copyrisht
ree4
byth€Amsi€."r"n,"d6liffi;?$ffdr,ffi
Derelqmental R)rcholoS/
1994.Vol. 30. No. 2. 2rl0-259
The Nature of the Influence of Speedon Adult
Age Differencesin Cognition
Timothy A. Salthouse
Two studieswere conducted to determine the relations among age,motor speed,perceptual speed,
and 3 measuresof cognitive performance: study time, decision time, and decision accuracy. Each
study involved over 240 adults between I 8 and over 80 yearsof agewho all performed a battery of
tests,including computer-administered
testsof memory,reasoning,and spatialability. The results
indicated that (a) increasedagewasassociatedwith lower accuracyaswell aswith longerstudy time
and decisiontime and (b) someofthe relations betweenageand decision accuracyand betweenage
and decisiontime appearto be mediated by a slowerrate ofexecuting cognitive operations.
A convincing argument that a construct is involved in the
mediation of the relationsbetweenageand cognition could be
basedon the followingcombinationof evidence:(a) demonstration ofa negativerelation betweenageand measuresofthe hypothesizedmediator,(b) demonstrationof a positive relation
betweenmeasuresof the mediator and measuresof cognition,
and (c) substantialattenuationofthe relationsbetweenageand
cognition after measuresof the mediator are statisticallycontrolled.Severaltheoreticalconstructshavebeenproposedaspotential mediaton of the relations betweenage and cognition,
with reducedattention(e.g.,Stankov,I 988)and failure ofinhibition (e.g.,Hasher& Zacks, 1988)amongthe most prominent
at the current time. Most of the researchconcerningtheseparticular constructshasbeenfocusedon establishingrelationsbetween age and measuresof the hypothesizedmediators.The
linkagebetweentheseconstructsand cognitivefunctioning has
seldombeendirectly investigated,and little or no evidenceis
availableconcerningthe magnitudeofthe attenuationofthe age
differencesin cognition when the variancein the measuresof
the hypothesizedmediatoris held constant.
Two theoreticalconstructsin which eachtype of evidenceis
availableareworkingmemory capacityand speedof processing
(e.g.,Salthouse,1991,1992a,1992b,1992e:
Salthouse
& Babcock, I 99 I ). However,thereis alsoevidencethat the attenuation
of the age-cognitionrelationsis greaterafter measuresof processingspeedare controlled than after measuresof working
memory are controlled,and that the relationsbetweenageand
working memory are substantiallyattenuatedwhen processing
speedmeasuresare controlled(Salthouse,1991, 1992a,1992qSalthouse& Babcock,1991).Thkentogether,theseresultssuggestthat processingspeedmaybe more fundamentalthan working memory asa mediatorof age-cognitionrelations.
This researchwassupportedby National Institute on Aging Grant
AG06826. I thank Vicky Coon, Jane Crawford, Jennifer Davidson,
Alan Kersten,Elinor Nixon, JamesRieder,Judi Rieder,and Jocelyn
Thomasfor assistance
in data collectionand Julie Earlesfor comments
on an earlierversionofthe manuscript.
Correspondence
concerningthis article shouldbe addressedto Timothy A. Salthouse,SchoolofPsychology,GeorgiaInstitute ofTechnology,Atlanta,Georgia30332-0170.
Considerableevidencenow existsindicatingthat a largeproportion ofthe age-relatedvariancein many different cognitive
variablesis sharedwith a measureof perceptualspeed.Among
the most pertinent resultsare the findingsthat the age-related
diffbrencesin various measuresof cognitive functioning are
greatlyreducedwhen statisticalcontrol proceduresare usedto
adjust for differencesin perceptualspeed.As an illustration of
this phenomenon,Thble I in Salthouse(1993b)contains44
comparisonsacrossa wide rangeof cognitivevariables.Agewas
associatedwith a mean of l6.2Voof the total variance in the
variables,but after the varianceassociatedwith measuresof
perceptualspeedwas held constant,age was associatedwith
only 3.6Voofthe variancein the cognitivevariables.
One interpretation of this pattern of resultsis basedon the
assumptionthat the well-documentedfinding that increased
with lowerscoreson many measuresof speeded
ageis associated
performancereflectsan age-relatedreductionin the speedwith
which many cognitiveoperationscan be executed.All cognitive
processesare not necessarilyaffectedby this age-relatedslowing, and theremay be more than one distinct speedfactor operating. However,it is assumedthat when the requiredoperations
are very simple,asin many perceptualspeedtasks,much of the
variation in performance is associatedwith the speedwith
which many elementarycognitiveoperationscan be executed.
It is alsohypothesizedthat this slowerprocessingimpairs higher
orderprocesses
suchasintegrationand abstractionbecauseless
relevantinformation is simultaneouslyavailablewhen needed.
This argumentwasillustratedabstractlyin a computersimulation describedin Salthouse( I 988),andthe ideashavebeenelab(1992a)andSalthouse
oratedin Salthouse
andBabcock(1991).
A basicpremiseis that ifdecay rate remainsconstantacrossage
but thereis an age-relatedslowingofthe rate ofactivation, then
someof the early information will no longerbe availableby the
time that later information has been processed,and that this
will be true to a greaterextent in older adults than in young
adults.A fundamentalimplication of this interpretationis that
slowerprocessingleadsto an impairment in the quality of deci
sionsand not simply in a longertime to reachand communicate
decisions.
The presentproject had three major goals.The first goal was
to determinewhetherthere is comparablespeedmediation of
240
24r
SPEED INFLUENCE
the agerelationson cognitivemeasuresobtainedwithout time
limits. Most of the previousstudieshaveusedtimed paper-andpenciltests,andthus it is possiblethat the attenuationofthe age
relationsaftercontrol of measuresof perceptualspeedmight be
smaller with power tests in which there are no external time
limits. There is someevidencethat this is not the case,but the
relevantdata are basedon only a few small-scalestudies(e.g.'
1993a).
Salthouse.
The secondmajor goal ofthe project was to investigatethe
type of speedmediation involved in the relationsbetweenage
and cognition. One theoreticallyinterestingdistinction is between motor speedand perceptualspeed.Motor speedtasks
typically haveminimal cognitiverequirementsand can be postulatedto primarily reflectthe speedof sensoryand motor proIn contrast,perceptualspeedtasksinvolve varioustypes
cesses.
of cognitive operations,such as comparison,substitution, or
transformation,in addition to sensoryand motor processes.
(1993b;alsoseeSalthouse,1992b)recentlyreported
Salthouse
that the attenuationof the age-cognitionrelationswas larger
when perceptualspeedmeasureswere controlled than when
motor speedmeasureswere controlled. One purpose of this
project wasto attempt to replicatethis pattern with the same
paper-and-pencil
speedmeasuresusedearlier and to extendit
to new speedmeasuresderived from computer-administered
tasks.
The degreeof cognitiveinvolvement in computer-administeredspeedtaskswasvariedby alteringthe numberofcognitive
operationsrequiredto perform the task.That is, the number of
digit-symbolpairswasmanipulatedin a digit-symbolsubstitution test,andthe numberof memory setitemswasmanipulated
in a memorysearchtest.Cognitiveinvolvementwasassumedto
be minimal in the simplestversionsof the taskbut progressively
greaterin tasksrequiring multiple comparison,association,
memory search,or substitutionoperations.The degreeof cognitive involvementwas also postulatedto be minimal in the
interceptparameterof the regressionfunctionsrelatingnumber
of operationsto reactiontime, but substantialin the slopeparameterof thosefunctionsbecausethe latter can be presumed
to reflectthe duration ofcognitive operationssuch as association or memory search.
A third major goal of the project wasto examinethe relation
amongage,various measuresof speed,and three measuresof
performancederived from computer-administeredcognitive
tests,namely,studytime, decisiontime, and decisionaccuracy.
There are severalpossiblewaysin which thesevariablescould
be interrelated,and eachhasdifferentimplicationsfor the manner in which a slowerspeedof processingmediatesthe relations
betweenageand measuresof cognitivefunctioning. For example, increasedagemight be associatedwith longerstudy or solution time and with longerdecisiontime, but not with lower
decisionaccuracy.A pattern ofthis type would suggestthat despite an age-relatedslowing of certain types of processing,
adults of all agesmay be equallyable to achievethe samelevel
of decisionaccuracywhen allowedsufficienttime. Conversely,
negativerelationsmight exist betweenageand decisionaccuracy independentofany relationsbetweenageand study time
or decisiontime. An outcomeof this type would obviouslybe
consistentwith the theoreticalperspectiveoutlined earlier becauseage-relatedeffectswould be evidentin the quality ofthe
decisionsin addition to effectson the time to reachor communicatedecisions.
Relationsmight also exist among the study time, decision
time, and decisionaccuracyvariables.For example,a speedaccuracytrade-off might be evident in the form of a positive
relation (higheraccuracyassociatedwith longertime) between
decisionaccuracyand eitherstudy time, decisiontime, or both.
Alternatively,the relation could be negative,indicating that
peoplewho are slow are also not very accurate.Finally, it is
alsoof interestto determinethe nature of the relationsbetween
variousspeedmeasuresand both studytime and decisiontime.
If a common speedfactor influenceseverytime measure,then
strongrelationsmight be expectedamongall measures.
Becausethe pattern of relationsamongthe variousmeasures
could vary acrosstests,it is important that analysesof the tlpe
just describedbe conducted with severaldifferent cognitive
tests.Moreover,it is alwaysdesirableto examinethe reliability
of the major findingsby attemptingto replicatethem in an independentsampleofsubjects.This project thereforeconsisted
oftwo separatestudies,both containing paper-and-penciland
speedtests,andthreecomputer-admincomputer-administered
isteredcognitivetests.Within eachstudy,the computer-administeredcognitivetests,which wereassumedto require memor!.
reasoning,or spatial ability, were designedto yield separate
measuresof study time, decisiontime, and decisionaccurac)'.
Three analytical methodswere used:hierarchicalmultiple regressionto determinethe amount ofage-relatedvariancebefore
and after control of the variancein different speedmeasures:
commonalityanalysisto partition the age-relatedvarianceinto
portionsunique to ageand sharedwith motor speed,perceptual
speed,or both; and path analysisto examinethe interrelations
amongthe age,speed,study time, decisiontime, and decision
accuracyvariables.
Study I
Method
Subjects. Table I summarizesthe characteristicsofthe 246 adults
betweenI 8 and 84 yearsofage who participatedin Study l. (Adults in
their 70sand 80sare reportedtogetherbecauseofthe small number of
individuals in each of theseagedecades.)The subjectswere recruited
clubs,orgafrom a variety ofsources,such as personalacquaintances,
and eachwaspaid for particinizations,or neighborhoodnewspapers,
pating in a singlesessionlastingapproximately2 to 3 hr. None of the
subjectswascurrently attendingschoolon a full-time basis.
"How
Two backgroundquestionsconcernedthe subject'seducation:
"Which
of
many yearsof formal educationhaveyou completed?"and
(<12,12, 13-15, 16, >16) best describesthe highest
five categories
grade(or degree)you havecompleted?"The correlation betweenresponsesto theseitems was .93. The entry in Thble I representsthe resultsfrom the questionofhow many yearsofeducation had beencompleted.This variablehad a correlationwith ageof -.20 (p < .0 I ).
health' One quesSix backgroundquestionsweredesignedto assess
rangingfrom I =
a
scale
health
on
ofone's
for
an
evaluation
asked
tion
excellentto 5 : poor. Three additional questionsalso used a 5-point
scaleandaskedfor ratingsofoverall health,satisfactionwith health,and
degreeof limitations of daily activitiesowing to health status.Correlationsamongthesemeasuresweremoderateto high (.47 to .78). Two
yes/noquestionsaskedwhetherthe individual had had surgeryfor cardiovascularproblemsor wastaking medicationfor high blood pressure.
242
TIMOTHY A. SALTHOUSE
Thble 1
D emographic Characteri stics of Research Part icipants
Eduation
(years)
Age
(yean)
Decade
Vo
female
M
Health'
SD
M
SD
Study I
20s
30s
40s
50s
60s
70s+
48
43
48
40
44
Total
z)
23.4
33.9
44.2
54.7
64.6
75.0
46
58
69
72
6l
65
14.7
15.5
14.8
t4.r
14.0
l3.l
2.1
1.6
2.1
2.2
2.6
2.2
1.8
2.2
2.0
2.6
2.0
2.4
0.'l
0.9
0.9
1.2
1.0
0.8
246
46.6
6l
14.5
2.2
2.t
1.0
Study2
20s
30s
40s
50s
60s
70s+
Total
35
58
50
46
36
25.t
34.0
44.6
54.2
64.5
75.8
46
59
66
73
52
69
15.0
15.8
r 5.6
14.9
15.7
14.3
t.7
2.3
2.3
2.2
2.5
2.4
t.8
1.8
2.0
2.0
1.9
2.0
0.7
0.8
0.9
0.8
0.9
1.0
258
48.7
60
15.3
2.3
1.9
0.8
JJ
' From | = excellenl and 5 -- poor.
Responses
to theseitemshad very low correlationswith the other items
(.04 to .27). The health variable in Table l refersto the first overall
healthrating,which had a correlationwith ageof. I 3 (p > .0 I ).
Procedure. Subjectsweretestedin groupsof I to 4, and for the computer-administered
testsa separatepersonalcomputerwasprovidedfor
eachsubject.All subjectsperformed the testsin the following order:
Boxes,PatternComparison,Number SeriesCompletion,Name Numbet CubeAssembly,Letter Comparison,Digit Copying,Digit Symbol,
PaperFolding,Matrix Reasoning,and AssociativeMemory. The abilities postulatedto be assessed
by the testsweremotor speed(Boxesand
Digit Copying),perceptualspeed(PatternComparison,LetterComparison, and Digit Symbol), reasoning(Number SeriesCompletion and
Matrix Reasoning),spatial visualization(Cube Assemblyand Paper
Folding),and memory(Name Number and AssociativeMemory).
The first seventestswerein a paper-and-pencil
format. The Boxestest
wasfrom Salthouse( I 993b).The form for this testconsistedof l0 rows
of l0 three-sidedsquareswith the top, bottom, left, or right sideopen.
The task for the subjectwasto draw a line acrossthe opensideto make
a closedbox, and the measureofperformancewasthe number ofboxes
drawn within 30 s.
The Digit Copy test was also from Salthouse(1993b).The form in
this testconsistedof l0 rowsof l0 pairsofboxes with a digit in the top
box and nothing in the bottom box. The taskwasto copythe digit from
the top box in the box immediatelybelowit, and the measureof performancewasthe numberof digitscopiedwithin 30 s.
The Letter Comparisontest wasfrom Salthouse(1991, 1993b)and
Salthouseand Babcock(1991), and it required the subjecrto inspect
pairsofthree, six, or nine lettersand then write an S ifthe two pairsare
the sameand a D if they are different. The test form consistedof a
singlecolumn of 2l pairsof letterswith a blank line betweenthem. The
measuresof perflormancewere the numbersof correct and incorrect
producedwithin 30 s.
responses
The PatternComparisontest wasalsofrom Salthouse( 199I, I 993b)
and Salthouseand Babcock( I 99I ). Subjectsin this test wereaskedto
inspectpairs ofline patternscomposedofthree, six, or nine line seg-
mentsand then to write an S if the pair of patternsis the sameand a D
ifthey are different.The test form consistedoftwo columnsof 15pattern pairs,eachwith a blank line betweenthe two membersof the pair.
The numberofcorrect responses
and the numberofincorrect responses
producedwithin 30 s servedasthe measuresofperformancein this test.
Threeofthe paper-and-pencil
testswereadministeredfor 2 min each.
The Number Seriestest wassimilar to the Number SeriesCompletion
testdescribedby Salthouseand Prill ( 1987).The test form consistedof
20 problems,eachinvolving a seriesof five elements.First-orderproblemswerebasedon a simplecontinuation(e.g.,2-4-6-8-lO-?),secondorder problemswerebasedon a relationamongthe differencesbetween
elementsratherthan amongthe elementsthemselves(e.g.,2-4-7-l l-16?), and alternating-orderproblems consistedof two interleavedrelations (e.g.,2-13-4-l l-6-?). Each successive
set of 5 problemshad I
first-orderproblem, 2 second-orderproblems,and 2 problemswith alternatingrelations.Subjectsansweredthe problemsby writing the best
continuationofthe serieson the testform.
The Cube Assemblytest wasoriginally basedon a task describedby
Shepardand Feng( I 972), and it hasbeenusedpreviouslyin Salthouse
( I 99I, I 992d).Problemsin the testconsistof a patternof six connected
squaresrepresentingan unfoldedcube.One ofthe squaresis markedas
the baseofthe cube,and two squarescontain arrows pointing to one
sideofthe square.The task is to decidewhetherthe arrows would be
pointing at one anotherifthe squareswereassembledinto a cube.The
testcontains24 problems,with an equalnumberof problemsin which
one,two, or three folds wererequiredto assemblethe cube.One problem ofeach type waspresentedbeforeanotherofthe sametype. Decisionswerecommunicatedby placinga checkin a column labeledYES
(indicatingthe arrows would touch) or in a column labeledNO (indicating they would not touch), locatedadjacentto the problem on the
testform.
The Name-Number test consistedof the presentationof l0 first
names(5 male and 5 female),eachpaired with a number betweenl0
and 99. The pairswerepresentedtogetherfor I min, and then the subject was presentedwith the list of namesin a reorderedsequenceand
was allowed I min to write the numbersassociatedwith the names.
Performancewasassessed
in terms ofthe numbersofcorrect and incorrectname-numberpairs.
All computer-administered
testswere precededby written instructions and severalpracticetrials, and all exceptthe first test had a primary emphasison accuracyrather than speed.The Digit Symbol test
wasbasedon the test describedin Salthouse(1992c\.Nine. 6. 3. or 0
digit-symbolpairswerepresentedin a codetable in the top of the computer screen,and a pair of items, either a digit and a symbol or two
digits, appearedin the middle of the screen.The subjectswere instructedto respondwith the rightmost slash(/) key on the bottom row
of the keyboardif the items were physicallyidentical or matchedaccording to the codetable,and with the leftmost(Z) key on the bottom
row of the keyboardif the items did not match. One practiceblock of
l8 trials waspresentedwith nine digits and nine symbols,followedby
eight experimentalblocks of 90 trials each.The number of symbols
acrossthe eight blocks were 9, 6, 3, 0, 0, 3, 6, and 9, respectively.In
conditionswith either3 or 6 symbols,oneof the blockshad the symbols
pairedwith the first n digits (wheren is 3 or 6), and the other block had
the symbolspaired with the last n digits. The remainingdigits had the
symbol in the codetable replacedwith identicaldigits (e.g.,2 with 2, 4
with 4, and soon). Trial selectionwasbasedon all nine digits regardless
of condition, and thus approximatelyone third and two thirds of the
involvedcomtrials in the conditionswith 6 and 3 symbols,resp€ctively,
parisonsof pairsof digits ratherthan a digit pairedwith a symbol.One
halfofthe trials in eachblock requireda positiveresponse(becausethe
membersof the pair matched),and one half required a negativeresponse(becausethe membersofthe pair did not match).Subjectswere
instructedto respondasrapidly and accuratelyaspossible.
243
SPEED INFLUENCE
The computer-administered
PaperFoldingtest wasbasedon the test
ofthe samename describedin severalearlier articles(i.e., Salthouse,
Babcock,Mitchell, Palmon,& Skovronek,1990;Salthouse,Babcock,
Skovronek,Mitchell, & Palmon, 1990;Salthouse,Mitchell, Skovronek,
& Babcock,I 989).Trials in this taskwereinitiated by pressingthe ENTER key on the keyboard.This led to a dynamicdisplayof the fint fold,
and subsequentlolds or the location ofthe hole punch weredisplayed
pressofthe ENTER key.After the displayofthe
after eachsuccessive
punch location,anotherpressofthe ENTER key resultedin a display
ofa patternofholes accompaniedby the words NO on the lowerleft of
the screenand YES on the lower right of the screen.Decisionswere
communicatedby pressinglhe Z or slashkey,respectively.
Three trial
typesweredistinguishedon the basisofthe number offolds (one,two,
or three)presentedbeforethe displayofa hole punch. Subjectscould
inspecteachdisplayofthe product ofa fold or the holepunch aslongas
desiredand couldtakeaslongasnecessary
to makea decision.The total
time inspectingthe foldsand examiningthe position of the holepunch
servedas the measureof study time, and the time to respondto the
patternofholes servedasthe decisiontime. A practiceblock of3 trials
containeda detailedexplanationofthe task, and it could be repeated
as often as desired.This wasfollowedby two blocksof24 trials each,
composedof 8 trials with eachnumber of folds arrangedin a random
order.
The Matrix Reasoningtest wasbasedon the test describedin Salthouse( I 993a),which in turn wasbasedon the RavenProgressive
Matricestest.Problemsconsistedof a 3 X 3 matrix with geometricpatterns
in eachof eight cells and a set of eight patternsrepresentingpossible
completions
of the missingcell in the matrix.The matrix andthe completion alternativeswere presentedsuccessively
in separatescreenson
the computer.Studytime wasmeasuredasthe time to inspectthe matrix, and decisiontime wasmeasuredasthe time from the presentation
of the answeralternativesto the registrationof the numeric response
indicatingwhich ofthe answeralternativeswasselected.Subjectscould
inspectthe matrix and the setofalternativesaslongasdesiredbut could
not return to the matrix after advancingto the display of the answer
alternatives.
The practiceblock of 3 trials wasrepeatable,and it wasfollowedby
two experimentalblocksof I 8 trials each.Threetrial typesweredistinguishedby the number of relevantrelationsamongthe elementsin the
matrix(ci Salthouse,
I 993a).Sixtrialsin eachexperimental
blockcontained eachnumberofrelations, and they werepresentedin a random
order.
The AssociativeMemory test wasa continuouspaired-associate
task
designedto measurethe ability to remember associationsbetween
words and digits. The test involved the presentationsof either a word
pairedwith a digit (from the setofone, two, or three)or a singleword.
When a word and a digit were presented,the subjectwas allowedto
inspectthe pair for aslongasdesired.Whena word waspresentedalone,
the subjectwasto type the digit that had beenpreviouslypresentedwith
that word. The time devotedto the initial inspectionof the word-digit
pair wasusedasthe measureof studytime, and the time to entera digit
in responseto the testword wasusedasthe measureofdecisiontime.
A practicelist of 6 pairswaspresented,followedby an experimental
list of90 pairswith 24 tests(8 eachat lagsofzero, two, or four intervening items).The stimuluswordswerenounsbetweenfour and eight letters in length with Kucera-Francisfrequenciesof l0 or greaterwith
aboveaverageratingsin concreteness
and imagery,from the Toronto
Word Pool(Friendly,Franklin, Hoffman,& Rubin, 1982).
Resultsand Discussiort
Because
of the manystatisticalcomparisons
and the relativelylargesamplesize,analphalevelof .01wasadopted
for all
statistical
significance
testsreportedin thisarticle.
Table2
Summary StatisticsforPrimary Depmdmt Variables,Study I
R2
Variable
Boxes
Digit Copy
Letter Comparison
PatternComparison
Digit Symbol-O(s)
Digit Symbol-9(s)
Intercept(s)
Slope(s)
Correct- incorrect
Number Series
CubeAssembly
Name Number
Eocorrect
PaperFolding
Matrix Reasoning
AssociativeMemory
Decisiontime (in s)
PaperFolding
Matrix Reasoning
AssociativeMemory
Studytime (in s)
PaperFolding
Matrix Reasoning
AssociativeMemory
M
Est.
Rel,
Linear
age
Quadratic
age
.78"
.84"
.38"
.52'
.94b
.95b
.86b
.44b
.290*
.28I i
. 2 5l i
.374+
.262|
.374i
.294*
.ll5i
.006
.030r
.018
.001
.046*
.02I r
.027*
.001
4.23 .67"
4.70 .70"
3 . 8 1 .46
.It8*
.09I |
.070*
.004
.012
.006
.215]
.t49*
.07I |
.007
.009
.001
.336'
.241i
.2314
.005
.009
.050r
SD
50.5 l3.l
51.5 tt.2
9.4
3.4
t5.4
3.9
0.'16 0.23
1.50 0.40
1.05 0.30
0.05
0.03
2.49
4.02
l.l5
69.7
57.5
67.5
I 1.9
21.9
t2.2
.72.
.88"
.45"
2 . 4 1 0 . 8 2 .89'
6.00 3.94 .93"
2 . 8 8 t . 4 6 .93'
6.24 3.55 .93" .057'
26.89 14.42 .90" . 0 6 1 t
| . ' 7 6 l . t 1 . 9 6 ' .023
.001
.017
.007
Note. Est.Rel.= estimated
reliabilities.
" Alternate-forms
correlationfrom a sampleof 2 l2 collegestudents.
bCorrelationbetweenscoreslrom first and secondadministrations
formula. " Computedfrom correboostedby the Spearman-Brown
lationsacross
with formulain Kenney( 1979,
threelevelsof complexity
p. 132):Reliability= n(average
r)lll + (n - l)(average
r)1.
*p<.01.
Table 2 contains the means,standarddeviations,estimated
reliabilities,and R2 valuesfor the linear and quadratic agerelations for the primary dependentvariables.Quadratic trends
wereevaluatedby an age-squared
term enteredafter the linear
ageterm in a multiple regressionequation and after both the
variableshad beencenteredto means
ageand the age-squared
of zero to reducepotential multicollinearity problems(Cohen
& Cohen, 1983). Becausethe quadratic trends were always
small in relation to the linear trends,they wereignoredin subsequentanalyses.
Most reliabilities were in the respectablerange, although
those for the Name Number measureand for the measureof
decisionaccuracyin the AssociativeMemory test were much
lowerthan desirable.In both casesit appearsthat the tasksmay
have been too difficult for many of the researchparticipants
becausethe averagelevelsof performancewerequite low. Reliability estimatesfor the Letter Comparisonand PatternComparison variableswere low in the pilot sample of collegestudents,perhapsbecauseofthe restrictedagerangein this group.
However,thesevariableshad correlationswith other variables
in this samplethat were higher than the estimatedreliability,
and thus the reliability in the presentsamplewaslikely greater
than that derivedfrom the studentsample.As an example,the
244
TIMOTHY A. SALTHOUSE
correlationsof the LetterComparisonand PatternComparison
variableswith agewere-.50 and -.61, respectively,
andthe correlationbetweenthe two variableswas.55.
pmcil tests. Performancein the paper-and-penPaper-andcil testswasinitially analyzedin terms of the number of correct
responses,
the number of incorrect r€sponses,
and the number
of correct responses
minus the number of incorrect responses.
The age relationswere weak with the measureof number of
incorrect responses,
as the agecorrelationswere -.03 for Pattern Comparison,.09 for Letter Comparison,.13 for Number
Series,. l8 for Cube Assembly,and .06 for Name Number Association.Only the correlation for Cube Assemblywassignificantlydifferentfrom zero.The agerelationsweresimilar for the
measuresof number correct and number correct minus number incorrect, and the correlationsbetweenthe two measures
weregenerallyhigh: PatternComparison,r : .96; Letter Comparison,r : .96; Number Series,r = .86; Cube Assembly,r :
.71; and Name Numbe4 r = .86. To providean adjustmentfor
guessing,all subsequentanalysesusedthe variable of number
correctminus number incorrect for the paper-and-pencil
tests.
Preliminary Age(by decade)X Complexity Level analysesof
variance(ANOVAs)wereconductedon the data from the three
computer-administeredcognitive tests to determine whether
the agerelationsvariedaccordingto taskcomplexity(i.e.,number of folds in PaperFolding, number of relationsamong elementsin Matrix Reasoning,and presentation-testlag in AssociativeMemory). Perhapsbecauseof the small number of trials
at each complexity level, the Age X Complexity interactions
werenot significantwith the decisionaccuracymeasurein any
of the tests.Moreover,this wasalsotrue in restrictedsamplesof
subjectswho all had accuracyin the simplest condition (i.e.,
one fold, one relation,or lag 0) abovethe meanfrom the entire
sample.Only the meansacrossall three complexity levelsare
thereforeconsideredin subsequentanalyses.
Scoresfrom the paper-and-pencilspeedtestsand the mean
responsetimes in the Digit Symbol test with zero (DigSym-0)
and nine (DigSym-9)symbolswereconvertedto standarddeviation units on the basisof the entire sampledistribution and
were plotted as a function ofdecade in Figure l. Becausethe
.
Digit Symbol measuresare expressedin units of time per item
rather than number of items in a fixed period of time, higher
scoreson thesemeasurescorr€spondto poorer performance.
Inspectionof Figure I revealsthat the patternswith eachmeasureare very similar in that the averagein the decadeofthe 20s
is about *.5 (or -.5 for the Digit Symbol measures)and the
averagein the decadeof the 70s is about - I .0 (or * I .0 for the
Digit Symbol measures).The tendencyfor the function for the
Digit Symbolmeasuresto be positivelyacceleratedaccountsfor
the presenceofthe significantquadraticagetrendsin thesemeasuresreportedin Table2.
The sametype of conversionto standarddeviationunits was
conductedfor the measuresof number correct minus number
incorrect in the three paper-and-pencil
cognitivetests,with the
meansby decadeplotted in Figure 2. As in Figure 1, the age
trendsarenearlymonotonic,with meansthat rangefrom about
+.5 in the decadeof the 20s to between-.5 and -1.0 in the
decadeofthe 70s.
Digil symbol. Mean reaction time and mean percentageof
errors in the Digit Symbol test are plotted asa function of num-
.|.5
Boxes
--.l-
Dlglgtv
LetCom
...4...
o
.€
c
f,
c
t
0.5
PatCom
DigS;m-0
aF-:
.o
-"-l
E
o
o
DigSIm-g
.-:-'l'.
\ 1 1 _ .
0
E
(6
o
{.5
c
.l-
t'ot'
u--.
(u
a
^
.1.5
2
0
3
0
4
0
5
0
6
0
7
0
8
0
Age
Chronological
Figurel. Meanstandarddeviationscoresby decadefor the speed
measures,
Studyl. DigCopy: DigitCopy;LetCom= LetterCompariDigSym-0= Digit Symbolwith
son;PatCom: PatternComparison;
zerosymbols;
DigSym-9: DigitSymbolwith ninesymbols.
ber of symbolsand agedecadein Figure 3. Both variableswere
analyzedby separaterepeatedmeasuresANOVAsin which age
wascategorizedby decadeand numberof symbolswasa withinsubjectsvariable.Only the main effectof number of symbols
wassignificantin the analysisof errors,F(3,720): 19.38,MS"
= 3.21. All three effectswere significantin the analysisof re-
CubsAssm
--aNumSsr
o
c
l
c
NameNum
. .t.
o'5
"'\ r.
-.\
'..
\ . \ . ' ">r k "- " ' . X . . "
o
l
(E
A
o
o
P
-tl.
R
x
t .:r.-..
*. i..
ij {.5
c
ct
fl
-ra
t..'r
a
*
-1
-1.5
2
0
3
0
l
m
5
0
6
0
7
0
8
0
Chronological
Age
Figure 2. Mean standard deviation scoresby decadefor the number
correct minus the number incorrect scoresin three paper-and-pencil
cognitivetests,Study l. CubeAssm: CubeAssembly;NumSer: Number SeriesCompletion;NameNum : Name-Number test.
245
SPEED INFLUENCE
DigitSymbol
PaperFolding
os€bols
.t
6 15m
o)
o
g
o
E
-.1
"
*"-+
r '.
l
.'
t
......-r
..r'
'
.l
..t
I
3 Syq$olsT-t
6 sJlbols I
A
9 Symbols
&
=o
0.5
\
o
--ll"
- \ r
a_.\
(E
1"-""
A
F l m
o)
tn
c
o
o_
lt,
o)
(E soo
o
o
s R
6 g
--]-
StutIImo
f
c
.L'
Porcsnta6
--a- Core{
Dscision'Iime
I
o
E
r
'0.s
€
c(U
a
-1
f'
L
..
,,,\
, ...;)-----'t' ,
\
\
r $
z p
20
30
70
8o
U
Chronological
Age
c#onorolor n?"
Figure3. Meanreactiontime andmeanpercentage
of errorsin the
Digit SymbolSubstitution
testas a functionof the numberof digif
symbolpairsby decade,
StudyL
sponsetimes:agedecade,F(5,240) : 28.79,MS": 24g,ttDt
numberof symbols,
F(3,720) = 1,799.20,
MS" : 14,100;and
Age DecadeX Number of Symbols,F(14,720) : 9.O2,MS.
= 14,100.The patternin Figure3 suggests
that the significant
interaction in the responsetime variable is a consequenceof
largeragerelationson trials with more symbols.The agecorrelationswereconsistent
with this interpretation,astheywere.51
for zerosymbols,.59 for threesymbols,.59 for six symbols,and
.61for nine symbols.
Onemannerin whichthe Digit Symboltestcanbe conceptualizedis to assumethat performancein the nine-symbolversion
ofthe testreflectsprocesses
ofencoding,responding,and search
of the codetable,and that performancein the zero-symbolversionofthe testonly requiresprocesses
ofencodingand responding. Accordingto this interpretation,the slopeofthe function
relatingthe numberof symbolsto responsetime representsthe
time to decideto searchthe code table and to carry out the
search.One or both of theseprocessesshould occur on one
third. two thirds. or all of the trials whenthe codetablecontains
three, six, or nine symbols,respectively.Regressionequations
relating number of symbols (betweenthree and nine) to responsetime were therefore computed for each subject. The
mean of the correlationswas .95, indicating that the fit of the
regressionequationswasgenerallygood. The meanof the slope
parameterswas 5l ms per symbol. The intercept of theseregressionfunctions can be hypothesizedto representthe time
neededto respondwhen no searchprocesses
are required.The
meanof the interceptparameterswas 1,049ms, which wassubstantiallygreaterthan the mean responsetime in the DigSym0 condition (i.e., 760 ms). One possibleinterpretation of this
discrepancyis that the additionaltime in the interceptparameter in relation to the actual time to respondwith zero symbols
representsuncertaintyaboutwhen,and hoq to searchthe code
table.
Both the slopeand the interceptparameterswerelargerwith
Figure4. Meanstandarddeviationscoresby decadefor the study
time,decision
time,anddecision
accuracy
measures
in thePaperFoldingtest,Studyl.
increasedage(cf. Table 2), as was the differencebetweenthe
intercept and the DigSym-Otime (i.e., agecorrelation : .22).
Theseresultssuggestthat increasedageis associated
with slower
encoding and responseprocesses(DigSym-0 and intercept),
slowersearchof the codetable (slope),and a longertime to decide to searchthe codetable (diffbrencebetweenthe intercept
and DigSym-0).
Computer-administeredcognitive tests. For each of the
computer-administered
cognitivetests,meanstudy time, mean
decisiontime, and meandecisionaccuracyacrossall complexity levelswereconvertedinto z scores,and the meanswereplotted asa function ofdecade.Resultsfrom the PaperFoldingtest
are illustrated in Figure 4, those from the Matrix Reasoning
test in Figure 5, and thosefrom the AssociativeMemory test in
Matrix Reasoning
Por€ntaos Correct
+
DecisionTime
--]-
stu-d.f,Ire
o
-_
I
c
o
.E
A
o
o
-q
o
0.5
-t.
o
-o.5
c
(!
a
z
J
3
0
,
O
5
0
6
0
7
O
e
O
ChronologicalAge
Figure 5. Mean standard deviation scores by decade for the study
time, decisiontime, and decisionaccuracymeasuresin the Matrix Reasoningtest,Study l.
246
TIMOTHY A. SALTHOUSE
AssociativeMemory
Series,Matrix Reasoningdecisionaccuracy,and PaperFolding
accuracy.In all cases,the effectswerein the direction ofgreater
Docbi$Tlmo
educationassociatedwith higher scores.More educationwas
Stud\limo
alsoassociatedwith longerstudytimes in the Matrix Reasoning
o
.E
test but with shorter decisiontimes in the PaperFolding and
:)
AssociativeMemory tests and with shorter DigSym-0 times.
0.5
c
o
Better self-reportedhealth wasassociatedwith higher scoreson
r!
'5
Boxesand Matrix Reasoningdecisionaccuracyand with faster
o
o
o
DigSym-0 and Digit Symbol intercept scores.Women pertt
formed at significantlylowerlevelsthan men on Number Series,
tU
p
{.5
Cube Assembly,and PaperFoldingdecisionaccuracy,but they
(t
performedsignificantlybetterthan men on Letter Comparison.
a
Most important for subsequentanalyses,none of the interactions betweenageand thesepredictorsweresignificant,indicating that the agetrendswerenot moderatedby thesefactors.
m 30
'
80
A confirmatory factor analysisspecifyingtwo correlatedfac"ilono,ln,o,L"
tors was conductedon the four paper-and-pencilspeedmeasures(i.e., Boxesand Digit Copy as measuresof motor speed
Figure6. Meanstandarddeviationscoresby decadefor the study
and Letter Comparisonand Pattem Comparisonas measures
time,decision
time,anddecision
accuracy
measures
in theAssociative ofperceptual speed)to verify the proposeddistinction between
Memorytest,Studyl.
motor speedand perceptualspeed.The fit ofthe modelwasnot
impressive,x20, N : 246) : 5.02,adjustedGFI = .900,adjusted RMS - .142, and the correlation betweenthe motor
Figure 6. It is apparentin each figure that the agetrends are
speedand perceptualspeedfactorswasquite high (i.e.,.913).
generallymonotonic and that there are substantialageeffects
However,when the correlationbetweenfactorswasfixed to 1.0
on the measureof decisionaccuracyaswell as the measuresof
and the analysiswas repeated,the fit of the model was signifidecisiontime and study time. Theseresultsthereforeindicate
cantly poorer,differenceX2(I, N = 246) : 4.94),implying that
that, in conditionsin which accuracyis emphasizedand subalthoughthe correlationbetweenthe two factorsis very high, it
jects are allowedto proceedat their own pace,increasedageis
is lessthan 1.0.
associated
with lessaccuratedecisionsaswell aswith more time
Although the resultsof the confirmatory factor analysisdid
usedto reachand communicatethe decisions.
not provideconvincingsupportfor the distinction betweenmoRegressionanalyses. A seriesofmultiple regressionanalytor speedand perceptualspeedin this study,the resultsofother
ses was conducted to evaluate the relative contribution of
analysesthat werebasedon the sameor very similar measures
different factorsto the agedifferencesin the primary perfor(e.g.,Salthouse,1993a,1993b)and the resultsofan identical
mancevariables.To determine whethereducationand health
analysisconductedon the data of Study 2 wereconsistentwith
could be adequatelyrepresentedby compositevariables,I conthe hypothesizeddistinction.I thereforedecidedto treat the two
ducteda confirmatory factor analysisspecifyingtwo factorson
setsof variablesas representingdistinct constructsdespitethe
the two educationvariables(number of yearsof formal educaweakresultsfrom the conlirmatory factor analysis.Becausethe
tion and the classificationofthe highestgradeor degreecomstandardizedweightsfor the variableson their respectivefactors
pleted)and on four healthvariables(two ratingsofthe individweresimilar (i.e.,Boxes: .80, Digit Copy : .90, LetterComual'sown health,onerating reflectingdegreeofsatisfactionwith
parison= .74,and PatternComparison: .74),the average
of
one'shealth,and one rating indicatingdegreeofhealth-related
the relevantz scoreswasusedas a compositevariablefor each
limitations). The fit of the model wasgood, as revealedby the
construct.
followingindices:x2(8,N : 246) : 10.46,adjustedgoodnessTwo variablesfrom the Digit Symboltest-DigSym-O repreof-fix index (GFI) : .964, and adjusted root-mean-square sentingminimal cognitivedemandsand DigSym-9representing
(RMS) : .036. The correlation betweenthe education and
greatercognitiveinvolvement-were also used as speedmeahealthfactorswas-20. Becausethe standardizedweightsofthe
suresin the regressionanalyses.Although I originally planned
variableson their respectivefactorswere similar (i.e., .94 and
to usethe slopeand interceptofthe functionsrelatingresponse
.98for educationand .8 I to .90 for health,except.56 for healthtime to number of digit symbol pairs as additional speedmearelatedactivity limitations), compositescoresfor the education
sures,the low reliability of the slopeparameterand its weak
and health constructswere createdby averagingthe relevantz
relation with age (cf. Table 2) diminished the value of these
scores.
analyses,and consequentlythe intercept and slope variables
Each of the variablesin Thble 2 was examinedfor the preswere not included as predictors in the subsequentregression
enceof main effectsof gender,health, and educationand for
analyses.
interactionsofthesevariableswith age.The predictorvariables
Two separatesetsofanalyseswere conductedto yield inforwereall centeredto meansof zero to avoid problemsof multimation about both the moderatingand the mediatingeffectsof
collinearityand to facilitateinterpretationsofany interactions.
speed.One type of analysiswasdesignedto examinemoderatSignificantmain effectsof educationwereevidentin the following effects,as revealedby significant interactions of age and
ing variables:Boxes,Digit Copy,Letter Comparison,Number
speed.Interactionsofthis type would indicate that the age-rePtrcrnb8'Corec't
L
247
SPEED INFLUENCE
wereasfollows:Digit Copy(.0 16),PaperFoldingdecisronaccuracy (.023),Matrix Reasoningdecisiontime (.028),Associative
Memory decision time (.080), DigSym-O (.068), DigSym-9
(.028),and Digit Symbol intercept (.038).Interactionsinvolving age and DigSym-0 were significant with Cube Assembly
(.035),Matrix Reasoningstudytime (.035),DigSym-9(.010),
and Digit Symbol intercept (.011). Finally, two variableshad
significantinteractionsbetweenageand DigSym-9:Associative
Memory decisiontime (.026) and DigSym-0 (.045). Note that
all but two (i.e.,PaperFoldingdecisionaccuracyand CubeAssemblycorrect-minus-incorrect)of theseinteractionsinvolved
time or speedmeasuresasthe criterion variable.
The assessment
of mediationaleffectswas basedon a comparisonofthe proportion ofvariance(asreflectedin increments
in R2 correspondingto squaredsemipartialcorrelations)associated with age before and after the varianceassociatedwith
the measureof the hypothesizedmediator was controlled.For
example,the influenceof variationsin healthand educationon
the agedifferencesin the primary variablescan be determined
by comparing the proportion of varianceassociatedwith age
before(column 4 in Thble2) and after(column I in Table3) the
compositemeasuresof health and educationwere controlled.
Examination of thesevaluesrevealsthat there wassomeattenuation ofthe agerelations,particularly for the reasoningmeasuresof Number Series(i.e., R2 of .l l8 to .059)and Matrix
(i.e.,R2of .149to .080).However,
it is alsoapparent
Reasoning
lated influencesvary accordingto the levelofspeed,and hence
that speedmoderatesthe influenceofage. The secondtype of
analysiswasintendedto examinemediatingeffects,as revealed
by contrastsofthe magnitudeofthe age-relatedvariancebefore
and after control of the measureof speed.To the extent that
statisticalcontrol of a speedmeasureresults in a substantial
attenuationofthe age-relatedvariancein a criterion variable,it
can be inferred that the speedmeasureprobably playsa mediatingrole in the relationsbetweenageandthe criterion variable.
In the analysesofthe interactionterms, both the ageand the
speedvariableswerecenteredto meansofzero, and the crossproduct interactionterm wasenteredin the regressionequation
after both the age and speedvariables.If the interaction was
statisticallysignificant.the R2 associated
with the interaction
was then determined.All but two of the interactionswere in
the direction of smallerage-relatedinfluencesat fasterlevelsof
speed(or equivalently,largereffectsof speedat older ages).The
two exceptionswerewith the Cube Assemblyand Matrix Reasoning study time measures,in which the age-relatedeffects
were larger among subjectswith faster DigSym-0 scores.The
variableswith significantinteractionsbetweenageand the composite motor speedvariable,with the increment in R2 associatedwith the interactionpresentedin parentheses,
wereas follows: AssociativeMemory decision time (.056), DigSym-0
(.049),and DigSym-9(.018). Variableswith significantinteractions involving ageand the compositeperceptualspeedvariable
Table3
R2for Age After Control of Demographic and Speed Variables,Study I
R2 for aee after control of:
Criterion
Boxes
Digit Copy
Letter Comparison
PatternComparison
Digit Symbol-O
Digit Symbol-9
Intercept
Slope
Correct- incorrect
Number Series
CubeAssembly
NameNumber
9ocorrecl
PaperFolding
Matrix Reasoning
AssociativeMemory
Decisiontime
PaperFolding
Matrix Reasoning
AssociativeMemory
Studytime
PaperFolding
Matrix Reasoning
AssociativeMemory
Health.
education.
motor
speed
Health.
education.
perceptual
speed
Health,
education.
Dig.it
Svmbol-O
Health,
education.
Digit
Svmbol-9
.321*
. 18 7 *
.299*
.21l*
.l05r
.000
.000
.034i
.093*
.054*
.105+
.0'17+
.032*
.030
.01l
.005
.005
.026*
.049*
.o47+
.008
.108r
.075r
.063r
. 1 73 '
.075*
.035r
.02'7*
.094i
.001
.058i
.022*
.04'7+
.001
.002
.059*
.062*
.048*
.028r
.045*
.025
.003
.018
.007
.033i
.036*
.014
.009
.009
.016
.l6l+
.090r
.047*
.078*
.028*
.016
.041*
.010
.004
.073*
.024*
.ot4
.033*
.007
.009
.268t
.lg6r
.168*
.136*
.078+
.065*
.080*
.o43*
.036r
.l12+
.088r
.044*
.070+
.063+
.080r
.020
.045*
.039*
. 0 1l
. 0 31 *
.026+
. 0l 0
.048*
.069r
.01I
. 0 51 *
.036*
.007
Health,
education
.212*
.197*
. l 9 l*
Note. Dashes indicate no data.
*p<.01.
.055i
.021r
248
TIMOTHY A. SALTHOUSE
from the entries in the first column of Table 3 that the residual
agerelations are still significanfly greaterthan zero for most of
the variables.
TWotypesofcomparisons are of interest in Table 3. One consistsofcontrasts ofthe valuesin the secondthrough the fifth
columns with the valuesin the first column, and the other consistsof contrasts of the values in the columns representingthe
two types ofspeed. The overall pattern can be describedquite
simply by stating that the age-relatedvariance is smaller after
control ofa speedvariable in addition to the health and education variables(columns2 through 5) than only after control of
health and education (column l), and that the residual age-related variance is smaller after control of speedmeasureswith
greatercognitive involvement than after control of speedmeasureswith minimal cognitiveinvolvement(columns3 vs. 2 and
columns5 vs.4). As an example,the averageR2associatedwith
agefor the three paper-and-pencilcognitive measureswas .056
afterhealthand educationwerecontrolled,but it was.033(4 l Zo
attenuation) after motor speedwas also controlled, and it was
only .009 (83.9Voattenuation)after perceptualspeedwas controlled in addition to health and education.The averagevalue
for the measureof decisionaccuracyin the computer-administered cognitive tests was .096, and this was reduced to .041
(57.3Eoattenuation)after control of motor speedand to .0lg
(8l.3Voattenuation)after control ofperceptualspeed.For every
variable except the two used to create the composite motor
speedindex (i.e., Boxesand Digit Cqy), the residual age-relatedvariancewassmalleraftercontrol ofperceptualspeedthan
after control of motor speed.Comparisonof the valuesin the
fourth and fifth columns revealsthat a similar pattern existed
with the Digit Symbol measuresin that the attenuationof the
age-relatedvariancewas largerwith the measurepresumedto
havegreatercognitiveinvolvement(i.e.,DigSym-9).
Note that the influence ofperceptual speedactually appears
to be larger on the accuracy mqrsures than on the measuresof
study time or decisiontime. For example,the attenuation of the
age-relatedvariance in averagedecision accuracy after control
ofperceptualspeedwas8 1.37o,but the correspondingvaluefor
the averagestudy time measurewas 6l .37oand that for the averagedecisiontime measurewas74.4Vo.
Theseresultstherefore
suggestthat, ifanything, the relations betweenperceptualspeed
and decision accuracy may be strongerthan those betweenperceptualspeedand eitherstudy time ordecisiontime.
The residual age-relatedvariance in DigSym-9 after control
ofperceptual speedwas significantlygreaterthan zero, as was
the age-relatedvariance in the perceptual speedmeasures(Letter Comparison and Pattern Comparison) after control of DigSym-9. This is somewhatsurprising becausethese measures
werepresumedto involve very similar typesof comparisonprocesses.
Methodologicaldifferencesassociated
with the format of
administration (i.e., paper-and-pencilvs. computer-administered) may be responsiblefor the significantresidualagevariancein thesemeasures.
The R2in the cognitivevariablesassociated
with the composite perceptualspeedvariable and with the DigSym-9 variable
was also examinedbeforeand after control ofage, health,and
education to evaluatethe magnitude of the speedinfluence
when other sourcesof individual differenceswere controlled.
The top portion of Thble 4 summarizesthe resultsfor the correct-minus-incorrectmeasurein three paper-and-pencil
cognitive testsand for the decisionaccuracy measurein the three
computer-administered
cognitivetests.The resultsindicatethat
a significantrelation existsbetweenperceptualspeedand some
measuresof cognitiveperformance,evenamongindividualsfor
whom the variation associatedwith age,health,and education
is controlled. However,the magnitudeof the relation is much
Table4
R2Associated With PerceptualSpeedand Digit Symbot Before
and After Control of Other Variables
Perceptualspeed
Criterion
Alone
After age,
health,and
education
Digit symbol
Alone
After age,
health,and
education
StudyI
Correct - incorrect
Number Series
CubeAssembly
Name Number
.207*
.088*
.085*
.053*
.01I
.023
.15'7+
.125*
.063*
.031*
.036*
.008
.224*
.2t4*
.l05r
.038*
.044+
.035*
.257*
.239+
.088*
.065*
.068*
.021
.l3gi
.054+
.l6g*
.100*
Vo cOfi€,Cl
PaperFolding
Matrix Reasoning
AssociativeMemory
Study2
%,COrIeCt
SpatialRotation
Matrix Reasoning
AssociativeMemory
*p < .ol.
.141*
.166*
.134*
.049*
.100*
.040r
.202*
.196*
SPEED INFLUENCE
Table5
Resultsof CommonalityAnalysesConductedon Decision
AccuracyMeasuresin Study I
Predictor variable
Variable
Age
MSpd
PSpd
PaperFolding accuracyascriterion
Uniqueto age
Uniqueto MSpd
Unique to PSpd
Common to Ageand MSpd
Common to Ageand PSpd
Common to MSpd and PSpd
Common to Age,MSpd, and PSpd
Total effects
,038
.002
.030
.007
.044
.007
.t26
.024
.t26
.044
.024
.t26
.2t5
.159
-zz+
Matrix Reasoningaccuracyascriterion
unique to age
Uniqueto MSpd
Uniqueto PSpd
Common to ageand MSpd
Common to ageand PSpd
Commonto MSpdand PSpd
Commonto Age,MSpd,and PSpd
Total effects
.009
.035
.006
.024
.006
. ll 0
.045
. ll 0
.024
.045
. rl 0
.t49
.t'10
.214
AssociativeMemory accuracyascriterion
Uniqueto age
Uniqueto MSpd
Unique to PSpd
Commonto ageand MSpd
Commonto ageand PSpd
Commonto MSpdand PSpd
Commonto Age,MSpd,and PSpd
.005
Total effects
.002
.022
.001
. 0 13
.001
.052
.018
.052
. 0 13
.0r8
.052
.071
.073
.105
Note. MSpd= motorspeed;
PSpd= perceptual
speed.
smallerthan that evident when the age-relatedvarianceis included, suggestingthat the age-relatedvariation in speedis a
major contributor to the overall relationsbetweenperceptual
speedand cognitionobservedin this study.
Commonalityanalyses. Another analytical procedure applied to the decisionaccuracymeasureswascommonalityanalysis (Pedhazur,1982). The method describedby Salthouse
( I 993b)wasused,in which the total effectsofage on a criterion
variableweredecomposedinto a unique influenceof ageand
into common influencessharedwith either motor speed,perceptualspeed,or both. Measuresofspeedin theseanalyseswere
the compositespeedmeasuresthat were basedon the paperand-pencilspeedtests.
Summary information for the commonality analysesconductedon the decisionaccuracymeasuresin the three computer-administeredcognitivetestsis presentedin Table 5. Because
the entriesin the first column representthe partitioning of the
variance,they areofgreatestinterestin this context.
age-related
Three points shouldbe noted about the information in this table. First, the varianceuniquely associatedwith ageis only a
small proportion ofthe total age-relatedvariancein the crite-
249
rion variable.This is consistentwith the resultsofthe hierarchical regressionanalysesbecauseit indicatesthat much ofthe agerelatedvarianceis sharedwith one or more measuresof speed.
Second,the proportion ofage-relatedvariancesharedwith perceptualspeedis substantiallygreaterthan the prqortion of agerelated variancesharedwith motor speed.This is also consistent with the hierarchicalregressionresultsbecaus€it indicates
that perceptualspeedhasa greaterinfluenceon the age-cognition relations than does motor speed.And finally, one of the
largestproportions of varianceis that common to age,motor
speed,and perceptualspeed.This finding extendsthe earlier
analysesby revealingthat a considerableamount of the agerelated variance is not uniquely associatedwith one type of
speed.
Path analyses. The initial step in the path analyseswas a
confirmatory factor analysison nine cognitivevariables:study
time, decisiontime, and decisionaccuracyfor eachof the three
computer-administeredcognitive tests. Three factors (study
time, decisiontime, and decisionaccuracy)werespecified,with
correlationsallowedbetweenfactors.The fit of the model was
ratherpoor: y2124,N : 246) : 117.43,adjustedGFI : .828
and adjustedRMS : .123. Examinationof the residualsrevealedthat the poor fit wasattributableto relativelyhigh correlations among the variablesfrom the sametest. Becausethis
pattern implies that the relations among the variablesmight
differ acrosstests,separateanalyseswereconductedon the data
from eachtest.
Two setsofanalyseswere conductedon the data from each
test,one with the compositemotor speedand perceptualspeed
variables,and the other with the DigSym-Oand DigSym-9variables.The model determinationprocedurebeganby postulating pathsfrom ageto all variables:from motor speedto perceptual speed,from perceptualspeedto study time, decisiontime,
and decisionaccuracy,and from both study time and decision
time to decisionaccuracy,with a bidirectional path (correlation) betweenstudytime and decisiontime (seeFigure 7). Paths
with coefficientsdifferent from zero by lessthan two standard
errorsweredeleted.Pathsbetweenmotor speedand study time
and betweenmotor speedand decisiontime werethen addedif
the resultingpath coefficientdiffered from zero by more than
two standarderrors.Coefficientsfor thosepathsin Figure7 that
were significantand three measuresofthe fit ofthe final path
model for eachtest are reportedin Thble6.
Four points shouldbe noted with respectto the resultsofthe
path analysessummarizedin Table6. First, the modelswith the
two setsofspeed measures(basedon paper-and-pencilproceversionsof the Digit Symbol
duresand computer-administered
test)werequite similar and did not differ in any substantialrespect.(Note that the differencein signsis due to high scores
representingbetter performancein the paper-and-pencilspeed
measuresbut poorer performancein the Digit Symbol speed
measures.)Second,therewerelittle or no relationsbetweenmotor speedand any ofthe cognitivevariables(seePaths7, 8, and
9 in Table 6). This is consistentwith the inferencethat motor
speedis not a very important mediator of the age-cognition
relations.Third, perceptualspeedhad a consistentinfluenceon
both decisionaccuracyand decisiontime but no effecton study
time. Theseresultsimply that the variation in study time is attributable to different factors than those responsiblefor the
I
I
I
t
250
TIMOTHY A. SALTHOUSE
I
I
Figure 7. Structural diagram illustrating possiblepaths among variablesin the computer-administered
cognitivetests.
rate personalcomputerswereprovidedfor eachsubjectfor the computer-administeredtests.The testswereperformedin the following order
by all subjects:Boxes,PatternComparison,Letter Comparison,Digit
Copying,Digit Symbolwith zerosymbols,Digit Symbolwith nine symbols, AssociativeMemory, SpatialRotation, Matrix Reasoning,Memory SearchWith Digits, and Memory SearchWith Letters.The Boxes
motor speed,and
and Digit Copyingtestswereagainpostulatedto assess
the PatternComparisonand Letter Comparisontestswerepostulatedto
perceptualspeed.The Digit Symbol test with zero symbolswas
assess
usedas an additional measureof motor speed,with the Digit Symbol
test with nine symbolsrepresentingperceptualand motor speed.The
AssociativeMemory,SpatialRotation,and Matrix Reasoningtestswere
Study 2
intendedto assessmemory, spatial visualization,and reasoningabiliThe primary purpos€of Study 2 wasto replicateand extend
The two memory searchtestsweredesignedto yield
ties, respectively.
the resultsof Study l. Computer-administeredcognitivetests
measurescorrespondingto encoding and response(intercept) and
search(slope)processes.
with lowerlevelsof difficulty than thoseof Study I wereexamThe paper-and-pencil
speedtests(Boxes,Digit Copying,Letter Comined to avoid a possiblemeasurementfloor in older adults,and
parison,and PatternComparison)wereidenticalto thoseusedin Study
new computer-administered
testswereincludedto provideadDigit Symbol
I, aswerethe two versionsof the computer-administered
ditional measuresof speed.
test. Unlike Study l, however,eachversionof the Digit Symbol test in
this study was presentedfor only one 90-trial block after an l8-trial
Method
practiceblock.
Two new computer-administered speed tests were memory search
Subjects.Thecharacteristics
ofthe 258adults,age20 to 87,who
taskswith digits and with letters.For both typesof stimulusmaterial,8
participated
in thisstudyaresummarized
in Tablel. Subjects
in this
in a major metropolitan practicetrials werefollowedby two blocksof48 trials each,with 6 posstudywererecruitedfrom advertisements
newspaper
in a singlesession
ofapprox- itive and 6 negativetrials at each set size between one and four. The
andwerepaidfor participating
memory set items weredisplayedfor 2 s in the top middle of the comquestions
were
imately2 to 3 hr. Background
askedofall participants
identicalto thosedescribed
in Studyl. Correlations
amongthealterna- puter screen,and after a 0.5-sdelay,the targetstimulusappearedin the
were communicatedby pressingthe
middle of the screen.Responses
variables
were.89for education
tivemeasures
ofthe background
and
.48to .78for health.Thecorrelations
between
ageandthe measures slash key for yes and the Z key for no. Both speedand accuracy were
emphasized.
reportedin TableI were-.08 for education
and. I 0 for health(bothps
The AssociativeMemory testwasidenticalto the test usedin Study I
>.10).
exceptthat the lagsbetweenpresentationand test ofthe stimulusitems
Notethatthesamplein thisstudyhada higheraverage
levelofeduwere 0, l, and 2 pairs instead of 0, 2, and 4 pairs. This changewas
cationthanthesamplein Studyl, particularlyfor adultsin theolder
implementedbecauseaccuracywasrather low, and nearly equivalent,
in whichtheaverage
isnearlyI yeargreater
for
decades
thantheaverage
with lagsof 2 and 4 pairs in Study l. A practiceblock o[ 9 items was
in Studyl.
thoseageranges
weretestedin groupsof I to 6 each,andsepa- followedby 90 items consistingofeight testsat eachofthree lags.
Procedure.Subjects
variationin perceptualspeed.And finally,negativerelationsbetweendecisiontime and decisionaccuracywereevidentin each
test, indicating that peqle who are lessaccuratealso tend to
takelongerto make their decisions(or that more accuratepeoplearefasterin theirdecisions).
BecauseStudy 2 was very similar, further discussionof the
resultsof this study will be deferredto the GeneralDiscussion,
wherethe resultsof both studiescan be intesrated and interpretedtogether.
I
I
251
SPEEDINFLUENCE
Table 6
SignificantPathCofficientsfor PathsIllustrated in Figure 7, Study I
Paper Folding
Path
P&P
DigSym
MatrixReasoning
P&P
AssociativeMemory
DigSym
P&P
DigSym
I (Age-MSpd)
2 (Age-PSpd)
3 (MSpd-PSpd)
-.58
-.34
.51
.51
.29
.64
-.58
*.34
.51
.51
.29
.64
-.58
-.34
.51
.51
.29
.64
4 (Age-Study Time)
5 (Age-DecAcc)
6 (Age-DecTime)
.24
-.25
.39
.24
-.26
.34
.26
-.t9
.30
.26
-. l8
.30
.23
-.16
.17
7 (Mspd-Study Time)
8 (MSpd-DecAcc)
9 (MSpd-DecTime)
l0 (PSpd-StudyTime)
I I (PSpd-DecAcc)
l2 (PSpd-DecTime)
l3 (StudyTime-DecTime)
l4 (StudyTime-DecAcc)
l5 (DecTime-DecAcc)
Model fit indices
x2ldf
AdjustedGFI
AdjustedRMS
.19
.;
-.31
-.zs
.39
.26
.36
.29
.34
-.24
2.to/4
.985
.000
7.95/4
.945
.068
.15
.28
-.33
-,,
-.31
.29
.39
-.18
.31
.39
-.17
.33
.52
-.21
.33
.52
-.18
.t
6.0814
.957
.051
--5I
4.'t913 t2.9t16
.94r
.9s5
.o7l
.057
.44
20.381s
.889
.l14
Note. P&P = composite measuresof motor speed(MSpd) and perceptual speed(PSpd) from the paporand-penciltests;Digsym = Digrt Symbol4 (for motor speed)and Digit Symbol-9(for perceptualspeed)
variables;DecAcc : decisionaccuracy;DecTime : decisiontime; GFI : goodness-of-fitindex; RMS :
Dashesindicatethe coefficientswerenot significant.
root-mean-square.
The Matrix Reasoningtest differedfrom that usedin Study I by replacingthe contentsof the matrix cells with setsof lettersand digits
insteadof geometricpatternsand by presentingonly four answeralternativesinsteadofeight. The cell contentswerechangedto try to make
it easierfor subjectsto identify the relationsamongthe elements.Three
typesoftrials weredistinguishedby containingone, two, or three elements (digits or letters)per cell. Relationsamong the elementswere
determinedby addition or subtractionin either the numeric or alphabetic sequencein stepsof one, two, or three. For example,one of the
two-elementproblemsconsistedof 22R, l8T and l4V in the first row,
20O, l6Q, and l2S in the secondrow, and l8L and l4N in the third
row, with answeralternativesof l6K, l8L, l0B and 6Q. Six practice
trials werepresented,followedby two blocksof30 trials each, l0 with
eachnumberof elementsper cell.
The Spatial Rotation test wasbasedon a task usedby Salthouse,Babcock, Mitchell, et al., (1990) and consistedof same-differentrecognition judgmentsofsix-segmentline patternsafter rotationsofO", 90", or
I 80".The initial stimuluspattern could be inspectedfor as long as desired,andthen two flagsrepresentingthe orientationofthe secondstimulus in relation to the first stimulus were presented.The left flag was
alwaysvertical, and ifthe right flag wasalso vertical then the orientation
discrepancybetweenthe initial and teststimuluswas0'. Ifthe right flag
washorizontal, then the orientation discrepancywas90", and ifthe right
flagwasinverted,then the orientationdiscrepancywas 180".The duration that the subjectviewedthe initial patternand the duration that he
or sheviewedthe display ofthe flagsindicating the relative orientations
of the initial and test stimuli werecombinedto representstudy time,
and the time to respondto the test pattern was usedas the measureof
decisiontime. Responseswere communicated by pressingthe slashkey
for sametrials and by pressingthe Z key for different trials. A practice
block of six trial3 wasfollowedby two blocksof 30 trials each.Within
eachblock, there were five sameand five different trials at eachorientation, presentedin a randomarrangement.
Results and Discussion
Means,standarddeviations,estimatedreliabilities,and R2for
linear and quadratic age relations for the primary dependent
measuresare reportedin Table7. As in Study 1,the age(linear)
and age-squared(quadratic)terms were centeredto minimize
collinearity.The correlationbetweenthe number correct score
and the number correct minus the number incorrect scorewas
.95 in both PatternComparisonand Letter Comparisontests,
and thus the number correct minus the number incorrect m€asurewasusedin subs€quentanalysesto adjustfor guessing.
Scoreson the four paper-and-p€ncilspeedt€stsand the DigSym-0and DigSym-9m€asureswereconvertedto z scores,and
the meanswereplotted asa function of decadein Figure 8. It is
apparentthat the generalpatternis similar to Figure 1,although
the agerelations in this study are somewhatsmaller than those
of the previousstudy,perhapsbecausethe older adults in this
samplewere more selectwith respectto amount of education
(cf. Table l).
Memory search. Mean responsetime and mean percentage
of errors as a function cf number of items in the memory set
areplotted for eachdecadein Figure9. Both variableswith each
type of stimulus material were analyzed by separaterepeated
measuresANOVAs in which agewascategorizedby decadeand
set size was a within-subjects variable. Only the age decade
252
TIMOTHY A. SALTHOUSE
1.5
Table7
Summary StatisticsforPrimary DependentVariables,Studv2
Boxes
--l-
O
R2
Variable
Boxes
Digit Copy
Letter Comparison
PatternComparison
Digit Symbol-0(s)
Digit Symbol-9(s)
Memory Search
Digits, intercept
Digits, slope
Letters,intercept
Letters,slope
VoCOrTeCl
SpatialRotation
Matrix Reasoning
AssociativeMemory
Decisiontime
SpatialRotation
Matrix Reasoning
AssociativeMemory
Studytime
SpatialRotation
Matrix Reasoning
Associative
Memory
M
SD
Est.
Rel.
Linear
age
Quadratic
age
47.t
50.7
10.5
16.0
0.75
1.5l
t4.0
10.8
3.1
4.5
0.21
0.42
.78"
.84.
.38.
.52"
.94b
.95b
.074*
.116r
.t29*
.265*
.l3l*
.291t
.004
.054*
.027*
.004
.015
. 0 1g *
l
o
c
c
i F
o'5
.9
(U
A
o
o
€
a {.s
DigSlm-9
1/
a - i
,..4--..-.._ *..-*".
LetCom
. 4..
Patoom
DigS.lm-o
o,/
,/z
- i;;-'+'
Dlglgtv
t.
*
,t'-.a'''''-'*
'i'
\
E
0.92
0.06
0.85
0.06
0.48
0.06
0.41
0.06
79.0
88.8
80.0
t2.4
16.8
t3.9
.92.
.59"
.88"
.23"
.164*
.002
.132*
.004
.016
.000
.010
.000
.8ld
.g4d
.079r
.009
.071+
.008
.079*
.007
1 . 5I .g4d
1 . 9 7 .94d
1 . 7 7 .g7d
.325*
.231*
.201r
.014
.055*
.038i
7 . 9 5 4 . 5 7 .g7d
23.55 tt.73 . g g "
2.t9
L 3 8 .g6d
.120*
.244*
.028*
.005
.001
.000
2.66
3.30
2.57
.66"
Note. Est.Rel.= estimated
reliabilities.
'Alternate-forms
correlationfrom a sampleof 212 collegestudents.
bValuefromStudyL "
Correlation
betwienscores
fromlirstandsecond administrationsboosted
formula.
dComputedfrom correlationsthe by Spearman-Brown
acrossthreelevelsof complexitywith
formulain Kenney
= n(average'r)lU
( 1979,
p. I 32):Reliability
+ (n I )(average
r)1.
*p<.01.
effectwith the leuerstimuli,F(5, 252): 5.53,MS" = 123.9n,
wassignificantin the analysesofthe error data. In the reaction
time analyses,the effectofage decadewas significantfor both
digits,F(5, 252)= 14.25,MS,: 592,253,
andletters,F(5,252)
= 12.75, MS,: 479,505,aswastheeffectof setsize:digits,
F(3,
756): 126.91,MS, = 12,864,and letrers,F(3, l.56)= 130.44,
MS" = 12,621.The Age Decadex Set Sizeinteractionwasnot
significantwith eitherdigits or letters(both Fs < 1.20).
The absenceof a significantAge X Set Sizeinteractionwith
either stimulus material was unexpected,but it is consistent
with the lack ofa significantagerelationon the slopesofthe Set
SizeX Response
Time functionsreportedin Table7. This failure to detectsignificantage-relatedeffectson the slopesdoes
not app€arto be causedby unsystematicrelationsbetweenthe
numberof items in the memory setand responsetime, because
the mean correlationsbetweenset sizeand reactiontime were
.73 for both letten and digits. Moreover,the slopeparameters
werenot completelylacking in reliability, becausethe correla_
tion betweenthem was .46, a value significantlygreaterthan
zero.
One possibleexplanationfor the failure to find significant
Age X SetSizeinteractionsmaybe that someof the slowestand,
likely amongthe oldest,subjectsmight haverespondedin the
o
U'
a?
-1
3
0
4
0
5
0
6
0
7
0
Chronological
Age
Figure8. Meanstandarddeviationscoresby decadefor the speed
measures,
Study2. DigCopy: DigitCopy;LetCom= LetterCompari= Digit Symbolwith
son;PatCom= PatternComparison;
DigSym-O
zerosymbols;
DigSym-9: DigitSymbolwith ninesymbols.
samemanner to all trials regardlessof set size.The analyses
werethereforerepeatedaftereliminatingthe data from subjects
with mean responsetimes greaterthan 1.5s, which is approximatelyone standarddeviationabovethe meanresponsetime of
the entire sample.The correlationsbetweenageand the slope
measuresin this restrictedsampleof 228 adultswerestill very
low (i.e., .05 for digits and .12 for letters),despitea moderate
correlation (.47) betweenthe two slopes.Finally, the Age DecadeX SetSizeinteractionswerestill not significantwith either
the digit or letter stimuli in this restrictedsample(i.e., both Fs
< 1.4).
Computer-administered
cognitivetests. Only meansacross
the threecomplexitylevels(i.e.,angulardisparity in SpatialRotation, number of elementsper cell in Matrix Reasoning,and
presentation-testlag in AssociativeMemory) are reported for
the computer-administeredcognitive tests, becauseonly one
Age (by decade)X Complexity interactionwassignificantin either the entire sampleor in subsamplesof subjectswith means
in the simplestcondition abovethe sample mean. The single
exceptionwasan interactionfor the decisionaccuracymeasure
in the SpatialRotation test,F( 10, 504): 2.44,M& = .009,but
this was difficult to interpret becauseit was not monotonic as
the agecorrelationswere-. I 8 for 0" rotations, -.29 for 90" rotations,and-.24 for 180"rotations.
The meanz scoresfor studytime, decisiontime, and decision
accuracyare plotted by decadefor the Spatial Rotation test in
Figure 10, for the Matrix Reasoningtest in Figure I l, and for
the AssociativeMemory test in Figure 12.The ageeffectswere
significantin every variablein the Spatial Rotation and AssociativeMemory tests.The linear agetrend wasnot significantin
the decisionaccuracymeasurein the Matrix Reasoningtest,but
the quadraticagetrend wassignificant(cf. Thble7).
253
SPEED INFLUENCE
Digits
SoatialRotation
s$.1
1.5
I
----
Psffitaoe Cortrt
Set8la2 n
Msion
Tims
--l-
stPff.3e
o
S€!sF6 4 g
15o
l
c o 5
o
0,
o
g
(l,
E
F
(,
o
c
o
ct
o
o
cE
Studllime
o
'=
d
e
1m0
o
E
(!
E
tr
C'
-0.5
u)
e &
Eoo
o
a
8 8
r B
2 x
E
U
$
3
3
o
€
5
0
@
7
50
0
60
g)
70
Ghronological
Age
Age
Chronological
l'igure 10. Meanstandarddeviationscoresby decadefor the study
measures
in theSpatialRotime,decision
time,anddecision
accuracy
tationtest,Study2.
L€tters
."ll- t
I
S€lr,:a 2 SSGIEOl?|
6.
ot
o
S€tsla 4 E
1s00
g
q)
E
F
q,
o
g
1000
o
o.
U'
0)
E
g
tr
soo
8 E
6 oe
4
L
z p
U
m
3{t
40
50
8{l
70
fit of the model was significantlyworse,differencex2(1,N:
258) : 3 1.I 3. Becausethe standardizedfactor weightingswere
similar (i.e., .73 for Boxes, .84 for Digit Copy, .72 for Letter
Comparison,and .86 for Pattern Comparison),the averagez
scorefor the Boxesand Digit Copymeasureswasusedto representmotor speed,and the averagez scorefor the PatternComparisonand Letter Comparisonmeasureswasusedto represent
perceptualspeed.
Eachof the l9 variablesin Table7 wasexaminedfor the presenceof main effectsofgender, health, and education,and for
interactionsofthese predictorswith age.The significanteffects
in the regressionanalysesand the direction ofthe effectswereas
follows: for health, better self-reportedhealth was associated
80
Age
Chronological
MatrixReasoning
Figure9. Meanreaction
timeandmeanpercentage
of errorsasa functionof memorysetsizebydecade
fordigits(top)andletters(bottom)in
theMemorySearch
test,Study2.
t.5
Pd6niao6
-t- Corr*l
Dsision Timo
--]-
Studv
lime
...1...
at,
'E
Regressionanalyses. A confirmatory factor analysisconductedon the four healthand two educationvariablesrevealed
a goodfit: 1218,N: 258) : 12.83,adjustedGFI : .959,and
adjustedRMS : .049. The correlation betweenthe education
and health factorswas -.23. Becausethe standardizedfactor
weightsweresimilar (i.e.,.92 and.97for the educationvariables
and .79 to .92 for the healthvariables,except.56 for the healthrelatedactivity limitation variable),the constructswererepresentedby the averageofthe relevantz scores.
A confirmatory factor analysiswas also conductedon the
measuresfrom the four paper-and-pencilspeedmeasures.In
contrastto the resultsofstudy l, the fit wasfairly good: x2(I , N
: 258): 1.44,adjustedGFI: .972,andadjustedRMS : .063.
The correlationbetweenthe motor speedand perceptualspeed
factorswas .75, but when this correlationwas fixed at 1.0,the
l
s
o
0.5
'16 A o
o
E
!".'l''"''1"-"'''
(u
o -o.5
E
(tt
a
,l
.1.5
m
3
0
,
o
5
0
6
0
7
0
8
0
ChronologicalAge
Figure 11. Mean standarddeviation scoresby decadefor the study
time, decisiontime, and decisionaccuracymeasuresin the Matrix Reasoningtest,Study2.
254
TIMOTHY A. SALTHOUSE
Associative
Memory
(.028),Matrix Reasoningdecisiontime (.023),and Associative
Memory decisiontime (.094). Finally, interactionsof ageand
DigSym-9 were evident in Pattern Comparison (.024), Digit
sqqnm6
Memory Searchintercept (.015), Matrix Reasoningdecision
o
E
time (.048), and AssociativeMemory decisiontime (.026). As
f,
in Study l, most of the Age X Speedinteractionswereon mea0.5
c
o
suresof time ratherthan measuresof accuracy.
(6
The proportionsofvariance associatedwith ageafter control
o
0
o
of
health, education,and the four speedvariablesare summalf
rized in Table 8. It is apparentthat the generalpattern is very
aU
!
o.5
similar to that of Study 1 in that the attenuation of the age.U
U'
related variancewas greaterwhen speedmeasureswere controlled in addition to healthand education,and the attenuation
wasgreatestafter control of the speedmeasureswith the most
.t.5
cognitiveinvolvement.
m e'
"
80
The R2valuesassociatedwith the perceptualspeedmeasures
c#onor[i""rln"
in the prediction ofdecision accuracybeforeand after control
ofage, health,and educationare reportedin the bottom ofTaFigure12. Meanstandarddeviationscoresby decadefor the study
ble 4. The resultsaregenerallyconsistentwith thosefrom Study
time,decision
time,anddecision
accuracy
measures
in theAssociative I in that the amount of varianceassociatedwith the speed
meaMemorytest,Study2.
suresis reducedbut not eliminated when the other sourcesof
varianceare controlled.
Commonalityanalyses. Resultsfrom the sametype of comwith higherscoresin Digit Copy and SpatialRotation decision
monality analysesthat wereperformedin Study I are summaaccuracy;for education,greateramountsofeducation wereasrized in Thble9. Note that the earlierresultsare replicatedwith
sociatedwith higherscoreson Boxes,Digit Copy,Letter Comrespectto (a) a small portion of varianceuniquely associated
parison, PatternComparison,Spatial Rotation decisionaccuwith agein relation to the total age-relatedvariance,(b) a larger
racy,Matrix Reasoningdecisionaccuracy,AssociativeMemory
proportion of variance shared between age and perceptual
decisionaccuracy,and longerSpatial Rotation study time, but
speedthan betweenageand motor speed,and (c) a relatively
with shorterMatrix Reasoningdecisiontime and shorterDiglarge proportion of variancesharedamong age,motor speed,
Sym-0 time. The only significantinteraction was betweenage
and perceptualspeed.The only exceptionsto thesepatternsare
and the compositeeducationvariableon Matrix Reasoningdein the Matrix Reasoningtest in which therewasvery little agecisiontime, in the directionoflargereffectsofeducationat older
relatedvariancein the measureofdecisionaccuracy.
ages.
Path analyses. As in Study l, the initial step in the path
Womenwere significantlyslowerthan men in Spatial Rotaanalyseswas a confirmatory factor analysison the nine cognition decisiontime and Matrix Reasoningstudy time. Age and
tive variablesspecifyingfactorsof studytime, decisiontime, and
genderinteractedon Matrix Reasoningdecisionaccuracyand
decisionaccuracy.Consistentwith the resultsof the previous
on Matrix Reasoningdecisiontime (in both cases,the advanstudy,the fit of the modelwaspoor: y2124,N: 258),: 2l3.gg,
tagefor menwaslargeramongolderadultsthan amongyounger
adjustedGFI : .724,and adjustedRMS : .169, and correadults).
lations among the residualsfor measuresfrom the same test
Moderatingeffectsof speedwere investigatedby examining
werehigh. The testswerethereforeexaminedseparately,
followinteractionsofage and speedafter the predictorshad beencening the sameprocedural stepsdescribedin Study l. The sigteredto a meanof zeroand the main effectswerepartialedout.
nificant path coefficientsand the goodness-of-fitindicesfor the
All interactionswerein the direction of smallerage-relatedinfinal path modelsare summarizedin Table 10.
fluencesat fasterlevelsofspeed (or greaterinfluencesofspeed
In general,the resultsin Thble l0 are quite similar to those
at older ages).Significant interactions involving age and the
from Study I (summarizedin Thble5). That is, as in the previcompositemotor speedvariable,with the incrementin R2assoous study,there weresmall or inconsistentinfluencesof motor
ciatedwith the interactionpresentedin parentheses,
wereevispeedon the cognitive variablesand tittle or no influence of
dent in Letter Memory Searchintercept(.026),Letter Memory
perceptualspeedon study time, but therewasa consistentrelaSearchslope(.043),Matrix Reasoningdecisionaccuracy(.038),
tion betweenperceptualspeedand both decisiontime and deciMatrix Reasoningdecisiontime (.079),and AssociativeMemsion accuracy.
ory decisiontime (.049). Significantinteractionsbetweenage
and the compositeperceptualspeedvariable were evident in
General Discussion
Digit Copy(.021),Digit MemorySearchintercept(.020),Letter
Memory Searchintercept(.024),Matrix ReasoningdecisionacThe initial sectionof the GeneralDiscussionfocuseson the
curacy (.049),Matrix Reasoningdecisiontime (.077),and Asthree goalsofprimary interestin this project: (a) Is there evisociativeMemory decisiontime (.023). Variableswith signifidenceofspeedmediationofthe age-relatedeffectson cognitive
cant interactionsinvolving ageand DigSym-0wereDigit Memmeasureswithout time limits? (b) What is the nature of the
ory Searchintercept (.026), Letter Memory Searchintercept
speedprimarily responsiblefor mediating age-cognition rePdmtaog
Correcl
+
D€dsion lime
--+-
255
SPEEDINFLUENCE
Table 8
R2for Age After Control of Demographic and SpeedVariables,Study 2
R2for ageafter control of:
Criterion
Boxes
Digit Copy
Letter Comparison
PatternComparison
Digit Symbol-O
Digit Symbol-9
Memory search
Digits, intercept
Digits, slope
Letters,intercept
Letters,slope
Mreaction time
Health,
education
Health,
education,
motor speed
Health,
education,
perceptual
speed
Health.
education.
Digit
Symbol4
Health.
education.
DBrt
Symbol-9
.038'
.o47|
.064*
.005
.01I
.00s
.063r
.000
.063*
.096*
.l 14|
.239*
.125*
.2'15|
.001
.001
.048*
.ll7r
.076*
.164|
.003
.007
.007*
.008+
.037*
.076*
.154i
.002
.120*
.004
. 1 74 *
.076*
.000
.049+
.007
.086i
.039*
.000
.022*
.006
.042*
.039*
.001
.024r
.002
.041'
.000
.000
.000
.004
.000
.062r
.003
.056*
.034i
.002
.041i
. 0 13
.01I
.01l
.o29|
.005
.01l
.008
.030*
.001
325r
.205i
.188r
.263*
.132*
.ll8r
.166*
.086*
.073*
.223i
.125+
.057t
.l l5i
.136*
.233*
. 0 31 r
.125+
.086*
.122*
.218*
.019
.088r
. 15 9 *
.006
.l4li
.093r
Vo COfieCt
SpatialRotation
Matrix Reasoning
AssociativeMemory
Decisiontime
SpatialRotation
Matrix Reasoning
AssociativeMemory
Studytime
SpatialRotation
Matrix Reasoning
AssociativeMemory
.l l4f
.023
.008
.053*
.019*
nodata.
Note. Dashesindicate
*p<.01.
lations?and (c) How are measuresof speed,studytime, decision
time, and decisionaccuracyrelatedto one anotherand to age?
Speed Mediation on Measures Without Time Limits
Before describingthe evidencerelevantto the influence of
speed on the age differences in cognitive measuresobtained
without time limits, it is first desirableto review the evidence
indicating that age-relateddifferencesdo exist in measuresof
decisionaccuracyunderconditionsof little or no time pressure.
This evidenceis provided in Tables2 and 6, in which the R2
associatedwith agewas significantlygreaterthan zero for all
of the percentagecorrect measuresexceptthat for the Matrix
Reasoningtest in Study 2. The significantagetrends for these
measures,togetherwith the nearlymonotonic patternsevident
in Figures4 through 6 and FiguresI 0 through I 2, indicatethat
age-relatedeffectsare definitely apparentin measuresofdecision accuracy,in addition to other measuresof performance
suchasdecisiontime.
The resultsof both Studies I and 2 indicate that theseage
differencesin decisionaccuracyare substantiallyreducedwhen
measuresof perceptual speed are statistically controlled. In
Study I the mean R2 associatedwith agewas .096 after health
and educationwerecontrolled and .018 after perceptualspeed
wascontrolled, valueswhich are equivalentto an attenuation of
valuesin Study 2 were .040 and .012,
81.37o.Corresponding
This magnitudeof attenrepresentingan attenuationof 70.0Vo.
uation is about the sameas that observedin paper-and-pencil
cognitivetests,asthe attenuationofthe age-relatedvariancefor
the Number Series,Cube Assembly,and Name-Number tests
in Study I was83.97o.Moreover,the proportionalreduction of
the age-relatedvariancein decisionaccuracywasactuallylarger
than that observedwith measuresof decisiontime. That is, the
averagepercentagereductionsin the age-relatedvariancein decision time after control of perceptualspeedwere 74.5Voin
Study I and54.8Voin Study2.
The answerto the first question addressedin thesestudies
thereforeseemsquite clearin that the resultsindicatethat there
is apparently as much speed mediation of the age-related
differencesin decisionaccuracyasofthe age-relateddifferences
in decisiontime or ofthe age-relateddifferencesin performance
measuresobtained from timed paper-and-penciltests.It can
thus be concludedthat the involvementofspeedin the relations
betweenageand cognition is not restricted to timed or speeded
measuresof cognitivefunctioning.
Type of Speed Mediation
The key distinction betweenmeasuresofspeed investigated
in thesestudieswasbasedon the relative cognitive requirements
256
TIMOTHY A. SALTHOUSE
Table9
Resultsof CommonalityAnalysesConductedon Decision
AccuracyMeasuresin Study 2
Predictor variable
Variable
Age
MSpd
PSpd
SpatialRotation accuracyascriterion
Unique to age
Unique to MSpd
Unique to PSpd
Common to ageand MSpd
Common to ageand PSpd
Common to MSpd and PSpd
Common to age,MSpd, and PSpd
.010
Total effects
. 0 1l
.034
.003
.025
.003
.041
.041
.o4l
.025
.041
.o4l
.079
.096
.l4l
Matrix Reasoningaccuracyascriterion
Uniqueto age
Uniqueto MSpd
Uniqueto PSpd
Commonto ageand MSpd
Common to ageand PSpd
Commonto MSpdand PSpo
Common to age,MSpd, & PSpd
Total effects
.019
.039
-.005
-.017
-.005
.070
.0t2
.r 0 l
.012
-.017
.t 0 l
.012
.009
.147
.166
AssociativeMemory accuracyascriterion
Uniqueto age
Uniqueto MSpd
Uniqueto PSpd
Commonto ageand MSpd
Common to ageand PSpd
Commonto MSpdand PSpd
Commonto age,MSpd,and PSpd
.010
Total effects
.000
.054
.000
.032
.000
.029
.019
.029
.032
.019
.029
.07|
.048
.tJ4
Note. MSpd= motorspeed;
PSpd= perceptual
speed.
in the tasks used to measureprocessingspeed.Cognitive demandswerepresumedto be low when the subjectonly needed
to draw lines, copy digits, or decidewhether two digits were
physicallyidentical,but the demandswere hypothesizedto be
much greaterwhen the subjectwasrequiredto comparesetsof
lettersor patternsor to associatedigitswith symbols.I originally
intended to use the slopeand intercept parametersfrom the
functionsrelatingreactiontime to the hypothesizednumber of
cognitiveoperationsin the visualsearch(Digit Symbolin Study
l) and memory search(in Study 2) tasksas additional speed
measures.However,I abandonedthis plan afterdiscoveringthat
the slopeparametershad weak relationswith ageand low reliability,becauseit would havebeenunreasonableto expectthese
variablesto mediate age relations with other variableswhen
they had very small relationswith ageand when only a small
proportionof theirtotal variancewassystematic.
The distinction betweenmotor speedand perceptualspeed
in the paper-and-pencil
testswas somewhatequivocalbecause
compositemeasuresof theseconstructswerehighly correlated
with one anothet particularly in Study l. Although this indicatesthat conclusionsregardingtypesofspeedmust be consid-
eredtentative,the pattern ofresults wasnevertheless
consistent
acrossnumerouscomparisonsin the two studies.Furthermore,
it seemslikely that evenlargerdifferencesbetweenthe influence
ofmotor speedand perceptualspeedwould be expectedifmeasuresof theseconstructscould be identified that were not as
highly correlatedasthosein the presentstudies.
Three typesof analyseswereconductedto evaluatethe relative importance of motor speedand perceptualspeedin the
age-cognitionrelations.One analysisconsistedof the examination ofthe residualage-relatedvariancewhen the speedmeasure was statisticallycontrolled. The reasoningwas that the
smaller the residual age-relatedvariance,the larger the presumed influence of speedin the age-cognitionrelations.The
resultsin Thbles3 and 7 indicate that the residualage-related
variancewas nearly alwayslargerwhen motor speedmeasures
were controlled than when perceptualspeedmeasureswere
controlled, thus suggestingthat the influence of perceptual
speedwasgreaterthan that ofmotor speed.
Commonality analysisconductedon the decisionaccuracy
measuresfrom the computer-administeredcognitivetestswas
the secondtype of analysisrelevantto the comparisonof motor
speedand perceptualspeed.The resultssummarizedin Tables
5 and 9 indicatethat the variancecommon to ageand perceptual speedwas nearly alwayslargerthan that common to age
and motor speed.The only exceptionwaswith the Matrix Reasoningmeasurein Study 2, in which the total ageeffectswere
very small.
Pathanalyseswerethe third type ofanalysisusedto evaluate
the relative importance of motor speedand perceptualspeed
in the age-cognitionrelations.The resultsin Thbles6 and l0
indicate that there were no significant paths betweenmotor
speedand decisionaccuracybut that the pathsbetweenperceptual speedand decisionaccuracywere significant in the final
modelsfor all tests.
When consideredtogether,the resultsof thesethree different
typesofanalysesseemto providea compellingcasethat perceptual speedis more important than motor speedasa mediatorof
age-cognition relations. Becausethe primary difference between the two types of speedmeasuresappearsto be in the
amount of cognitiveinvolvement,it seemsreasonableto infer
that it is the speedofcognitive operationsthat primarily contributes to the relations betweenase and measuresof cosnitive
functioning.
Relations Among Measures
Tables2 and 6 and Figures4 through 6 and l0 through 12
indicatethat, with only two exceptions,significantagerelations
wereevidentin the study time, decisiontime, and decisionaccuracymeasuresin everytest.Relationsamongthesemeasures
and among ageand the two types of speedwere examinedby
meansof path analyses.
The path analysisresults,6asedon an integrationofthe findings reported in Thbles6 and 10, are first consideredwith respectto the significantpaths leadingto decisionaccuracy.The
negativepath from decisiontime to decisionaccuracyindicates
that longertime to make a decisionwasassociatedwith lessaccuratedecisions.This is oppositeto the pattern expectedfrom
a speed-accuracytrade-offbecausethis finding indicatesthat
257
SPEEDINFLUENCE
Table l0
Significant Path Coeficientsfor Paths lllustated in Figure 7, Study 2
Spatial Rotation
Path
P&P
DigSym
I (Aee-MSpd)
2 (Age-PSpd)
3 (MSpd-PSpd)
-.34
-.33
.46
.36
4 (Age-StudyTime)
5 (Age-DecAcc)
6 (Age-DecTime)
.35
-. l8
.35
-.19
.41
.JJ
.57
7 (MSpd-Study Time)
8 (MSpd-DecAcc)
9 (MSpd-DecTime)
MatrixReasoning
P&P
AssociativeMemory
DigSym
P&P
DigSym
.36
-.34
-.33
.46
.36
.33
.57
-.34
-.33
.46
.JJ
.57
.49
.20
.28
.17
-.37
.38
.27
-.24
.19
-.35
.25
-.53
-30
-.5l
.24
.38
-.3'l
.24
.37
-.27
| 1.56/4
.924
.089
5.80is
.970
.026
8.92/s
.952
.060
3.9914
.9'73
.000
.49
.16
.Jt
.33
.t7
-.17
l0 (PSpd-StudyTime)
I I (PSpd-DecAcc)
l2 (PSpd-DecTime)
.26
-.20
I 3 (StudyTime-DecTime)
l4 (StudyTime-DecAcc)
l5 (DecTime-DecAcc)
.58
.48
-.25
Model fit indices
x'/df
AdjustedGFI
AdiustedRMS
4.49/4
.970
.025
;
.31
.60
.47
-11
t.0214
.993
.000
.34
-.zJ
.JJ
Note. P&P = compositemeasuresof motor speed(MSpd) and perceptualspeed(PSpd)from the paperand-penciltests;DigSym = Digit Symbol-O(for motor speed)andthe Digit Symbol-9(for perceptualspeed)
variables;DecAcc = decisionaccuracy;DecTime : decisiontime; GFI = goodness-of-fitindex; RMS =
root-mean-square.
Dashesindicatethat coefficientswerenot significant.
peoplewho are lessaccuratein their decisionsalso take longer
to make thosedecisions.The positivepath from study time to
decisionaccuracyindicatesthat a longertime working on the
problemswas associatedwith a higher level of accuracy.The
path from perceptualspeedto decisionaccuracywasin the direction offaster perceptualspeedassociatedwith higheraccuracy. This relation is independentof that betweenperceptual
speedand decisiontime, which was in the direction of faster
perceptualspeedassociatedwith fasterdecisions.
In light ofthe precedinginformation, severalinferencescan
be maderegardingthe age-relatedinfluenceson decisionaccuracy.First, thereappearsto be somedirect' age-relatedeffecton
decisionaccuracy,although this effectwas inconsistentacross
the two setsof speedmeasuresin the AssociativeMemory test
in Study I, and the relevantpath coefficientswere not significant in the modelfor the Matrix Reasoningtestin Study2. Seceffectwasapparentlymediated
ond,very little ofthe age-related
throughthe studytime variablebecausealthoughincreasedage
was associatedwith longer study time, longer study time was
associatedwith higher accuracy,and yet increasedagewasassociated with lower accuracy.This pattern raisesthe possibility
that the agedifferencesmight havebeenlargerif studytime had
not been positivelyassociatedwith age,but unfortunately no
independentevidencerelevantto this issueis availablein these
data.Third, it is possiblethat someof the age-relatedinfluences
are mediatedthrough slowerdecisiontime, but it seemsmore
likely that both slowerdecisionsand lessaccuratedecisionsare
a consequence
of a common third factor ratherthan that slower
decisionscauselower accuracy.Finally, it seemsprobablethat
there is somemediation of the age-relatedeffectson decision
accuracythrough slowercognitiveoperationspeedbecauseof
the negativerelation betweenageand perceptualspeedand the
positiverelation betweenperceptualspeedand decisionaccuracy. The net result ofthese two relationscould be that older
adultsare lessaccuratein their cognitivedecisionsbecausethey
are slowerin executingrelevantcognitiveoperations.The speed
influenceis presumedto be largelya result of cognitiveoperations becausethere was no significantrelation betweenmotor
speedand decisionaccuracy.
Miscellaneous
There are a number of additional resultsfrom StudiesI and
2 that warrant somediscussion.First, significantinteractions
betweenageand speedwere evident with severalof the performance measuresin both studies.Interactionsof this type are
theoreticallyinterestingbecausethey indicatethat fasterspeed
is associatedwith smallerage-relatedinfluences.However,the
fact that interactionsof ageand perceptualspeedwerenot significant in four previous studiesreported in Salthouse(1991,
I 993)suggests
that the resultsofthesestudiesshouldbe considt Note that direct in this context doesnot mean unmediatedby any
facton, but merely not mediatedby other measuresincluded in this
analysis.
258
TIMOTHY A. SALTHOUSE
eredtentative.lt is also important to note that most of the interactionsin the presentstudy were evident with other speed
measuresor with the study time or decisiontime measures,as
the only interactionswith accuracymeasureswerewith the Paper Folding test in Study I and the Matrix Reasoningtest in
Study2. One possibleinterpretationoftheseresultsis that moderatingeffectsofspeed,in the form ofAge X Speedinteractions,
are simply anotherconsequence
of age-relatedslowingin which
peoplewho are slow in somemeasuresare also slow in other
measures.
A secondinterestingresult from the presentstudiesis that
the age-relatedeffectsin the Matrix Reasoningtestsweremuch
smaller in the versionof the test with lettersand digits in the
matrix cellsthan in the versionwith geometricpatternsin the
cells(i.e..the R2for agewas.009in the versionwith lettersand
digits but .149 in the version with geometric patterns).It is
tempting in view of this pattern to suggestthat there may be a
specialage-relateddifficulty in identifying relations involving
geometricpatterns.However,such a conclusionwould be premature becausetherewerenumerousotherdifferencesbetween
the two versionsofthe test that could havecontributed to the
differentpatternof results(e.g.,only two typesof relativelysimple relationswereusedwith lettersand digits,whereasa variety
of relationswere usedwith geometricpatterns,the letter-digit
problemsvariedin terms of the numberof elementsand not
necessarilywith respectto the number of different relations,
and choiceswere made among four alternativesin the letterdigit versionof the testbut amongeight alternativesin the geometric patternversion).
Another noteworthyfinding in thesestudiesconcernsthe resultsin Table4. which indicatedthat the relationsbetweenperceptualspeedand cognition weresignificantevenafter the age
variationhad beencontrolled.This is consistentwith the results
ofotherresearchers
suchasJensen(e.g.,I 987)andVernon(e.g.,
1983).However,it is important to note that the influenceof
perceptualspeedwasmuch largerwhen agewasnot controlled
becauseofthe substantialrelation betweenageand perceptual
speed.The role ofage variation in the relationsbetweenspeed
and cognitionis alsoevidentin the commonalityanalyses
becauseentriesin the third column of Thbles5 and 9 indicatethat
a substantialproportion of the variancein decisionaccuracy
associated
with perceptualspeedis alsosharedwith age.
Finally, the effectsofpresentation-testlag in the Associative
Memory testsin the two studiesdeservesomecomment.Ofparticular interestis the existenceofsignificant age-relatedeffects
in decisionaccuracyat Lags | , 2, and4 when the analyseswere
restrictedto subjectswith 1007oaccuracyAt Lag 0.2The existenceof a significantmain effectof agein theseanalysesimplies
that increasedagemay be associatedwith a fasterlossofinformation oververy short intervals,evenas short as one intervening item. However,the fact that the interactionsbetweenage
and lag were not significantsuggeststhat most of the loss of
information occursalmostimmediately,becausethereis apparently little additional lossbetweenone and two or betweentwo
and four interveningitems.
Conclusion
The resultsof this study confirm earlierfindingsthat a large
proportion ofthe age-relatedvariancein cognitiveperformance
is sharedwith measuresof the speedwith which simple operations can be executed.Moreover,previousresultsare extended
by the discoverythat the influenceofspeedwasasgreaton measuresofdecisionaccuracyobtainedunderconditionsofno time
pressureas on measuresof decisiontime or of the number of
producedwithin a specifiedtime. And, as in
correct responses
earlier studies(e.g.,Salthouse,1993b),the relevantspeedappearsto be relatedto the rate at which cognitiveoperationscan
be executed,and not merely to the time required for sensory
and motor processes.
The resultsofthesestudiesare consistentwith the interpretation that a slowerspeedofprocessingaffectsthe quality ofcognitive performanceby reducingthe amount of simultaneously
availableinformation (cf. Salthouse,1988, 1992a;Salthouse&
Babcock,199I ). That is, the evidencenow seemsfairly compelling that slowerprocessingspeedmay function as a proximal
mediatorof the relationsbetweenvariousmeasuresof cognitive
functioning and age during adulthood. However,further researchis necessaryto distinguishthis interpretation from alternativeexplanations
ofthe speed-cognition
relation(e.g.,on
the basisofconstructs suchas inhibitory control or attentional
selectivity).Additional researchis also required to identify the
causesofthe relationsbetweenageand speeddocumentedin
theseand in numerousother studies.Although many questions
remain, there now seemslittle doubt that processingspeedis a
major factor in the age-relateddifferencesin severaltypes of
cognitivefunctioning.
' Resultsfrom the analysisof varianceon the data from I 54
subjects
in StudyI wereasfollows:agedecade,
-F(5,I 48) = 5.3I, M.S": 474.8'1,
p < .01;lag,F(1, 148): 3.60;andAgeDecadex Lag,F(5, 148)= 1.67,
MS" = 271.rU. Resultsfrom the analysison the data from I 76 subjects
in Study2 wereasfollows:agedecade,.F(5, I 70) = 5.5l, M S. = 522.63,
p < .01;lag,F(1, 170)= 31.98,p < .01;andAgeDecadex Lag,F(5,
l 70)= 0. I 3, MS" = 22g.rt.
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ReceivedJanuary7, 1993
RevisionreceivedMay I 3, 1993
AcceptedMay2l,l993 r