Psychonomic Bulletin & Review
1996,3 (3),287-299
Constraintson theories of cognitive aging
TIMOTHYA. SAI]THOUSE
Georgia Insti,tute of Technology,Atlanta, Georgia
There is currently little consensusregardingwhat must be explained by theories of cognitive aging.
In the present article, four empirical generalizationsthat seem to imply certain constraints in theorizing are identified. These generalizations,and their possible implications or constraints, are that
(l) age-relateddifferences are found in a wide range of cognitive variables, implying that either a
large number of specific factors or a small number of generalfactors must be coniributing to the agerelated differences; (2) the age-relatedinfluences on different cognitive variables are not independent, and unique age-relatedinfluences appear to be few in number and small in magnitude, implying that some fairly general factors need to be postulated to account for the shared age-related
influences; (3) only a small proportion of distinct age-relatedvariance occurs late in practice and at
long presentationdurations, implying that adequateexplanationsmust include faciors operating
when the individuals are just beginning to perform the task and when the stimuli can first be registered; and (4) measuresof how quickly very simple cognitive tasks can be performed share conJiderable age-relatedvariance with many cognitive variables, implying that factors related to simple
processingefficiencyneedto be incorporatedinto the explanations.
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Researchconcernedwith the relations betweenadult
age and cognitive performancehas been increasingdramaticallyoverthe lastseveraldecades.Despitethe rapid
expansionof research,however,there is still little consensusregardingthe reasonsfor the negativerelations
that aretypically reportedbetweenchronologicalageand
the measuresof memory,reasoning,and spatialability
sometimesreferredto as comprisingTypeA (Hebb, 1942)
or fluid (Horn & Cattell, 1963)cognition.The primary
purposeof this articleis to describeseveralsetsof empirical resultsthat appearto placeimportantconstraintson
theoreticalexplanationsof age-relatedcognitivedecline
phenomena.
It is helpful to beginby describingthe broadphenomenonin needofexplanationby theoriesofcognitiveaging.
Considerthe distributionof scoreson a cognitivetest,
suchas immediatefree recallof a list of unrelatedwords.
In a recentexperiment(Salthouse,1993b),a total of 305
adultsbetweenl9 and 84 yearsof age attemptedto remembertwo l2-word lists (presentedauditorilyat a rate
of I word every 2 sec), and their averagescoresacross
the two lists rangedfrom near zero to perfect (top panel
of Figure I ). Becausethe sampleincludedpeopleof different ages,the distribution can be disaggregatedby age.
That is, the individualscan be orderedby their ages,and
then the scoresplottedby age(as in the bottom panelof
Figure I ). This type of disaggregation
typicallyresulrsin
considerable
variabrlityat eachage,but with an average
This researchwas supportedby National Institute on Aging Grant
R37 AG6826 to T.A.S. I would like to thank three reviewersfor their
c o n s t r u c t l v ec o m m e n t so n a n e a r l i e rv e r s i o no f t h i s m a n u s c r i o t T
. he
a u t h o r ' sm a i l i n g a d d r e s si s S c h o o l o f P s y c h o l o g yG
, e o r g i aI n s t i t u t e
o f T e c h n o l o g y ,A t l a n t a , G A 3 0 3 3 2 - 0 1 7 0( e - m a i l : t i m . s a l t h o u s e ( d
psych.gatech
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trend that is clearly negative, indicating that increased
age is associatedwith lower performance.For example,
in this particulardata set, the R2 value for age in a regressionequationwas .162,and thusa moderateproportion of the total variance in the free-recallmeasurewas
associated
with chronologicalage.
Similar patternsof sharedvariancewith agehavebeen
found for many cognitive variables.To illustrate, problems in the Raven'sAdvanced ProgressiveMatrices Test
consistof a 3 X 3 matrix of symbolsor geometricelementsin all but one of the cells of a matrix. The task for
the examineeis to use abstractreasoningto identify the
patternthat providesthe bestcompletionof the missing
cell. A recentstudyinvolving221 adultsbetween20 and
80 yearsof age (Salthouse,1993a)found that 32.2ohof
the variancein the Raven'sscore was associatedwith
chronological
age,and in a similarstudy(Babcock,1994)
2l 2% of the variancein the Raven'sscorewas found to
be relatedto age.
There is clearly substantialscatterin the data of Figure l, and the proportionsof varianceassociatedwith
agearealwayssubstantiallylessthan 1.0.Becausemany
researchersmay not be comfortablethinking in terms of
proportions of variance,it is reasonableto question the
magnitude of the age-relatedeffects in Type A or fluid
measuresof cognitivefunctioning. Fortunately,thesevaluescanbe placedin contextby referenceto Cohen( I 988),
who, in his influential book on power analysis,has suggestedthat in the behavioralsciencesproportionsofvarianceof .01 are small,thoseof .09 aremedium,and those
of .25 are large. The effectsjust describedare therefore
in the medium-to-largerange with respectto behavioral
scienceresearch.
The phenomenonof age-relatedcognitivedecline in
Type A or fluid aspectsof cognition is not only moder-
287
Copyright 1996PsychonomicSociety,Inc.
288
SALTHOUSE
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measures,procedures,and samplesof participants.Thc
emphasiswill thereforebe on patternsof resultsobtained
from severalindependentstudiesand different methodological proceduresrather than on results from a single
study or analytical method.
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BASED CONSTRAINTS
A l t h o u g h m a n y r e s e a r c h e r sa, n d e s p e c i a l l yt h o s e
trainedin experimentalratherthanmultivariatetraditions,
tend to focus on single dependentvariables,the agerelatedcognitivedeclinephenomenonis actuallyquite
broad,becausea greatmany cognitivevariableshavebeen
found to exhibit age-relateddifferences.The breadthof
by inspectingthe conthe phenomenoncan be assessed
tentsof majorjournalsin the field (e.g.,Psvchologt'und
Aging and Journal of Gerontologv: Psvchologicul Sciences\and notingthe rangeof variablesin which signit-icantagedifferenceshavebeenreported.To illustrate.in
the last5 yearsyoungadultshavebeenreported.in thc-sc'
journals,to performsignificantlybetterthanolderadults
in the following cognitivetasks:memory for *ords. prosc.
pictures.faces.source.activities.locapairedassociates,
tions,phonenumbers,routes,grocerylists.and golfshot
information;reasoningwith seriescompletion.matrl\.
analogy,letter sets,and categorizationproblems:block
rotation.and intcdesign,paperfolding,objectassembly.
gration spatialtasks;divided, selectivc.and.focusedatcomprehcntention;and miscellaneoustasksassessin-s
sion, following instructions.and seriallearning.
v
\-
Age
Chronological
Figure l. Distribution of scores in a I 2-word free-recall task in
a sample of305 adults. Data from Salthouse (1993b).
0.8
0.6
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ately large but also robust, becauseit has been docuE
with
replicated
1920
and
has
been
at
least
mentedsince
8 o'2
many differenttypes of tests,with both cross-sectional C"
and longitudinaldata-collectionprocedures,in several
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(u 0
differentcultures,and in a varietyofspecies(e.g.,for reviews, see Birren & Schaie,1996,Craik & Salthouse, E i.2
(U
1992,andSalthouse,l99l). One of the major questions
-0.4
6
in the field at the currenttime is: how canthesenegative
age relationsbe explained?That is, what is responsible
-0.6
for the lower levels of cognitive performanceoften associatedwith increasedage?
.0.8
The goal in this article is not to describea specific the-1' 2 0 3 0 4 0 5 0 6 0 7 0 8 0
ory or explanation,but insteadto identify severalbroad
constraintsthat presumablymust be satisfied by any
cognitivedeclinepheplausibletheoryofthe age-related
Age
Chronological
nomenon.The rationalefor this approachis the assumpFigure 2. Mean standard scores by age decade for six cognitive
tion that it may be easierto reach a consensuson theoData for the free-recall and paired associatestasks are
m€asures.
retical explanationsif, first, there is agreementon the
from Salthouse (1993b), data for the Wisconsin Card Sorting and
must
satisfy.
broad constraintsthat plausibletheories
Shipley Abstraction tasks are from Salthouse. Fristoe, and Rhee
To qualifo astrue constraints,the relevantresultsshould (in press), and data for the Surface Development and Paper Foldbe robust, with numerousreplicationsacrossdifferent ing tasks are from Salthouse and Mitchell (1990).
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CONSTRAINTSON THEORIESOF COGNITIVEAGING
\.
The scopeofthe phenomenoncan also be appreciated
by examining the age trends for different variables in
moderatelylarge samplesof adults from a wide rangeof
ages.For example,Figure 2 illustratesthe agerelations for
six different variables(i.e., number correct in free recall
of two lists of 12 words each, number correct in paired
associatesmemory of 6 word pairs, percent perseverative errors in the WisconsinCard Sorting Test,and number ofcorrect responsesin the Shipley Abstraction Test,
in the SurfaceDevelopmentTest,and in the PaperFolding Test)from three separatestudies.The original scores
on eachofthe various testswere first convertedto z scores
to produce units on a comparablescale,and then the
meanswere plotted by decade.Note that the age trends
are very similar for measuresof memory ability (paired
associate
and freerecall),reasoningability (ShipleyAbstractionand Wisconsin Card Sorting), and spatial ability (paperfolding and surfacedevelopment).For eachof
theseabilities thereis a differenceof approximatelyI SD
betweenpeoplein their 20sandpeoplein their 70s.Similar age trendsin an age-heterogeneous
sampleof 1,628
adults across l7 different cognitive measureshave also
recentlybeenreportedby Schaieand Willis ( 1993).
The existenceof statisticallysignificant, and often
roughly comparable,age-relateddifferencesacrosssuch
a wide varietyof cognitivemeasuresleadsto the first constrainton theorizingabout cognitiveaging phenomena.
Constraint I
Either a small number of ./airly broad and general
mechanismsor a large number of specific mechanisms
are needed to account for the age-related diJ.ferences
found across a wide range oJ'cognitive variables-
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that is, becausethe phenomenonofage-relatedcognitive
decline encompasses
such a large number of cognitive
variables,explanationsof the phenomenonmust either
incorporatea largenumberof factorswith highly specific
effectsor a relativelysmall numberof factorswith broadreachingconsequences.
Theoriespostulatingdeficits in
a few processes
specificto a limited numberof cognitive
taskswill thereforenot sufficeto providea completeaccount of the age-relatedcognitivedeclinephenomenon.
In light of the wide rangeof variablesexhibitingsignificant age relations,and of the apparentsimilarity of
the age patternsacrossdifferent variablesin moderately
largesamples,the questionarisesasto the extentto which
age-relatedeffects on different variablesare independent. The issueof independence
is also relevantto the
numberof distinctmechanismsnecessary
to accountfor
cognitive aging phenomena,becausemany separate
mechanismswould presumablybe neededif most of the
age-relatedeffectswere found to be independent.In contrast,a common or generalage-relatedfactor would probably be implicatedif largeproportionsof the age-related
effectswere found to be shared.
In the past there has been a tendencyamong many
cognitive researchersto assumethat all age-relatedeffects were attributableto specific deficits, with these
289
deficits possibly even localizablein discreteprocessing
stagesor components.Becausethe focus was often on
single dependentvariables,such as an index of performance on a particular type of memory task, the issueof
sharedage-relatedinfluenceswas never seriouslyevaluated sincetherewas no meansof separatingcommon (or
shared)and specific (or unique) age-relatedeffects.
Broader interpretationshave sometimesbeen considered, but they were often dismissedbecauseof results
(e.g.,the existenceof age X conditioninteractions)interpretedas suggestingthat a generalfactor was not sufficient to account for all of the observedeffects. For a
variety ofreasons(e.g.,failure to considerthe role ofdifferentialreliability of factorswith a multiplicative influence, of processesthat might vary in their reliance on a
generalfactor,and ofthe possibility that both generaland
specific influencesmight operatesimultaneously),these
analysesmay not have been optimal (Salthouse,1991,
p p . 2 9 l - 3 0 0 ; S a l t h o u s e& C o o n , 1 9 9 4 ) .I n a n y c a s e ,
however,it seemsmore productiveto evaluatethe relative
contribution of different types of influencesrather than
to attemptto distinguishbetweenextremeall-or-noneinterpretations(such as only specific or only general).
Contemporary researchconcernedwith aging and
cognitioncan be characterized
as consistingofa surplus
of sensitivityevidencebut a shortageof specificityevidence.Claims of sensitivityare basedon evidencethat
the variableor theoreticalprocessis significantly related
to age.As noted above,there are many reportsof significant age relationsacrossa wide rangeof cognitive variables,and thus age sensitivity has been convincingly
demonstratedfor many variables.The term specificity in
this contextcan be usedto refer to evidencethat the agerelated influenceson one variable are distinct from, and
independentof, the age-relatedinfluenceson other variables.Becauseof the dominanceof researchbasedon
small-sample,
extreme-groupdesignsfocusingon a single dependentvariable,very little researchrelevantto
the issueofspecificity is currentlyavailablein the field
ofcognitive aging. This is unfortunatebecauseconvtncing evidenceof specificity is neededbefore interpretations basedon separateand distinctage-relatedinfluences
can be consideredplausible.That is, ifa largeproportion
ofthe age-relatedeffectson different cognitive variables
is found to be shared, or in common, then attempts to
identify mechanismsspecific to one of the variablesmay
merely be describingsymptoms of a much broaderphenomenon.Moreover,evenif only someofthe age-related
influencesare shared,the magnitudeof the uniqueagerelated effects that remain to be explained by taskspecific mechanismswill dependon how much of the
total effectsare attributableto more generalfactors.
lndependenceis often assessed
with correlationalprocedures,becausethe squareofthe correlationindicates
the proportion of variancein two variablesthat is shared.
However,becausethe current interest is in sharedagerelated influences,the relevant variance is not the total
amount of variance; instead, it correspondsonly to the
amount of age-relatedvariancethat is shared.For exam-
290
SALTHOUSE
ple, ifthe proportionofage-relatedvarianceis .162,then
the question of interest in the presentcontext is how
much of this varianceis sharedwith other variables.The
relevant proportions of variance can be estimatedwith
correlation/regressionproceduresbecauseprediction of
the criterion variablewhen age is the only predictorvariable in the regressionequation indicates the total agerelated variance,and the increment in variance associated with age after partialling out the effects of another
control variable indicatesthe unique age-relatedvaria n c e . S u b t r a c t i o no f t h e u n i q u e a g e - r e l a t e dv a n a n c e
from the total age-relatedvariance and division by the
total age-relatedvariancethereforeyields the proportion
of age-relatedvariancein the criterion variablethat is
shared,or in common,with the othervariable.(SeeSalthouse,1992,1994b,in press-a,for furtherdiscussionof
theseprocedures.)
If only a small proportionof the age-relatedvanance
in a given variableis sharedwith anothervariable,then
most of the age-relatedinfluenceson that variablecan
be inferredto be independent,distinct,and potentially
specific. However,if the ratio of shared(or common)
age-related
varianceto total age-related
varianceis high,
then one can infer that most of the age-relatedeffectson
the two variablesare shared.
To ensuremaximum generalizability,it is important
to examinetheseproportionsacrossmany combinations
of variables.Among the criteriadesirablein datasetsto
be usedfor this purposcare:( I ) multiplevariablesshould
be availablefrom the sameindividualsor else no independenceanalysesare possible;(2) the variablesshould
haveat leastmoderatereliability to ensurethat there is
sufTicientsystematicvarianceto be sharedwith other
variables;(3) the sampleshouldhavea wide age range,
and preferablyconsist of a continuousdistribution of
ages,to ensureaccurateassessments
of the age-related
influences;and (4) the samplesshouldbe largeenough
to ensurereasonablypreciseestimatesof the relevant
proportionsofvariance.Severalstudiesfrom my laboratory havethe requisitecharacteristics,
and thus datafrom
thosestudiescanbe examinedto estimateproportionsof
age-relatedvariancesharedacrossdifferent cognitive
variables.
It is useful to illustratetheseprocedureswith an example of the relevantcomputations.In a recent study
( S a l t h o u s eF, r i s t o e ,& R h e e ,i n p r e s s ) ,2 5 9 a d u l t sb e tween I 8 and 94 years of age performed tasksof inductive reasoning(i.e.,ShipleyAbstraction)and verbalmemory (i.e., paired associates)
that are usuallyassumedto
representdistinct cognitiveabilities.An initial regressi^onanalysison the abstractionmeasurerevealedthat the
R' associatedwith age was .199, indicatingthat l9.9Vo
of the variancein this measurewas relatedto age.A hierarchicalregressionequationin which the paired associatesmemory measurewas controlledbeforethe effects
of age on the abstractionmeasurewere examinedrevealedthat the incrementin R2 associated
with age was
.062.An estimateof the sharedage-relatedvariancecan
be derivedby subtractionofthis value,which represents
v
the uniqueage-relatedvariance,from the total age-related
varianceof . I 99 to yield a valueof .137. In this particular case,then, 68.8% (i.e., . I 371.199)of the age-related
variance in the abstractionmeasurecan be inferred to
have been sharedwith the age-relatedvariancein the
pairedassociatememory measure.Becausethe amount
ofage-relatedvarianceis not necessarilyidenticalfor the
two variables,the estimatesof uniqueand sharedproportions need not be equivalent.In fact, the percentageof
age-relatedvariancefor the paired associatesmemory
measureestimatedto havebeen sharedwith that in the
abstractionmeasurewas 58.9% (i.e., .1421
.241).
A recentarticleby Salthouse( 1994b)reportedresults
of analysessimilar to these,conductedon 855 pairs of
variablesobtainedfrom l3 separatestudies.The variables
were derived from a wide variety of tasks,ranging from
reactiontime to numberof items correcton the Raven's
Progressive
MatricesTest,and rangingfrom accuracyin
paired associatesmemory tasks to accuracy in paper
folding spatialtasks.The meanof these855 valueswas
. 5 0 0 ( m e d i a n o f . 5 2 0 ) , i n d i c a t i n gt h a t a n a v e r a g eo f
about50% ofthe age-related
variancein many cognitive
variablesis shared,or in common.Becausean averageof
only l9o/oof the total variancefor these same variables
was shared,it can be concludedthat the simplecorrelation betweentwo variablesis not sufficientto determine
t h e e x t e n tt o w h i c h t h o s ev a r i a b l e ss h a r ea g e - r e l a t e d
vanance.
T h e f r e q u e n c yd i s t r i b u t i o n f o r t h e p r o p o r t i o n so f
s h a r e dv a r i a n c ea m o n g l 6 v a r i a b l e s( 1 2 0 p a i r s )i n t h e
Salthouse,
Fristoe,and Rhec(in press)studyis portrayed
in Figure3. Notice that the patternwas nearlyidentical
to that found in the Salthouse( I 994b)analysesin that an
averageofover 50% ofthe age-relatedvariancein pairs
of variableswas shared.The similarity in outcomesis
particularlynoteworthybecausethe variablesin the Salthouse,Fristoe,and Rhee (in press)study were derived
from neuropsychological
testsoften postulatedto be sensitiveto functioningin diff'erentregionsof the brain. For
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Proportion ol Sharod Age-Rolated Variance
Figure 3. Distribution of proportions of shared age-related
variance from 120 pairs ofvariables in Salthouse, Fristoe, and
Rhee's (in press) study.
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CONSTRAINTSON THEORIESOF COGNITIVEAGING
291
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tv
example,the Wisconsin Card Sorting Test and the FAS
fluency test have been hypothesizedto be sensitive to
frontal lobe damage,visual spatial tests such as the
WAIS-R Block Design and Object Assembly tests have
been hypothesizedto be sensitiveto right parietal lobe
damage,and damageto the medial temporal lobe hasbeen
postulatedto affect performanceon verbal learning and
memory tests such as paired associatesand free recall.
The resultsjust describedindicatethat the age-related
effectson what appearto be quite different variablesare
not independent.That is, an averageof approximately
halfofthe age-relatedinfluenceson a givencognitivevariable appearto be sharedwith other cognitive variables,
even when those variableshave little or no resemblance
to one anotherand when they are usually interpretedas
representingdistinctcognitiveabilitiesor reflectingfunctioning in differentbrain regions.
Another analyticalprocedurethat can be usedto generateestimatesof common and unique age-relatedinfluencesis one proposedby Kliegl and Mayr ( l992) based
on a structuralequationmodel with a single common
factor. Within this model, both general(i.e., mediated
throughthe common factor)and specific(i.e., unmediated,or direct) age-relatedeffectsare postulatedto exist.
Furthermore,the relativecontributionsof each type of
influcncecan be estimatedfrom standardized
pathcoeff i c i e n t s d e r i v e d f r o m t h e s t r u c t u r a lm o d e l . T h a t i s ,
within this framework,the generalinfluenceis estimated
by the productofthe path coefficientsbetweenage and
the common factor and betweenthe common factor and
the individualvariable,and the estimateof the specific
influencecorrespondsto the coefficient betweenageand
the individualvariable.
Becausethe common factor in this type of model is
definedby the variableswith significantloadings,it can
be interpretedas representingwhat all of the variables
havein common.The interestingquestionin the present
contextconcernsthe magnitudeof the relationsbetween
age and the individual variablesafter the relation betweenageand an estimateofwhat all of the variableshave
in commonhasbeentakeninto consideration.Ifthose distinct agerelationsare largerelativeto the total age-related
effectson the variable,then substantialuniqueor specific
age-relatedinfluencescan be inferred to exist. However,
if the distinct (or direct) relation betweenage and the
variableis very small, then therewould be little evidence
for specific age-relatedinfluencesaboveand beyondthe
age-relatedinfluencessharedamong all of the variables.
A variety ofstructural equationmodeling procedures
(e.g.,EQS, LISREL) can be usedto deriverhe estimares
for the relevantpath coefficients.Becausethe prerequisitesfor thesetypesof analysesaresimilarto thosementioned earlier(i.e.,moderatelylargesamplesfrom a wide
age rangewith severalvariablesavailablefrom eachparticipant),the procedureswill againbe illustratedwith data
from my laboratory.(But see Lindenberger& Baltes,
1994,and Lindenberger,Mayq & Kliegl, 1993,for particularly elegantexamplesof this type of analysis.)Re-
sults from four independentdata sets are illustrated in
Figures4 and5. Figure 44, containsdata from Salthouse
(1993a),with measuresof perceptualspeed,working
memory, and inductive reasoning from 221 adults between 20 and 80 yearsofage. The seconddata set, portrayed in Figure 48, consistsof measuresof perceptual
speedand three setsof verbal and spatial memory measuresfrom 173 adultsbetween l8 and 88 yearsofage
(Salthouse,I 995a).The datasetrepresentedin Figure54,
consistsofmeasuresfrom neuropsychologicaltestsfrom
a sample of 259 adults between l8 and 94 years of age
(Salthouse,Fristoe,& Rhee,in press).Finally,the dataset
in Figure 5B consistsof measuresof conceptidentification, associativelearning, working memory, perceptual
comparisonspeed,and visual acuity from 197 adultsbetween l8 and92 yearsof age(Salthouse,Hancock,Meinz,
& Hambrick,in press).
The models summarizedin Figures 4 and 5 were all
generatedin the same manner. First the data from the
study were convertedinto a covariancematrix, and then
a single common factor rnodel was specified with relations from age to the common factor. Relationsbetween
variablessharingsimilar methodswere next examined
and includedin the model if the coefficientsdifferedfrom
zero by more than 2 standarderrors. Successivemodels
were then examinedin which direct relationswere specified betweenage and each individual variable,and relations with coefficients differing from zero by more than
2 standarderrors were retained in the model. The final
models,representedin Figures4 and 5, thereforeportray
all of the significant relations betweenage and the observedvariables.Becausethere was little attemptto representpossiblerelationsamongsubsetsof the variables,
the modelscan be consideredrelativelycrude summaries
of the structureof thedata.lHowever.the imoortantissue
from the currentperspectiveconcernsthe relativemagnitudesof the mediated,or common,and the direct,or
specific,age-relatedinfluences.Notice that a similar pattern is apparentin each data set in that there is a large
common or generalinfluenceon all variables,along with
small specific age-relatedinfluenceson a few of the variables.zTheseresultssuggestthat thereare relatively few
uniquerelationsbetweenageand the individual variables
beyondthose sharedamong all variables.
The two analytical methodsdescribedaboveare both
quiterecent,and consequently
their potentiallimitations
have not yet been fully explored. Furthermore,because
relatively few studieshavebeen conductedwith the requisite data,the resultsillustratedwere all derived from a
single investigator'slaboratory.Despite thesequalifications, the outcomes of both types of analysesare quite
consistentin suggestingthat the age-relatedinfluences
on many differentcognitivevariablesarenot independent.
That is, the moderate-to-largeproportionsof sharedagerelated variance and the small-to-nonexistentdirect relations between age and individual cognitive variables
after taking into account the relation of age to a single
common factor both suggestthat the age-relatedeffects
292
SALTHOUSE
\'
\,
Figure 4. Single common factor structural models for data (A) from Salthouse (1993b) and
(B) from Salthouse (1995a). Variables in Panel A are: DigSym = WAIS-R Digit Symbol Substitution score; Letcom = Letter Comparison; Patcom = Pattern Comparison; Shipley =
Shipley Abstraction Score; Raven = Raven's Progressive Matrices score; CSpan = computation span working memory score; and LSpan = listening span working memory score. Variables in Panel B are: PatCom = Pattern Comparison; LetCom = Letter Comparison; KT:V =
keeping track of verbal information; KT-S = keeping track of spatial information; EM-V =
element memory for verbal information; EM-S = elem€nt memory for spatial information;
MM-V = matrix memory for verbal information; and MM-S = matrix memory for spatial information.
on different^cognitivevariables are not independentof
one another.rTheseresultslead to the secondimoortant
constrainton theoriesofcognitive aging.
Constraint 2
Somefairly general or broad mechanismsare apparently needed to account.for the lack of independencein
the age-related influences on cognitive variables
in other words, becausea large proportion of the agerelatedeffectson different cognitivevariablesappearsto
be shared,theoriesbasedexclusivelyon specificmechanismswill not be sufficient to accountfor cognitiveaging
phenomena.Although somespecific age-relatedmechanisms appearto exist, they must be supplementedby
broaderor more generalmechanismsin order to account
for the commonality apparentin the age-relatedeffects
on different cognitive variables.
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CONSTRAINTSON THEORIESOF COGNITIVEAGING
293
\-
Figure 5. Single common factor structural models for data (A) from Salthouse, Fristoe, and
Rhee (in press) and (B) from salthouse, Hancock, et al. (in press). variables in panel A are:
DigSym = wAlS-R Digit symbol substitution score; Letcom = Letter comparison; patCom = Pattern comparison; PAI = Trial I in Paired Associates Memory; pA2 = Trial 2 in
Paired Associates Memory; RVLT2 = Trial 2 in the Rey Auditory verbal Learning Test;
RVLT6 = Trial 6 in the Rey Auditory verbal Learning Test; wcSTpE
= percent perseverative errors in the Wisconsin Card Sorting Test; WCSTCL = perc€nt conceptual level responses
in the wisconsin Card Sorting Test; objAssm = wAIS-R object Assembly score; BlkDes =
wAIS-R Block Design score; F60 = number of words beginning with F produced in 60 sec; and
560 = number of words beginning with S produced in 60 sec. Variables in panel B are:
= number of category responsesin the wisconsin card Sorting Test; Assocpc =
wcsr:-Nc
percentage correct in associative learning; NB2 = percentage correct in reporting items twoback in a sequence; NBI = percentage correct in reporting items one-back in a sequencel
wM-N = numeric (computation span) working memory score; wM-v
= verbal (reading
span) working memory score; DSRT = digit symbol reaction time; DDRT = digit digit reaction time; Patcom = pattern comparison; LetCom = letter comparisonl vision-R = visual
acuity in the right eye; and Vision-L = visual acuity in the left eye.
ly
An obviousnext question,in light of the evidencesuggestingthat a common or generalage-relatedfactor exists, concernsthe nature ofthat factor. One approachto
investigatingthe natureofthe generalfactor involvesex-
amining where, in an ordered sequence,independent
age-relatedeffects occur (Salthouse,in press-b). The
issue of primary interest in these sequentialanalysesis
how much of the age-relatedvariance in later variables
294
SALTHOUSE
\,
in the sequenceis sharedwith, and presumablymediated
through,age-relatedeffectson variablesearlier in the sequence.Consider the possible interpretationsif the sequenceofvariables correspondsto successivelevels of
practice on the task, or to progressivelylonger stimulus
durations.If only a small proportion of the age-related
variancein variableslate in practice,or in variablescorrespondingto long stimulus presentationdurations,is
sharedwith variablesearly in practice or with variables
correspondingto short stimulus presentationdurations,
then one could infer that distinctage-relatedinfluences
emergeas a function of increasedpracticeor longer presentationdurations. For example, some types of higher
order processingor strategiesmight develop with practice on the task,or may be effectiveonly after the presentation durationof the stimuli exceedsa minimum value.
However,if a substantialproportion of the age-related
variancein latervariablesin an orderedsequenceis shared
with variablesearlier in the sequence,then one could
infer that the factorsresponsiblefor many of the agerelated effects are presentvery early in practice and as
soonas the relevantstimuli can be registered.
Perhapsthe simplestmethodof determiningthe amount
ofindependentage-related
varianceon a particularvariable in a sequenceis to use hierarchicalregressionproceduresin which the variancein the prior variablein the
sequenceis controlledbeforethe amountofage-related
variancein the targetvariableis assessed.
The residual
age-relatedvariancein this situationindicatesthe agerelatedinfluencethat is independent
of the prior variable
in the sequence,and it can be expressedas a proportion
by dividing the independentage-relatedvarianceby the
total age-relatedvariancefor that variable.
Analysesofthis type requireaccessto the raw data,or
at leastto a completecorrelationmatrix, from studiesin
which eitheramountof practiceor the time of stimulus
presentationhavebeenmanipulatedin samplesof adults
ofdifferent ages.Resultsfrom severalsuch studies,includingthoseby Charnessand Campbell( 1988),Cooper
(1994),and Rogers,Fisk, and Hertzog(1994),were recently describedby Salthouse(in press-b).Figures6 and
7 illustratetheseand relatedresultsin the form ofthe percentage(i.e.,the proportioncomputedas describedabove
multiplied by 100) of the age-relatedvariancefor each
variablein the sequencethat was independentofthe agerelatedvariancein the previousvariablein the sequence.
The data in the upper left panel ofFigure 6 represent
performancein fairly complex multiple-task(i.e., synthetic work) or mental squaringstudiesacrosssuccessive
25-min (syntheticwork) or 38-trial (mental squaring)
sessions.The upperright panel containsdatafrom visual
and memory searchreactiontime taskscollapsedacross
setsof 240 or 600 trials. Data in the bottom two panels
of Figure 6 correspondto singletrials in free recall,maze
learning, or associativelearning tasks.Although the results basedon single trials are clearly much noisier than
thosein which eachdatapoint is basedon a greaternumber of observations,a similar pattern of greatly reduced
unique age-relatedvarianceacrosssuccessivepoints in
practiceis evidentin every panel.It can thereforebe concluded that most of the independentage-relatedinfluencesin severaldifferent types ofcognitive tasksare apparentin the earliestphasesoftask performance.
Resultsfrom studiesmanipulatingthe amountof time
relevantstimuli in the task were presentedare illustrated
in Figure 7 . Each point in thesefigures reflectsthe average level of performanceacrossa moderatenumber of
trials at a given stimulus duration in studiesin which
stimulusdurationvariedas a within-subjectsmanipulation. Despitethe variationin tasksand stimuli, a clear
patternofmost ofthe unique age-relatedvarianceoccurring at the shortestpresentationdurationsis apparentin
each function.
The resultssummarizedin the last two figures indicate that very little distinct age-relatedeffects appearto
occur on measuresofperformancerepresentinglater sessionsof practiceor longerstimulusdurations.This leads
to the third constraintfor theoriesof cognitiveaging.
Constraint 3
Factorsoperatingwhile stimuli are initially being registered,or in the early sessionsof practice on the task,
need to be postulated to acc'ount.fbrmuch o/ the agerelated efkcts in at least severalcognitive tasks--that is, becausea very largeproportionofthe age-related
influenceslatein practiceandwith long stimuluspresentation durationsare apparentlymediatedthrough inlluencesoperatingearlyin practiceand with shortpresentation durations,plausibletheoriesofcognitiveagingneed
to incorporatemechanismswith earlyandrapid influences.
An alternativeapproachto investigatingthe natureof
the hypothesizedcommon factor consistsof examining
the extentto which the age-relatedvariancein the cognitive variablesof interestis reducedafler controlling for
the variancein variablesthat might be postulatedto function as mediatorsof the age-cognitionrelations.Selection of potentialmediatorscould bejustified on theoretical grounds,or couldbe basedon empiricalcriteriasuch
as the variablesthat either appearto be the simplestor
havethe highestloadingson the commonfactor.Hierarchical regressionanalysescannext be conductedin which
the variance in the presumablyfundamentalmeasureis
controlledbeforethe relationof ageto the othermeasures
is examined.The plausibilityof a variable'sacting as a
mediator of the relationsof age to other variablescan be
inferred to increasein proportion to the degreeto which
the age-relatedvariancein the criterionvariableis reduced
after the variance in the potential mediating variable is
controlled.
A relativelylarge number of recentstudieshave reported results of statisticalcontrol analyseswhen measuresof working memory or processingspeedhaveserved
as the controlledvariables.Becausetasksdesignedto assessprocessingspeedcan be arguedto be simpler than
thoseassessingworking memory, and becauseresultsof
!
!
\,
CONSTRAINTSON THEORIESOF COGNITIVEAGING
295
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studies summarized in Salthouse (in press-b) and from Salthouse, Hambrick, Lukas, and Dell (in press).
\,
statisticalcontrol analysesindicate that there is greater
reduction of the age-relatedvariance in measuresof
working memory after control of measuresof speedthan
vice versa(e.g.,Salthouse,
in press a), the followingdiscussionwill focuson researchin which measurespostulatedto reflect processingspeedservedas the controlled
variable.a
A wide variety of speedvariableshave been used in
thesetypes of analyses,ranging from measuresof simple reactiontime to measuresof decisiontime in moderately complexcognitivetasks(e.g.,Bieman-Copland&
Charness,1994;Bors & Forrin, 1995;Bryan &Luszcz,
in press;Graf & Uttl, 1995;Hartley, 1986, 1993;Hertzog, 1989; Hultsch,Hertzog,& Dixon, 1990; Hultsch,
Hertzog, Small, McDonald-Miszczak,& Dixon, 1992:
K w o n g - S e e& R y a n , 1 9 9 5 ;L i n d e n b e r g eer t a l . , 1 9 9 3 ;
N e t t e l b e c k& R a b b i t t ,1 9 9 2 ;S c h a i e ,1 9 8 9 ,1 9 9 0 ) .A l though nearly all ofthe relevantstudieshavereportedat
leastmoderateattenuationof the age-relatedvariancein
the criterion cognitive variableafter control ofthe speed
measure,the degreeof attenuationappearsto be greatestwith speedmeasuresfrom taskswith elementarycognitive requirements(Salthouse,1993b,1994c).This could
be becausetasks such as simple reaction time, marking
lines,or copying digits tend to emphasizeperipheralsensory and motor factors,and performancein complextasks
may be heavily influencedby amount of relevantknowledgeand varioushigherordercognitiveabilities.In contrast,tasksinvolving simplesearch,comparison,and substitution operationsclearly have a cognitive component,
but are likely to be only minimally influencedby quantity of knowledgeor levelof spatial,reasoning,or memory
296
SALTHOUSE
\,
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Figure 7. Percentagesof independent age-related variance at progressively longer stimulus presentation durations. Data from studies summarized in Salthouse (in press-b) and from Salthouse and Hancock (t995).
abilities.In thepsychometricabilitiesliterature,thesetasks
are consideredto assessperceptualspeed(includedare
suchtestsas FindingAs, IdenticalPictures,NumberComparison,Visual Matching, and varioussubstitutiontests).
Two tasksthat have been used in many recent studies
to assessperceptualspeedinvolve the presentationof
pairs of lettersor line patternswith the researchparticipant instructedto classify them as same or dilJbrentas
rapidly as possible.Becausethe measuresofperformance
on these tasks typically have moderateto high correlations with one another(e.g.,in the rangeof .70),a more
reliable compositespeedindex can be formed by averaging the z scoresfrom the two tasks.
Resultsfrom severalstudiesin which the age-related
variancein different cognitive measureshas been compared before and after control of the compositeletter
comparison/pattern
comparisonspeedindex arereported
in TableI ofSalthouse( I 993b)and in Table5 ofSalthouse
(in press-a).The analysesin the Salthouse(1993b)article indicatedthat almost 80% of the age-relatedvanance
in variousmeasuresof reasoningand spatialabilitieswas
eliminatedafter control of measuresof perceptualspeed.
Similar reductionsof the age-relateddifferencesin measures of memory performance were reported by Salthouse (in press-a). To illustrate, the percentagereduction in age-relatedvarianceranged from 87 to 96 for
measuresof free recall, from 58 to 84 for measuresof associativelearning, from 83 to 100 for measuresof asso-
ciative memory,and from 78 to 97 for measuresof workphenomenonis also
ing memory.This speed-attenuation
evident with criterion variablesoften consideredto reflect higher order cognitivefunctioning.For example,the
age-relatedvariancein performanceon the Raven'sProgressiveMatrices Testwas reducedby 82.0% after control of the letter comparison/patterncomparison speed
index in a studyby Salthouse(1993b)and by 60.8%in a
studyby Babcock(1994).The reductionin the age-related
variancein the numberof categoriesmeasurein the WisconsinCard Sorting Testafter control of this samespeed
index was 75.4"/oin a study involving 259 adults,reported
by Salthouse,
Fristoe,and Rhee(in press),and 85.5%in
a studyinvolving 197adults,reportedby Salthouse,Hancock,et al. (in press).Finally,the age-related
variancein
the WAIS-R Block Design and Object AssemblyTests
was reducedby 86.3% and87.60/o,
respectively,after control of the letter comparison/patterncomparison speed
index in the Salthouse,Fristoe,and Rhee(in press)study.
The results summarizedabove indicate that there is
considerableoverlap of the age-relatedinfluenceson
very simple speededtasks and on complex cognitive
tasks,even when the latter are administeredunder selfp a c e dc o n d i t i o n s( e . g . ,S a l t h o u s e1, 9 9 3 a , 1 9 9 4 c S
; althouse,Fristoe,& Rhee,in press).There are at least two
possible interpretationsof these well-documentedrelations. One is that measuresof performancein simple
tasksprimarily reflect how quickly basic operatronscan
v
\,
CONSTRAINTSON THEORIESOF COGNITIVEAGING
be executed,and that processingspeedis a critical mediating factor contributingto the age differencesin many
differentcognitivevariables(e.g.,Salthouse,in press-a).
An alternativeinterpretationis that speedis not necessarilythe critical causalfactor responsiblefor the agecognition relations,but rather that there are one or more
other factors that influence basic processingefficiency,
and that the only way effects on processingefficiency
can be manifestedin thesetypesof very elementarytasks
is in terms of a reduction in the speedof performanceof
the operations.That is, most of the tasks used to assess
perceptualspeedare so simple that errors are relatively
infrequent,and nearly everyonewould perform without
m i s t a k e si f t h e r e w a s n o t i m e p r e s s u r e .A s a c o n s e quence,virtually all ofthe individual differencesin these
tasksare evidentin the speedwith which the requisite
operationscan be completedratherthan in the quality or
accuracyof performance,but this does not necessarily
meanthat the primarycauseof thesedifferencesis an alteration in one or more processing-speed
factors.
Both interpretationsagreethat simple processingefficiencyis compromisedwith increasedage,but they differ in that in the first interpretationa slower processing
speedis postulatedto be the critical mediating factor,
whereasin the latter interpretationspeedof performance
is viewed merely as the mannerin which differencesin
processingefficiencyare exhibited.Additionalresearch
is neededto distinguishbetweenthesepossibilities,but
it is importantnot to lose sight of the fact that whatever
their cause,thesevery simplemeasures
of processingefficiency have been found to share large proportions of
age-related
variancewith complexmeasures
of cognitive
performance.This leadsto the fourth and lastconstraint
fiortheoriesof cognitiveaging.
Constraint 4
Factors related to simple processing fficiency need
to be incorporated in explanations oJ'age-relatedcognitive ddferencesthat is, becausestatisticalcontrol ofvariablesreflecting
an individual's efficiency at carrying out elementary
cognitive operationshas been found to reduce the agerelated variancein a wide variety of cognitive variables
by between50ohand 100%,factorscontributing to basic
processingefficiency must play a prominentrole in comprehensivetheoriesof cognitiveaging.
IMPLICATIONS
v
FOR FUTURE R.ESEARCH
Ifthe constraintsdescribedaboveare acceptedas reasonable,then they presumablymust be incorporatedin
any plausible theory attempting to account for agerelatedcognitivedeclinephenomena.Theoriesfocusing
exclusivelyon processes
specificto a particulartype of
c o g n i t i v ef u n c t i o n i n g( e . g . ,d e l i b e r a t er e c o l l e c t i o ni n
memory, or mental rotation in spatialtasks)or on higher
order processes(e.g.,metacognitiveevaluations,or overt
297
compensatorystrategies)will thereforeneed to be supplementedbefore they can be consideredcompletetheories of cognitive aging. Furthermore,to the extent that
the constraintsare valid, they suggesttwo important directions for future research.One line ofresearch should
be directed at investigatingthe sourcesof the age relations on measuresof simple processingefficiency and of
the mechanismsby which they affect cognitivefunctioning. The secondfocus for future researchshould be investigation of the mechanismsresponsiblefor specific
age-relatedinfluences.That is, in addition to learning
more about the nature of the hypothesized general or
common factor and how it exertsits influence, research
should also be directed toward examining the operation
of mechanismsthat are independentof the generalfactor.
There are at leasttwo major reasonswhy it can be arguedthat the highestpriority for futureresearchand theorizing should be understandingthe natureofage-related
differencesin simpleprocessingefficiency.First,specific
influencesare, by definition, more limited in scopethan
generalinfluences,and thus havea more restrictedrange
of explanatorypower.And second,limitations at a basic
levelmay influencethe type or effectiveness
of any higher
levelprocessingthat canbe carriedout. Analysesofspecific age-relatedinfluenceswould thereforelikely be
meaningful only to the extent that procedureshave first
been employedto control or adjust for any generalagerelatedinfluencesthat might exist. In view of the large
amount of evidence indicating that general age-related
factorscontributeto the observedage-relateddifferences
in many cognitivevariables,researchersinterestedin investigatingspecific age-relatedinfluenceswould be well
advisedto considerthe impactofbroaderinfluencesbefore placingmuch confidencein their interpretations
of
specificinfluences.For example,to ensurethat the effects
ofinterestare truly specificand independentofbroader
or more general factors, these researchersmight focus
on explaining the residual age-relatedvariance that remainsafterthe influenceof measuresof simpleprocessing efficiencyhavebeenstatisticallycontrolled.
An initial step in researchaimed at investigatinggeneral age-relatedinfluencesmight consistof specifying
possiblesourcesof age-relateddifferencesin simple processingefficiency. Among the categoriesof explanation
that could be consideredare nonspecific factors such as
level of motivation (e.g., amount of interestin, or effort
expendedon, the task) or cautiousness
(e.g.,relativeemphasison accuracyor quality comparedwith speed),input
and outputfactorssuchas sensoryabilities(e.g.,sensitivity to environmentalstimulation)and motor abilities(e.g.,
quicknessof emitting or controllingovertresponses),
and
cognitivesystemcharacteristicssuchas working memory
(e.g.,the ability to maintaininformationaboutthe task requirementswhile alsofluently performingthe relevantoperations),attention(e.g.,the ability to allocate,inhibit,
sustain,or redirectattentionto relevantaspectsof the
task), and processingspeed(e.g.,the rate at which many
differentprocessingoperationscan be executed).
298
SALTHOUSE
\,
The next step in this type of researchmight involve a
detailed examination of one or more of the candidate
sourcesofage-relateddifferences.There area numberof
ways in which this investigationcould proceed,but several broad principles or guidelines can be identified.
Much of the previous researchexamining the variables
listed abovehas been limited in its informativenessbecauseone or more of theseprinciples havebeenneglected.
One guideline is that two or more measuresof the relevant constructshould be assessedto minimize the influence of method-specificvariance,maximize the contribution of the theoreticallyinterestingconstructvariance,
and increasethe reliability of the assessment.
When only
a single variable is used to assessthe construct,it is impossibleto distinguishthe influencesassociatedwith the
materials,procedures,and forms of assessmentfrom
thoseattributableto the theoreticalconstructof primary
interest.Reliability can also be improvedby aggregation
acrossdifferentvariablesas well as by aggregationacross
additional observationsinvolving the same variable. A
secondguideline is that both correlational and experimental proceduresshould be employedwheneverpossible. Correlational proceduresare useful to evaluatethe
explanatorypower of the hypothesizedmediator by determining the relative magnitudesof the mediated and
unmediatedrelationsbetweenage and various measures
of cognitiveperformance.For example,a constructwould
probablynot be consideredplausibleas a mediatorif the
age-relatedvariancein the criterion variablewas not substantially reducedafter measuresof that constructwere
held constantby statisticalmeans.Furthermore,questions of independenceand specificity are most directly
addressedwith correlationalmethods.However,experimental proceduresare desirablefor the investigationof
the mechanismsresponsiblefor relationsbetweenage
and the hypothesizedconstructand betweenthe construct
and the cognitive measures.Finally, the researchshould
be replicatedacrossindependentsamplesand variations
in methodologyin order to establishthe robustnessand
generalizabilityof the major results.
SUMMARY
The primary focus of this article has been on summarizing the empirical evidencerelevant to what are proposedas four important constraintsthat must be consideredin explanationsof cognitiveaging phenomena.First,
becauseofthe great variety ofvariables exhibiting significant age differences,plausible theories need to incorporateeither a large number of highly specific agerelatedinfluencesor a small number of more general
influences.Second,becausea largeproportionofthe agerelatedvarianceon different cognitivevariableshasbeen
found to be sharedand not independent,plausibletheories needto postulatea generalfactor to accountfor this
lack ofindependence.
Third, becausemost ofthe independent age-relatedvariancein an orderedsequenceofvariablesoccursearly,major age-relateddeterminantsmust
be postulatedto be operatingas soon as the stimuli can
be registeredand at the earliest stagesofpractice. And
fourth, becausemeasuresof simpleprocessingefficiency
share considerableproportions of age-relatedvariance
with many complex cognitive measures,adequatetheoretical accountsmust include factors related to simple
processingefficiency. Finally, it was suggestedthat a high
priority for future researchshould be to investigatethe
natureof age-relateddifferencesin simpleprocessingefficiency and to discoverthe mechanismsby which cognitive performanceis affectedwhen the efficiency of elementaryaspectsof processingis compromised.
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NOTES
l . I n d i c e s o f t h e g o o d n e s so f f i t o f t h e m o d e l s w e r e a s f o l l o w s :
M o d e l i n F i g u r e 4 A , ,X 2 ( t t ) : 8 3 . 9 9 , S t d . R M R - . 0 5 0 , C F t : . 9 4 :
M o d e l i n F i g u r e4 8 , X 2 Q D - 6 5 . 2 7 .S t d . R M R : . 0 5 1 ,C F I : . 9 4 .
M o d e l i n F i g u r e5 4 , X 2 ( O g ): 1 3 5 . 8 0 ,S t d . R M R - . 0 5 6 . C F t : . 9 i :
M o d e l i n F i g u r e5 8 , X 2 ( J 9 ): 1 3 5 . 0 6 ,S t d . R M R : . 0 6 9 . C F I : . 9 4 .
2. The patternofresults for all data setswas also quite similar when
the following procedure,based on a principal-componentsanalysis,
was performed. First, a principal-componentsanalysiswas performed
on all variables;second,the first (unrotated)principal componentwas
extractedto serve as an index of the general factor in the set of variables;and third, a seriesofhierarchical regressionanalyseswere perf o r m e d i n w h i c h e a c h i n d i v i d u a lv a r i a b l es u c c e s s i v e l fyu n c t i o n e da s
the criterion variable,and the first principal componentwas usedas a
control variable before examining the variance associatedwith age.
The residual age-relatedvariancein theselatter analysesindicatesthe
age effects that are independentofthe generalor common factor, and
t h u s t h e y c a n b e c o n s i d e r e dt o b e s p e c i f i co r u n i q u e .
3 . I t s h o u l da l s ob e n o t e dt h a tt h c c o n c l u s i o nt h a t t h e a s e - r e l a t e d
influences on different variablesare not independentis coirsistentwith
l n t e r p r e t a t i o nosf a n a l y s e sb a s e do n t h e e x i s t e n c eo f s t r o n g s y s t e m a t i c
r e l a t i o n sb e t w e e nt h e m e a nl e v e l so f p e r f o r m a n c ea c r o s sc o n d i t i o n si n
s a m p l e so f y o u n g a n d o l d a d u l t s f o r b o t h s p e e dv a r i a b l e s( e . g . ,
C e r e l l a , 1 9 9 0 ; M y e r s o n , H a l e , W a g s t a f f ,P o o n ,& S m i t h , 1 9 9 0 )a n d
a c c u r a c yv a r i a b l e s( e . g . ,V e r h a e g h e n
& M a r c o e n .1 9 9 3 ) .
4 . I t i s i m p o r t a n tt o n o t et h a t t h e f o c u so n p r o c e s s i n gs p e e da s a p o tential mediator of age-cognition relations differs in at least two respectsfrom the approachofother theoristswho have been concerned
w i t h a g e d i f f e r e n c e si n m e a s u r e so f s p e e d( e . g . ,C e r e l l a ,1 9 9 0 ;M y e r s o n e t a l . , I 9 9 0 ) . F i r s t ,t h e t a r g e tv a r i a b l e st o b e e x p l a i n e di n t h e p r e s e n t a n a l y s e sc o n s i s to f a l m o s t a l l c o g n i t i v ev a r i a b l e sf o u n d t o b e r e l a t e dt o a g e i n a d u l t h o o d ,a n d n o t m e r e l yv a r i a b l e sm e a s u r e di n u n i t s
o f t i m e . A n d s e c o n d ,t h e r e s u l t so f p r i m a r y i n t e r e s th e r ea r e c o m p a r i s o n so f t h e a m o u n to f a g e - r e l a t e dv a r i a n c ei n t h e t a r g e tv a r i a b l eb e fore and after control ofan index ofspeed, ratherthan the number and
n a t u r eo f t h e f u n c t i o n sr e l a t i n gt h e m e a n s p e e d so f o n e a g e g r o u p t o
t h e m e a n s p e e d so f a n o t h e r a g e g r o u p .
( M a n u s c r i p tr e c e i v e dA u g u s t 3 , 1 9 9 5 ;
r c v r s i o na c c e p t e df o r p u b l i c a t i o nJ a n u a r y2 5 , I 9 9 6 . )