Journal of Gerontologt
1982,Vol. 37, No. 3,349-353
Time-Accuracy,Relationships
in young
and old Adultsl
Timothy A. Salthouse,phD, and Benjamin L. Somberg, phD2
The relationships between reaction time and classification accuracy were
compared in young (lg to 2l
years)-and old (6i0 to 84 years) adults in a choice reaction time
task, rio6r younjlno older adults showed
equivalent rates of increasing accuracy with greater time, but the temporal
iur"tjon "t which the accuracy
first exceeded the chance level was shorter for young than for older
adults. It was suggested that aging is
associat€d with a slowing of the information integralion and/or
respons" pr"p"."iion processes but not
with a slowing of the actual rate of information exiraction.
Key words: Speed-accuracy tradeoff, Processing capacity, Reaction
time, Age-related slowing, Human
f\ ,ng same classic paper (1869/ 1969)in which
r he introduced his now famous stage model
of reaction time, Donders also menti6ned the
problem of interpreting reaction time when in_
dividuals commit errors. For almost 100 vears
this problem of interpreting reaction time when
accuracy rs uncontrolled remained unsolved,
and it has been only in the last decade that
explicit procedures have been developed for the
simultaneous analysis of both speed^andaccu_
racy aspects of performance.
The procedural innovation of recent vears
involves examining reaction time and erroi rate
at several levels ofspeed and accuracy to deter_
mine the mathematical relationship between the
two and, then, using this relationship as a mea_
sure of performance capacity. The empirical
functio.ns relating reaction time and uccuru.y
have been termed speed-accuracy-operating
characterisrically by PLw 11969yarrd iat.n"y_
op^erating characreristics by Lappin and Disih
(1972) in recognition of their sjmilarity to the
receiver-operating characteristics of sienal de_
tection theory (e.g., Green & Swets, 1966).Like
receiver-operating
characteristics, different
points on the function are assumed to reflect
different decision criteria or response biases,
and, thus, the function itself can serve as a
strategy-independent measure of performance
capacity. Both Pachella 11974)and Wickelgren
(1977) have provided detailed discussionsoFrhe
methodological advantages of using complete
'This rcrarch
was supponedby National Instituteson Agitrg Crant Rol
Ac 00694-01to Dr. Salthriri*.
'Department
of Psychology,Universityof Missouri,Columbia,MO 6521l.
tradeoff functions in place of conventional re_
action time measures.
In addition to the methodological importance
of time-accuracy tradeoffs, piw (19'691 and
Wickelgren (1977) have pointed out rhat more
precise identification of the nature of an exper_
imental factor's influence might be possibl6 by
examination of the parametels of the time-ac_
curacy-operating_ characteristic. Recent empiri_
cal work (e.g., Salthouse, l98l) has indicated
that th€ operating characteristic can be reasonably described by three general parameters:the
mtercept, slope, and accuracy asymptote. A
schematic illustration of an idealized ooeratins
characteristic and the effects of varying'each oT
the three parameters is presented in Fieure t.
The shift in the point at which accuracyiegins
to increase with increased time, portray"d in
Figure lB, will be reflected in the iniercept
measure of a linear equation relating time to
accuracy for the middle-segment of the-function.
The change in the amount of increase in accuracy per unit time, depicted in Figure lC, will
be e-vident as a change in the slope measure of
the linear equation. And finally, ihe change in
the asymptotic high level of accuracy, rEpresented in Figure lD, can be summarizid bvthe
final measure of accuracy in whatever uniti are
employed.
The effect of adult age on time-accuracy-operating
.characteristic parameters is particularly
interesting since slower performanie is often
considered one of the primary behavioral characteristics ofaging, and yet very little is presently
known about the cause, or exact nature, of thii
reduction in speed. Moreover, previous research
349
SALTHOUSE AND SOMBERG
350
o
Hi9h
Fast
Reaction Time
Fieure l. Schematic illustration of idealized time-accuracy-6perating characteristic (A) and variations in intercept
(B), slope (C), and accuracy asymptote (D).
comparing time-accuracy-operating characteristici in adults of different ages has been inconsistent with respect to the parameter most influencedby increasedage.Rabbitt and Vyas (1970)
did not-report many details but suggested,that
older adulis did not differ from young adults in
the slope Parameter but may have differ-ed in
the int-ercept parameter. Salthouse (1979) reported three experiments with time-accuracybperating charaiteristics for young and older
adults, but the results wer€ not entirely consistent, and there was evidence of both intercept
and slope differences in various comparisons.
One problem with the Salthouse (1979) study
was that the regression parameters were not
computed from the individually determined
best-htting equations. Instead, all of the available data points were used for each participant,
and since iome individuals had data with either
very low (chance) or very high (perfect) accuracy, this procedure resulted in relatively poor
estimates of the true regression parameters for
individual participants. The present experiment
attempts to clarify the ambiguity currently surrounding the issue of which operating characteristic parameter is affected by increased ag_eby
the individually determined slope
comparing
and intercept Parameters of young and old
adults. Because-thePresent discrimination task
was quite easy, all pafticipants achieved near
perfeCt accuracy with long reaction times, and'
thus, comparisons of the accuracy asymptote
parameter per se are not meaningful. Of course,
ihe time at which the asymptote is reached is an
interesting and meaningful variable, but this can
be derived from, and hence is not independent
of, the intercept and slope parameters.
Definitive interpretations of the meaning of
the various parameters are not Vet possible,but
certain speculations seem reasonable on the
basisof the available evidence.For example, the
slope seemsto representthe rate of extracting
information to discriminate betr,r'eenalternative
representations because more discriminable
stimuli lead to steep€rslopesle.g.. Link & Tindall. l97l: Pachella& Fisher. 1969:Rabbitt &
Vyas, 1970;Swensson.l97lt. The rnterceptparameter apparently reDresentsthe duration of
all processesexcePt actual inlbrmation extraction as it has been found t.. tre sreater u'ith
variations of such factors as (at stimulus intensity (e.g., Lappin & Disch. l9-1. Pachella &
Fisher, 1969),(b) number of stimulus-response
alternatives(e.g.,Pachella& Fi:her. l9'1. Pew.
1969),and (c) distanceof the strmulu: litrm the
l9ll r li these
fovea (e.g.,Sterling & Salthe-ruse.
speculationsas to the meaning rrf the lntercept
and slope parametersare accepted.the rnrestigation of adult age effects should &llrr$ orl€ to
determine whether aging effect. dt.t-rtmtnatton
or information extraction Pr(x'ei:€\ le\.. more,
or equally as much as other Prr\*e\\.\ tnr.-l!ed
in speededresponses.
MErHoo
Participants.- Fortv college ttudent' ' lrt femalesand 20 males)betueen the aees.-i lr and
24 years (M : 18.'l) and 4O t'rlder adult' (26
fernales and 14 males) between ths 396' .'i 60
and 84 years (M : 69.I ) participaredIn a \rnsle
experimental session.Preliminan analr.c: revealed no sex differences or age bl :er lnteractions on the primary dependent vanabler and.
thus, the sex variable was ignored tn all ruh:equent analyses.Mean rau scoreson the \\'{lS
'1.5 lor the
vocabulary subtestwere 58.4 and
y o u n g a n d o l d a d u l t s .r e s p e c t i r e l r . l ( 7 E l _ i: . l - .
WAIS digit
! < .0OOt.Mean raw scoreson the
adults and
voung
for
65.9
were
iymbol subtest
46.4 for old adults,(78) : 1'33'p < '@01' Most
of the older adults were active or retired professionals, whereas all of the younger adults were
college students.All participants reported themselvei to be in reasonably good health'
Apparatus.-
A PDP-ll laboratory computer
controlled the Prescntr
lett-Packard modcl l l
decay P3l PhosPhor
from a resPons€ Panc
pushbutton telePhonc
iom-most (0) kev on r
All temporal measure
millisecond.
Procedure. - A lfI
consisting of four dots
"
with I sides,was Pres
the target stimulus. v
diaeonal arrow onentl
lorier right of the drs
target stimulus was tr
pait depressedthe tx
ifor the leftward P.rr
(for the rightward P
After the resPons€s a
displayed in which tl
the reiponse and thc
indicated. The Panx
attemPt to resPond r
reeion regardless trf
reiult. Tio trial blo
rated bY a short rest 1
with the desired trm
475 msec, with the t
msec stePsuntil it rca
is, in the first l0 tn
respond between 3'j
ond l0 trials he or s
325 and 425 msec. tn
275 and 375 msec. ar
remained at 125 to I
were Produced 'r'itl
point the time regrc
hieher values *'ith c
wiitrin the region. '
sponses had becn
responsesfell withrn
the time region cor
remaining trials. ln
no age differenccs I
required in the tro
eni procedure for
functions than Prc
investigations (Saltl
advantages of bein
much more ellicien
Rnsurrs
fc
The resPonscs
TIM E-ACCURACY RELATI ON SHI PS
controlled the presentationof stimuli on a Hew_
lett-Packard model l3llA display with a rapid
decay P3l phosphor and reiorded responses
from, a response_
panel containing two iO_tey
pushbutton telephone keyboards. bnly the bot_
to-m-most (0) key on each keyboard was used.
All temporal measurements were to the nearest
millisecond.
35r
9 8 0
o
o
Procedure. - A 1000-msecfixation stimulus,
o
consistingof four dots in the corners of a square o
with I o sides,was presentedimmediately before a
the target stimulus, which consisted oi a l.5o
diagonal arrow oriented toward the lower left or
lower right of the display. The direction of the
target stimulus was indicated when the partici_
pant depressedthe bottom-most key on ihe left
I
l
(for the leftward pointing arrow) br the right
200
250
3oo
350
400
(for the rightward pointlng arrow) keyboa-rd.
Reaction Time in msec
After the responsewas regisiereda time iine *as
Figure 2. Time-accuracy-operating
characteristic for
displayed in which the dlsired time resion for young and old adults computed by averaging
accuracy
the.responseand the actual responsetiire were a c r o s si n d i v i d u a l sa t e a c h o f s i x t i m e l n t e r v a l i indicated. The participants were instructed to
attempt to respond within the designated time
region regardless of the accuracy that mieht
acrossthe two trial blocks, were grouped in 50result. Two trial blocks were presented, seia- msec intervals from 175 to 475 msec, and the
rated by a_shorrrest period. A tlial block began percentage correct determined within each in_
with the desired tim-e region between 375 and terval. Complete time-accuracy functions, com475 msec, with the time region reduced in 50_ puted by averaging accuracy icross individuals
msec stepsuntil it reached 125to225 msec.That
at each time value, are illustrated in Figure 2.
is, in the first l0 trials the participant was to
Least squares linear regression equati6ns were
respond between 375 and 475 msec, in the sec- fitted to each p_articipanl's data aiter omitting
ond l0 trials he or she was to respond between points at floor (507o)andceiling (l00%o)levels to
325 and 425 msec,in the third l0irials between maximize the fit to a linear equation with at
275 and.375msec,and so forth. The time resion least three pairs of percentage correct and reacremained at 125 to 225 msec until l0 respo-rrses tlon time values.The correlations,indicatine the
-which
were produced within the interval, at
goodness of fit to the linear equation, raiged
point the-time r"€ion increased to successively from .834 to .999 with a median of .960 for'the
higher values with each additional l0 resDonses older adults and ranged from .845 to 1,000with
within the region, or until a total of 250 re- a median of .980 for the younger adults. The
sponses had been produced. If less than l0
mean slopes, reflecting the amount of increase
responsesfell within the designated time region, rn accuracy per millisecond of time, were .270
for young adults and .261 for older adults. t(7g)
the time region continued a-t that level foi all
:
remaining trials. Informal inspection indicated
..46.p > .5O.Time intercepts,computed by
no age differences in the number of responses using the regression parameters to pr-edict the
required in the two age groups. This is a differreaction time at 5OVoaccuracy, averaged 176
ent procedure for generating time-accuracy msec for young adults and 222 msec f6r older
functions. than previously em-ployed in aging a d u l t s ,t ( 7 8 ) : 4 . 7 0 , p < . 0 0 0 1 .
investigations (Salthouse,-t97c;),6ut it has"th6
Correlations were computed within each age
advantages of being easier to understand and group between age, vocabulary score, and dijit
much more efficient in the collection of data.
symbol score and the two dependent variables,
slope and intercept. The correlation between age
and intercept in the older adults was significant
REsurrs
(r : -.335, p < .05), but the directioriwas for
The responsesfor each participant, collapsed increased age to be associated
with faster interc
, w
I
352
SALTHOUSE AND SOMBERG
cepts. Since this is opposite to the overall age
trend, it probably can be dismissed as a sampling
fluctuation. No other correlations were sisnificant in either the older adult or young adult
samples. The lack of significant correlations between the intellectual measures and the dependent measures indicates that there is little relationship between these variables, and, thus, the
differences between the age groups on the intellectual tasks can not be used to explain any
performance differences between the young and
old groups.
DrscussroN
The major result in this experiment is that
young and old adults differ in the intercept but
not the slope of the time-accuracy-operating
characteristic.That is, although older adults require more time than young adults before their
accuracy begins to improve above a chance
level, the rate at which their accuracy increases
is the same as young adults.
The discovery that there is not an age difference in a maJor component of speededperformance is rather unusual in that substantial aee
differences have been found in most speed6d
measures.In view of the moderately large number of individuals in each age group, and the
discovery of a significant difference in the intercept parameter, we do not feel that the lack of
a statistically signihcant difference in the slope
parameter is due to a low-power test. Indeed, we
have computed that in order for the .009 slope
difference to reach the .05 level of sisnificance
with a power of .80, more than 600 iidividuals
in each age group would have been required.
Expressed somewhat differently, if the slope
difference between age groups was l3%, onehalf of the proportional age difference observed
with the time intercept measure, the likelihood
ofdetecting that difference in the current experiment was .95.
Other researchershave used the phrase "rate
of information extraction" in a somewhat different manner than the current usage. The primary manipulation in the earlier studies has
been the amount of information, defined in
information theory terms as the log (base 2) of
the number of stimulus-response alternatives.
Results from these studies have been mixed;
some investigators reported age differences in
only the intercept parameter (e.g., Crossman &
Szafran, 1956; Szafran, 1966), whereas others
reported both intercept and slope differences
(e.g., Suci et al., 1960). Welford (1977), in reviewing these and other similar studies, has offered speculations as to possible reasons for the
discrepancies, but as he himself admits, at the
current time they are merely speculations.There
is not yet any consensusconcerning the effects
ofadult age on the abstract "uncertainty reduction" measuresof information extraction.
In the present context rate of information
extraction simply refers to the amount of increasein classification accuracy per unit of time
with the same set of two possible stimuli and
two possible responses.Since very little information is available when responsesare produced
at chance(507o)accuracybut progressivelymore
information is acquired as accuracy increasesto
the asymptotic level, it seemsreasonableto interpret the slope parameter as a direct measure
of rate of gain of information.
One way of conceptualizing this information
extraction processis to imagine the sampling of
discrete "pieces" (e.g., features, elements, segments) of stimulus information. Accuracy would
be expected to increase in direct proportion to
the number and value of the accumulated pieces
of information. A chanse in either the number
of piecesobtained pe. uiit rime, or in the "quality" (value or relevance) of the pieces, could
lead to differencesin the slope parameter. Based
on the result (e.g.,Link & Tindall, l97l; Pachella & Fisher, 1969: Rabbitt & Vyas, 1970;
Swensson,1972)that the slopesare steeperwith
more discriminable stimuli. which presumably
contain more informative pieces relative to less
discriminable stimuli. it misht be concluded that
the principal mechanism iesponsible for slope
differences is the relevance or quality of the
information pieces extracted at each sample.
The surprising f,rnding of the current study is
that, regardlessof the mechanism primarily responsible for producing slope differences,it apparently is not affected by increased age. Another possibility, considered very unlikely, is
that age differences exist in opposite directions
in the two mechanisms such that they exactly
compensate for one another (e.g., fewer pieces
per unit time but each piece of greater relevance).
It is not clear why the rate of information
extraction or discrimination should be spared
from the effects of increasedage, whereas most
other processesseemto become slower with age.
One possibility is that the extraction processis
automatic and indeg.c
sourcesor capacitr tha
age. A problem in erah
that some researchen
Thomas, 1974)hare .ur
the time-accuracv funcl
processingcapacin. li
cepted,then the presenl
is not an age differenct
and. thus. the automatr
not meaningful in the p
concept of processine ,
generally acceptedfash
appear useful to incorpt
of other phenomena
Further researcht. n
more preciselythe natu
tributing 1s ths 5lope a:
eters. Based oD the prtr
the overall reaction llt
might be considered
However, the markedlt
the two parameters m:
tion desirable. if ft r t
identify and more cl€a
relevant to speeded p
affected by increased a
that should be inrestrc
are sample characten
sample was highlv edu
in verbal abilily) and t,
ent arrow discriminatr
compared with other ti
employed). Until the p
demonstrated to be ee
contexts they must be c
tive despitethe unequr
with the present task a
A secondary result r
is the replication of thc
that adult age differenc
simply be attributed tt
racy emphasis. This .r
frnding that young and
of performance e\.en
made at the same lc
accuracv.
TIM E-ACCURACY RELATI ONSH I PS
automatic and independent of processing re_
sourcesor capacity that may be declinineiith
a.ge.A problem in evaluating this hypothlsis is
that some researchers 1e.g.] S*eni ion, 1972;
Thomas, 1974)have sugges-ted
that the slope of
the time-accuracy function is itself a measu'reof
processingcapacity. If this interpretation is ac_
cepted,then the presentresultssuggestthat there
rs not-an age difference in procesiing capacity,
and. thus. the automaric efiortful diitinciion is
not meaningful in the present context. Until the
concep_tof processing capacity is defined in a
generally acceptedfashion, therefore, it does not
appear useful to incorporate it in ..explanations',
of other phenomena.
353
RrrrnrNcrs
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age in
the speed of information_intake and disirimination.
In
verzT 1Ed.-\.E-xperimental research in ageiil,
wrr<!h a u s e r ,
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_Speedand accuracy rn
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matron processtngresearch.In B. Kantowitz (Ed).
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m.oreprecisely the nature of the operations con_
man information processing: Tutorials in performance
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and
accuracy in absolutejudgments. Journal of Experimenmt
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Psychologlt, 1969. I l. 7 -9.
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identify and more clearly understand processes Pew. R. W. The speed-accuracyoperating characteristic.
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-to speeded peribrmance that' are not Rabbitt. P. M.^A., & Vyas. S. M. An elementary preliminary
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that should be investigited with ihis technique
Acta Psychologica. 1970. J3. 56 _76.
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rn verbal ability) and task complexity (the pres_
A comparative-influence stage analysii techniqle.
-is
zcta
ent arrow discrimination task
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J0, I r4-r
clemonstratedto be generalizabletd these other Suci, G. J., 1 8 .
Davidoff, M. D., & Surwillo, W. W. Reactron
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Swensson,R. G. The elusive-tradeoffJSpeed vs. accuracy
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rs the replicationof the Salthouse(lg7c])finding Szafran, J. Age differences in the rate ofgain ofinformation,
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