed,and memory;
no significant relation between age and cognition; and large
positiverelationsbetweenmotor speedand perceptualspeed
and betweenperceptualspeedand cognition. Moreover,it is
reassuringto note that the samepatternsare evidentwhen the
analysesare basedon unit-weightedcompositescores(Figure
3A')and on latent constructsdefined by a confirmatory factor
analysis(Figure3B).
The results from the structural analysesare related to the
primary goals of the project in the following manner. First,
examination of the paths leading to the memory variable revealsthat some,but not all, of the age-relatedvariancein memory is mediatedthrough slowerperceptualspeed.That is, unlike the cognitivevariable,a direct path existsbetweenageand
memory in addition to the indirect path through perceptual
speed.And, second,at leastwhen motor speedis assumedto
influenceperceptualspeed,the relationsbetweenmotor speed
and cognition are very small and are actually negativerather
than positive,whereasthe relationsbetweenperceptualspeed
and cognition are largeand positive.
Table 7
Resultsof Commonality AnalysesConductedon the Cognition
and Memory CompositeVariqbles
in Adult Sample
Predictor variable
Criterion
Cognition
Unique to age
Unique to motor speed
Unique to perceptualspeed
Common to ageand motor
speed
Common to ageand
perceptualspeed
Common to motor speed
and perceptualspeed
Common to age,motor
speed,and perceptual
speed
Total effects
Memory
Unique to age
Unique to motor speed
Unique to perceptualspeed
Common to ageand motor
speed
Common to ageand
perceptualspeed
Common to motor speed
and perceptualspeed
common to age,motor
speed,and perceptual
speed
Total effects
Age
Motor
speed
Perceptual
speed
.005
.018
.302
-.002
-.002
.0'74
.124
.202
.074
.045
.045
.124
.1 8 5
.t24
.545
.031
.000
.065
.001
.001
.049
.103
.1 8 4
.449
.044
.044
.r 0 3
.148
.r 0 3
.261
Commonality Analysis
Another method of partitioning the variance in a criterion
variableis commonalityanalysis(Pedhazur,1982).As applied
in the presentcontext, the goal of this techniqueis to decomposethe total effectsof ageon either the cognition or memory
compositevariableinto a unique contribution of ageand into
contributionsin common with motor speed,perceptualspeed,
or both. The unique influencecorrespondsto the age-related
variancethat is independentofboth motor speedand perceptual speed,and the common influence representsthe age-relatedvariancethat is sharedwith either motor speedor perceptual speedor both.
Table 7 contains the summary information from the commonality analysesconducted on the cognition and memory
compositevariables.Entries in the first column (Age)are of
greatestinterestbecausethey indicatethe partitioningofthe
age-relatedeffects.Two important points should be emphasizedabout thesedata. First, notice that only a small proportion ofthe total age-relatedeffectsis uniquely associatedwith
age(i.e.,.005vs..202for the cognitionvariableand.03l vs..184
for the memory variable).And second,noticethat the variance
common to ageand perceptualspeedis much larger than that
common to ageand motor speed(i.e.,.074 vs. -.002 for the
cognition variableand .049 vs. .001 for the memory variable).
In both respects,these resultsreinforce the conclusionsfrom
the hierarchicalregressionand path analysisprocedures.How-
ever,this analysisextendsthe earlieranalyses
by indicatingthat
the largestproportion of variancein the cognitionand memory
compositevariableswas sharedamong age,motor speed,and
perceptualspeed.
Relations Among Speed Measures
As describedin the introduction, regressionequationswere
computed relating the times of each adult participant to the
averagetimes of the 100studentsacrossthe samemeasuresof
speed.That is, the predictor or X valuesin the regressionequationswerethe meantimesof the 100students,and the criterion
or )z valueswere the times of the individual subject in those
same tasks.Intercept, slope,and correlation coefficientsindicating the goodnessof fit of the linear equationweretherefore
obtained for eachsubjectto representthe relation ofhis or her
times to the mean times of the referencegroup.
Meansof the regressionparameterswere .93 (,SD: .07) for
the correlation,I .40 (SD : 0.9I ) for the slope,and -0. I 3 (.SD:
0.54) for the intercept.The high averagecorrelation, together
with the fact that the magnitudeof the correlation coefficient
wasnot significantlyrelatedto age(i.e.,r - -.14), indicatesthat
the linear equationsprovided a reasonablecharacterizationof
the dataof most participants.The interceptparameterwassignificantly relatedto age(i.e.,r = - .19), but the absolutemagni-
734
TIMOTHY A. SALIHOUSE
tudeofthe effectwasquitesmall,becauseeachyearofage was
associatedwith a reduction in the intercept of only .006. The
slopeparameterhad a signihcantpositiveagerelation(i.e.,r:
.30)correspondingto an annualincreaseof.0l7.
Comparableanalyseswerealsoconductedon only the 7 perceptualspeedmeasures,
excludingthe 4 motorspeedmeasures.
Resultsof these analyseswere similar to those basedon all
speed measuresexcept that the correlation coefficient was
smaller(i.e.,r: .821.
intercept: -. I 3; slope: 1.45),suggesting
a
somewhatpoorer fit of the linear equation to the data. The
correlation betweenthe slopebasedon all I I speedmeasures
and that basedonly on the 7 perceptualspeedmeasureswas
.98.
To estimatethe reliabilityof theslopeparameterbasedon all
I I speedmeasures,the speedmeasureswere rank-orderedin
terms of averagetime and then separateslopescomputed for
the six odd-rankedmeasures
(i.e.,horizontalmarking,number
copying,numbertransformation,patterncomparison,number
completion,and letter comparison)and for the five evenranked measures(i.e.,vertical markings,letter copying,digit
symbol, letter completion, and letter transformation).The
meansfor the two slopeswere1.42and 1.38,respectively,
and
the correlationwas .48. Applicationof the Spearman-Brown
formulato this correlationresultedin an estimatedreliability
of the slopebasedon all I I speedmeasures
of .65.
Table8 containsa comparisonof the magnitudeofthe attenuation ofthe agerelationsacrossdifferentspeedmeasures
and
acrossdifferentcognitiveand memorymeasures.
Valuesin the
tableweredeterminedby computingthe R2associated
with age
whenit wasthe only variablein the equationand againwhenit
wasenteredafterthe variableslistedin the top row ofthe table.
The differencebetweenthe two varianceestimateswas then
divided by the total age-related
variance,and this value was
multipliedby 100.To illustrate,Table6 revealsthat the R2for
ageon the cognitionvariablewas.202when agewasthe only
predictor in the regressionequationbut that the increment in
R2 associatedwith ageafter controlling the influenceof motor
- .0S0)
speedwas.080.Dividing the differenceof .122(i.e...202
by .202yields.604,which whenmultipliedby 100resultsin the
first entry in Table8.
The recencymemory measureis excludedfrom Table 8 becausecomparisonsof the magnitudesof attenuationwith this
measurewould not be meaningfulgiventhe very small relation
betweenageand this measure(i.e.,r = -.08). Entrieslabeted
Averagein the last row and in the last column are included to
facilitatecomparisonsacrossmeasures,but it shouldbe emphasizedthat theseare not true averages,
becausethe valuesin the
columnsand rowsare not independent(e.g.,the compositecognition variableis derivedfrom the variableslabeledpMA Reasoning,PMA Space,integrativereasoning,and analogy).
It can be seenin Table8 that statisticalcontrol ofthe composite perceptualspeedmeasuregenerallyresultedin the greatest
attenuationof the age-relatedeffects,followed by a composite
basedon the LetterComparisonand PatternComparisonmeasures,and then by the Digit Symbolmeasure.The composite
motor speedmeasurewas relativelyineffectivein attenuating
the agerelationson anyof the cognitiveor memorymeasures,
and the two slopemeasuresfared the worst in terms of their
inferred mediationalinfluenceon the age-cognitionor agememory relations.
Theseresultsare relevantto the secondmajor goal of the
project in that they are informative about the relative importanceof differentmeasuresof speedas mediatorsof the relations betweenageand cognitionor memory.Basedon the data
containedin Table8, one can inler that perceptualspeedis
much more important than motor speedand that although
there is a systematicrelationbetweenthe speedsof adultsof
dilferentages,the slopeof this relationdoesnot appearto be
very importantasa mediatorof age-cognitionor age-memory
relations.
Table8
Attenuatkn oJAge-CognitionRelalionsas a F-unctionof the Measuresol
Speedand Cognitionin the Adult Sample
70 attenuation ofR2 for age
Criterion
Cognition
Memory
PMA Reasoning
PMA Space
Integrativereasoning
Analogy
Pairedassociates
Primacy
Asymptote
Average
Motor
speed
60.4
56.5
68.3
43.9
55.6
75.4
51.2
57.5
42.5
56.8
Perceptual
speed
98.5
82.6
100
89.2
93.3
94.2
80.2
73.2
66.4
86.4
Lettcr/pattern
95.5
80.4
98.8
87.8
88.9
98.6
15.9
68.6
60.4
83.9
Digit
symbol
89.I
73.4
94.6
"10.3
'19.3
100
Slope
pSlope
Average
46.0
34.2
54.5
39.2
34.1
59.4
3t.7
22.8
38.3
2'/.7
2t.5
39.1
2l.0
24.2
I 1.9
26.5
10.2
58.3
75.8
59.7
62.1
77.8
55.6
52.6
42.9
6t.7
/J.)
J l.)
59.5
57.5
17.5
32.7
18.7
38.9
Nole. Motor speedis a compositeof horizontalandverticalline markingand letterand numbercopying;
perceptualspeedisa compositeof letterand numbercompletion,letterand numbertransformation,
letter
and pattern comparison,and digit symbol;letter/patternis a compositeof letter and pattern comparison;
slopeis the linear regression
sloperelatingtimesof I I speedmeasures
to the averagetimesof t 00 college
students;PSlopeis the linearregression
sloperelatingtimesof7 perceptualspeedmeasures
to the average
timesof 100collegestudents.PMA : Primary MentalAbiliries.
SPEEDMEDIATION
General Discussion
T heoretical Construct s
Although the four constructsof primary interestin this project-motor speed,perceptualspeed,memory,and cognitionwere ficund to have moderate to large correlationswith one
another,they arenevertheless
distinguishable.That is, the measurementmodel illustrated in FigureI wasfound to providean
acceptablefit to the data, and the correlations between the
compositesin Table 5 were appreciablylower than the estimatedreliabilitiesof the composites.
The discovery of high correlations(i.e.,.74 for composites
and.88 for factor scores)between the perceptualspeedand
cognitionvariableswassomewhatsurprising,becausetheseare
generally assumed to represent separateand distinct constructs, but correlationsof similar magnitude have been reported in other studies.For example,in studiesinvolvingsamples ofolder adults,the correlationsreported betweenperceptual speedand inductivereasoningcompositeswere.78(Baltes,
Cornelius,Spiro,Nesselroade,
& Willis, 1980),.80 (Cornelius,
Willis, Nesselroade,
& Baltes,1983),and .78 (Schaie,Willis,
Hertzog,& Schulenberg,l9ST).
Schaie,Willis, Jay,and Chipuer
(1989)havealso reporteda correlationof.86 betweenperceptual speedand inductivereasoning(and.77 betweenperceptual
speedand spatialvisualization)in a sampleof 1,621adultsbetween22 and 95 yearsof age.A lateranalysisof thesedata with
a total of 1,628adults resultedin correlationswith perceptual
speedof .88 for inductivereasoningand.78 with a spatialfactor
(Schaie,Dutta, & Willis, 199I ). The resultsof all thesestudies
thereforesuggestthat there is considerableoverlapin what is
measuredby perceptualspeedtestsand timed testsof inductive
reasoning and spatial visualization, particularly in samples
containinga largeproportionofolder adults.
The motor speedand perceptualspeedconstructsalso appear to be distinct despitefairly high correlationsbetweenthe
factors(.812)and the compositevariables(.70).Schaieet al.
(199I ) havereportedsimilar resultswith a more complex measureofmotor speedbasedon the speedofcopying paragraphs
printed in uppercaseand lowercaselettersand on the speedof
writing synonymsand antonymsof familiar words.The correlation betweenthis motor speedfactor and a perceptualspeed
factor in their study was.9l3, and, as in the presentstudy,
analysesrevealedthat this valuewassignificantlylessthan 1.0.
Age Relations
The resultssummarized in Figure 2 and in Tables4 and 5
clearlyindicatethat increasedageis associatedwith slowerperformanceon manyspeededtasksand with lowerlevelsof performanceon certain memory and cognitivetasks.The agecorrelations with the compositemeasures(seeTable 5) ranged from
-.43 to -.55, indicatingthat between187oand 307oof the total
variance in thesemeasureswas systematicallyrelated to age.
These valuesare in the same range as those summarized in
Table I and are consistentwith much researchin the area of
agingand cognition (seeSalthouse,199 I b, for a recentreview).
The correlationbetweenageand the memory compositewas
-.43, but the age correlation was only *.08 for the recency
measure.The lack of a significantagerelationwith the recency
735
measurecould be interpretedas suggestingthat the factorsresponsiblefor the recencyeffect(e.g.,primary memory) may be
relativelyunafected by increasedage(e.g.,Craik, 1977).However,resultsfrom anothersimilar project are inconsistentwith
this interpretation.Ronnberg(1990)alsoadministeredl2-word
lists to adults from a wide rangeof agesand analyzedperformancein terms of recall of wordsfrom successive
thirds of the
list. Correlationswith agein that study were-.12, -.35, and
-.27 for the primacy,asymptote,and recencysegments,respectively,comparedwith the valuesof -.39, -.37. and -.08 in this
study The Ronnbergstudy thereforefound smaller age-related
influenceson recall of primacy items compared with recency
items,whereasthe reversewastrue in this study.Becauseparticipants in the Ronnbergstudy receivedeight lists of words and
participants in the presentstudy receivedonly two lists, the
discrepancyin the two setsof resultsmay be relatedeither to
the reliability of the measures(which would be greater with
more observations)or to sometype of age-differentialstrategy
shift acrosssuccessive
lists.
Speed Mediation
Consistentwith the resultsof the studiessummarizedin Table I , the age-relatedvariancein the measuresof cognitivefunctioning wasfound to be greatlyreducedafter statisticalcontrol
of an index of perceptualspeed.In fact, the resultswith the
compositevariablesindicatethat between807oand 1007oof the
age-relatedinfluenceson memory and cognition were eliminated by using statisticalproceduresto equateparticipantson
an index ofperceptual speed.Expressedsomewhatdifferently,
18.470
of the total variancein the memorycompositeand20.22o
of the total variancein the cognitioncompositewereassociated
with agebeforestatisticalcontrol ofthe perceptualspeedvariable,but after statisticalcontrol ofperceptualspeed,the age-associatedvariancewasonly 3.27ofor the memory compositeand
0.3Vofor the cognitioncomposite.
Althoughthe resultsof this studydo not by themselves
indicatehow speedmediatesthe influenceofage-relatedeffectson
memory and cognition, it is neverthelesspossibleto speculate
about the mechanismsthat might be involved.An initial assumption is that perceptualspeedmeasuressuch as those included in this study reflectthe rate at which the individual can
carry out many elementarymental operations.Given this assumption,one can speculatethat at leastsomeof the agedifferences in simple cognitive measuresmay be a direct consequenceof a slowerspeedof mental processingbecausethe required operations are relatively undemanding. Much of the
age-relatedinfluenceson the cognitivemeasuresin the present
study may be attributable to this type of influence, because
most of the items in thesetests would probably be answered
correctly by individuals of moderateto high ability working
without time constraints.In other words,with testsof low difficulty,a largeproportion ofthe variancein performancecan be
hypothesizedto be causedby variationsin the numberof items
attempted rather than to variations in the percentageof attempted items answeredcorrectly.
With more complex cognitivemeasures,the speedinfluence
may be largely indirect and perhapsmediated by an impairment in the functioningof working memory.The precisenature
736
TIMOTHY A. SALTHOUSE
of the workingmemoryimpairmentis still not clear,but it may
be relatedto a diminishedability to maintain the productsof
earlyprocessing
duringthe executionoflater processing.
Much
higherorder thinking involvingintegrationand abstractioncan
be postulatedto requirethe simultaneousavailabilityof relevant information,and the amountof simultaneously
available
informationis likely to be a direct functionof the effectiveness
of workingmemory.Threeobservations
areconsistentwith this
working-memorymediation interpretation.First, the influenceof workingmemoryhasbeenfoundto be greaterthan that
ofperceptualspeedfor difficultcognitivetestssuchasthe Shipley AbstractionTestand the RavenbAdvancedProgressive
Matrices Test (StudyI in Salthouse,1991a),whereasthe reverse
wastrue for easiercognitivetestssuchasthe integrativereasoning and geometricanalogiestestsincludedin this study(Studies 2 and 3 in Salthouse,l99la). Second,a similar patternof
greaterworking-memoryinvolvementand reducedinfluence
of perceptualspeedin moredifficultor complexconditionshas
beenfound in within-taskcomparisons.
That is, moredetailed
analyses
ofthe resultsfrom Studies2 and 3 in Salthouse
(l 99 I a)
revealedthat the influenceof working memory was greater
than that of perceptualspeedfor the more complexitems in
eachof the tests(Salthouse,
1992c).And third, the resultsof
severalindependentstudiesindicatethat the age-related
variancein measures
of working memory is greatlyattenuatedby
usingstatisticalcontrolproceduresto removethe varianceassociatedwith perceptualspeed(Salthouse,
l99la. 1992d;Salthouse& Babcock,l99l). This suggests
that speedmay be an
importantmediatorof the agedifferences
in at leastsomemeasuresof working memory.
It is not yet obviouswhat factorsbesidesperceptualspeed
contributeto the agedifferencesin memory functioning.One
possibilityis that working memory playsan important role,
much like that hypothesized
with complexor difficult reasoning or spatialproblems.Anotherpossibilityis that someof the
agedifferences
areattributableto variationsin the effectiveness
of particular mnemonicstrategiesor in the elficiencyof specihc processes
concernedwith encoding,retrieval,and so on.
Systematicinvestigationof the effectsof perceptualspeedon
adult agedifferencesin specilicmemory componentsand on
theefficiencyofselectedstrategies
is obviouslyneededto distinguishbetweenthesepossibilities.
Comparabi litv Wilh Previous Studies
Becausesomeof the sameperceptualspeedand cognitive
taskshavebeenusedbefore.the presentresultscan be comparedwith thoselrom the previousstudies.The attenuationof
the agedifferences
in integrativereasoningwith statisticalcontrol of the LetterComparison/Pattern
Comparisoncomposite
in this study was 88.97o,
and the correspondingvaluesin the
two relevantstudiesreportedin Salthouse(1991a)were86.77o
and 89.2VoValuesfor the analogiestask were 98.6%in this
study,and 99.5Vo
and94.lVoin the two earlierstudies.Hertzog
(l 989)and Schaie(l 989)useddifferentmeasures
of perceptual
speedin their studies,and thusthe valueswith the PMA Space
and PMA Reasoningtestscannot be compareddirectly,but
inspectionofthe valuesin TablesI and 8 revealsthat the Dat-
terns with thesemeasuresin this studyweregenerallysimilar to
thoseof the earlierstudies.
Becauseit was recently reported (Salthouse,1992b)that a
very large proportion of the age-relatedvariance in the Digit
Symbolmeasurewassharedwith a perceptualspeedcomposite
createdfrom the Letter Comparisonand PatternComparison
measures,the present data were examined to determine
whetherthis phenomenonwas alsoevidentin this study The
earlier results were replicated becausethe R2 for age in the
prediction of Digit Symbol performancewas.261 when it was
consideredalonebut wasonly .019whenconsideredafterstatisticalcontrolof the LetterComparison/Pattern
Comparison
composite.Although the residualagerelationwasstill significantly greaterthan zero, it was only 7Vaof the original value,
indicating that approximately93Voof the age-relatedvariance
in the Digit Symbolmeasurewassharedwith a compositeof the
two perceptualcomparisonspeedmeasures.
Comparison of Speed Measures
The discoverythat there was more attenuationof the relations betweenageand cognition after statisticalcontrol of perceptualspeedmeasuresinvolvingcomparisonor transformation operationsthanaftermotorspeedmeasures
requiringlittle
or no cognitiveoperationssuggests
that the speedof primary
interestin the mediationof relationsbetweenageandcognition
is perceptualor cognitivein natureratherthan motoric.Also
consistentwith this interpretationis the finding that, at least
for the sampleof adults involvinga wide rangeof ages,the
relationsbetweenthe compositemeasureswere,if anything,
slightlystrongerbetweenperceptualspeedand cognition(r:
.74) thanbetweenperceptualspeedand motor speed(r: .70).lt
thereforeappearsthat the aspectofprocessingspeedresponsible for the mediationof agedifferences
in cognitionis not that
associated
with sensoryor motor processes
but ratheris related
to the speedwith which simplecognitiveor mentaloperations
can be executed.
Statisticalcontrolof the slopeparameterled to only a small
attenuationof the age-cognitionrelations,particularlyin comparisonwith other speedmeasures.
As discussedin the introduction,an outcomeof this type is more consistentwith the
weakinterpretationof theslopeparameterin whichit is consideredto be an indirect reflectionofthe speedfaclor involvedin
age-cognitionrelations.The existenceof the systematicrelations among the speededvariablesimplies that the various
speedmeasures
arenot independentwith respectto age-related
influences,but the presentdataofferlittle supportfor the view
that the slopeis a direct indicatorofthe speedfactorpostulated
to be involvedin mediatingsomeof the agedifferences
in cognition. The lact that the estimatedreliabilityof the slope(i.e.,
.65)waslowerthan that for the otherspeedmeasures
reported
in Tables3 and 5 raisesthe possibilitythat the weakerattenuation of the agerelationswith the slopemeasuremight be attributableto the lowerreliabilityof this measurerelativeto that of
the directly observedmeasures.To investigatethe extent to
which differentialmeasurementreliability contributedto the
resultssummarizedin Table8, correctionsfor attenuationwere
appliedto the correlationsbetweenageand speedand between
speedand the compositemeasureof cognition.Thesedisatten-
SPEEDMEDIATION
uatedcorrelationswerethen usedin the computationofpartial
correlations between age and cognition after controlling the
relevantmeasureof speed.Finally, to expressthe resultsin a
form comparablewith that of Table8, the squareof the partial
correlationwassubtractedfrom the squareofthe age-cognition
correlation, the differencedivided by the squareof the agecognition correlation, and the quotient multiplied by 100 to
yield a measureof percentageattenuation of the age-related
variance.Valuescomputed in this manner were 93Tofor the
Digit Symbol measure,85Vofor the Letter Comparison measure,987ofor the PatternComparisonmeasure,and only 46Vo
for the slope measure.Theseresultsthereforesuggestthat the
discrepanciesin the magnitudeof the attenuationof agerelations with the slopemeasurecomparedwith other measuresare
not simply attributable to lower measurementreliability, and
they henceserveto weakenconfidencein the interpretationof
the slopeasan index ofthe magnitudeofan age-relatedreduction in rate of cognitiveor mental processing.
Conclusions
Oneconclusionfrom this studyis basedon the discoverythat
the age-relatedinfluences on several measuresof memory
functioning were greatly attenuatedafter statisticalcontrol of
measuresof perceptualspeed.It thereforeseemsreasonableto
infer that a substantialproportion ofthe adult agedifferences
in at leastsomemeasuresof memory appearto be mediatedby
the same speedfactors that have been found to mediate age
differencesin reasoningand spatialabilities.
A secondmajor conclusionis that the speedinvolvedin the
mediation of age-cognition relations does not merely reflect
sensory and motor processesbut instead is related to how
quickly simple mental or cognitiveoperationscan be executed.
It is not yet apparent whether cognitiveoperation speedis a
fundamentalconstructor whetherit is a consequence
of something evenmore basic,suchasa reductionin certain attentional
processes.What doesappearclear, however,is that there is a
strong associationbetween measuresof mental or cognitive
speedand the negativerelationsbetweenageand cognitiveperformance.
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Press.
AcceptedOctober13,1992t
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