Britisb Journal of PEchologlt(1993), 84, 771-199
@ 1993 Thc l)ritish PsychologicalSociety
111
Printed in Great Britain
Influence of working memory on adult ^ge
differences in matrix reasoning
Timothy
A. Salthouse*
.ftbool of Ps;'cbologr,Georgia In.rtitntt of Terltno/0g1"Atlanta, G''1' t0it2-0170'
USA
The four studies reported in this article, involving a total oi 401 adults ranging
between 18 and 80 1'earsof age, wcre designed to investigate how working memory
m i g h r m c d i a t e a d u l t a g e d i f f c r e n c c si n m a t r i s r c a s o n i n g t a s k s s u c h a s t h e R a v c n ' s
P r o g r e s s i v e N l a t r i c e sT e s t . E v . i d e n c eo f t h i s m e d i a t i o n i s a v a i l a b l ei n t h e 6 n d i n g t h a t
statistical control of an index of working memorv reduces the age-reiated variance
in matrix reasoning performance by approximately 70 per cent. Because the age
differences were nearly constant across items of varying difficulty, it was concludcd
that thc hctors responsible for variation in item difEculty were distinct from thosc
responsible for thc age differcnces. Howcvcr, young adults were found to bc more
acculate than older adults at recognizing information presented earlier in the matrix
reasoning trial, thereby supporting the intcrpretation that working memory exefts
its influence by contributing to the preservation of information during subsequent
proccssing.
Speculationsabour rhe role of working memorv in adult age differencesin cognition
can be traced at least as iar back as Welford's (1958) book (seeSalthouse,1990, for
a review of researchon adult age differencesin working memory). It has only been
in the last several ,vears, ho\r'ever, that convincing empirical evidence for the
influence of working memory on age differencesin cognition has become available.
Examples are recent studies by Salthouse(1,991a) and Salthouse,Mitchell, Skovronek
& Babcock (1989) in u'hich the magnitude of the age differencesin several measures
of cognitive functioning was found to be greatly attenuated b,v statistical control of
a measure clf working memorv.
Although the stadstical relations seem to be well documented, relatively little is
yet known about the processesresponsible for those relations. The principal goal of
the current research\\'as rherefore to invesrigatethe mechanismsby which working
memory might mediate rhe age differencesin a specific cognitive task. Three tlpes
of analyses are reported. The 6rst focuses on item variation because items can
be assumed to vary in the demands placed on working memory, and hence age x
item interactions might be expected if high-demand items exceed the reduced
working memory capacitiesof older adults, but are still u'ithin the capabilitiesof
young adults. A secor.d cvpe of analysisis based on an examination of the alternadves
selected on incorrectly answered items. Just as items can be postulated to vary in
their working memory demands, so might the probability of selecting particular foils
or incorrect alternatives differ according to the working memory requirements
* Rcqucsts for rcprints.
1,72
Tinotlry A. Saltboase
imposed by each incorrect alternative and the working memory capabilities of the
individual. Finally, because working memory is usually defined in terms of the
simultaneousstorageand processingof information, one should expect young adults,
who tend to have high levels of working memory, to be better able to preserve
previously presentedinformation than older adults, rvho are presumed to have lorver
Ievels of rvorking memory.
In addition to examining possible consequencesof different levels of s-orking
memory, the results of thesestudiescan also be used to investigateone possible cause
of age-relatedvariations in working memory. This is the idea that age differencesin
many cognitive tasks originate becauseo[ an age-relatedreduction in the speed oF
e x e c u t i n g r e l e v a n t c o E n i t i v e o p e r a t i o n s .S o t n e e v i d e n c ef o r t h i s i n t e r p r e t n t i o n r r ' l s
reported by Salthouse (1991a) and Salthouse & Babcock (1991) in u'hich age
differences in working memorv rvere substantially reduced b1' using staristical
procedures to equate people on a measure of perceptual comparison speed. The
contribution of perceptual speeclwas examinedin the current project bv conrrasting
the degree of attenuation of the age differencesin cognitive performance achieved by
statisticalcontrol of a working memorv measurewith that obtained with control of
a perceptual speed measure, and also by examining the additional attenuation
atttibutable to working memory after the variance associatedwith perceptual speed
had been removed.
Matrix reasoning tasks were selected as the criterion cognitive activity in this
proiect because:(a) matrix reasoning tests such as the Raven's ProgressiveNlatrices
are a common and highly g-loaded (e.g. Jensen,7982) measure of intelligence; (b)
substantialage-relateddifferencesin Raven's ProgressiveMatrices performance have
been reliably documented; (r) there are both theoretical and empirical reasons fbr
expecting working memory to be important in the solution of these kinds of
problems; (/) extensive development o[the Raven's Progressive N{atricesTest has
resulted in a systematicprogression of item difficulty from the early to the late items
in the test; and (a) many of the incorrect alternatives in the Raven's problems rvere
constructed to be informative about the causesof poor performance.
Research involving comparisons of adults of different ages on the Raven's
Progressive lVlatricesTest has recentl\-been reviewed by Salthouse (1992r). The
median correlation betu'een age and Rar.en's score across six studies involving
samples with a wide range of ages was -.61. Five studies wete located in which
groups of older adults, typically with a mean age of about 70 years,vrere contrasted
rvith groups of young adults, usuallr s'ith a mean algeof about 20 years. In each
study, the performance of the olcler adults could be expressed in units oi the
distribution of the performance of youne adults. The median across the five studies
was -2.84 standard deviation units. Both of theseestimatesof the magnitude of the
age differencesare among the largest reported for anv cognitive measure.
It has recently been reported thar performance on the Raven's Proqressive
IVlatricesTest has increasedover historical tirrre(Flynn, 1987; Raven & Court, 1989),
and some researchershave interpreted rhesepositive time-lag differencesas evidence
that age differences observed in cross-sectional comparisons are an artifact of
generational change. As discussedin Salthouse(199Lb),a discovery of generational
differencesin test performance does not by itself implv that maturational factors do
lYorking memzrJ, age and matrix reasoning
r73
not contribute to the observed age-related differences because such a conclusion
depends on several additional assumptionsthat are seldom tested. Regardlessof the
distal causeof performance differencesamong people of varying age, however, it is
important to identify the proximal processingcharacteristicsassociatedwith different
levels of performance. In other words, even if the age-related differencesare an
artifact of progressivelv higher test performance acrosssuccessivegenerations,it still
remains to be determined how individuals from earlier generations perform
differently from individuals from later generations. From the current perspective,
therefore, the goal is to specify the factors associatedwith differencesin the observed
level of functiooing, and not to determine the ultimate source or cause oF those
differences.
The potential importance of working memory in successfulperformance of matrix
r e a s o n i n gp r o b l e m s c a n b e i l l u s t r a t e db y c o n s i d e r i n gt h e s a m p l ep r o b l e m i n F i g . 1 .
Notice that all but one of the cells in the matrix of three rows and three columns is
6 l l e d r v i t h g e o m c t r i c f b r m s . T h c t a s k f o r t h e e x a m i n e ei s t o s e l e c tr v h i c h o i t h e e i g h t
answer alternatives presentedbelow the matrix provides the best completion of rhe
missing cell of the matrix. One way to conceptualize the processing required in
matrix reasoning problems such as this is in terms of the three components discussed
by Jacobs & Vandeventer (7972): discrimination among elements,identification of
relations and combination of relations. Working memory could be involved in each
of these components because cell attributes have to be preserved in order to
determine similarities and differences across cells, similarities and differences have to
be preserved in order to determine the relations among cells in a given row or
column, and relations have to be preserved in order to coordinate row and column
relations to predict the pattern of the missine cell. Another theoretical analvsis in
which an aspect of rvorking memory concerned with the management of subgoals
rvas postulated t() be critical for the solution of difficult matrix problems r.','as
also
recentlv published bv Carpenter, Just & Shell (1990). Finally, empirical support for
the hypothesized relation between working memory and matrix reasoning
performance is availablein the moderate (.30 to .59) correlations reponed bv Larson
a n d c o l l e a g u e s( e . g . L a r s o n , N l e r r i t t & W i l l i a m s , 1 9 8 8 ; L a r s o n & S a c c u z z o ,1 . 9 8 9 )
between Raven's perfbrmance and several measurespostulated to reflect rvorking
memorv abilities.
Evidence that items in the Raven's Test vary in item difficulty is available from
Raven, Court & Raven (1985). These investigators reported that the average
accuracvin the .\clvrrncedSet II version of the test rvas98 per cent for item 1, BB per
c e n t f l o r i t c m 1 0 , 5 9 p e r c e n r f l o r i t e m 2 0 , r n c l o n l y 2 6 p e r c e n t F ( ) ri t e m 3 0 . T h i s
substantialvariation in item difficulty meansthat comparisonscan be made at several
points alons the difficulty continuum. Moreover, to the extent that the item variation
is at least partiallv attributable to differential demands on working memorv, one
might expect the efibctsassociatedwith age to be greateston the most difllcult items.
In other rvords, if one o[ the reasonsfor the low accuracy.of difficult items is that
those items place greater demands on working memorv than lessdifficult items, then
accuracy on those items should provide the greatest discrimination across people of
different ages who are assumed to vary in their working memory abilities.
The sample problem in Fig. 1 can be used to illustrate horv the particular incorrect
174
Tinotlt1 A. Salthoase
lil 4
2
Ii
ill
2
lt + ftt i
8
o
t-_t
t
t
-
l
I
l
tt;t
I
II:TFI
Figure 1. Examplesof the type of problem in the Raven's Progressive Ivlatrices Test.
choicesselectedmight be informative about the causesfor poor performance. Notice
that rhe correct answer is alternative 4 because that pattern satis{ies the critical
prirrciple of one o[ each type of line thickness and line orientation in each row and
column. Alternative 6 is merely a repetition of a pattern from the matrix, and its
selection may reflect a response based on the property of familiarity rather than a
relevant principle. Alternatives t and 3 are also repetitions, but in addition can be
considered partial solutions becausethev would have been correct if one dimension
had not been neglected (i.e. line thickness in alternative 1, and line orientation in
alternative 3). Alternative 5 is another example of a partiallv complete solution, in
this case because the pattern does not incorporate the correct value for the relevant
dimension of line orientation. Finallv, alternatives 2, 7 and 8 are combinations
createdby applf ing an incorrect principle of addition. Some o[these error t],pesseem
m o r e l i k e l v t o b e a c o n s e q u e n co
e f r v o r k i n g m e m o r ) ' l i m i t a t i o n st h a n o t h e r s ,a n d t h u s
examination of the pattern of incorrect choices may prove informative about the
influence of working memory on matrix reasoning performance. For example, a
failure to notice a relevant attribute might occur equally' often for people with
effective and ineffective working memorv systems,but people rvith more limited
working rriemory systems might be expected to have a greater number of errors
associatedwith a failure to coordinate the simultaneousapplication of multiple rules.
Results from four studies are reported in this article. Study 1 is a more detailed
report of Study 1 from Salthouse (799La), and focuses on the influence of working
memory and age at the level of individual irems in the Raven's ProgressiveNlatrices
ll/orking memlry, age and matrix reasoning
175
Test. The matrix reasoning task was implemented on a computer in Studies 2
through 4 in order to obtain separatemeasuresof time and accuracy,and to allow
for the Presentation of probes of previously displayed information. Because
recognition probes could be presented with either simultaneous or sequential
displays of the st-imulusmatrix, and becauseboth methods differ substantiallyfrom
the more traditional paper-and-pencil format for presenting matrix reasoning
problems, a primarv Purpose of Studv 2 vras to explore interrelations among
measuresof pertbrmance in the difrerent presentationmodes. Study 3 then examined
accuracy of probe decisions after simultaneousdisplays of the marrix, and Study 4
examined probe decisions after sequentialdisplays of the matrix. Participants in all
studies also performed two perceptual speed tasks to allow comparisons of the
influence of perceptual speed and rvorkins memory as possible mediators of age
d i f f e r e n c e si n n i l t r i x r e a s o n i n g .
STUDY 1
T h e p u r p o s e t > [ t h i s i n i t i l l s t u c l r \ \ ' r l sr o e r r r l n i n et h e i n f l u e n c e so f a g e a n c l w o r k i n g
memory on perfttrmance of th.e Raven's Progressive Nlatrices Test at the level of
individual items. If the solution of certain items, or the selection of particular
incorrect alternatives,dependson the individual's working memory ability, then the
accuracy and error Patterns should vary as a function of age and level of working
memory.
Method
Sabjectt
Nervspaper advertisements rvere used to recruit adults interested in participating in a research project
concerned rvith relationsamong ageing, memory and cognition. Complete data were obtained from221
adults (61 per cent rr'omen) ranging from 20 to 80 r'ears ofage. F,ach decade rvas represented by betrveen
3 4 a n c l 3 9 i n d i v i c l u r r l s .A l l p a r t i c i p a n t s r e p o r t e d t h e n u m b e r o f y e a r so f e d u c a t i o n t h e y h a d r e c e i v e d ,a n d
rrted thcir hcalth on a fise-point scalc (ranging from 1 for cxcellent to 5 for poor). Nleans of these
v a r i a b l e s a n c l t h e i r c o r r e l a t i o n s r v i t h a g e s ' e r c 1 5 . 6 1 ' e a r sa n d r : - . 0 4
for education, and 2.04 and
r:
.20 (p < .01) for seli--rated health. Analyses revealed that the patterns among the variables of
primary interest \r'ere not signihcantly altered after adiusting for amount of education or rating of selfr e p o r t e d h e a l t h , : r n d c o n s e q u e n t l i ' t h e s e m e a s u r e sa r e r e p o r t e d p r i m a r i l y t o a s s i s ti n d e s c r i p t i o n o f t h e
rcsearch samplc.
P rr.tcedure
Research
participants
rveretestedin groupsofaboutfour to 30,andall performed
thetasksin thesame
s e q u e n c c .T h e t a s k s , i n t h c o r c l c r i n r r ' h i c h r h c t , r v e r e p r c s e n r e d ,w e r e : D i g i t S v m b o l S u b s t i t u t i o n T e s t
( \ l e c h s l er , 1 9 81 1 , L c t t e r C r r r n p i r r i s o n , P a t t e r n C o n r p r r r i s o n , C o m p u t a t i o n S p a n , L i s t e n i n g S p a n
-Iesr
,\bstrrction
( S h i p l c r ' , 1 9 8 6 ) r n d R a v e n ' s r \ d v a n c e c l P r o g r e s s i r . eN l a t r i c e s , S e t I l ( R a v e n , 1 9 6 2 ) .
The Digit Symbol and Shiplev Abstraction Tests rvere included for purposes unrelated to the current
p r o i e c t a n d r v i l l n o t b e d i s c u s s e df u r t h c r i n t h i s r e p o r t .
The Letter (}rmpartson, Pattern Comparison, Computation Span and Listening Span tasks were
irlcnticll t() th()se rlcscribcrl in Sirlthousc .\ Bebcock (1991). Thc I-ettcr Comparison and Pattcrn
( - o r r p a r i s o n t a s k s c o n s i s t c r l o f p a g c s c ( ) n t r i n i n g p a i r s o f t h r c c , s i x , o r n i n e l c r t e r s ,o r p a i r s o f p a r t c r n s
composcd of three, six or nine line segments.One-half of the pairs were identical, and one-half were
d i f f c r e n t b c c a u s c o i e c h a n q e i n o n e o f t h e l e t t e r s o r l i n e s e g m e n t s .T h e t a s k f o r t h e p a r t i c i p a n t w a s t o
classiiy each pair as SANIF, or DIFFERF,NT by writing an S or a D on a line between the two members
o F t h c p a i r a s r a p i c l l v a s p o s s i b l c . T r i a l s r , r ' i t ht h r e e , s i x o r n i n e e l e m e n t s w e r e s e p a r a t e l yt i m e d ( 3 0 s f o r
1,76
Tinothl ^1. Saltbouse
32 pairs), and the scores were averaged to provide a single measure for each tvpe of comparison (letter
or pattern).
The Computation Span and Listening Span tasks were designed to assess working memory by
r e q u i r i n g p a r t i c i p a n t s r o r e m e m b e r i n f o r m a t i o n s ' h i l e a l s o c a r r y i n g o u t s p e c i E e dp r o c e s s i n g . I n t h e
Computation Span task arithmetic problems s,ere presented auditorilv, and the task was to select the
answer to the arithmetic problem from three alternatives on the response form while also remembering
the last digit in each problem. Short sentenceswere auditorily presented in the Listening Span task, with
participants instructed to answer a question about rhe sentence, printed on the resPonseform along with
t h r e c a n s w c r a l t c r n a t i v c s , w h i l c a l s o r e m c m b c r i n q t h c l e s t r v o r d i n c x c h s e n t e n c e .T a r g e t i t c m s r v e r e
recalled by writing them, in the order in ',vhich tlrev were presented. on designatedlines on thc back
of the response form. The number of arithmetic problems or sentences increased from one to seven,
rvith three trials at each sequence length. An indiridual's span rvas determined bv the greatest number
o f d i g i t s o r r v o r d s t h a t c o u l d b e r e m e m b e r e d o n r t - o o f t h e t h r e e t r i a l s t o r a p e r t i c u l a r s e c l u e n c el e n g t h ,
given that he or she was also corrcct in the ansrvers to the relevxnt arithmetic and scntencc
c o m p r c h e n s i r ; n c l u c s t i o n s .T h i s l r r t t e r r e c l u i r e m e n re n s u r e c lt h : i t t h e s c o r e s r e P r c s e n t e cbl r > t h s t o r a g c a n c l
processing.
As noted above, thc Raven's Advanced Proqressive Nlatrices Test consists of displavs of 3 x 3
matrices of geometric forms rvith the bottom righr cell missing. The task for the examinee is to select
r h e c o r r e c r p a r r e r n r o c o m p l e t e t h c m i s s i n g c c l l r r o m a s e t o f e i g h t a l t e r n a t i v e sd i s p l a v e d b e l o r v t h c
m a t r i x . T h r e e s a m p l e p r r > b l e m s( l t e m s 6 , 8 a n c l l l f r c , m t h e R : r v e n ' s A d r a n c e d P r o g r e s s i v cN l a t r i c c s S c t
I) were provicled, tbllowed bv the 36 problcms oi Set lI. Twentv minutes rvere allowed to work the
problems in Set ll. Although a time limit of 40 min is usually recommended, the steep difficulty gradient
across successive items suggests that few responses rvere likely to have been correct on later items had
they been attemptcd. Furthermore, comparisons of the average number of items answered correctly in
college student samples with 20 min (a pilot studr, and Studies 2 and 4 of the present report), 40 min
(Larson & Saccuzzo, 1989; Palmer, Macleod, Hunt & Davidson, 1985) and no time-limit (Jensen,
1983, 1987; Paul, 1985) administrations revealed relatively small differences related to the time allowed
for completion of the items. Finally, similar age trends were reported by Heron & Chown (1967) with
20 min and 40 min administrations of the standard Raven's Progressive Matrices Test.
Results and discussion
Distributions of the frequency of number-correct scoreson the Raven's Progressive
7 3 a n d 7 1 , r e s p e c t i v e l y )a r e
Matrices Test for each of three age groups (N:77,
displayed in Fig. 2. Also portrayed in Fig. 2 for purposes of comParison is the
distribution of scores obtained in a pilot samPle of 83 college students (mean
age:19.9 years, mean of 1.3.7yearsof education). It is aPParentin this 6gure thnt
college studenrs have the highest scores.and that increasedage is ^ssociatedwith a
s - v s t e m a t idco r v n r v a r ds h i f t o f t h e e n t i r e d i s t r i b u t i o n . r
The initial srep in the analysesof rhc deta in'u'oh'edcreating comP()sitemc.lsures
of the v/orking memory and perceptualspeedconstructs.This was accomplishedby
averaging the individual's 1 scoresfrom the Listenin.qSpan and Computation Span
t a s k s t o p r o d u c e a w o r k i n g m e m o r v c o m p o s i t e ,a n d a v e r a g i n eh i s o r h e r l s c c l r e s
from the Lerter Comparison and Partern Comparison tasks to Proclucea PercePtual
speed comPosite.
Tabie 1 conrains the correlation marrix summarizing the relations among the
variablesof sublect age, rhe rvo composirevrriables, and both the number of corrcct
l Thc highcr scorcs frrr thc samplc r>i studcnrs rclativc :,, lhc samplc r>i rdulrs bctrvccn 20 rntl 39 lcers oi lqc rttar
be a conieguencc oftheir vounger age (i.e. mean of 19.9 rears vcrsus 29.1 vears), or ofthc fact that tlrcv had becn
s c l e c t c c ip a i t i a l h . r > n t h c b a s i s o t t i n t c l l c c t u a l a b i l i n ' f o r : d m i s s i o n t o a r c l a t i l c l t c o m p c t i t i v c u n i v c r s i t v . I f t h c l a t t c r
is the caie then comparisons between students and older adults recruited according to the procedures in this studv
may overestimate the absolute magnitude of age-relatcd differences.
a,a
',.:!
:,i:,tiiiiii
lVorking memzrJ, age and rtatrix
I
I
T
t2
I
I
I
I
I
30 I
j"
a
I
l8
)l
l0
l0
l0
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
E -l -s
o
Age 60-79
Age 40-59
Age 20-39
Students
20 l0
l0
L77
reasoning
l0
20
.10
l0
l0
Frequency( percentage)
F i g u r e 2 . D i s t r i b u t i o n o f s c o r c s o n t h e R a v e n ' s P r o . q r e s s i v eM a t r i c e s T e s t a s a f u n c t i o n o f a g e ,
Study 1.
responsesand the percentageof attempted items answered correctly in the Raven's
ProgressiveMatrices Test. It should be noted that eachmeasurehad at least moderate
reliability, and that all correlations were in the medium to large range. Moreover, the
signiFcant negative correlation between age and percentage oF items answered
correctlv indicates that nc>tall the age variation in Raven's performance is due to
differencesin the nurnber oi items attemDted.
Table 1. Correlation matrix for variables in Studv 1 (N : 221)
Variable
I
2
3
4
5
- .57*
(.el)
r\.qe
[{ [),\l no.(
RPM%C
WNIem
Spcctl
,\lc,Irl
SD
-.36-
.u+'
(.86)
+8.5
17.4
)
I .1.(
o.L
(;1.3
23.-
- .54*
.694
.60*
(.71)
- .61*
.62*
.45*
.s9*
( . 85 )
0.00
0.88
0.00
0.93
+ p <.01.
\ r l r . R c l i l b i l r r i cisn r h c . l i , t q , t r r l lusc r c c s t i m a t c bt lr u s i n gr h c S p c a r m a n ' B r o r rf'rnr r m u l lt r . rb o o s rt l r e
c ( ) r r c l r l r i o n l r c r r v c c n t h c r r r , , c ( ) n r P ( ) r r c n tn l c : l s r r r c s{ t i ) r l ) c r c c p t u r l S p c c d a n t l \ \ ' o r k i n g \ l c m o r r ' ) ( ) r
b c t \ \ ' e c n t h c s c o r c s t i r r o t l c l : r n c lc v c n i t e m s ( t o r t h e n u m b c r - c o r r c c t a n d p c r c e n t a g e - c o r r e c tv a r i a b l e s ) .
K e r , .S p e e d : r \ v e m g c ( ) i \ - s c ( ) r c sf i r r L e t t e r ( J o m p a r i s o na n c l P a t t c r n C o m p a r i s o n ; V N { e m : A v e r a g e
o f 1 s c o r e s t b r C o m p u t a t i o n S p ' a na n c l L i s t c n i n g S p a n ; R a v n o . C : N u m b e r o [ i t e m s c o r r e c t i n R a v c n ' s
T e s r ; R a v T n C : P e r c c n t a $ { co f a t t e m p t e c l i t e m s c o r r e c t i n R a v c n ' s T c s t .
PS \
8J
1.78
Tinotbl A. Salthoase
A seriesof hierarchical multiple regressionanalyseswas conducted to determine
the amount of variancein measuresof Raven's performance associatedrvith age when
considered alone, and after controlling the variance associatedwith the composite
measureof working memory andf or the composite measureof perceptual speed.The
R2 values in these analysesare summarized in the top row of Table 2, u'here it can
be seen that partialling the variance associatedwith working memory reduced the R2
for age from .322 to .053. This degree of attenuation of the age effects is clearlv
consistent with a mediational influence of working memory on the age dii{erencesin
matrix reasoning. It is also apparent in Table 2 that the attenuation oi the age
differenceswas nearly as large after statisticalcontrol of the perceptualspeedvariable.
Implications oi this finding rvill be considered in the General Discussion.
T a b l e 2 , R ' r e s t i m a t e sa s s o c i a t e c,l , r ' i t h a g e i n p r e d i c t i o n o f m l t r i x
oerformance
Studv
Variable
A l l subjects
Raven's Num. Correct
1
Alone
.322*
.678*
.347*
.229*
.375*
Onlv subjects satisfying accuracy criterion
Raven's Num. Correct
.303*
1
.701*
2
Raven's Num. Correct
.258*
Simult. Nlatrix Acc.
.li8
Se<1ucnt.N{atrix Acc.
.273Simult. Nlatrix Acc.
a
Raven's Num. Correcr
Simuk. Nlatrix Acc.
Sequent. Matrix Acc.
Simult. Nlatrix Acc.
.\ fter
\\'Mem
r\tier
PSpeed
reltsoninu
After
\\ IIem &
PSpeed
.053*
.389*
. 10 8 *
.066
.086*
.056*
.201,*
.062
.021
.111*
.017*
.762*
.031
.007
.021
. 10 9 *
.482*
.1,57+
.049
.083*
. 13 4 *
.111
.005
.058
.048*
.117*
.107
.002
.039
.t) I
*p<.01.
In an attempt to minimize the possibilit,vthat the reiations between rvorking
m e m o r \ ra n d R i l v e n ' sp e r f o r m a n c em i q h t h a v e b e e na c o n s e ( l l r e n coef a f e i l u r e o n t h e
p a r t o [ s o m e s u b j e c t st o u n d e t s t a n dt u l l v t h e t a s k r e q u i r e m e n t s ,t h e a n a l v s e sw e r e
repeatedafter eliminating subjects with errors on either of the 6rst two items in the
Raven's Set II problems. Results from chis restricted sample of 766 sr-rbjectsare
s u m m a r i z e di n t h e b o t t o m p o r t i o n o i T a b l e 2 . N o t i c e t h a t t h e p a t t e r n i s q u a l i t a t i v e l v
verl' similar to that evident in the complete sample.
Additional analyseswere conducted ro examine performance on the Raven's Test
at the level of individual items. These analyseswere limited to items 1 through 22
becauseferver than 50 per cent of the researchparticipants responcledtci later items,
and thc rangc o[ agcs tirr thosc whr> cliclresponclwxs f]reatly restricteclbec:rusefew
o l d e r i n d i v i d u a l s a t t e m p t e dm a n y o f t h e l a t e r i t e m s .
The percentageso[ correct responsesas a function t-rfitem across the three age
groups are displayedin Fig. 3. The most striking featureof thesedata is that although
W
1,79
IVorking memzrJ, ageand ntatrix reasoning
100
Aee 20-39
90
40-59
Aee
----*---
*
Aee60+
80
i
8 o o
e
c
o{J
5
L 4 0
30
l0
l0
0
2 3 4
|
5 6
7
8 9 l 0 l l 1 2 l 3 l + 1 51 61 7 t 8 1 92 0 2 t 2 2
Item number
F i g u r e 3 . M e a n a c c u r a c y f o r i n d i v i d u a l i t e m s i n t h e R a s e n ' s ProgressiveNlatricesTest as a function
ofage, Study 1.
Working memory
0.5
____o-
W o r k i n g m e m o r y .A g c
0.5
-----o--.Age
--f-
0.3
A g e .W o r k i n g m e m o r y
-----E----
0.2
0.1
o
0
o
U
-0.1
- 0.2
- 0.3
-0-.1
- 0.5
|
2
f
4
5 6
7 8 9 10il121314151617l819202t22
Item number
F i g u r e 4 . C o r r e l a t i o n s o f a g e a n d w o r k i n e m e m ( ) r r s ' i r h : r c c u r a c vo f i n d i v i d u a l i t e m s o n t h e R a v e n ' s
P r o . g r c s s i v cN l l r r i c c s T c s t , S t u c h ' L
1
I
i
.t
; . : :\ '
.:
180
Tinothl A. Salthorce
Table 3. First and secondmost freouentlv chosen incorrect alternativesfor each item
by age group
Number
oI errors
Item nt,. \-
1
3
o
I )
t:)
1
1.7
1
I
-
15
25
26
24
19
21
32
23
39
21
21
a . l
7 J 6
8
8
1
i
2
2
I
8
7
8
8
1,7
7
2
2
i
8
7
5
5
4
8
5
)
B
5
7
7
2
3
),t
4
7
2
2
5
8
1
t
1
l
8
7
2
4
lvI
8
9
10
11
12
21
15
18
13
13
lJ
)!
)t
+J
5
14
16
19
18
29
27
20
25
25
19
27
29
27
19
A
aa
aA
30
24
29
27
l
3
4
9
i;
-)
lJ
6
11
1
1
l
15
zI
16
17
18
19
20
11
17
2)
23
30
zl
Jl
22
37
o
NI
9
14
20
23
l0
14
19
20
30
14
21
1
2nd frequent
1st frequent
8
5
3
1
5
2
I
8
I
1,7
2,4,6
1,5,6
2
1,7
6,8
5
6 , 7, 8
6
3
8
1
2
4
3 r
i
7
7
1,3,4
8
6
4,7
4,7
6
4
5
1,6,7,8
4
4
l
1
5
3
1
5
L
)
4
l
4
3
2
4,6
3,8
6,7
7
7,4
1
4
5
6
4
4
R
? i
4
J
1
8
)
5
41
6
6
'7
6
6
\
a1 /
4
3
8
o
NI
t h e r e i s s u b s r a n r i avl a r i a t i o n i n a v e r a s el e v e l o f a c c u r a c y ,r a n g i n g f r o m a b o u t 8 5 p e r
cenr ()n item 1 to approsimatelv 35 per cent on item 22, rhe functions for the three
g r ' ( ) u p sa p p c x r r e n r r r r k a b l vp a r a l l e l .T h i s i n r p r e s s i o nr v a sr e i n f o r c e dr v i t h t h e r e s u l t s
of a group (young, middle, old) x item (items 1. to 22) analysis of variance. Both
main effccts oi age group f Q,218) : 30.94, N{SE : 1.07, and item,
: ) - l - . 6 9 , \ l S l : : ( ) . 1 - - rs)' e r c s i g n i f i c a n t( , , < . 0 1 ) i n t h i s a n a l v s i s ,b u t
l-(21,-+578
t h c i r i n t c r a c t i o r ru ' ' . r sn t > t ( F ( 4 2 , . 1 5 7 8: ) 1 . 4 1 ; .
A second analvsis consisted of determining the simple and partial correlations
between accuracv tbr each item and the age and rvorking memory variables.These
correlations, displaved in Fig. 4, sen'e to conErm the inferencefrom Fig. 3 of nearlv
consr..rntage etfecrs rcr()ss irems. It is also interesting that partialling u'orking
menrory trom the age correlations reduced most of them to De r zero, but that the
reduction in s'orkinq memorv correlations after partialling age q'as much smaller.
Medians of the 22 correlations were - .22 for age alone, - .04 for zge after partialling
working memor\-, .35 for working memorv alone, and .26 for working memorv after
partialling rgc.
l{/orking merlzt), age and matrix reasoning
181
Patterns of errors on items with orert responses(i.e. excluding errors of omission)
were also examined. Analyses were conducted to determine whether subjects of
varying agesdiffered in the particular incorrect alternativesselectedwith the greatest
frequencv. Table 3 contains the identities of the alternatives for each item with the
highest, and second highest, frequency of occurrence in each age group. It is
apparent that there \\'as a great deal of consistency in the particular incorrect
alternatives chosen bv adults of different ages. The young and middle-aged groups
selectedthe same incorrect alternatir-emost frequentiy on ali 22 items, and there was
agreement between rhe younu and old groups, and between the middle-aged and old
g r o u p s , o n 1 9 o [ t h e 2 2 i t e m s . F u r t h e r m o r e ,t h e r e w a s a g r e e m e n ti n t h e a l t e r n a t i v e s
s e l e c t e dt ' i t h e i t h e r t h e h i g h e s to r t h e s e c o n chl i g h e s tf r e q u e n c vi n 2 1 o f t h e 2 2 i t e m s
both for middle-aged and old groups, and tbr young and old groups.
Discussion
The results sumrn:rrized in Tables 1 and 2 confirm previous results concerning
relations among age, working memory, and measures of cognitive performance.
Specifically, the finding that the influence of. age on cognitive performance was
markedly reduced after controlling the variance associated with a measure of
working memory suggeststhat working memory plays an important role in the age
difference in at least this cognitive rask.
Average solution accuracy varied considerably across the items examined, and it
seemsreasonableto hypothesize that at leastsome of the item variation might have been
due to increased rvorking memory demands. If age differences are largely mediated
by reductions in u'orking memon', then it might have been expected that the
differences would be greater for the most difficult items that place the largest
demands on workinq memorv. Contrarv to this prediction, horvever, the analvses
revealed that the age relations were remarkably constant across the range of .items
examined. An apparent implication oithese findings is that the factors responsiblefor
the variation in item difficulty are independent of the factors responsible for the
effectsassociatedu-irh working memory and adult age. Of course, it is not knorvn
rvhether similar results rvould have been observed in samples with higher averalle
l e v e l s o f r e a s o n i n gp e r t i r r m : r n c eo, f r f i t h a d b e e n p < > s s i b lteo e x t e n d t h c a n a l v s c st c r
even more difficult items, but the parterns in Figs 2 and 3 suggest that the influences
of age and working memorv are relativelv constant in this set of data.
T h e a n a l v s e so i t h e e r r o r p a t t e r n sl l s o i a i l e c lt o p r o v i d e a n v e r - i d e n c eo f c l c f i c i t si n
p a r t i c u l a rk i n d s o I p r o c e s s i n g ,o r r e s t r i c t e dt o s p e c i f i cr e l a t i o n a p
l r i n c i p l e s .r \ l t h o u g h
some incorrect alternarives were consistently selectedmore often than others, the
same general patterns were evident acrossthe three age groups. It therefore appears
that the factors responsiblefor causingsome incorrect alternativesto be chosen more
i r e q u e n t l v t h a n o t h c r s w c r e ( ) p e r a t i n r i:n s i m i l a r w a y s r e g a r d l e s so f t h c i n c l i v i r l u r l ' s
^9"The configuration of results iust describedpresentsa challengefor interpretation.
On the one hand, there is evidence of moderate to large relations between the
measureso[ working memorv and matrix reasoning performance, but on the other
hand, the data indicate that these relationsare no greater for diftrcult (lorv accuracv)
182
Tinotlry A. Salthoase
problems than for easy (high accuracy) problems. At least three distinct explanations
could be proposed to account for these findings. First, it is possible that the lack of
a differential relation acrossitems of varving difficulty is a consequenceof some type
of methodological artifact. For example, the fact that the most difficult items
occurred later in the problem sequencemeans that ferver of them were probablv
attempted by the slower subfects,rvho may also have had less effective r.vorking
memorv svstems. An attempt lr'as made to minimize distortions of this kind bv
restricting the analysesto items attempted by the majority of the subjects,but it is
neverthelessstill possible that various kinds of measurementinsensitivitv may ha.,'e
conrributed to the lack of dill'erentialrelations o[ age and working memorv acr()ss
items.
A second potential explanation is that much of the variation in item dilficultv mav
be attributable to factors unrelated to working memor\'. That is, the rvorking
memorv influence might have been nearlv the same for all items, but item dilficultv
o f t h e a t r r i b u t e s ,F a n r i l i a r i t lo I
c o u l c l h a v e v z r r i e db e c a u s eo f t a c t o r ss u c h x s s a l i e r r c e
the relational rules, etc.
A third interpretation focuseson the meaning of the relation observed between
the working memory measuresand performanceon the matrix reasoning test. That is,
it could be speculatedthat this relation did not originate becauseof the involvement
of working memory in the reasoning test, but rather was a consequenceof a third
variable involved in both the working memory and reasoning tests. As an example,
instead of the relation occurring becauseof reliance on working memory in the
matrix task, it could have originated becauseof a temporal aspect in both the matrix
reasoning test and in the working memorli tests.Consistentwith this view is the fact
that the 20 min time limit for the Raven's Test was too short for most respondents
to attempt all items, and the group administration of the working memory tests
necessitatedthe imposition of limits on the rime between presentation of successive
stimuli and the time allowed for production of responses.It is therefore conceivable
that at least some of the relations observed in this study were a reflection o[ the
common requirements of having to work rapidly, and were not a direct consequence
of working mem()r\r involvement in the Raven's lVlatrix Test.
STUDY 2
The remaining studies in this proiect were designed in part to resolve some of the
i n r e r p r e t a t i o n r l; r m b i g u i t i e sa s s o c i a t e cwli t h t h e r e s u l t so f S t u d y 'l . F e a t u r e so I r l - r e s e
s t u d i e si n t e n d e d t o r r d d r e s st h e c o n c e r n sd i s c u s s e da b o v e r v e r e : ( a ) b < > t ht h e u ' o r k i n g
memory and matrix reasoning tests were administeredon a computer with subjects
allowed as much time as desiredto respond; aod (b) matrix problems createdto vary
svstematicallv according to the number of relations among matrix elements u'ere
p r e s e n t e ciin a r a n d o m l v a r r a n g e ds e c l u e n c e .
Examples of the problems used in Studies2 and 3 are illust'iatedin Fig. 5. Notice
that the problems ','arv with respectto the number of unique relations amons cell
attributes. That is, cells in the problem on the left vary only in the number of vertical
lines, cells in the middle problem vary in the number of 6lled squares and in the
n u m b e r o t s u r r o u n d i n g s q u a r e s ,a n d c e l l s i n t h e p r o b l e m o n t h e r i g h t v a r v i n t h e
l{/orking me/ltzrJ, ageand rnatrix reaszning
ooo
oo@
o o tr
I
r
I
t
t
F--l
t r l
II
ldJ
/'^\
["Tl i\/--\ott o\/ \qz
l-p-l
l\.,
(
)
I,'\
*
/q
qE/
&
Two rehti(rns
Threerclations
One relation
Figure 5. Sanrplc probiems u'ith onc, tw() anrl three relations.
distribution oi major shape (circle, squareand diamond), in the distribution of
i n n e r p a t t e r n s( f i l l e d a n c lo p e n c i r c l e s ) ,a n d i n t h e d i s t r i b u t i o n o f i n n e r l i n e s ( v e r t i c a l ,
horizontirl and diagonal).
I i t h e p r r > b l c n r sw i t h m o r e r e l a t i o n si m p o s eq r e a t e rd e m a n c l so n w o r k i n g m e m o r \ ,
rhan problenrs w'ith ferver relations, thcn one might expect progressively higher
correlations between working memory and decis.ionaccuracy as the number of
relations in the problem increased.Furthermore, if adult age differencesin matrix
reasoning are attributable to limitations of rvorking memory, then the magnitude of
the age differencesshould also increaseas a function of the number of relations in the
problem.
Another purpose of Studies 2,3 and 4 rvasto examine the implication that people
with higher scores on the working memorv measures should be more accurate at
recognizing previouslv presented information than people with lorver working
memorv scores. Although the information probe procedure is conceptuallv verv
simple, ir can become complicated in practice becauseof the difficult,vof specit-r'ing
the appropriate tvpe of previously processedinformation to be probed. For example,
the most relevant processingin marrix reasoningtasks may be intermediate bet*'een
the initial encoding of the cell attributes and determination of the pattern for the
missing cell. Unfortunatelv, probes concerning the status of information about
similaririesor differencesacr()sscells,row or column relations,etc., would be difficult
to interpret with<>urs()meassurancethat the probed information had, in tact, existed
i n m c n r o r y a t a n e a r l i e rt i m e . T h a t i s , b e c a u s es o m e s u b i e c t sm a v n o t g e n e r a t et h e s e
intermediate information states, and because people might vary in how the
intermediate information is represented memoriallv, there can be formidable
d i f l l c u l t i c s a s s o c i a t e d. , v i t h p r o b i n g t h e s r a r l r so F i n t o r m a t i o n a s s u m e dt o e x i s t i n
u'r>rkins memory at an e:rrliertime. The solucion t() this problem adopted in
the current studies invoh'ed administering probes about previouslv presented
infrrrmation-that is, probes of the patterns presentedin speciEccells of the matrix.
This approach to probing earlier information is not optimal becauseit is based on
the unvc'rifiedassumption that explicitlv presenteclintbrmation is retainedin w<>rking
memory in a relatively untransformed.stare.It may be equally plausible to suggest
that information in working memorv is alrvavstransformed in some fashion, and
does not merely duplicate the information available in the external stimulus.
Although these concerns are legitimate, certain assumptions are necessaryif the
W
Tinotlry A. Salthouse
184
Moreol':r'" the validity of the
status of previous information is to be probed'
in working
concerning the existence-of previously presented information
"rr"-p,iori
information
and
may depend"on how, and ..ri-,en,the stimulus displays
*.-o.y
in Fig. 6'
pi.r..r,ed. Consider the r.uo presentation methods illustrated
;;J.r'"..
Simultaneous
II ltl
/-a
J
i
Standard
I
ll
ll a
ll ,-nI
watrtr
t
)
3
4
5
Figure 6. Illustration oi
matrix reasoning task'
standard and recognition probe displays in the computer-administered
in the lett oi Fig' (r involvcs
The simultaneousversic)noi the matrix t^sk Portrayed
i n d i c a t e st h a t h e o r s h e i s
t h e p r e s e n t a t i o no [ t h e s t i m u l u s m a t r i x u n t i l t h e s u b i e c t
a recognition probe.for
,.^dy to view the answer alternatives,and then substituting
with this procedure
the ansrveralternativeson some of the trials. A potential problem
existed in rvorking
is that even if the unrransformed cell informati-onhad previously
the. subiect had completed
memor)', it mav have been cliscarded by the time
This probiem
the matrif and was readv to view the answer alternatives'
p.o..rri.rg
'-igt,
in the right of Fig' 6
be ivoidecl rvith the sequential-versionof the task portrayed
to,be interrupted
because this mode of pr.r.ni"tion allows the subiect's processing
the contents of
regarding
Information
cell.
viewed
bv a probe of " p..iiously
l.
t
lYorking memlrJ, age and matrix reasoning
185
previously vierved cells may be more likely to still reside in working memory if the
probe is presented while the subject remains engaged in processing the stimulus
matrix.
Before investigating possibleage-relateddifferencesin probe recognition accuracy
ir was tirst considered desirable to examine relations among performance in the
Raven's Progressive lVlatricesTest and the trr-o computer-administered matrix tasks
illustrared in Fig. 6 when they were presentedrvithout anv probe trials. Study 2 was
therefore conducted to examine the relations among the matrix reasoning measures
in the three presentation modes. The simultaneoustask was then administered with
recognition probes in Studr' 3, and the sequentialtask rvith recognition probes was
a d m i n i s r e r e di n S t u c h '4 .
Method
Srblecti
D e s c r i p t i r - e c h a r a c t c r i s t i c so f t h c 3 0 r ' o u n g a d u l t s a n d 3 t l o l d e r a d u l t s r v h o p a r t i c i p a t e d i n t h i s s t u d y a r e
s u m m l n z ; , 1 i n ' f r r b l c . l . ' f h c r o u r r g r d u l r s r v c r c c o l i c q c s t u d e n t s ,a n d t h e o l d e r a d u l t s r v e r c v o l u n t e c r s
r c c r u i t c d i r o m n c s s p a p c r i r d v e r t i s c n r c n t sa n d r c f c r r : r l s t i o m o t h e r p a r t i c i p a n t s . Y e a r s o i c d u c a t i o r r
rcters to the number of years of formal education the participants reported having completed. Self-rated
health is a subjective evaluation of one's health on a Ere-point scale ranging from 1 for excellent to 5
ior poor. Digit-s,vmbol time is the median time in s per digit-symbol pair, and digit-digit time is the
median time in s per digit-digit pair.
Procedur,
thetasksin thesame6xedorder:Raven's
All subiecrs
performed
Advanced
Progressive
Nfatrices
; Digit
S r m b o l ; D i g i t D i g i t ; R e a d i n g S p a n ; C o m p u t a t i o n S p a n ; S i m u l t a n e o u s M a t r i x ; a n d S e q u e n t i a lN f a t r i x .
Each task s'as precedcd bv instructions and several practice trials to attempt to ensure that the subjects
c l e a r h ' u r r . l e r s t o o d r v l r a r t h e v r v e r c s u p p o s e c lt o b e d o i n g .
T h e R . r r e n ' s A d v a n c c c l P r o g r e s s i v eM a t r i c e s T e s t r r a s a d m i n i s t e r e d i n t h e s a m e m a n n e r ( i . e . s ' i t h t h e
s i l m c t i n l c l i m i t s ' a n dt h e s a m c p r a c t i c e p r o b l e m s ) a s r n S r u d r 1 . T h e D i g i t - S y m b o l T e s t w a s x c o m p u t e r administered version of the Digit-Symbol Substitution Test (Wechsler, 1981).The code rable with the
nine digit-svmbol pairs was presented on the top of the computer screen, and a single digit-symbol pair
s'as presented in the middle of the screen. On half of the trials the digit-symbol pair was correct, in
t h e t t h e p . r r r m a t c h e c lt h a t p r c s e n t e d i n t h e c o d e t a b l e , a n d o n h a l f o f t h e t r i a l s t h e d i g i t - s v m b o l p a i r
s ' a s i n c o r r e c t . F i r - c t r i a l s < > F c a c thv p e w e r e p r e s e n t e dr v i t h e a c h o f t h e n i n e d i g i t s ( 1 t h r o u g h 9 ) . S u b i e c t s
s'ere instructed to classifvthc pair as C()RRI1CT or I\CORRE,CT as rapidlv as possible bv pressing
-/'ker
tirr correct antl thc'Z'key for incorrect.
tlre
The Di-eit-Digit Test was similar to the Digit-Symbol Test except that the code table consisted of
paiirs of ide ntical digits, and the test stimulus consistcd of a pair of digits. On half of the trials the two
r l i , l i t s i n r i : c p a i r s e r c i t l c n t i c a l ,a n t l o n h a l f o f t h c t r i l l s t h e d i g i t s w e r c d i f f c r e n t . F i v e t r i a l s o f e a c h t v p c
rvere prescntcd u'ith cach of thc nine cligitsas the top member of the pair. Subjectswere instructed to
c i . . r s s i r yt ['r c p a i r a s C ( ) R R l i ( ] ' I o r I N C ( ) R R l l C ' I ' a s r a p i d i l a s p < . r s s i b lbey p r e s s i n g t h e ' / ' k e y
tbr same
()r c()rrecr. and thc 'Z' key for diFerent or incorrcct.
The Re.rding Span and Computrtion Span tasks were adaptations, with the same stimulus materials,
oi the tto rvotking mcmor) tasks used in Studv 1. Each required the research participant to
clcntonstr.t:t succcssiul proccssirrg whilc also remenrbering information. The Reading Span task
c t > n s i s t e rtl , i d i s p l a l s ( ) f s c n t c n c c s ,e a c h a c c o m p a n i e db r a s h o r t q u e s t i o n a n d t h r e e a . l t e r n a r i v ea n s w ' e r s .
Subjects s'ere instructed to read the sentence, type in the number designating the corrett answer ro the
c l u e s t i o n . . r n d r e m e m b c r t h c l a s t r v o r d o f t h c s c n t c n c e .T h e C o m p u t a t i o n S p a n t a s k c o n s i s t e do f d i s p l a y s
of arithmetic problems with three alternative answers. Subiects 'ilere instructed to solve the arithmetic
problcm, tlpc in thc numbcr dcsignating the correct ansver to the question, and remember the last
d i - q i t i n t h c p r o b l c m . N o l i n r i t r v a s i m p o s e c lo n t h e d u r a r i o n c a c h s e n t e n c eo r a r i t h m e t i c p r o b l e m c o u l d
'5
Tinothl A. Salthoase
186
Table 4. Characteristicsof the samplesin Studies2 through 4
Studv3
Studr 2
Samplesize
Young
old
7o Female
Young
old
Ag.
Young
old
Yrlrs oi education
Young
old
S c l f - r a t e dh c a l t h
Young
OId
D i g i t - S 1 ' m b o l ' f i m e( s )
Young
old
Digit-Digit Time (s)
Young
old
Computation Span
Young
old
Reading Span
Young
old
30
30
30
30
30
30
5U
53
50
50
50
57
2 0 . 3( 1 5 )
6 r . 5( r . 9 )
1 9 . 8( l . l )
6 0 . 8( s . 3 )
1e.7( l .-)
63.4(1.6)
i4.l (l.i)
1 5 . 1( 2 . i )
li.e (1.0)
1 s . 4( 2 . 3 )
l ] . 5( r . + )
1 s . o( 2 . 2 )
1 . 6( 0 . 7 )
l.? (ti.9)
1 . 4( 0 . 6 )
L'J(0.7)
l.s (0.6)
1.9( L{n)\
1 . 2 0( 0 . 1 7 )
l.el (0.4i)
1 . 1 70 . l e )
l.97 (0.36)
l.l3 (0.22)
1.63(0.28)
0.54 (0.06)
0.78 (0.26)
0 . 5 5( 0 . 0 7 )
0 . 7 9( 0 . 1 9 )
4.e(1.e)
3.1(2.4)
4.7 (2.0)
2.1 (2.0)
3.2(1.6)
2.2(1.6)
3.4(1.6)
1 . 8( 1 . 3 )
Raren Progrcssive llatrices Numbcr Corrcct
23.1(2.9)
Young
old
Studv 4
1 3 . 1( 5 . 1 )
2 0 . 5( 3 . 3 )
l 1 . e( 5 . e )
Na/a. Valucs in prrenthcscsare standarddcviations.
be viewed, but subiects were encouraged not to sPend too much time on any given display. Pressing the
IINTF.R ker- atier viewing the sente-nceor arirhmetic displav resulted in the Presentation of the next
itcm.
i t e m i n t h e . . q u . n . " , o r t i c w o r d R I I C i \ L L a c c ( ) n r p r n i e db v a b l a n k l i n e . f o r e a c h t o - b e - r e c a l l e d
bcirrrc
S p a n s r v e r c c l e i e r m i n c c lb y i n c r e a s i n gt h c n u m b e r o f s e n t e n c c so r a r i t h m c t i c p r o b l e m s p r c s e n t e d
'fhree
t r i a l s \ \ ' e r ep r e s e n t e dr v i t h e a c h s e q u e n c cl e n g t h , i n : r n r t s c e n t l i n go r c l c r , t r n t i l
thc recall instrucrion.
trials tbr a givcn
the subiect was incorrect on either the processing or the recall on two oi the three
that could be
or
digits
words
of
number
largest
the
wa;therefore
span
sequen;e length. The subiect's
r e c l u i r e t lp r o c c s s i n Q '
a c c u r a r e l v r c i e l l e d ( ) n 1 r l e x s tt . " o o f t h r c e t r i a l s r r h i l e a l s o c o r r e c t l v p e r f r r r m i n t t h c
In:rtrix tesks.\\'irhin
T r u , , s c t s o i 3 0 p r o b l e m s c x c h \ \ ' e r ec o n s t r u c r e d t b r t h c c o m p u t c r - a c l r t i n i s t c r e t l
anclsix hrrtl thrcc
e a c h s c t , l 2 o f t l r e p r o b l e m s h a d o n e r e l e v a n t r e i x t i ( ) n , i 2 h i r c lt r v o r e l c v r n t r c l a t i o r r s ,
sequential) was
or
(simultaneous
version
task
to
set
problem
of
relevant relations. The assignment
effccts or interactions
balanced across subiects in el'ch age group. (Preliminary analvses revealed no main
sevcn incorrect answcr
o f s t i m u l u s s e r a n d h e n c e t h i s v a r i a b l e i s i g n o r e d i n s u b s e q u e n ta n a l v s e s . )T h e
such es tiilurc to
a l t e r n a t i v e s t b r e a c h p r < t b l e m. u . . " a o n r t r r . , e d t r , r c p r c s c n t a r l t n g c o f l i k c l v e r r r r r s .
c
t
c
'
r
c
l
l
t
i
o
n
,
i
n
c
o
r
r
c
c
t
o
f
a
n
a
p
p
l
i
c
c
t
i
o
n
noticc a relevanr attributc,
that the tasks
Instructions in both ,r.rrions of the computer-administerecl matrix tasks emPh:rsized
carlicr exccpt
perfr>rmed
N{atrices.Tcst
Proqressive
Rn'en's
paper-and-pencil
were verv similar to the
to devote as much time
that the problems were n;w presentld on the comPuter. Subiects were allowed
but thev were n()t
as desired ro inspecting the 6rst display in the simultaneous version of the task,
vcrsion of thc
a l l o w e d t o r e r u r n t o r h e m a r r i x a f t e r - v i e w i n g t h c a n s r v e r: r l t e r n a t i v e s .l n t h c s c c l t r c n t i a l
pcr
tri:rl :rs lorv
cxanrinctl
cclls
of
matrix
number
total
keep
the
to
task the subiects \vere enc()uragecl
i
I
II
I
I
M
lVorking me///zrJ, ageand matrix reasoning
187
Table 5. Nlean inspection time, decision time, and accuracy in the simultaneousand
sequenrial matrix tasks, Studies 2, 3 and 4
Simultaneous
Nlean
SD
Sequential
Nlean
SD
Inspectiont i m e ( s )
Study 2
Younq
()td
(s8)
S t u d y3
Young
ord
(s8)
Sttrclv4
Young
ord
(s8)
12.24
3.35
13.14
27.62
6.21.*
14.68
29.65
13.97
5.75
19.03
39.:1
7.09*
2.88
10.49
'7 <)l*
6.01
15.39
11.89
2 7. 9 7
5.18*
Decisiondme (s)
Strrrlrr ?
Young
old
(s8)
Study 3
Young
()lct
(s8)
2.95
0.57
1.66
5.03
6.49x
2.92
0.75
3.02
6.30
5.95*
0.65
3.50
2.14
6.55
7.47*
Sruclr'4
\-oung
2.54
0.39
5.33
6.39
3.94"
otd
(s8)
Decision accurac\' (percentage correct)
S r u c l v2
\ ' , r r rn g
Otcl
(s8)
S r t r r l v3
Younq
()lcl
(s8)
9._5
84.6
2t.2
63.0
5.08*
70.-
15..1
JZ.3
Zl. I
3.80*
12.4
14.6
15.6
54.1
5.47*
S t u d y4
\'ounq
( )l(i
(s8)
/ <.t)i.
89.6
54.5
7.2
25.3
7.32*
188
Tinotlt1' A. Salthoarc
and frrr as long a
as possible, but they vrere allowed to inspect the pattern in any cell as man)' times,
t
o
r
e
t
urn to the mxtrix
a
l
l
o
r
v
e
d
n
o
t
w
e
r
e
s
u
b
j
e
c
t
s
v
e
r
s
i
o
n
,
i
n
t
h
c
s
i
m
u
l
t
a
n
e
o
u
s
duration, as desired. As
d i s p l a y a f t e r v i e r v i n g t h e a n s r v e ra l t c r n a t i v e s .
Results and discussion
Descriptive statisrics for several of the performance measures are summarized in
Table 4. The age differences in the time ancl span measures were statisticallv
significant 1p < .0t1, as was the difference on the Raven's Progressive Matrices
measure (xU /s > 3.0).
Means ancl standard der.iations for the time and accuracv measures from the
c o m p u r e r m a t r i x r a s k sa r e d i s p l a r - e di n T a b l e 5 . I n s p e c t i o n t i m e r e f e r s t t > t h e t i m e
. p . . , t . , . ^ - i n i n s t h e s t i m u l u sm a r r i x , a n d d e c i s i o nt i m e r e f e r st o t h e i n t e r v a l t r o m t h e
display oI the answer alternarivesuntil the responseindicating the subject's decision.
It is apparenr from rhese clata rhat r>lderadults took signihcantlv more time than
young od,tl,t in both the inspection and decision phasesof the trial' Horvever, it is
i . n p , , i " n , r ( ) n ( ) r e t h l t t l . r c c l c c i s i o n sr e s u l t i n q t r o m t h i s g r e x r c r t i m e u ' e r e s t i l l
s i-The
g n i 6 c a n t l yl' e s sa c c u r a t et h a n t h o s e t > f l o u n g a c l u l t s '
correlation matrix containing the correlations among the maior variables
is presented in Table 6. Note that the correlations among the measuresof matrix
,easoning performance, and the correlations of these measureswith the comPosite
working-memory measure,are all statisticallysignificant, and moderate to large in
m"g.ritJd.. The hrst result suggesrsthar common processesare probably involved in
the three matrix tasks clespitJin. q,,tit. different Presentation formats' The second
are
result confirms the finding of Study 1 that higher working memory scores
performance.
reasoning
matrir
successfui
associatedwith more
Several hierarchical re.qressionanalvseswere conductecl in order to cxamine the
relations ^m()ng ^g., ru,-riki.tgnlem()rv irnclmatrix reasoning pertbrmance' For each
u'hen
o F r h e v e r s i < > nosf t h e m a t r i x t a s k , t h e R l a s s o c i a t e dr v i t h a r : er v a sc l e t e r m i n e d
t
l
i
r
"
'
o
rking
m
e
a
s
u
r
c
s
c
o
m
p
o
s
i
t
e
t
h
e
o
[
c
o
n
t
r
o
l
s
t
a
t
i
s
t
i
c
a
l
a
f
t
e
r
a
n
d
c O n s i d e r e da l < > n e
these
<>f
Results
combination'
in
and
seParatel)',
speed
memory and perceptual
analvsesare summarized in the second,third and tburth rows of Table2' along with
( ) n ec a n
t h e i e s u l t so i a p a r a l l e ls e t o t - a n a l v s ebsa s e do n d a t a f r o m s u b j e c t sf o r r v h o m
have some confidence that thel' clelrli' understoocl the task recluirements
\\'ts
( c c l r r c s p 1 l n c l i r rrUo t v s o f l l o t t t , t r t p l n c l ) . I . , r ' i c l c n c et > l t h i s u n c l c r s t : t n t l i r - t q
manit-eitedby erroriesspertbrmanceon problems I and2 in the Raven's Progressive
oneMatrices Test, or by ac.oracv equal or greater than 75 Per cent on the simplest
t
l
t
t
m
l
'
t
c
r so F
T
h
c
t
c
s
t
s
.
n
t
l
t
r
i
r
s
c
c
l
r
r
e
n
t
i
a
l
r
i
r
r
c
l
s
i
m
u
l
r
i
r
n
e
o
L
l
s
i
i
t
h
c
relatirn pnrblcms
29
the
23
Frrr
tntl
resPectivelr',
\vere,
criteria
rhese
meeting
aclults
v()Llng ancl crlcl
the
1
2
f
<
>
r
1
7
a
n
c
l
a
n
d
t
e
s
t
,
m
a
t
r
i
x
t
h
e
s
i
m
u
l
t
a
n
e
g
u
s
t
b
r
1
6
a
n
d
it^rr..,', Test,29
2
is
oi
Table
rows
relel-ant
the
in
aPParent
resulr
maior
The
test.
sequential matrix
the
same
exhibited
performance
reasoning
Pattern
matrix
of
that all three measures
Thc larger
6 F a t t e n u a r e cal q e c l i f f e r e n c e: sr t r e rs t a t i s r i c r rclr > n t r r >olf r v o r k i n g m c l l l ( ) r \ ' .
a
are
probably
I
Studv
to
relative
study
in
this
Test
Raven's
age effects on the
the
is
that
point
important
the
but
design,
Pattern
groups
extreme
.i.,r.q.r.n.. of rhe
was the case
of attenuation ot- the age diti-erenceswas very similar' Furthermore' as
in at least as
resulted
variable
speed
perceptual
ofthe
cl;.rtrol
in Study 1, staristical
189
lf,/orking memlrJ, ageand matrix reasoning
Table 6. Correlation matrix for variables in Study 2 (N :
60)
Variable
- .82*
(.e4)
1 Age
2 RPNI
3 SimAcc
.l SeqAcc
5 Repet.
(r WNIem
7 Speed
\leen
SD
-.59x
.80*
(.88)
-.48*
.72+
.73*
(.84)
.Ta
-.35*
- .77
-.08
X
- .46*
.59*
.64*
.54*
-.26
(.63)
.76*
- .70*
-.56*
- . 5 1*
.Zgx
- .47*
0.00
0.86
0.00
0.91
(.7e)
40.9
21.5
I8.2
6. r-
73.E
19.6
6r.5
20.9
8.0
6.2
' p <.01.
- \ r t e . R c l i , r l r i l i t i c si 1 r i r c t l i r g o n : r l s s c r c c s r i r n r r c r l b v u s i n { t h e S p e a r m e n - B r o r v n l i r r m u l l i o b o r l s t t h c
c 6 r r e l a t i g n b e t v c c n r h c t r v o c ( ) r ' n p ( ) n e n r n c : l s L r r c s( t i r r [ ) e r c e p t u a l S p e e d a n d W ' o r k i n g \ [ e m o r v ) o r
bcrrvccn the scorcs titr odti an(l cVcn itcms (tirr the matrix reesoning measures).
Ke7. RPNI: Number correct in the Raven Progressive rVatrices'Test; SimAcc: Accuracy in the
s i i r u l t a n e o u s c o n d i t i o n o f t h e c o m p u t e r m a t r i c e s t a s k ; S e q A c c : A c c u r a c l r i n t h e s e < l u e n t i acl o n d i t i o n
of the computer matrices task; Repet. : Average number of repetitive cell examinations in the
Working memory composite createdby
s e q u e n r i a lc o n d i t . i o n o f t h e c o m p u t e r m a t r i c e s t a s k ; V M e m :
atiraging { scores fronr the Reading Span and Computation Span tasks; Speed: Speed composite
tasks.
created bv averaging t scores tiom the Digit-Svmbol and Digit-Digit
much arrenuation of the age differencesin matrix reasoning as did the rvorking
memor\' \'arixble.
D e c i s i o na c c u r a c vw a s a l s o a n a l v s e da c c o r d i n gt o t h e n u m b e r o f a t t r i b u t er e l a t i o n s
i n t h e p r o b l e m . N l c a n a c c L l r a c ivn t h e s i r n u l t a n e o u sc o n d i t i o n i s d i s p l a . u " ei nd t h e t o p
panel of Fig. 7, and mean accuracv in the successivecondition is displared in the
to,ro- panel of this figure. The lack of differential age effectsapParentin the figure
rvas confirmed bv the absenceof significant (i.e. F < 1) age x problem tvPe X
conditi()n interactionsin an age (l'oung, olcl) x condition (simultaneous,sequential)
x p r o b l e m t v p c ( 1, 2 r > r3 r e l a t i o n s )a n a l v s i so f v a r i a n c e .
Correlations r,verealso c<;mputeclbetrveen rvorking memory and accuracv ti>r
problems with each number of relations. The correlations (all signiEcantatl <.01)
ior problems rvith one, r\\'o and three relations were .56, .60 and .51 for the
s i n r , - i l t , r , r e < ,c.or sn c l i r i o r r ,r n c l . . 1 6 ,. 5 4 a n c l . 4 0 i n t h e s e c l u e n t i acl o n c l i t i o n .T h e s c
r e s u l t s . l r cc ( ) n s i s t c n rt v i t h t l r c n c a r l r ,c ( ) n s t a n tr v o r k i n g n t e m o r v c ( ) r r e l a t i ( ) nasc r o s s
items evident in Fig. 4.
Becausesubjects in the sequential condition made overt keypress resPonsesto
e x a m i n et h e c o n r e n r sr > fe a c hm a t r i x c e l l , t h e p a t t e r n o f c e l l e x a m i n a t i o n sc o u l d a l s o
l t e a n a l v s c d .( ) f r h c t \ \ : ( )r v p e so f c c l l c \ a n l i n a t i o n s - u n i q u e o r f i r s t e x a m i n x r i o n so f
a cell, and repetitive or redunclant cell examinations-the latter are oi greatest
i n t e r e s t i n t h i s c ( ) n r e x r .I t c a n b e s e e n i n T a b l e 6 t h a t t h e r e w a s a s i g n i f i c a n t
correlation between age and number of repetitive cell examinations.It is tempting to
infer that the greater number of redundant cell examinations on the part of older
Tinotly A. Salthouse
190
Sinrultaneous
T
3
o
o
I roo
6
Nunrberof relations
in the
rclults :rs rr tunction o[ the number of relations
Figute 7, Ilc:rn accuracv for vout]u ancl olcl
standard error' l' voung; E' old'
o
n
e
t
o
c
o
r
r
c
s
p
o
n
d
b
^
t
t
"
t
h
a
b
o
v
e
problem, Studv 2. Lines
a diminished ability to Presefve
adults reflects an attempt ro comPensate for
the Iow correlation betrveenthe number
Hor',,e',,er,
iniormation in working *...,.u.
mJemorv mcasure (i'e'
of repetitive cell exariinations ancl the cornposi:: :'"tUli*
'
0
9
a c l u l t s )i s i n c o n s i s t e n t
t
'
l
c
l
c
r
t
i
r
r
- . 2 6 , a , n do' n l v - . 1 2 i o r v ( ) u t l s a c l u l t se n d
examinations may be
cell
repeatedwith this interpretation. Ali.rnative causesof the
about row or
hyp-otheses
verifying
difrficultiesin hisher-order processing such as
i
n
t
b
r
m
a
tion in one's
r
l
f
s
t
'
l
t
r
:
s
thc
c o l u m n r e l a t r o n s ,o r l a c k o i c o n t i d r n c e l b o u t
nlem()r\'.
ThereaPPeartobethreemaiorfindingsfromthisstudv.The6rstisthattheearlier
age' working memory and matrix
results of^ moclerately larue ielations 1T""*
without external time limits'
reasonin{I performance rvere confirn.redin ,i.^*t.t
c
( ) m m ( ) t ]t e m p o r a l I i m i t a t i o n
a
t
r
t
f h e s e r e l a t i < ; n st h e r c f i r r c c a n n ( ) t b c a t t r i b u t c c l
memory and matrix
working
the
in
imposed by the group-administration procedures
results oF Study 1
the
of
replication
reasoning tasks. A .f.."a -^i"r fin.ling is the
problems oi
across
.""t:11,
nearly
that the age and working memorv influenc.eswere
Finally, the
requirements)'
rvorking memory
rarving difficultv lunJ-f.r,r-ablv,
lVorking memorJ,age and matrix reasoning
191
discoven- that the age and working memory influenceswere similar acrossthe three
marrix tasks,and that the measuresof performance were significantlv correlatedwith
one another, suggest that common processeswere involved in each task despite the
ouite different methods of presentation.
STUDY 3
The prinrarv purpose of Study 3 was to investigate the interrelations among age,
m e a s l l r e so f t h e a c c u r a c vo f d e c i s i o n sc o n c e r n i n g p r o b e d i n f b r m l t i o n , a c c u r x c vo n
the simultaneous matrix task, and perfbrmance on the rvorking memory tasks. If
r e t e n t i o n o i e a r l i c r i n f o r m a t i o n i s i m p o r t a n t f o r s r - r c c e s s f pu el r i b r m r n c e o n m e t r i x
reasoningrests,then one would expect moderate positive correlations between probe
accuracv and matrix performance. Furthermore, if limirations of rvorking memorv
contribute ro poor matrix performancebecauseof an inabilitv to preserveinformation
d u r i n s p r o c e s s i n g , t h e n m o c l e r a t ep o s i t i v e c ( ) r r e l a t i ( ) n sr r ' o u l c l a l s o b e e x p e c t e c l
between probe accuracyand scoreson the working memorv tasks.Irinally, ii one of
the causesof adult age differencesin the matrix test is a reduced ability to preserve
eariier presentedinformation during subsequentprocessing, then older adults would
be expected to be less accurate than young adults in these probe decisions.
Method
Snbjects
D e s c r i p t i v e c h a r a c t e r i s t i c so f t h e 3 0 y o u n g a d u l t s a n d 3 0 o l d e r a d u l t s s ' h o p a r t i c i p a t e d i n t h i s s r u d t a r e
s u m m a r i z e c li n T a b l e 4 . T h e s a m p l e sw e r e r e c r u i t e d i n t h e s a m e n l r n n c r c l e s c n b e ciln S r u d r ' 2 , b u t n o n e
o f t h c i n c l i v i t l u l l s h a d p a r t i c i p a t e d i n n p r e v i o u s s t u d v c o n c e r n e c lr v i t h e i t h c r s ' o r k i n . q m c m o r l r r r m a t r i x
rc:rsoning.
P rocedure
Rcacling Span;
A I I s u b j e c t s p e r f i r r m e d t h e t a s k s i n t h e f < r l k > r v i n go r c l e r : D i s i t - S v m b ( ) l ; D i e i t - D i s i t ;
C o m p u r a t i o n S p l n ; a n c l S i m u l t a n e r > u sI l a t r i x . A l l t a s k s r v c r c i d c n t i c l l r o t h o s c i n S t L r . l v? c s c c p t r h ; r t
t h e s i m u l t a n e o u s m a t r i x t a s k l l s o c o n t a i n e d p r o l r e s o f t h e c o n t c n t s o i p r c r - i o u s l v d i s p L r v c c lc e l l s .
Prior to performing the matrix task on the computer the subjects studied a set of 6r'e practice
problcms (Numbers Dl, D2, D3, C4 and E3 from thc Raven's Standard Prosressive \latrices)
d i s p l a v c c li n r b o o k l c t . l l e l o r v e a c h p r o b l c m r v e s e c l c s c r i p t i o no i r h c r r t r r i l ) u r c i l r r t l r c l l t i , r n r c l c v t n t t r r
t h e s o l u t i o n o f t h e p r o b l e m , a n c l a n e x p l a n a t i o n o f r v h v t h c c l c s i g n i r r e <tln s r v e r r , ' ' a sc o r r c c t . T h e
S i m u l r a n c r > u s^ \ l a t r i x t a s k r v a s t h e n d e s c r i b e d , w i t h s p e c i a l e m p h a s i s o r r r h c p r o b c r r i a l s .
T r v o b l o c k s o f 3 0 t r i a l s e a c h w e r e p r e s e n t e di n t h e S i m u l t a n e o u s N l a t r i x t a s k . \ \ ' i t h i n e a c h b l o c k , 2 0
t r i a l s r v e r e s t a n d a r d t r i a l s i n t h a t t h e m a t r i x w a s f o l l o r v c d b y - t h e s c t o f c i g h t a n s r v e ra l t e r n a t i l e s , a n d
10 trials rvere cell probes in which the matrix was followed bv a probe conccrning the contents oF a
p t r t i c u l a r c el l . \ \ ' i t h i n c a c h s t i m u l u s s c t , c : r c h o [ t h e e i g h t n r l t r i x c e l l s \ \ ' r r sp r ( ) l ) c ( lc i t h c r o n c c ( ) r t \ \ ' i c c ,
a n d t h e p r o b e s o c c u r r e c lo n f o u r t r i a l s w i t h o n e r e l e v a n t r e l a t i o n , f < r u r t r i e l s s i t h t r v t . tr e l c v e n t r e l a t i o n s ,
and trvo trials with three relevant relations.
T h c p r r > b c sc o n s i s t e d o f d i s p l a l s o f a g e o n r e t r i c p a t t e r n i n o n e o f t h c c c l l s L r i t h e m r r r r i s a c c r r m p : r n i c d
'
'SAlv{E'
on the lower left and lower riqht of the displav,respectively.
by the words DIFFERF,NT' and
( ) n e h a l f o f r h e p r < > b e sc o n s i s t e d o f t h e s a m e p t t t e r n p r e s e n t e dc a r l i e r i n t h a t c e l l , a n d o n e h a l f c o n s i s t e d
o f a c l i f f e r e n tp a t t e r n ( e i t h e r t h e p a t t e r n f r o m o n e o f t h c o t h c r c c l l s i n t h c m a t r i x , o r a s l i s h t l v a l t c r c c i
W
792
Tinothl A. Saltboase
version of the original pattern). Decisions to the probe stimuli were communicated bv pressing the
bottom left kev ('Z') or DIFFF,RI1NT for the bottom right kev ('/') for SAMF,.
Results and discussion
Descriptive statistics on several of the performance measuresare summarized in
Tables 4 and 5. As in Study 2, all the age differenceswere significant (p < .01) in
the perceptual speed, working memory and matrix reasoning measures.
Results from the hierarchical regressionanalvses,summarized in the fifth row of
Table 2, resembled those from Studies 1. and 2. Anallzsesrestricted to subiects (22
young adults and 7 older adults) with accuracv of at least 75 per cent on problems
with a single relarion were also similar. In both analysesthe variance in reas<;ning
performance associatedwith age was substantiallyattenuatedafter statisticalcontrol
of th. composite measuresof either working memorv or PercePtualspeed.
Accuracy'in the probe recosnition trials rverlged 70.3 Per cent (SD:11.(t) For
y o u n g a d u l t sa o d 5 7 . 3 p e r c e n t ( S D : 1 . 2 . 5 f) o r o l d e r a d u l t s( l ( 5 8 ) : 4 . 1 8 ,p < . 0 1 ) .
An age x cell pos.ition analysis of variance was also conducted to determine whether
the age differences varied as a function of the particular matrix cell whose contents
wereteing probed. Both main effectsin this analysiswere significant (i.e. Fs > 6.4),
: 849.47).
as vrell as the age x cell position interaction (F(7,406) :4.28, MSE
Inspection of the cell means revealed that the interaction was attributable to both
yoo.,g and old adults performing near chance for one cell position (middle cell in the
iop row), but with young subiects performing more accurately than older subjects for
alf other cell positions. Examination of the stimulus Patterns revealed that the
DIFFERE,NTlrials in this cell rvere created bv rather subtle changes compared to
those in the other cells, and thus an atypically difficult SI\NiE/DIFFE,RENT
discrimination mav have been responsiblefor the low decisionaccuracvin top middle
cell.
The correlation matrix containing the correlations among the maior variables in
this study is presented in Table 7. Notice that, as in the previous studies, the
correlations among age, working memory and matrix reasoning performance are all
moderatelv high. It should also be emphasizedthat the probe accuracv measure is
positivelv' correlated .,r'ith both working memorv and matrix reasonins, btrt
negadvely correlated with subiect age.
M.^nt of the percenragecorrect measure in each age grouP for problems with one,
trvo and three relations are displaved in Fig. 8. The interaction of aqe x problem
type in an analvsisof variance was not significant (i.e. F < 1). Correlations betlveen
working memory and mean accuracyfor problems with one, two and three relations
were .60, .55 and .45, respectively.In both respectsthese results replicate those of
Study 2.
The primarv nerv resulrs from this study concern the probe recognition measure.
As exptctecl, this measure was positively correlated with workinll memorv and
matrix reasoning performance, and negativelv correlated with subiect age' These
results are consistent with the hypothesis that working memory med.iatesage
differences in matrix reasoning tasks because of its role in preserving earlier
information during subsequentprocessing.
rii,i*:jj-ix,
..;;s.".
t93
IVorking memlrJ, age and matrix reasoning
Table 7. Correlation matrix for variables in Studv 3 (N : 60)
V
1
2
3
4
5
a
r
Age
SimAcc
ProbeAcc
WNlem
Speed
i
x
.10.3
21.0
lvlean
sD
a
b
l
e
1
-.61*
(.86)
- .50*
.67+
(.47)
64.6
1 7. 2
6i.8
13.6
2
3
-.63',
.61*
.50*
(.71)
0.00
0.88
4
5
.80*
-.51*
- .49*
-.46*
(.e2)
0.00
0.96
* p <.01.
N p r r . R e l i a b i l i t i e s i n t h e c l i a g o n a l sr v c r c e s t i m e t c c lb v u s i n g t h e S p e a r n r a n - B r o u n f o r m u l a t o b o o s t t h e
correlarion between the two comp()nent measures (for Perceptual Speed and Working Memory) or bv
, 132): reliabilit): N(avg.r)/[1+(N-l)(':rvg.r)1,
u s i n g t h e f r r r m u l ad e s c r i b c db v K c r r n e r ' ( 1 9 7 9 p
s,ith corrclations bets'ccn mcasurcs rvitlr one. trvo:rncl thrce rclations ior the Sim,\cc and ProbeAcc
variables.
Ka7. SimAcc : Accuracy in simultaneous condition of computer matrix task; ProbeAcc : Accuracy in
cell recognition probes; WIvIem - Working memory composite created by averaging 1 scores from
Reading Span and Computation Span tasks; Speed: Speed composite created by averaging t scores
tasks.
from Digit-Symbol and Digit-Digit
100
80
6
o b u
o
{s
o
Numbcr of relltions
Figure 8. Nlean xccurac) frrr voung and olcl lclults as a tunction of the number oF rclations in thc
problem, Study 3. Lines above each bar correspond to one standard error. I, young; E, old.
STUDY 4
Aithough the resultsof Study 3 seemto implicate a mediationalinfluenceof rvorking
memory, it was somewhat surprising that accuracyof the probe recognition decisions
was rather low in both age groups (i.e. 70.3 ^nd 57,3 per cent for young and old
adults, respectively).One interpretation of the relativelv low levelsof probe accuracy
in the previous study is that information mav be discarded when it is no longer
I
1,94
Tinothl A- Salthoase
necessaryfor processing.That is, becausethe probes in Study 3 ..verenot Presented
until the subject indicated that he or she was ready to view the answer alternatives
and make a decision, it is possible that the cell information had already been purged
from memory by the time the probe was Presented. This possibility can be
investigated by intertupting the processing by the Pfesentation of a probe about
previousiv viewed information. In order to ensure that subiectswere still engagedin
processingat rhe time the probe was presented,the sequentialversion of the matrix
task was used in this study.
The availability of measuresof recognition probe accuracvand of the number of
reperitive cell examinationsin the inspection of the stimulus matrix also provides an
opportunitv to determine the relation between these two variables.If the redundant
cell inspections occur because the previously viewed information is no longer
available, then one might expect a negative correlation between the two measures
because better preservation of information, as reflected bv high probe accuracv
s c o r e s ,s h o r , r l cble a s s o c i a t e dw i t h a s m a l l e r n u m b e r o f r e p e a t e dc e l l e x a m i n a t i o n s '
Becauseaccuracyin the sequentialversion of the matrix reasoningtask in Studr 2
was fairly low even among young adults (t.e. 70.7 Per cent), an easier set of
stimulus items was used in the present experiment. These were the problems used in
an earliet study by Salthouse & Skovronek ('1992),in which young adults averaged
90.7 per cent in the simultaneous conditions and 88.0 per cent in the sequential
condiiion. In order to verify that performance on these new items was related to
performance on the paper-and-pencilRaven's test, all subiects also performed the
Raven's Advanced Progressive Matrices Test. However, becauseof a desire to keep
the average length of the experimental session less than 1.5 hours, neither of the
working memory tasks nor the Digit-Digit task were administeredto subjectsin this
study.
Method
Sabjects
Descriptive characteristics ofthe 30 young adults and 30 older adults who participated in this studv are
s u m m a r i r e d i n T a b l e 4 . N o n e o f t h e s u b j e c t s h a d p a r t i c i p a t e d i n a n ; - o f t h e p r c v i o u s s t u c l i c si n t h i s
projcct, but eech rvas recruited according to the procedures described in Srudr'2.
Procedare
A l l s s b j c c t s l ; 1 : , ; 3 nt b e s c s s i o nl > v p e r f o r m i n . q t h e R a v e n ' s P r o g r e s s i v c ) f a t r i c e s T c s t a t l m i n i s t c r c c li n t h c
'fhev
thcn performed both thc standard \\'AIS-R Digits a m c n r a n n c r d c s c r i b c c li n S t u d i e s 1 a n d 2 .
S y m b < > l S u b s r i t u t i o n T e s t , a n d t h c c o m p u t e r - a d r l r i n i s r c r e dc l i g i t - s v m b o l v e r s i o r r d c s c r i l : e r l c a r l j c r ,
follorved by the scquential version of thc computcr matrix tesr.
Each subiect performed three blocks of 18 rrials each in the Sequential Nlatrix task, preceded bv a
block of six practice trials. The matrix problems in this study resembled those used in Studies 2 antl 3,
b u t w e r c n , r , a , r n r t r r l a t a dt o d i f f e r s v s t c m a t i c a l l l r v i t h r e s p c c t t < >t h c n u m l ; c r r > f r c l e l ' : i n t r c l a t i o n s -. fShics
t r i a l s i n e a c h o i p e r i n - r e n t a lb l o c k w c r e i n t e r r u p t e d b v t h c p r e s c n t a t i r > no f c c l l r c c o . g n i t i t t np r r - r b c s "
probes were similar to those of Study 3, but were not identical because different sets of problems rvere
u s e d i n t h i s s t u d y ' .T h c p a r t i c u l a r m a t r i x c e l l p r o b c d i n t h e c e l l r e c o g n i t i o n t r i a l s v a r i e d r a n c l o m l r . b u t
always occurred after two other cells had been examined since the previous vierving of the target cell.
No recognition probe rvas presented if the subject did not examine the critical ccll, or if he or she prcsscd
the IINTI]R kev to view rhe answer alrernatives before examining t\!o aclditional cells.
IVorking memzrJ, ageand matrix reasoning
195
Results and discussion
Descriptive sratisticssummarized in Tables 4 and 5 indicate that, as in the previous
studies,the young adults answeredmore Raven's items correctly, and rvere fasterand
more accurate in the computer matrix task then older adults. It can also be seen in
Table 5 that although the voung adults apparently benefited from the change to a
d i f f e r e n t s e t o [ s t i m u l u s i t e m s ( i . e . a c c u r a c yi n t h e s e q u e n t i a cl o n d i t i o n w a s 7 0 . 7 p e r
c e n r i n S r u d y 2 a n d 8 9 . 6 p e r c e n t i n t h i s s t u d y ) , t h e o l d e r a d u l t s s t i l l a v e r a g e dl e s s
than 55 per cent correct decisions.
il r\IS-R Digit -S,vmbol
S u b j e c t si n t h i s s t u d v a l s o p e r f o r m e d t h e p a p e r - a n d - p e n c W
:
9 . 8 ) f o r y o u n g a d u l t s ,a n d
S u b s t i t u t i o nT e s t . S c t > r eos n t h i s t e s t a v e r a g e d l 2 . 0 ( S D
5 1 . 8 ( S D : 1 2 . 1 ) f i r r o f t e r a c l u l t s ( ( 5 8 ) : 7 . 1 2 , p < . 0 1 ) . T h e s e s c o r e s \ r ' er e
converted to units of s per item by dividing them into 90 (the number of s allowed
to perform the test), and then the 1 score for this measurewas averaged with the 1
score frr>m thc computer-administeredDigit-Symbol measure to fbrm a composite
p e r c c p t L t xsl p e e d r - : r r i r r b l c .
H i e r a r c h i c a l r c g r e s s i o n a n a l y s e sr e v e a l e d t h a t s t a t i s t i c z rcl o n t r o l o f p e r c e p t r - r a l
speed reduced, but did not eliminate, the age diferences in matrix reasoning
performance. That is, the R2 associatedvrith age in the prediction of Raven's
performance was .538 when considered alone, and .112 after control of perceptual
speed. Corresponding values for the sequential matrix task were .630 and .094,
respectivelv. These results are consistent with those of the previous studies, as
summarized in Table 2.
Analyses of the cell examinations and of the probe accuracy measure revealed
patterns similar to those reported in Studies 2 and 3. Speci6cally,voung adults,
compared to older adults, averased fewer repetitive cell examinations(i.e. mean of
4 . 2 , S D : 3 . 7 r ' s . m e a n o f 7 . 6 , S D : 7 . 3 , / [ 5 8 ] : 2 . 2 5 ) , a n d 'm o r e a c c u r a t eP r o b e
r e c < > s n i t i o nd e c i s i < > n(si . e . m e a n o f 8 4 . 8 P e r c e n t , S D : 1 2 . 8\ r s ' m e a n o f 5 8 . 4 p e r
cent, SD : 18.2, l[58] : 6.49). For the young adults, accuracy of the recognition
probe decisionswas greater in this study than in Study 3 (i.e. 84.8 vs. 70.3 Pef cent),
but there was little differencein the accuracvof older adults across the two studies
(i.e. 58.4 vs. 57.3 per cent).
The correlation matrix iirr the maior variablesin this study is presentedin Table 8.
T h e h i g h c o r r e l r r t i t > nb e r t , e e n t h e n u m b e r o f c o r r e c t r e s p ( ) n s e si n t h e R l t ' e n ' s
Progressive Nlarrices Test and accuracy in the sequential matrix test suggests that, as
in Study 2, common processescontribute to performancein both types of tests.Also,
s ctt'een the probe recognition
l i k e i n S t u c l v . 3 . t h c m < > c l e r a r ehl vi g h c o r r e l a t i r > n b
a c c u r a c v m e a s u r e a n d p e r t b r n r a n c ei n b o t h m a t r i x r e a s o n i n g t a s k s i n d i c a t e t h a t
people who achieve high scores on the matrix reasoning tasks are also better than
p e o p l e w i t h l o r v e r s c o r e sa t p r e s e r v i n gp r e v i o u s l y p r e s e n t e di n f o r m a t i o n .
It can be seen in Table 8 that the correlation between the averaged number of
r e p e t i t i v e c e l l e x a m i n a r i o n sa n d a c c u r a c vi n t h e p r o b e r e c o g n i t i o n t r i a l s w a s r a t h e r
low (i.e. - .21.), and not significantly different from 0. lf the repetitive cell
examinarions represent an attempt to preserve information that is being lost, then
one might have expected a large negative correlation. The failure to find more
repetitive cell examinations among subiects rvith low probe accuracy scores casts
'196
Tinothl A. Salthouse
Table 8. Correlationmatrix For variables in Study 4 (N : 60)
Variable
1
2
3
4
5
6
-.73*
Age
RPN,T
SeqAcc
ProbeAcc
Repet.
Speed
)[ean
SD
X
- .19*
.81*
( e4)
-.70*
.60*
.t+
X
.32*
-.45*
-.19
-
a1
.L t
X
.'79*
11*
- .64*
?/*
(.8s)
4l-5
22.7
1,6.2
6.4
72.1
25.5
1 1. 6
20.5
5.9
6.0
i).0()
0.92
* p <'01.
N o l e . R e l i a b i l i t i e s i n t h e c l i a g o n a l sr v e r e e s t i m a t e d b v u s i n g t h e S p e a r n . r l n B r o r v n f i r r m u l l t o b ( ) o s t t h e
correlarion berrveen thc tw'o comp()nenr mcasurcs (for Perceptual Speed) or bv using thc f<rrmula
rrith corrclrttions
d c s c r i l r c rbl r K c n n c r ' ( 1 9 1 9 . p . 1 3 2 ) : r c l i 1 l l > i l i:r ) \ ' ( : r v S .a / U + ( \ ' - l ) ( r \ s . r ) ] .
bet\-een measurcs rvith one, t$.o and three relations [r>rthe SeclAccr-ariable.
in the
Kg,. RPNI: Number correct in the Raven Proqressive N{atrices fest; Se<1Acc: Accuracv
seluential condition of the computer matrix task; ProbeAcc: Accuracv in cell recognition probes;
computer
R " p . t . : A v e r a g e n u m b e r o F r e p e t i t i v e c e l l e x a m i n a t i o n s i n t h e s e q u e n t i x lc o o d i t i o n o f t h e
Speed composite created b.v averaging t scores from paper-and-pencil and
m"irix task; Sfeed:
computer Digit-Symbol tasks.
doubt on rhis interpretation, although it is possible that the correlation was small
because of low reliability of the measures. Unfortunately, no estimates of the
reliability of the probe accuracy or repetitive cell exirmination measures were
available in this study.
GENERAL
DISCUSSION
The results o[ these studies replicated the findinss ot- manr earlier stuclicsresardins
substantialage-relateddeclineson performanceon the Raven's ProgressiveN{arrices
Test. The afe correlation of -.57 in Studv 1, and the discovery that the average
-3.6 (Studv2) and -2.6 (Studr'4) voung
o l c l e ra d u l t r c h i e r . e csl c o r e se q u i v a l e n tt o
a d u l r s t a n d a r cdl e r . i a t i o nu n i t s , a r e b o t h c o n s i s t c n tr v i t h t h e r e s u l t ss r - r m n r r t r i z ei nc lt h e
introduction.
The present results also extend the earlier results, hou-et'er,by revealing _thatthe
age differencesare evident in measuresof accuracv, and do not simplv reflect the
n i r m l r c . o t i t e n r sx t r e n r p r e ( IT. h i s r v a sr p p a r e n t i n t h e e r t r r l l s i st > f t h e p c l c c n t a q eo F
v e ^ s u r c si n e : r c h
a t t e m p t e c il t e m s a n s r v e i e ccl o r r e c t l v i n S t u d l ' 1 , a n c li n t h e . a c c u r a c m
did take more
adults
Older
tasks.
reasoninq
matrix
of rhe computer-administered
but they
decisions,
their
to
make
and
matrices
the
inspect
to
adults
voung
time than
adult
standard
in
voung
expressed
When
decisions.
in
those
accurare
less
also
were
c i e r - i a t i 6 nq n i t s , t f i e a c c L r r a c cv l i f { e r c n c cisn t h e c o n r p u t c r I n : l t r i \ t l s k s ( c f . T a b l e 5 )
a v e r : r g e d- 2 . 2 7 , - 1 . 1 9 , - 1 ' 6 0 a n d - 4 . 8 8 u n i t s .
Another findine consistent rvith the results of other studies is that statistical
conrrol of a measure of working memorv greatly attenuatedthe magnitude <>ithe
bv "vhich the age
age-related effects on cognitive Performance. The Percenta.qes
W
lY/orking memzrJ, ageand matrix reasoning
1.97
effectswere attenuated, as computed from the values in Table 2, were 83.5 per cent
(Study 1) and 42.6per cent (Study 2) for the Raven's ProgressiveMatrices Test,68.9
per cent (Study 2) and 77.1 per cent (Study 3) for the simultaneousmatrix task, and
71.1,per cent (Study 2) for the sequentialmatrix task. It therefore appearsclear that
working memory is an important factor in the age differencesin these kinds of matrix
reasoning tasks.
Three types of analvsesu'ere carried out to examine horv rvorking memory might
mediate age differencesin matrix reasoning.One set of analvsesfocused on betveenitem variation becauseof the assumption that at leastsome of the accuracydifferences
across items might be attributable to the demands placed on working memory.
C o n t r a r y t o e x p e c t a t i o n ,h o r v e v e r ,t h e r r l e e f r ' e c t rsv e r en e a r l v c o n s t a n ta c r o s si t e m s
. h i s i s e v i d e n ti n F i g s 3 , 7 a n d 8 r e p r e s e n t i n g
v a r v i n g c o n s i d e r a b l vi n m e a n a c c u r a c vT
results from paper-and-pencil, simultaneous comPuter, and sequential computer
a d m i n i s t r a t i o n sA
. s e c o n ds e to f a n a l v s e cs o n c e n t r a t e do n e r r o r p a t t e r n s .E x a m i n a t i o n
of the frequencv with which incorrect alternatives \vere selected(cf. Table 3) also
[ a i l e c l t o p r o v i c l e e v i d e n c e o f d i f f e r e n t p : r t t e r n s o f e r r o n e o u s r e s P o n s e s .. . \ n
implication oi borh sets oI resuks is rhat the factors responsibletbr age differences
are nor the sameas those contributing to the variation in item difficulty. As suggested
in the discussion of Study 1, item variation in average accuracymay reflect factors
such as the salience of the attributes and awareness of specific relational rules more
than differential demands on working memory.
The third set of analysesdesigned to investigate how working memofy might
mediate adult age differences in matrix reasoning involved the probe recognition
measures. If people with low levels of working memory do not function well in
cognitive tasks becausethev are not very successfulin presen'ing information rvhile
also carrving out processing, then thev should be expectedto be less accurate than
people with higher working memor)' levels at recognizing probes o[ previouslv
presented in[ormation. This hypothesis \\rassuPPorted in both Studies 3 and 4 as
older adults were found to be signilicantly less accurateat recognizing the contents
of previously examined matrix cells than young adults. Moreover, becausethe probe
recognition measurewas correlated with both the measuresof rvorking memorv and
the measures of cognitive performance, these results are comPatible with the
inrerpretatioo thzt one of the wavs in rvhich .,r'orkinq memorv exerts its medieting
influence is bv afl'ectingthe Preservationof inti>rmation during processing.
The finding of age differences in the accuracy oF recognizing information
presentedearlier in the context of a cognitive task may have to be qualified because
n u x g e c l i f f e r c n c e si n a n t c l s u r c o f p r t l b c r e c t l g n i t i o n a c c t t r x c vr v e r e r e p o r t e c lb r '
S a f t h o u s e& S k o v r o n e k ( 1 9 9 2 ) . r \ c u b e c o m p : r r i s o n st a s k r v : r su s e d i n t h a t p r o i e c t ,
and young and old adults rr,'erefound to be equivalent in the accuracy of recognizing
the contents of previouslv viewed cube faces. One possible explanation for this
discrepancv is that age differences in the preservation of information may be
pronounced only rvhen the combinecl storage and processing requirements are
demanding. That is, the matrix tasks in the current studiesinvolved unique difficultto-describe geometric panerns in each of eight cells, whereasthe stimuli in the cube
comparisons task consisted oF only three to six familiar letters. Furthermore,
Salthouse (1992a) recenrlv found that the age differences in the accuracy of
198
Tinothl A. Salthoase
an integrative
recognizing previously presented intbrmation in the context of
performing
subiects
from
,.^roni.rg ,.-"rk*.r. gr.",iy reduced by eiiminating the data
was
evident
result
poorly ii the simpleit condition of the reasoning task. A similar
of
measure
a
employing
in "diitio.r^l analysesof data from Studies 3 and 4 because
and
3
in
Study
accuracy with the simplest problems (i.e. one-relation problems
in Studv 4) as a covariate reduced the age differences
roughli equivalent p.ott.-r
per cent. The
i n i , r . ' p r o b . r e c o g n i t i o n a c c u r a c t r ' m e a s u r eb v a p p r o x i m a t e l y 5 0
earlier inphe.ro-enon of ^ge diff.rences in the recognition of inFormation presented
of
amount
of
the
"r, on-going .ogiitirr. task may therefoie vary as a function
or
the
motivational
information in the task, ancl of .ith.. th. cognitive capabilities
involvement of the subiects.
the aee
r\n imp<-lrtantremnining qLrestionconcerns the factors responsible [or
&
Salthouse
I99la;
differencesin working memory. Previtlus research(Salthouse,
the
incorporating
Babcock, 1991), incl.,iinq a report conreining additional.analyses
the age differencesdata from Studies 2 and'3 (Safthouse, 7992a), has revealed that
o f m e e s u r e so f
i n s , r > r k i n g n t c n - l o f vx r e g r e r t l v i r t t e n L l r t e db v s t a t i s t i c a l_ c o n t r t l l
the perceptual
that
per..pt,.,^l'spcecl.The ,.r.rii. summarized in Table 2 also indicate
to rvhich
degree
in
the
ip..d and working memory variablesrvere nearly equivalent
is, the
That
they influenced the age-related effects on matrix reasoning performanceto
similar
very
.,r"ti., of R2 for"g. ^f,., statisticalcontrol of working memory-were
few
cases
a
in
only
and
those obtained afier statistical control of perceptual speed,
after control of both
was the arrenuarion of the age influence appreciably greater
that an important
suggest
perceptual speedand rvorking memor)'. These findings all
measures of
determinant of the age differ"encesin cognitive functioning,.including
can be
oPerations
cognitive
working memory, is"the speed with rvhfth elementarv
oPerations
cognitive
execut;. The mechanirms by which the rate oi performing
yet been identified' but
affectsrvorktng memorv ancl other ctlgnitive tasks have not
analr"sisof age
reductionistic
the results oI these ^n.i,rthe. stucliesln.lic"te that the
on speed of
fbcus
to
a
least
at
differencesin cognirion can, and should, be extended
information processingas an explanatorv construct'
Acknolvledgements
(]rent,-\(106826 lrvould like to thenk
T l t l 5 r u 5 c r r c r l. , \ ' : i :\ u P l i r ) r t ( . (!l r r \ r r r i o r r i r l l n s t i r u r c o n . \ g i n g
a n c l : r n a l y s i so i c l a t a .
R . l j a b c t l c k , J . J a c k s o r i r r r t l J . S h : r r v t i , l r i r s s i s t : r n c ci n c o l l c c t i o n
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