The Processing-Speed Theory of Adult Age Differences in Cognition

Transcription

1 Psychologicl Review Copyright 1996 by the Americn Psychologicl Assocition, Inc. 1996, Vol. 103, No. 3, X/96/$3.00 The Processing-Speed Theory of Adult Age Differences in Cognition Timothy A. Slthouse Georgi Institute of Technology A theory is proposed to ccount for some of the ge-relted differences reported in mesures of Type A or fluid cognition. The centrl hypothesis in the theory is tht incresed ge in dulthood is ssocited with decrese in the speed with which mny processing opertions cn be executed nd tht this reduction in speed leds to impirments in cognitive functioning becuse of wht re termed the limited time mechnism nd the simultneity mechnism. Tht is, cognitive performnce is degrded when processing is slow becuse relevnt opertions cnnot be successfully executed (limited time) nd becuse the products of erly processing my no longer be vilble when lter processing is complete (simultneity). Severl types of evidence, such s the discovery of considerble shred ge-relted vrince cross vrious mesures of speed nd lrge ttenution of the ge-relted influences on cognitive mesures fter sttisticl control of mesures of speed, re consistent with this theory. The purpose of the current rticle is to describe, nd discuss the evidence relevnt to, the processing-speed theory of cognitive ging phenomen. The fundmentl ssumption in the theory is tht mjor fctor contributing to ge-relted differences in memory nd other spects of cognitive functioning is reduction with incresed ge in the speed with which mny cognitive opertions cn be executed (Slthouse, 1985b). In this rticle, discussion of evidence relevnt to the theory is restricted to the dult portion of the life spn, but the bsic mechnism my be relevnt cross the entire life spn becuse similr ides hve been proposed by Kil (e.g., 1986, 1991; Kil & Prk, 1992 ) regrding the development of cognitive functioning during childhood. Becuse the success of theory cnnot be evluted if the gol one hopes to chieve is never clerly specified, I begin by briefly describing the phenomenon tht the present theory is intended to explin. Some of the best-documented findings in the literture on ging nd cognition re the ge-relted differences in Type A (Hebb, 1942) or fluid (Cttell, 1943; Horn, 1982; Horn & Cttell, 1963) cognition, which include wide vriety of mesures of memory, resoning, nd sptil bilities. The reltions between ge nd cognition hve been well documented since the erliest mentl testing of dults (e.g., Foster & Tylor, 1920; Jones & Conrd, 1933), nd they re redily pprent in the results from the stndrdiztion dt in psychometric nd neuropsychologicl test btteries (e.g., see Slthouse, 1991c, chp. 2, for review). Becuse the smples for the stndrdiztion dt in these test btteries re typiclly lrge nd representtive, nd becuse the performnce mesures re Preprtion of this rticle ws supported by Ntionl Institute on Aging Grnt R37 AG I would like to thnk John Dunlosky, Julie Erles, Dn Fisk, Leh Light, Ulmn Lindenberger, nd Dvid Mdden for helpful comments on erlier versions of this rticle. Correspondence concerning this rticle should be ddressed to Timothy A. Slthouse, School of Psychology, Georgi Institute of Technology, Atlnt, Georgi Electronic mil my be sent vi Internet to tim.slthouse@psych.gtech.edu. of estblished relibility nd spn brod rnge of cognitive bilities, the generl phenomenon of negtive reltions between ge nd Type A or fluid cognition cn be considered quite robust. Performnce on tests of cognitive bility is lso meningful trget or criterion phenomenon becuse cognitive btteries hve proven useful for prediction nd ssessment outside of the lbortory nd in noncdemic settings (e.g., Ghiselli, 1973; Hunter & Hunter, 1984). A focus on cognitive test performnce therefore provides reltively prsimonious linkge to relworld ctivities. The prediction is not perfect, but significnt reltions to rel-world functioning hve been empiriclly estblished; thus, if the ge-relted influences on these mesures cn be explined, t lest some of the ge-relted effects in extrlbortory ctivities might lso be explinble (Slthouse, 1992c). Although the rnge of cognitive mesures is extensive, it is importnt to emphsize tht the present gol is not to explin ll determinnts of cognitive functioning but, rther, to ccount for the differences in cognitive functioning tht re systemticlly relted to dult ge. The phenomenon to be explined is thus the ge-relted vrition in behvior, nd not the behvior itself (Slthouse, 1991 c, 1992d). Ultimtely, of course, more comprehensive theories should encompss ll dimensions of cognitive phenomen, but n explntion of the reltions between dult ge nd Type A or fluid spects of cognition is by itself n extremely formidble gol t the present time. The rticle is orgnized in two mjor sections. The first section summrizes the primry ssumptions of the processingspeed theory. Evidence relevnt to criticl hypotheses of the theory is then described in the second section. Theoreticl Assumptions One substntive ssumption of the current perspective is tht performnce in mny cognitive tsks is limited by reltively generl processing constrints, in ddition to restrictions of knowledge (declrtive, procedurl, nd strtegic), nd vri- 403

2 404 SALTHOUSE tions in the efficiency or effectiveness of specific processes. Some relevnt limittions my be prtilly overcome by experience, nd indeed one view of expertise is tht it serves to circumvent processing constrints or limittions (Slthouse, 1991). Nevertheless, it is ssumed tht generl limittions frequently impose constrints on mny types of processing nd, hence, tht they hve consequences for the performnce of lrge vriety of cognitive tsks. It is sometimes sserted tht generl mechnisms re not plusible s explntions of dult ge differences in cognitive functioning becuse of evidence presumed to implicte selective or differentil ge-relted effects, such s Age X Tretment sttisticl interctions. However, the ssumption of one or more firly generl ge-relted fctors does not preclude the occurrence of significnt interctions becuse interctions cn originte s result of () the existence of specific or locl ge-relted influences in ddition to the hypothesized brod or generl influences (Slthouse, 1992d), (b) differentil relince of processes or mesures on the generl or common fctor(s) (e.g., Slthouse & Coon, 1994), (c) multiplictive or proportionl influence of the generl fctor(s) such tht the bsolute differences between ge groups increse with the mgnitude of the tretment effect (e.g., Cerell, 1990; Cerell, Poon,& Willims, 1980; Slthouse, 1985), or (d) sttisticl rtifct ttributble to differentil discriminting power (e.g., relibility, power, nd region in the mesurement rnge) of the vribles (e.g., Slthouse, 1985b, 1991c). Prticulrly when one does not ssert tht generl fctors re the exclusive source of ge-relted differences in cognition, therefore, the existence of wht pper to be selective or differentil ge-relted effects in the form of sttisticl interctions is not t ll inconsistent with the existence of common or generl fctors. A second substntive ssumption of the processing-speed theory is tht speed of processing is criticl processing constrint ssocited with incresed ge. From the current perspective, the speed with which n individul performs cognitive ctivity is not simply function of the processes required in tht ctivity but lso reflection of his or her bility to rpidly crry out mny different types of processing opertions. A slower speed of executing mny cognitive opertions is not ssumed to be the exclusive source of ge-relted differences, becuse other gerelted influences re lso postulted to exist. Nevertheless, reduction with incresed ge in the speed with which mny cognitive opertions cn be executed is hypothesized to be mjor contributor to the dult ge differences in mny mesures of cognition ( Slthouse, 1980, 1985b, 1991 b, 1992b, 1994d). ~ Becuse this is fundmentl spect of the theory, much of the reminder of the rticle is devoted to the elbortion nd justifiction of this ssumption. Two distinct mechnisms re postulted to be responsible for the reltion between speed nd cognition. The limited time mechnism is ssumed to operte becuse relevnt cognitive opertions re executed too slowly to be successfully completed in the vilble time, nd the simultneity mechnism is hypothesized to operte becuse slow processing reduces the mount of simultneously vilble informtion needed for higher level processing. A metphor for the limited time mechnism is n ssembly line becuse if relevnt processing opertions re not successfully completed within prticulr tempo- rl window, then the qulity of the finl product is likely to be impired becuse lter processing opertions would be either less effective or only prtilly completed. Some type of juggling ctivity might be metphor for the simultneity mechnism becuse the fundmentl principle is tht mny complex ctivities require synchroniztion of the constituent tsks, nd synchroniztion is esier when the relevnt processing opertions cn be executed rpidly. Limited Time Mechnism The bsis for the limited time mechnism is simply tht the time to perform lter opertions is gretly restricted when lrge proportion of the vilble time is occupied by the execution of erly opertions. This mechnism is primrily relevnt when there re externl time limits or other restrictions on the time vilble for processing, such s the presence of concurrent demnds on processing. Some cognitive tsks (or tests) hve reltively low level of difficulty, such tht the primry determinnt of individul differences in performnce is likely to be the speed of performing relevnt opertions. For these types of tsks no specil explntion ppers to be needed to ccount for the reltion between speed nd mesures of very simple cognition becuse performnce on the cognitive mesure could merely be nother mnifesttion of slow processing. The limited time mechnism my lso operte in more complicted cognitive tsks in which the qulity or ccurcy of performnce is ffected by the number of opertions (e.g., ssocitions, elbortions, nd rehersls) tht cn be crried out in the vilble time (Slthouse, 1980, 1982; Slthouse & Kil, 1983). If complex opertions re dependent on the products of simpler opertions, nd fewer of those products re vilble becuse of slower execution speed, the effects of slow processing cn be expected to be most pronounced on the speed nd ccurcy of complex opertions. A mechnism of this type my therefore ccount for wht is sometimes referred to s the complexity effect, or the positive reltion between tsk complexity nd the mgnitude of ge differences in both speed nd ccurcy mesures of tsk performnce (Slthouse, 1982, 1985b, 1991 c; Slthouse & Kil, 1983). Becuse grdul reduction in the speed of bsic processes with incresed ge is likely to be ccompnied by numerous dpttions, the consequences of slower processing re not lwys esy to predict (Slthouse, 1985b). This point cn be illustrted by considering wht my be n nlogous sitution in reverse, in the form of the evolutions of computer progrms tht hve occurred s successive genertions of computers hve become progressively fster nd more powerful. The enormous increses in performnce hve not simply been ttributble to increses in the speed of executing the sme progrms, becuse mjor modifictions in the nture of the progrms hve lso Note tht not ll cognitive opertions re ssumed to be necessrily ffected by slower processing nd tht role for nonspeed influences is explicitly cknowledged. The theory described here is thus not ccurtely chrcterized by clims such s the following: "Slowing of informtion processing.., is single mster fctor underlying involutionl chnges in ll cognitive skills" (Nettelbeck & Rbbitt, 1992, p. 191 ).

3 PROCESSING-SPEED THEORY 405 occurred to cpitlize on the fster speed ( nd lrger memories) of newer computers. Similr types of dpttions in the form of ltertions in strtegy, relince on prestored solutions insted of novel problem solving, nd so forth could lso occur in the humn processing system s it becomes progressively slower nd less efficient with incresed ge. Despite the complictions ssocited with identifying ll of the consequences of slower rte of processing, however, the bsic principle underlying the limited time mechnism is quite simple; nmely, more processing frequently results in higher levels of performnce, nd the opportunity to ccomplish lrger mount of processing is greter when the speed of processing is fster. Simultneity Mechnism The second hypothesized mechnism for the reltion between processing speed nd qulity of cognitive performnce is bsed on the ide tht the products of erly processing my be lost by the time tht lter processing is completed. To the extent tht this is the cse, relevnt informtion my no longer be vilble when it is needed. Processing deficits could therefore emerge becuse of discrepncies between the time course of loss of informtion nd the speed with which criticl opertions such s encoding, elbortion, serch, rehersl, retrievl, integrtion, or bstrction cn be executed (Slthouse, 1982, 1985b, 1988, 1992b). A key ssumption of the simultneity mechnism is tht informtion decreses in vilbility (i.e., quntity or qulity) over time s function of either decy or displcement. Moreover, under rpidly chnging conditions, the informtion could lso become obsolete in tht it my no longer be ccurte or pertinent by the time it becomes vilble. In either cse, when the rte of executing opertions is slow, relevnt informtion is less likely to be useful becuse it is more impoverished or degrded by the time tht preceding opertions re finlly completed. Moreover, this will occur regrdless of the mount of time llowed for processing becuse the criticl limittions re bsed on internl dynmics rther thn on the reltion between internl (i.e., processing speed) nd externl (e.g., stimulus presenttion time) fctors. Performnce on tsks ssumed to ssess working memory cpcity might be postulted to reflect functioning of the simultneity mechnism becuse working memory is sometimes conceptulized s consisting of informtion tht is currently vilble for storge or processing, or both. However, it is importnt to distinguish the mount of simultneously vilble informtion, which my be indexed by mesures of working memory, from possible cuses of ge-relted reductions in tht mount. A criticl hypothesis in the processing-speed theory is tht n ge-relted decrese in speed is one of the mjor cuses of the vritions in working memory ssocited with incresed ge (e.g., Slthouse, 1992; Slthouse & Bbcock, 1991 ). As discussed lter, there is considerble evidence in support of this hypothesis becuse sttisticl control of mesures of processing speed hs been found to gretly reduce the mount of ge-relted vrince in mesures of working memory (see lso Slthouse, 1994b). From the perspective of the processing-speed theory, it is the slower speed of ctivting or processing informtion rther thn the rte of informtion loss or decy tht is primrily responsible for ge-relted consequences of the simultneity mechnism (Slthouse, 1992, 1994b; Slthouse & Bbcock, 1991 ). In fct, reserch with tsks such s continuous recognition or continuous pired-ssocites memory suggests tht forgetting functions re very similr cross the dult ge rnge (see Slthouse, 1992, for review). However, it should be noted tht simultneous vilbility of informtion cn lso be reduced becuse of disruptions in the synchroniztion of neurl signls or ptterns of ctivtion, nd not only becuse of chnges in the rtes of decy or informtion loss. For exmple, ltertions in the vribility of timing t elementry levels might lso led to decreses in the quntity or qulity of informtion bsed on multiple intercting inputs. The simultneity mechnism should therefore not simply be viewed s ttributble to forgetting becuse ny fctor tht ffects the synchroniztion of relevnt inputs lso hs the potentil to lter the mount (nd qulity) of simultneously vilble informtion. The importnce of simultneous vilbility of relevnt informtion is not novel ide, becuse it hs been mentioned in one form or nother for t lest 60 yers. For exmple, the concept is similr to specultions by Eysenck ( 1987 ), Jensen (e.g., 1982, 1987 ), nd Vernon ( 1983, 1987 ). The ide of trde-off between loss of informtion nd speed of relevnt processing is lso fundmentl to the notion of n rticultory loop in Bddeley's (e.g., 1986) model of working memory. Anlogous rguments in discussions relted to ging hve been mde by Birren (e.g., 1965, 1974) nd Jones (1956). To illustrte, Jones ( 1956, p. 138) suggested tht problem-solving effectiveness is impired when lower level opertions re too slow nd erlier steps re lost before the relevnt informtion cn be integrted. Perhps the first discussion of the simultneity mechnism ws in the following pssge by Lemmon (1927): It is possible tht the qulity of intelligence my depend upon the number of connections, but lso upon the speedwith which those connections re formed. Nerve centers (e.g., ssocition centers) cnnot remin excited indefinitely t mximum intensity; consequently in the cse of the person who forms connections slowly it is possible tht the excittion of the first ssocition centers to be ffected will hve diminished nd disppered before the ltter centers come into ply. Thus only limited number of centers re cooperting t ny one time. The person who forms connections quickly, however, is pt to hve more ssocition centers intercting t once, since the lter centers re roused before the erlier ones hd chnce to lose their effectiveness. But the most intelligent response is, in generl, the one in which the determintion of which the gretest number of fctors hve been tken into considertion. In neurl terms this my well men the response in the determintion of which the gretest number of ssocition centers hve cooperted, nd the number of simultneously ctive centers my in turn depend to some extent upon the speed with which nervous impulses re conducted from center to center nd through synpses within the centers. (p. 35) Another erly description of the simultneity mechnism ws provided by Trvis nd Hunter ( 1928 ): Intelligence is probbly best defined s the bility to see reltionships nd menings by hving ccess to s mny lterntives or judgments s possible t pproximtely the sme instnt of time. This would necessitte the rection ptterns which subserve the

4 406 SALTHOUSE judgments to be ctive within n extremely short intervl of time. The "feeble-minded" individul hs reltively speking, such slow conduction rte tht one rection pttern becomes inctive by the time nother becomes ctive, thus doing wy with the very fctor, reltive simultneity of ctivity, which mkes possible the seeing of reltionship between idetionl elements. (p. 352 ) An importnt impliction of the simultneity mechnism is tht the dynmic cpcity of processing "structures" or "systems" such s working memory will be ffected, with likely impirments of higher order processes such s bstrction, elbortion, or integrtion, becuse not ll of the relevnt informtion will be vilble in usble form when it is needed (Slthouse, 1992b). Furthermore, degrdtion of these processes will led either to incresed errors or to time-consuming repetitions of criticl processing opertions (cf. Myr & Kliegl, 1993). Speed effects on cognitive functioning thus my be indirect becuse they lter the effectiveness of process (such s bstrction, elbortion, or integrtion) tht directly ffects cognitive performnce. Becuse the simultneity mechnism is so fundmentl, it could hve n impct on mny spects of cognition, including performnce in tsks without externl time constrints. From the current perspective, therefore, Pek nd Boring (1926) were correct in suggesting tht power tests re not necessrily those tht do not involve speed but my simply be those tht do not tke speed into ccount. Some evidence of the sufficiency of the simultneity mechnism cn be obtined from computtionl models incorporting vritions in the speed of propgtion of ctivtion or in the speed of firing productions (e.g., Slthouse, 1985b, 1988; see lso McKy & Burke, 1990, for dditionl discussion of very similr mechnism). Prediction of the specific consequences of processing-speed limittion requires detiled understnding of, or willingness to mke mny ssumptions bout, the processes involved in prticulr tsk. It my lso be difficult to distinguish the contribution of other spects of the model from the speed prmeter being mnipulted for the prticulr consequences tht re predicted. Tht is, the consequences could vry ccording to the type of processing lgorithm or representtion system used, even when the method of mnipulting the criticl vrible, in this cse processing speed, is identicl (cf. Slthouse, 1988). Despite these limittions, the bsolute differences in vrious indexes of performnce between fst nd slow processing systems re often lrger when the mount of processing increses (Slthouse, 1988). Furthermore, if there re externl time limits on the usefulness (i.e., ccurcy or relevnce) of the informtion or decreses in its vilbility becuse of displcement or decy, then qulittive impirments in certin types of processing cn lso be expected. It is lso noteworthy tht n importnt chrcteristic of reduction in processing speed exhibited by computtionl models is grceful degrdtion of performnce (Slthouse, 1985b, 1988). Tht is, reductions in the speed of processing seldom result in the totl or ctstrophic loss of prticulr kind of processing but, insted, tend to led to brod or diffuse reduction in the efficiency of mny types of processing. At lest in reltively generl mnner, therefore, nlyses of speed mnipultions in computtionl models re consistent with the ssumptions of the processing-speed theory. In summry, two mechnisms hve been postulted to c- count for the speed-cognition reltion. The principle underlying the limited time mechnism is tht necessry opertions my not be completed if the processing is slow. The simultneity mechnism is bsed on the ide tht if the processing is too slow, then not ll relevnt informtion will be vilble when needed, leding to impirments of criticl opertions tht could result in either high rte of errors or time-consuming repetitions of criticl opertions. Evidence Empiricl evidence relevnt to the processing speed theory is discussed in the context of three mjor hypotheses: () Agerelted slowing is not exclusively determined by specific nd independent deficits; (b) processing speed functions s meditor of some of the reltions between ge nd mesures of cognitive functioning; nd (c) the limited time nd simultneity mechnisms re primrily responsible for the reltions between speed nd cognitive functioning. However, before discussing these hypotheses, I briefly summrize the ge-relted slowing phenomenon, nd describe the method by which processing speed hs been ssessed. Slowing with ge is often considered one of the best-documented nd lest controversil behviorl phenomen of ging. One illustrtion of the slowing phenomenon is the medin correltion of.45 between ge nd mesures of speed cross very wide rnge of behviorl ctivities reported by Slthouse (1985). The ge-relted slowing phenomenon is lso evident in nlyses of the ge trends from perceptul speed tests in psychometric test btteries such s the Digit Symbol Substitution Test from the Wechsler Adult Intelligence Scle-Revised (see Slthouse, 1992e) nd the Visul Mtching nd Cross Out Tests from the Woodcock-Johnson Cognitive Ability Tests (see Kil & Slthouse, 1994). Performnce in the Finding A's nd Identicl Pictures tests (Ekstrom, French, Hrmn, & Dermen, 1976) hs lso been found to be negtively relted to ge in both cross-sectionl nd longitudinl comprison, by Schie (1989) nd Schie nd Willis (1993). Not only hve these reserchers reported pronounced ge trends in ech type of comprison, but Schie (1989) hs suggested tht, in contrst to the sitution with mny cognitive vribles, the ge-relted declines re ctully greter in longitudinl comprisons thn in cross-sectionl comprisons. Figure 1 illustrtes the ge-relted slowing phenomenon with dt from smple of 221 dults between 20 nd 80 yers of ge (Slthouse, 1993b, Study l) on two pper-nd-pencil perceptul speed tsks (i.e., Letter Comprison nd Pttern Comprison, described subsequently). The verticl xis in this figure is the verge of the two perceptul speed mesures expressed in stndrd devition units, with higher scores representing fster performnce. These results re typicl of mny in the literture in tht strong systemtic reltion is usully found in which incresed ge is ssocited with lrgely monotonic, nd pproximtely liner, decrese in speed of performnce. Becuse the processing speed construct is fundmentl to the theory, it is importnt to consider how this construct hs been ssessed in recent studies. Severl criteri hve been proposed to guide the selection of mesures used to ssess processing speed (e.g., Slthouse, 1985b, 1991c, 1992b). For exmple, one

5 PROCESSING-SPEED THEORY I z = (Age), r2=.371 I ee QO "" I /.'.,,'. o ' -'t ":. I ~ o -2-3 Chronologicl Age Figure/. Reltion between ge nd composite mesure of processing speed (dt from Slthouse, 1993b, Study 1 ). criterion is tht the tsks used to ssess processing speed should be reltively simple, such tht most of the individul differences in performnce re ttributble to how quickly one cn crry out the relevnt opertions rther thn to vritions in mount of knowledge or in other cognitive bilities. When more complex mesures re used, such s lexicl decision speed or reding speed (e.g., Hrtley, 1986, 1993; Hultsch, Hertzog, & Dixon, 1990; Hultsch, Hertzog, Smll, McDonld-Miszczk, & Dixon, 1992), it is difficult to determine how much of the vrition in the mesures is due to differences in the speed with which elementry cognitive opertions cn be executed s opposed to differences in the qulity or quntity of semntic knowledge or differences in the level of more generl verbl bilities. However, the speed mesure should not merely represent input nd output processes or sensory nd motor processes, or else it my not reflect the durtion of relevnt cognitive opertions. Finlly, s with the ssessment of ny theoreticl construct, it is generlly desirble tht the construct be evluted with severl mesures to minimize the specific vrince ssocited with single mesures nd to emphsize the common, construct-relevnt vrince. Relince on multiple mesures lso hs the dvntge of incresing the relibility of the ssessment becuse of ggregtion (Rushton, Brinerd, & Pressley, 1983 ). Much of the reserch described subsequently hs used vrious combintions of seven mesures to ssess processing speed. One mesure is the score on the Digit Symbol Substitution Test (Wechsler, 1981 ). This is pper-nd-pencil test consisting of code tble with pirs of digits nd symbols nd rows of double boxes with digit in the top box nd nothing in the bottom box. The tsk for the reserch prticipnt is to refer to the code tble to write the symbol in the bottom box tht is ssocited with the digit in the top box. Performnce on the test is represented by the number of correct symbols written in 90 s. Two perceptul speed mesures require comprisons of pirs of letters (Letter Comprison) or pirs of line ptterns (Pttern Comprison). In ech cse, the pper-nd-pencil test form consists of pirs of items with horizontl line between the members of the pir. The tsk for the prticipnt is to write n S (for sme) or D (for different) on the line between the two members of the pir nd to complete s mny of the items s possible within specified time (usully 30 s). Two dditionl pper-nd-pencil tests were designed to involve miniml cognitive opertions, but with stimulus nd response requirements similr to the perceptul speed tests. One mesure (Digit Copying) ssesses how quickly individuls cn copy digits, nd nother (Boxes) ssesses how quickly they cn drw lines in specified loctions. Finlly, in severl projects processing speed hs been ssessed with two computer-dministered rection time tsks. These tsks re bsed on the Digit Symbol Substitution Test in tht they consist of code tble t the top of the screen nd probe stimulus in the middle of the screen. In the Digit Symbol version of the tsk, the code tble contins pirs of digits nd symbols, nd the probe stimulus consists of single digit-symbol pir. In the Digit Digit version of the tsk, the code tble contins pirs of identicl digits, nd hence is superfluous, nd the probe stimulus consists of single pir of digits. In both tsks, the reserch prticipnt is to press one key on the keybord if the probe stimuli mtch, either with respect to ssocitionl equivlence (Digit Symbol) or in terms of physicl identity (Digit Digit), nd to press different key if they do not mtch. In ddition to exhibiting moderte to lrge reltions with ge ( see lter discussion), ll of these mesures hve been found to hve respectble test-retest relibilities. To illustrte, in smple of 240 dults between 19 nd 82 yers of ge (Slthouse, 1994, Study 1 ), the immedite test-retest correltions were.86 for Boxes,.86 for Digit Copying,.58 for Letter Comprison,.73 for Pttern Comprison,.61 for Digit Digit rection time, nd.93 for Digit Symbol rection time. Vlues from smple of 131 dults between 17 nd 79 yers of ge (Slthouse, Fristoe, Linewever, & Coon, 1995, Study 2) were.93 for Boxes,.93 for Digit Copying,.60 for Letter Comprison,.78 for Pttern Comprison,.69 for Digit Digit rection time, nd.89 for Digit Symbol rection time. Hypothesis 1: Age-relted slowing is brod phenomenon nd is not simply ttributble to specific nd independent processing deficits. A key hypothesis of the processing-speed theory is tht gerelted speed differences of the type just discussed originte t lest prtilly becuse of smll number of firly generl or common fctors rther thn exclusively from lrge number of specific nd locl fctors. One reson for the ssumption of substntil shred or common influence is tht mny mesures of processing speed hve been found to be relted to incresed ge, nd not merely those restricted to few tsks or to few types of cognitive opertions. More importnt, evidence discussed lter indictes tht the ge-relted influences on mny speed mesures re not independent but, insted, hve considerble shred or common vrince. There re two primry implictions of the hypothesis tht common ge-relted influences contribute to mesures of processing speed. The first is tht it should be possible to predict the ge differences in prticulr speed mesures from knowledge of the ge differences in other speed mesures. The second impliction is tht the ge-relted effects in different speed mesures re not expected to be independent, rther, they re s-

6 408 SALTHOUSE sumed to hve considerble mount of shred ge-relted vrince. Anlyticl procedures bsed on the exmintion of systemtic reltions nd on sttisticl control techniques cn be used to exmine these implictions. Anlyses of Systemtic Reltions In recent yers, there hs been considerble interest, nd controversy, regrding the existence nd interprettion of systemtic reltions between men levels of performnce in different ge groups (e.g., Cerell, 1985, 1990, 1991, 1994; Fisk & Fisher, 1994; Fisk, Fisher, & Rogers, 1992; Hle, Lim, & Myerson, 1991; Lver & Burke, 1993; Mdden, Pierce, & Allen, 1992, 1993; Myr & Kliegl, 1993; Myerson, Hle, Wgstff, Poon,& Smith, 1990; Myerson, Wgstff, & Hle, 1994; Perfect, 1994). The method of exmining ge-comprtive dt in which the tsk or condition mens of one group re plotted ginst those of nother group ws originlly described by Brinley (1965), who used it to express reltions with both ccurcy mesures nd speed mesures. Most subsequent reserchers using this method hve focused on speed mesures, nd heted debtes hve risen concerning the mening of these reltions. One of the mjor issues of contention is whether the primry contribution of portrying condition mens of two groups s function of one nother is to illuminte globl ge-relted influences or to obscure specific ge-relted effects. From the perspective of the processing-speed theory, systemtic reltions re interesting primrily becuse of their potentil to generte estimtes of the reltive contributions of generl nd specific, or common nd unique, ge-relted influences. Tht is, given certin ssumptions, the reltions between the men levels of performnce in two ge groups my llow distinction between common nd unique ge-relted effects (Slthouse, 1992b, 1992d). The rtionle hs been described s follows: Only if t lest some of the ge-relted effects on ech vrible were determined by fctor common to other relevnt vribles does it seem resonble to expect ge differences on one vrible to be relted to ge differences on other vribles. "'Generl" or "common" in this context thus implies lck of independence, in the sense tht knowing the mgnitude of the ge differences on one vrible provides informtion bout the mgnitude of the ge differences on other vribles. (Slthouse, 1992d, p. 330) One ppliction of systemtic reltion nlyses to distinguish common nd unique ge-relted influences ws described by Mdden et l. ( 1992; see lso 1993). These investigtors used the performnce of young dults nd the systemtic reltions from set of vribles to predict the men vlues of older dults in given condition. The method is bsed on the ssumption tht the systemtic reltion reflects the influence of the common or generl speed fctor for tht smple nd those vribles. If this ssumption is vlid, then djusting ech score of the members of one ge group by the prmeters of the function relting the men scores in the two groups cn be interpreted s removing the common or generl influence. If the djustment does in fct eliminte the effects of the common or generl fctor, then the mgnitude of the remining differences between the originl scores in one group nd the djusted scores in the other group provides n estimte of the contribution of unique or specific ge-relted influences on the trget vrible (Sithouse, 1991 c, 1992b, 1992d). A similr method ws pplied in recent study by Slthouse nd Kersten (1993), nd it resulted in the elimintion of most of the ge-relted differences cross vriety of speed mesures. Furthermore, very similr results were obtined even when the djustment ws bsed on different types of speed tsks (i.e., those derived from pper-nd-pencil procedures rther thn from rection time tsks). This outcome not only is consistent with the existence of the hypothesized common speed influence but suggests tht, for some mesures, nerly ll of the ge-relted influences my be ttributble to the common or generl fctor. One possible objection to the djustment of scores by the prmeters of the systemtic reltion is tht this method my not be very sensitive to specific ge-relted effects tht re smll reltive to ny generl ge-relted influences tht might exist (e.g., Fisk et L, 1992). Although this concern is vlid, exceptions to the generl pttern were detected in both the Mdden et l. (1992) nd the Slthouse nd Kersten (1993) studies. For exmple, in the Slthouse nd Kersten (1993) study, the time tken by older dults to perform the Digit Symbol rection time tsk fter n opportunity to lern the ssocitions between digit-symbol pirs ws greter thn tht expected from the systemtic reltion. According to the resoning underlying the nlyticl method, therefore, it cn be inferred tht specific or unique ge-relted influences contributed to the ge differences on this mesure, in ddition to the generl or common influences tht were postulted to be responsible for the systemtic reltion. It is importnt to note tht the reltions between the men performnce of young nd old dults need not be described by single function to produce moderte to high levels of predictbility. Tht is, lthough some reserchers hve relied on the number of distinct quntittive functions relting the performnce of young nd old dults s the bsis for distinguishing between generl nd specific ge-relted effects or between single nd multiple speed fctors (e.g., Kliegl, Myr, & Krmpe, 1994; Lim, Hle, & Myerson, 1991; Myr & Kliegl, 1993; Myerson et l., 1990), distinctions mong lterntive functions re only of secondry interest from the current perspective. The question of primry importnce in the processing-speed theory is the extent to which the ge-relted effects in some vribles re independent of, or not predictble from, the ge-relted effects in other vribles. If there is considerble independence nd lck of predictbility, then specific influences would be inferred to predominte over generl or common influences. In contrst, if the vribles were found to shre lrge proportion of their ge-relted vrince, nd if the ge differences in some vribles were highly predictble from the ge differences in other vribles, then generl or common influences would be inferred to be of greter reltive importnce. This rgument cn be illustrted with dt from two conditions in speeded verifiction rithmetic tsk (Slthouse & Coon, 1994, Study 2). Between zero nd seven rithmetic opertions were presented in this study in either sequentil condition (e.g., = 2; flse) or hierrchicl condition in which temporry preservtion of intermedite products ws required (e.g., [5-3) + 4] - 1 = 4; flse).

7 PROCESSING-SPEED THEORY V s s" o Seq~ntil Hierrchicl "6" E ~ I-- u) c o o. O9 CC ~D Old ~ -o~4.~".o r ==.99 2 I 0 0 I I I I I I I I I Young Response Time (sec) Figure 2. Men time of older dults s function of men time of young dults in sequentil nd hierrchicl rithmetic tsks (dt from Slthouse & Coon, 1994, Study 2 ). The systemtic reltion functions for the sequentil nd hierrchicl rithmetic dt in this study re portryed in Figure 2. Seprte regression lines re illustrted for the conditions in ech tsk becuse the interction of condition (sequentil or hierrchicl) with time of the young dults ws sttisticlly significnt (cf. Slthouse, 1985, 1991 c, 1992d, 1992f). Becuse ll prticipnts in this study lso performed two pper-nd-pencil perceptul speed tsks (Letter Comprison nd Pttern Comprison) nd two rection time tsks (Digit Digit nd Digit Symbol), rtios of perceptul speed nd rection time speed mesures were computed to serve s dditionl estimtes of the hypothesized generl speed fctor for these prticipnts. Tble 1 summrizes the ctul (originl) group differences for ll speed mesures nd the differences between ctul vlues nd predicted vlues for older dults fter djustments for the generl influence ccording to ech of the equtions shown in the notes to the tble. The vlues in the tble re d units, which correspond to the men difference between the groups divided by the pooled stndrd devition (Cohen, 1988 ). Inspection of Tble 1 revels tht lmost ll of the differences involving n djustment re smller thn the initil differences (i.e., the men effect size for the originl scores ws 1.75 units, nd the grnd mens for ll other conditions, displyed in the tble notes, were between nd 0.40). The degree of prediction is certinly not perfect, nd exmintion of the mesures with consistently lrge residul differences my be informtive bout the nture of the specific ge-relted influences operting in these vribles. However, the importnt point for the current rgument is tht the mgnitude of the ge differences in nerly every vrible ws gretly reduced fter djusting for the estimted contribution of common speed fctor. On verge, therefore, there ppers to be moderte predictbility of the ge differences in certin speed mesures from knowledge of the pttern of ge differences in other speed mesures. Becuse there were different systemtic functions in Figure 2, it is informtive to exmine the degree to which the ge-relted vrince in the mesures from these conditions ws independent. Tht is, even though there re distinct quntittive reltions for the sequentil nd hierrchicl mesures, it is possible to exmine the mount of ge-relted vrince the mesures from the two functions hve in common. Estimtes of the shred ge-relted vrince cn be derived by determining the proportion of ge-relted vrince in the mesures from the condition with the lrger ge differences (i.e., hierrchicl ) tht is shred with the mesures from the condition with the smller ge differences (i.e., sequentil). Moreover, these computtions cn be crried out both for the men vlues cross ech condition nd for pirs of mesures with the sme number of rithmetic opertions. Results of the computtions re summrized in Tble 2. Two points should be noted bout the entries in this tble. First, estimtes of the shred ge-relted vrince re modertely high, with n estimte of.871 bsed on the computtions of the men vlues nd men cross estimtes from different

8 410 SALTHOUSE Tble l Effect Sizes Before nd After Adjustment for the Influence of Generl Speed Fctor Number of rithmetic opertions Condition M Sequentil Originl 2.15* 2.05* 1.59" 1.56" 1.43" 1.28* 1.09* 1.29" 1.56 Eqution I b * -0.95* -0.92* " -0.88* Eqution 2 c 0.64* 0.57* * -0.62* -0.78* -0.60* Eqution 3 o Eqution 4 e l* * " " " " Eqution 5 r 1.16* 0.75* * l* * - I. 18* * Hierrchicl Originl 2.24* 2.30* 2.08* 1.76" 1.92* 1.76* 1.82" 1.67" 1.94 Eqution I b * * * Eqution 2 c 0.69* 0.81" * 0.69* 0.86* 0.62* 0.68 Eqution 3 d * 0.68* 1.29" 1.11" 1.27" 1.08" 0.81 Eqution 4 e Eqution 5 f 1.17* 0.97* * M d = b Rtio of perceptul speed: Old = Young (1/.62) (M d = 0.05). c Rtio of rection time speed: Old = Young 1.51 (M d = 0.22). d Regression eqution for sequentil condition: Old = (Young 1.23) +.55 (M d = 0.40). e Regression eqution for hierrchicl condition: Old = (Young 1.96) -.34 (M d = -0.51). f Regression eqution for both conditions: Old = (Young 1.72) -.37 (Md = 0.07). *p<.01. numbers of operuons of.817. Despite the quntittive difference in the functions, therefore, the vlues representing the two functions shred n verge of more thn 80% of their ge-relted vrince. 2 Second, the proportions of shred ge-relted vrince tend to decrese s the number of rithmetic opertions increses. This decrese my reflect n incresed involvement of novel or distinct ge-relted processes (perhps relted to working memory nd the temporry preservtion of informtion while processing other informtion) when the problems contin four or more opertions. Even when it ppers tht other ge-relted influences re operting, however, it is importnt to note tht more thn 50% of the ge-relted vrince is shred with speed mesures tht re presumbly unffected by those influences? The dt reported in Figure 2 nd in Tbles 1 nd 2 suggest tht the quntittive prmeters of the systemtic functions re not necessrily informtive bout the existence, or reltive con- Tble 2 Estimtes of Proportions of Age-Relted Vrince in the Hierrchicl Arithmetic Tsk Age-relted vrince Number of Proportion of opertions Alone After sequentil vrince shred M tribution, of common ge-relted speed fctor. Although those prmeters hve descriptive vlue nd my be useful for estimting the contribution of the hypothesized generl fctor(s) on prticulr vrible, they do not directly indicte the extent to which the ge-relted influences in different vribles re distinct nd independent of one nother. In summry, the considerble literture documenting the existence of systemtic reltions between men times of young nd old dults is viewed s consistent with the hypothesis of generl ge-relted slowing fctor. The current perspective differs from tht espoused by other theorists, however, in tht nlyses of systemtic reltions re not necessrily ssumed to be informtive bout the number of independent ge-relted influences; insted, they re postulted to be primrily useful s 2 Myr nd Kliegl (1993) reported tht slightly more thn 6% of the vrince in mesures from tsks involving coordintive complexity ws independent of tht in mesures from tsks involving sequentil complexity. However, becuse they did not report the totl ge-relted vrince in the coordintive complexity mesures, estimtes of the proportions of shred ge-relted vrince could not be derived from the informtion in their rticle. Figure 8 in tht rticle lso illustrtes results of n djustment nlogous to those reported in Tble 2 of this rticle in which similr pttern ws pprent (i.e., under-prediction of the effects in the complex condition from n djustment bsed on results in the simple condition ). 3 A very similr pttern of results ws obtined in contrst of sequentil rithmetic performed lone nd performed while lso remembering four letters (Slthouse et l., 1995). Tht is, the regression equtions for the two sets of vribles differed significntly in slope (i.e., Old = I. 11 [Young], r 2 =.99, for rithmetic lone, nd Old = [Young], r 2 =.99, for rithmetic with concurrent letter memory), the mgnitude of the ge difference in d units ws gretly reduced fter djustment for the influence of the common fctor, nd lrge proportion of the ge-relted vrince in the concurrent rithmetic mesures ws shred with the single-tsk rithmetic mesures.

9 PROCESSING-SPEED THEORY 411 Controlled Vnble ~ Age Criterion Vrible Figure 3. Illustrtion of regions of vrince for ge nd two vribles. The circles represent the totl vrince in the vribles, nd the regions of overlp correspond to proportions of shred vrince. mens of identifying vribles with potentilly specific gerelted influences. Sttisticl Control Procedures Becuse mny speed mesures hve been found to hve negtive reltions with ge, fundmentl question within the processing-speed theory concerns the number of seprte nd distinct ge-relted influences on speed. Tht is, re there mny independent nd unique ge-relted influences, or re there, insted or in ddition, reltively smll number of fctors with firly brod consequences? As noted erlier, centrl hypothesis of the processing-speed theory is tht some version of the ltter interprettion is the most plusible nd, hence, tht there should be substntil commonlity, or overlp, of the ge-relted influences on mny different speed mesures. In other words, rther thn being completely independent, it is hypothesized tht much of the ge-relted vrince in ny given speed mesure is shred with the ge-relted vrince in other speed mesures. One wy of investigting the degree of commonlity mong speed mesures is through use of sttisticl control methods. The logic of sttisticl control procedures in the present context cn be described by reference to Figure 3 (see lso Slthouse, 1992b, 1992d, 1994c, for further discussion of the rtionle). This figure represents the totl vrince, nd the regions of shred or overlpping vrince, in three vribles. Note tht the proportion of vrince in the criterion vrible tht is shred with the ge vrible corresponds to the rtio (b + d)/( +f+ b + d). In similr mnner, the proportion of vrince in the criterion vrible tht is shred with the controlled vrible corresponds to the rtio ( + b)/( +f+ b + d). However, it is lso pprent in Figure 3 tht the proportion of ge-relted vrince in the criterion vrible tht is shred with the controlled vrible corresponds to the rtio b/(b + d). It is this ltter quntity tht is of gretest interest in the current context becuse the prediction from the processing-speed theory is tht the ge-relted influences on mny speed vribles re not independent nd, hence, tht the vribles will shre lrge proportion of their ge-relted vrince. In other words, the rtio b/(b + d) is predicted to be reltively lrge when the two vribles both reflect speed of processing. In contrst, if seprte nd distinct ge-relted influences re responsible for the ge differences in every speed mesure, then most of the ge-relted vrince in the vribles will be independent, nd the rtio b/(b + d) will be smll. Both correltion nd hierrchicl regression procedures cn be used to derive estimtes of the proportions of vrince illustrted in Figure 3. Tht is, the squre of the correltion between ge nd the criterion vrible corresponds to the proportion of the criterion vrince shred with ge (i.e., [b + d]/[ +f+ b + d]). Hierrchicl regression techniques, in which the vrince in the controlled vrible is removed before the reltion of ge to the criterion vrible is exmined, cn be used to derive the squre of the semiprtil correltion (i.e., d/[ +f+ b + d]). Finlly, subtrcting the second quntity from the first, nd then dividing by the first, yields n estimte of the proportion of ge-relted vrince in the criterion vrible tht is shred with the controlled vrible (i.e., b/[b + d]). These nlyses cn be illustrted with n exmple reported in Slthouse (1994c). The primry dt in tht report were from lrge (N = 910) smple of dults cross wide ge rnge. The two speed mesures were the Digit Symbol Substitution Test nd composite perceptul speed mesure formed by verging z scores from the Letter Comprison nd Pttern Comprison tsks. The correltion between the Digit Symbol Substitution Test nd composite perceptul speed vribles ws.73, indicting tht 54% (i.e.,.732) of the totl vrince in ech vrible ws shred. The R 2 vlue ssocited with ge in the Digit Symbol Substitution Test ws.289, but the increment in R 2 ssocited with ge fter control of the perceptul speed mesure ws only.008. It cn therefore be inferred tht 97.2%--[ )/.289] X 100--of the ge-relted vrince in the Digit Symbol Substitution Test ws shred with the composite perceptul speed mesure. Becuse the proportions of totl ge-relted vrince in the vribles need not be identicl (i.e., b + d is not necessrily equl to b + c), estimtes of the proportion of shred ge-relted vrince in two vribles re not necessrily symmetric. In fct, when the nlyses in the dt set just described were reversed, the ge-ssocited R 2 vlue in the perceptul speed mesure ws.412, but the increment in R 2 ssocited with ge fter control of the Digit Symbol Substitution Test ws.086. This leds to n estimte tht 79.1%--[ )/.412] X 100--of the ge-relted vrince in the composite perceptul speed mesure ws shred with the ge-relted vrince in the Digit Symbol Substitution Test. A very similr pttern of shred ge-relted vrince ws found in the dt from n independent smple of 305 dults reported in the Slthouse (1994c) rticle. Tht is, in this smple 92.3% of the ge-relted vrince in the Digit Symbol Substitution Test ws shred with the perceptul speed mesure, nd 77.3% of the ge-relted vrince in the perceptul speed mesure ws shred with the Digit Symbol Substitution Test. In contrst, becuse the correltion between the two mesures ws.68, only 46% of the totl vrince in ech mesure ws shred with the other mesure. The results from these two dt sets therefore indicte tht very lrge percentge of the ge-relted vrince in t lest these prticulr speed mesures ws shred, nd hence reltively little ws independent or unique to ech mesure. Procedures similr to those just described hve lso been conducted on vriety of different speed mesures from two sep-

10 412 SALTHOUSE Tble 3 Proportions of Shred Age-Relted Vrince in Speed Mesures: Slthouse (1993d; N = 305) Criterion vrible Controlled vrible Age r 1. Horizontl Mrking Verticl Mrking Digit Copying Letter Copying Digit Comprison Letter Comprison Digit Trnsformtion Letter Trnsformtion Letter Comprison Pttern Comprison Digit Symbol rte dt sets; results re summrized in Tbles 3 nd 4. Tble 3 contins results from 11 speed mesures obtined from the 305 dults reported in the Slthouse (1993d) rticle. All mesures from tht study were derived from pper-nd-pencil tests. Tble 4 contins results from 4 pper-nd-pencil tests nd 2 rection time tests from totl of 744 dults who hd prticipted in one of three recent studies (i.e., Slthouse, 1994d, Studies 1 nd 2; Slthouse, 1994, Study 1 ). In ll cses, the entries in Tbles 3 nd 4 correspond to proportions of shred ge-relted vrince computed by subtrcting the increment in R 2 ssocited with ge fter eliminting the vrince in the controlled vrible from the totl R 2 ssocited with ge nd then dividing this difference by the totl R 2 ssocited with ge. As in the exmples described erlier, these vlues indicte how much of the ge-relted vrince in one vrible (represented in the columns) is shred, or in common with, the ge-relted vrince in nother vrible (represented in the rows). The medin for the vlues in Tble 3 ws.842, nd tht for the vlues in Tble 4 ws.628. Only the vlues obtined fter the control for Digit Trnsformtion nd Letter Trnsformtion mesures were consistently lower thn.5, nd this my reflect the fct tht these two vribles hd reltively low correltions with ge (i.e., -.23 nd -.24, respectively, s compred with rnge of -.38 to -.59 for ll other vribles). The mount of ge-relted vrince tht cn be shred between two vribles is obviously limited by the totl ge-relted vrince in ech vrible. Becuse ll of the mesures in Tbles 3 nd 4 re single vribles, the ge-relted vrince is not esily prtitioned into tht ttributble to the hypothesized construct, in this cse common speed fctor, nd tht specific to the prticulr methods, mterils, nd mesures. Nevertheless, the results summrized in the two tbles revel tht there is substntil overlp of the ge-relted vrince in the individul mesures of processing speed, with n verge of nerly 75% of the ge-relted vrince in these vribles shred with other vribles. Very similr resuits hve lso been reported in two recent studies. Slthouse nd Meinz (1995) found tht n verge of 86.3% of the gerelted vrince ws shred cross 2 rection time, 2 pper-ndpencil, nd 10 vocl speed mesures. And Slthouse (1996) found tht n verge of pproximtely 62% of the ge-relted vrince in 19 different speed mesures involving vocl, written, nd rection time responses ws shred. A second method tht cn be used to investigte the degree of commonlity of ge-relted vrince in mesures of speed is bsed on structurl eqution model with single ltent speed construct relted to ll speed mesures nd with reltions from ge to the ltent speed construct nd to ech individul speed mesure. Within model of this type, estimtes of the common ge-relted influence on ech speed mesure cn be obtined from the product of the pth coefficients from ge to the corn- Tble 4 Proportions of Shred Age-Relted Vrince in Speed Mesures: Erles nd Slthouse (1995; N = 744) Criterion vrible Controlled vrible Age r 1. Boxes Digit Copying Letter Comprison Pttern Comprison Digit Digit rection time Digit Symbol rection time

11 PROCESSING-SPEED THEORY 413 mon speed fctor nd from the common fctor to the individul speed mesures. The direct pth coefficients from ge to the individul speed mesures serve s estimtes of the specific or unique ge-relted influences on the mesures. Slthouse (1996) recently pplied this method to four independent dt sets nd, in ll cses, found very similr results. For every vrible, the estimte of the common or shred gerelted influence ws much lrger thn the estimte of the unique or specific ge-relted influence. Moreover, the unique ge-relted influence ws significntly greter thn zero for only 18 of the 53 vribles cross the four dt sets. It is importnt to point out tht generl or common gerelted influence is lso likely to be operting with mesures often postulted to reflect the durtion of discrete nd specific cognitive processes. In fct, results from severl nlyses suggest tht 50% or more of the ge-relted vrince in mesures of purportedly specific informtion-processing components is ttributble to common or generl speed fctor. Anlyses leding to this conclusion cn be illustrted with dt from n rticle by Slthouse nd Prill (1987) involving series completion tsk. In the condition of gretest interest in the present context, ech element in the problem ws presented successively, nd the time tken by the prticipnt in exmining ech element ws monitored by computer. Two different types of problems were distinguished on the bsis of the bstrctness of the reltions mong elements. Problems with first-order reltions mong elements consisted of simple continution sequence (e.g., ??). In contrst, problems with second-order reltions hd the invrince or constncy t the second level of bstrction, in the difference mong differences (e.g., ??). A mesure of bstrction time cn be derived from the differ- ence in inspection or processing time in the two types of problems, prticulrly t the third element in the sequence, where the problems re first distinguishble. Men inspection times for correct trils for young nd old dults in the two types of problems re illustrted in Figure 4. It is pprent in Figure 4 tht older dults were slower thn young dults cross every item in the sequence for both types of problems. Of prticulr interest re the much longer times in the third, fourth, nd fifth elements in the second-order problems becuse these durtions presumbly reflect the time needed to infer or bstrct reltions mong items. Becuse these durtions re longer for older dults thn for young dults, some of the lower ccurcy of older dults on the second-order problems (i.e., 35.8% correct, s compred with 68.6% correct for young dults) my be ttributble to greter probbility of forgetting erly items in the sequence during the longer period needed to identify the reltions mong elements. The first two rows in Tble 5 contin the vlues leding to estimtes of the proportion of ge-relted vrince in the tskspecific speed mesures tht ws shred with speed mesure from seprte tsk (i.e., Digit Symbol Substitution Test score). Note tht sttisticl control nlyses of the type described erlier yield estimtes tht 49.1% of the ge-relted vrince in the bstrction mesure, nd 62.5% of the ge-relted vrince in the men inspection time mesure, ws shred with the Digit Symbol speed mesure. The remining entries in Tble 5 re bsed on studies with mixture of tsk-specific speed mesures. Two distinct ptterns re evident in these dt. One is similr to tht described erlier in tht the ge-relted vrince in the tsk-specific mesure ws gretly reduced fter control of the vrince in nother speed Q f ',, Young Old 1st Order ~ 0 2nd Order i 6 oo "0 5 C 0 O (1) 4 O~ 3 / / / t, ",." " 0, 0 s.- i s" 0 I I I I I I Element Number Figure 4. Time to inspect successive series completion elements for young nd old dults in first-order nd second-order bstrction problems (dt from Slthouse & Prill, 1987, Study 2).

12 414 SALTHOUSE Tble 5 Estimtes of Shred Age-Relted Vrince in Different Speed Mesures Study nd criterion vrible Alone Age-relted vrince After control of Proportion of vrince shred with Slthouse & Prill (1987), series completion (N = 48) Men inspection time Difference: 2nd order minus I st order Digit Symbol Digit Symbol Slthouse (1987), geometric nlogies (N = 48) Men inspection-decision time Slope of time-element: complete problem Slope of time-element: first 2 terms Digit Symbol Digit Symbol Slthouse & Coon (1993), reordered letter memory spn, Study 1 (N = 55) Men recll time Reorder time RTS RTS Slthouse & Coon (1993), reordered letter memory spn, Study 2 (N = 71) Men recll time Reorder time Encoding time RTS RTS Slthouse & Kersten (1993), symbolic rithmetic (N = 104) Symbol rithmetic RT Digit rithmetic RT RTS DART RTS DART.911 Slthouse & Coon (1994), Study l, subtrction RT (N = 240) Borrow RT No borrow RT RTS NBRT RTS NBRT.980 Slthouse & Coon (1994), Study 2, rithmetic with 1 to 7 opertions (N = 80) Sequentil rithmetic intercept Slope Hierrchicl rithmetic intercept Slope IRT Intercept b.531 IRT Intercept b.579 Slthouse et l. (1995), rithmetic with 1 to 4 opertions (N = 131) Single-tsk rithmetic intercept Slope Dul-tsk rithmetic intercept Slope IRT Intercept RT.455,833, Intercept b b Slthouse (1994d), digit symbol with 3, 6, nd 9 digit-symbol pirs, Study 1 (N = 246) Intercept Slope DDRT Intercept DDRT Intercept b Slthouse (1994d), digit memory serch with 1 to 4 items, Study 2 (N = 258) Intercept Slope RTS Intercept RTS Intercept Slthouse (1994d), letter memory serch with 1 to 4 items, Study 2 (N = 258) Intercept Slope RTS Intercept b RTS Intercept b

13 PROCESSING-SPEED THEORY 415 Tble 5 (continued) Study nd criterion vrible Alone Age-relted vrince After control of Proportion of vrince shred with Slthouse & Meinz (1995), Stroop interference (incongruent - neutrl; N = 242) RTS RTS Color Number Position Slthouse (1996), Stroop interference (incongruent - neutrl; N = 172) Color RTS RTS Note. RTS = rection time speed; = perceptul speed; DART = digit rithmetic rection time; RT = rection time; NBRT = no borrow rection time; IRT = identifiction rection time; DDRT = Digit Digit rection time. Vrible not vilble or not relevnt in the nlysis, b Estimtes of shred vrince not meningful s result of n pprent suppression reltionship becuse the ge-relted vrince incresed rther thn decresed fter control of the other vrible. mesure (i.e., symbol rithmetic rection time, digit rithmetic rection time, borrow rection time, no borrow rection time, sequentil rithmetic intercept, Digit Symbol intercept, memory serch intercept, nd Stroop color interference). The second pttern is tht the ge-relted vrince in the criterion vrible incresed rther thn decresed fter control of the vrince in the other speed vrible (i.e., sequentil rithmetic slope, hierrchicl rithmetic intercept, single-tsk nd dultsk rithmetic slope, Digit Symbol slope, nd memory serch slope). Instnces with the second pttern indicte tht sttisticl control need not lwys reduce the mount of ge-relted vrince becuse it cn lso "relese" the ge-relted vrince tht hd been suppressed becuse of negtive reltion between the two speed mesures. For exmple, the intercept could operte s third vrible tht obscures the reltions between ge nd the slope unless its effects re tken into considertion. Even though the ge-relted vrince in these cses incresed rther thn decresed fter sttisticl control of the other mesure, it is importnt to note tht the results re still consistent with the interprettion tht the ge-relted influences on the speed mesures were not independent. Sttisticl control cn lter the ge reltions, in either negtive or positive direction, only if t lest some of the ge-relted vrince in the mesures is shred, nd not ll is unique or specific. A very similr pttern in which lrge proportion of gerelted vrince in presumbly specific speed mesures ws shred with more generl processing-speed mesures ws lso reported by Slthouse (1996). In tht study, fctor nlysis procedures were used to derive n estimte of the generl speed fctor, nd the specific mesures represented the time to serch code tble nd substitute items, to serch nd retrieve n item from memory, to reorder items in memory, to rticulte or reherse items, nd so forth. Sttisticl control of the generl speed fctor substntilly reduced the ge-relted vrince for ll of the mesures with significnt ge reltions, implying tht mny of the ge-relted influences in the specific mesures were shred with the generl speed fctor. The results just discussed, nd summrized in Tbles 3-5, led to the conclusion tht moderte to lrge proportion of the ge-relted vrince in mny speed vribles is shred, or in common, rther thn being completely independent nd distinct. Moreover, the ge-relted influences re pprently not restricted to those reflecting overll performnce in simple tsks becuse similr ptterns re evident with mesures presumed to reflect the durtion of specific cognitive opertions in modertely complex tsks. These results re thus consistent with the hypothesis of the processing-speed theory tht smll number of common fctors contribute to the ge-relted differences in mny speed mesures. In summry, two importnt implictions of the hypothesis tht ge-relted slowing is generl phenomenon pper to hve convincing support. The impliction tht the direction nd mgnitude of the ge differences in certin speed mesures re predictble from knowledge of the ge differences in other speed mesures is supported by the results described erlier involving systemtic reltions. And the impliction tht the ge-relted influences on different speed mesures re not independent is supported by the finding tht mny speed mesures shre considerble proportion of their ge-relted vrince. This evidence is clerly consistent with the proposl tht smll number of common fctors contribute to the ge-relted influences in mny mesures of speed. Becuse there hs been frequent confusion on the issue of generl slowing, it is importnt to be explicit bout wht is not implied from the current perspective. Although ge-relted slowing is ssumed to be ubiquitous, it is not necessrily ssumed to be universl, uniform, or unitry. Ech of these ltter chrcteristics is considered in turn. First, the hypothesized common or generl speed fctors re not necessrily universl. Tht is, some mesures my not exhibit ge-relted slowing becuse it is not ssumed tht every mesure scled in units of time is ffected by common or generl influence(s) (Kil & Slthouse, 1994; Slthouse, 1985b, 1992b, 1996; Slthouse & Somberg, 1982). Becuse not ll speed mesures re postulted to be influenced by the hypothesized common speed fctor(s), discovery tht some speed mesures hve little or no ge differences would not be inconsistent with the hypothesis tht common fctors ffect mny other speed mesures. Ultimtely, of course, explntions re needed to ccount for why some speed mesures re relted

14 416 SALTHOUSE 0.8 Study 1 v Study 2..~... G) < 0.6 t-.o_ t- O I I I I Correltion with Word Knowledge Figure 5. Functions illustrting the reltion between the mgnitude of the correltion with ge nd the correltion with mesure of word knowledge for seven speed mesures in studies conducted by Slthouse (1993c). to ge, wheres others re not. For the purpose of the current rgument, however, the importnt point is tht universlity is not necessry concomitnt of the existence of fctors with reltively brod influences. A second ssumption of the processing-speed theory is tht ge differences on different speed mesures should not necessrily be expected to be uniform. Insted, the ge-relted effects cn be expected to vry in mgnitude becuse of the opertion of other influences, even if common underlying mechnism is involved (cf. Slthouse, 1992b, 1992d; Slthouse & Coon, 1994). Considerble evidence indictes tht vriety of fctors contribute both to the bsolute level of speeded performnce nd to the reltions between ge nd mesures of speeded performnce. As n exmple, reserch on typing hs reveled tht the reltions between ge nd mesures of speed (i.e., interkey intervl) systemticlly vry s function of the mount of preview of to-be-typed text vilble during typing (cf. Slthouse, 1984, Figure 4). In the Slthouse (1984) project, the correltion between ge nd medin interkey intervl ws bout.5 with visible window of one chrcter, nd it decresed to ner 0 with unlimited preview. Another illustrtion of the influence of other fctors on gespeed reltions is vilble in the results of recent project (Slthouse, 1993c), portryed in Figure 5. The vribles in the two studies in this project were severl mesures of perceptul speed (e.g., Letter Comprison, Pttern Comprison, nd Digit Symbol Substitution Test) nd mesures from other timed tests presumed to require word knowledge (e.g., vrious word fluency tsks nd tsks such s ngrms). It is obvious in both studies tht the mgnitude of the reltions between ge nd the speed mesure decresed s the involvement of word knowledge (ssessed by scores on two vocbulry tests) in the tsk in- cresed. One interprettion of this pttern is tht speed-dependent processing requirements were reduced s the mount of relevnt knowledge incresed, thereby resulting in decrese in the reltion of ge to the mesure. For exmple, when more knowledge is vilble, fewer trnsformtions or novel processing opertions might be required becuse much of the relevnt informtion (or "solutions") my lredy exist in the individul's knowledge system. The typing results (Slthouse, 1984) nd the dt in Figure 5 re merely two illustrtions tht the reltion between ge nd mesures of speed vries s function of other fctors. Results of this type cn be viewed s confirming the well-ccepted principle tht virtully every performnce mesure hs multiple determinnts. Tht is, one-to-one reltions between prticulr hypotheticl process nd behviorl vrible re extremely rre, nd thus most vribles cn be ssumed to be ffected by severl different influences. Identicl ge reltions on different speed mesures should therefore not be expected unless the mesures hve the sme determinnts, with exctly the sme weightings or reltive importnce, nd the mesures re equivlent in relibility nd sensitivity. 4 4 Age-speed reltions will lso vry ccording to the relibility of the speed mesure becuse lrge ge reltions cnnot occur if there is little systemtic vrince in the mesure tht is vilble for ssocition with other vribles. As n exmple, the finding of Mdden et l. (1993) tht priming difference scores (i.e., priming rection time minus unrelted or neutrl rection time) hd relibilities of ner zero suggests tht lck of systemtic vrince my be one reson for the low correltions between ge nd mesures of priming. Also consistent with this interprettion re the reports by Slthouse (1994) of correltions in two studies of.51 nd.85 between the relibility of the mesure nd the bsolute mgnitude of the correltion of the mesure with ge.

15 PROCESSING-SPEED THEORY 417 A third ssumption of the processing-speed perspective is tht there is not necessrily single, or unitry, speed fctor. Insted, severl common fctors could exist, s long s the number is substntilly smller thn the number of relevnt speed mesures (Kil & Slthouse, 1994; Slthouse, 1992b, 1995c). Results of studies conducted by Erles nd Slthouse (1995), Hertzog (1989), Slthouse ( 1993c, 1994d), Tomer nd Cunninghm (1993), nd White nd Cunninghm (1987) suggesting tht severl speed fctors cn be distinguished in smples of young nd old dults re therefore not incomptible with the present perspective. An nlogy my help to illustrte this point. Severl different types of speed ffect the performnce of computer, including the processor clock rte; the speed of specilized mthemticl or grphics co-processors; hrd disk ccess time; input rte from devices such s keybords, scnners, or modems; nd output rte to devices such s disply monitors, printers, plotters, or modems. Nevertheless, knowledge of smll number of speed "fctors" llows performnce on n extremely lrge number of tsks to be predicted quite ccurtely. A centrl hypothesis of the processing-speed theory is tht the humn cognitive system cn lso be conceptulized s hving reltively smll number of speed fctors tht re relted to ge nd tht contribute to the efficiency of mny cognitive processes. This is in contrst to the view, which is often implicit, tht every process or mesure hs n independent ge-relted influence. A crucil point from the current perspective, therefore, is tht the ge reltions in ll speed mesures should not be expected to be of the sme mgnitude, in either bsolute or proportionl terms. Insted, the proposl is tht mny, but not necessrily ll, of those mesures shre substntil ge-relted vrince becuse of the influence of common determinnts or fctors. Hypothesis 2: Processing speed functions s n importnt meditor of the reltions between ge nd mesures of cognitive functioning. Becuse it is ssumed, nd the vilble evidence seems consistent with the ssumption, tht there re generl ge-relted effects on speed of processing, it is hypothesized tht there re effects not only on the speed of mny cognitive opertions but lso on the qulity of the products of those opertions. Two ctegories of evidence re relevnt to the hypothesized meditioni role of processing speed in ge-cognition reltions: results from pth nlyses nd results from sttisticl control of n index of processing speed. Pth Anlyses Becuse pth models cn illustrte the complete pttern of interreltionships mong vribles, pth nlyses re vluble s mens of indicting the reltions mong severl vribles. Pth models should not be considered definitive becuse they cn vry in the degree to which they represent or fit the dt, nd lterntive structurl models often provide eqully good fits to the dt (McCllum, Wegener, Uchino, & Fbrigr, 1993). Nevertheless, pth nlyses cn be informtive bout the presence or bsence of prticulr reltions, nd hence they re of obvious relevnce to theories postulting tht construct like processing speed medites some of the ge-relted effects on mesures of cognitive performnce. As expected from the processing-speed theory, pth nlyses hve reveled strong reltions between ge nd speed, moderte reltions between speed nd vrious mesures of cognitive functioning, nd either wek reltion or no direct reltion between ge nd mesures of cognitive functioning. Exmples with vrious cognitive mesures s the criterion vrible hve been described in Lindenberger, Myr, nd Kliegl (1993) nd Slthouse ( 1991b, 1992b, 1992f, 1993d, 1994), nd those with working memory s the criterion cognitive construct hve been reported in Slthouse (1994c) nd Slthouse nd Bbcock ( 1991 ). A recent project by Slthouse (1994d) cn be used to illustrte the fetures, nd potentil contributions of the pth-nlytic pproch. Results from two independent studies with slightly different cognitive tests were reported in this rticle, with smple sizes of 246 (Study 1) nd 258 (Study 2) dults rnging from 18 to 87 yers of ge. The prticipnts in ech study performed pper-nd-pencil sensorimotor speed (Digit Copy nd Boxes) nd perceptul speed (Letter Comprison nd Pttern Comprison) tsks, s well s tests of memory, resoning, nd sptil bility. Becuse the cognitive tests were dministered on computers, it ws lso possible to obtin seprte mesures of study or solution time, decision time, nd decision ccurcy from ech of the cognitive mesures to represent distinct spects of cognitive performnce. Figure 6 illustrtes the best-fitting pth model from the project, bsed on composite mesures formed by verging z scores cross the three cognitive tests in ech study. The degrees of freedom in the model were low becuse the number of estimted prmeters ws close to the number of vilble covrinces, but the model nevertheless provided good fit to the dt (e.g., Adjusted Goodness of Fit Index model determintion vlues of.987 in Study 1 nd.955 in Study 2). All pth coefficients in Figure 6 differed from zero by more thn two stndrd errors, except for the pth between ge nd decision ccurcy in Study 2. No pths not represented in the figure hd coefficients significntly different from zero in either study. Severl importnt results should be noted bout this figure. First, there were moderte to strong reltions between ge nd perceptul speed nd between perceptul speed nd decision ccurcy, but there were wek reltions between ge nd decision ccurcy. These fetures re ll consistent with the key ssumption of the theory tht slower speed of processing prtilly medites the dult ge differences in vriety of cognitive tsks. In ddition, however, Figure 6 illustrtes tht sensorimotor speed ws relted to perceptul speed nd decision time but not to decision ccurcy. Peripherl (i.e., input nd output) spects of speed therefore do not pper to be directly involved in the medition of the reltions between ge nd decision ccurcy. Furthermore, study time ws not relted to perceptul speed, but it ws relted both to ge nd to decision ccurcy. This pttern suggests tht, with incresed ge, more time ws spent working on the items nd tht longer time devoted to the items ws ssocited with higher ccurcy. However, becuse study or solution time ws not relted to perceptul speed, it my reflect strtegic or stylistic fctors rther thn effects ssocited with slower speed of executing relevnt processing opertions. Finlly, it is noteworthy tht perceptul speed ws re-

16 418 SALTHOUSE.30/ /.32.51/ /.3O -.14/ / Figure 6. Pth digrm illustrting reltions mong vribles in two studies reported by Slthouse (1994d). Coefficients re reported in the formt Study 1/Study 2. lted to decision ccurcy but not to decision time. This is dditionl evidence tht processing speed, s indexed by the perceptul speed mesures, ffects the qulity of cognitive processing nd not simply the speed with which decisions bout the products of the processing cn be communicted. Although only smll number of relevnt pth nlyses hve been reported, the vilble results hve been quite consistent with the predictions of the processing-speed theory. In prticulr, moderte reltions hve been found between ge nd mesures of speed nd between speed mesures nd mesures of cognition, but wek to nonexistent reltions hve been found between ge nd cognition. An dditionl contribution of pth nlyses pprent in the preceding exmple is tht becuse the pth nlyses indicte how severl different vribles re interrelted, they re informtive bout how speed-medited influences occur. Sttisticl Control Procedures One impliction of the hypothesis tht processing speed is meditor of ge-cognition reltions is tht ge-relted effects would be expected to be much smller if the vrition in the hypothesized meditor could be eliminted. An idel investigtive procedure would probbly involve experimentl mnipultion of the level of the meditor, but this does not pper fesible with vribles such s processing speed tht re presumed to reflect reltively stble processing chrcteristics of n individul (Slthouse, 1992, 1992b). Attempts cn be mde to mtch individuls of different ges on mesures of speed; s illustrted lter, however, this is not lwys successful, nd it typiclly reduces the sttisticl power of the comprisons becuse of the decresed smple size. The most prcticl method of investigting hypothesized meditionl reltions therefore ppers to be some type of sttisticl control procedure in which the vrince in n index of the hypothesized meditor is held constnt by sttisticl methods. It is importnt to note tht sttisticl control procedures will reduce the ge-relted effects on criterion vrible only if the mesure of the hypothesized meditor is relted both to ge nd to the criterion vrible. If the meditor is relted only to ge, then there will be no effect of its control on the criterion vrible; if the meditor is relted only to the criterion vrible, then its control will hve no effect on the reltion between ge nd the criterion vrible. This is evident in Figure 3, which shows tht the controlled vrible cn contribute to the medition of ge effects in the criterion vrible only if the region of double overlp (i.e., Region b in Figure 3 ) is greter thn zero. One method of sttisticl control involves the use of hierrchicl regression procedures similr to those described erlier. Tht is, the totl mount of ge-relted vrince in the criterion vrible is determined, nd then the mount of unique or independent ge-relted vrince is ssessed by controlling the vrince in mesure of the hypothesized meditor. If the mount of unique or independent ge-relted vrince is lrge reltive to the totl ge-relted vrince, then considerble indepen-

17 PROCESSING-SPEED THEORY 419 dence of the ge-relted influences in the controlled (hypothesized meditor) nd criterion vribles cn be inferred. However, if the unique ge-relted vrince is smll reltive to the totl ge-relted vrince, then one cn infer tht there is substntil commonlity of influences in the two sets of mesures. This second type of outcome is consistent with the medition of t lest some of the ge effects in the criterion vrible through the controlled vrible (e.g., Slthouse, 1992, 1992b; Slthouse & Bbcock, 1991 ). Appliction of sttisticl control methods does require severl ssumptions rnging from sttisticl (Cohen & Cohen, 1983) to substntive in nture. One of the ltter is tht the current level of the controlled vrible, but not its etiology or developmentl history, is relevnt ( Slthouse, 1991 c, 1992). It is lso importnt to estblish relistic expecttions regrding the outcome of sttisticl control nlyses becuse sttisticl significnce tests in these types of nlyses typiclly refer to the mount of vrince tht is not explined by the controlled vrible rther thn the mount tht is explined. The ge-relted vrince would be completely eliminted, with no residul vrince, only if the controlled nd criterion vribles shred ll of their ge-relted vrince. This is n extremely demnding criterion becuse it would require not only tht ll vrince ttributble to the theoreticl construct, but lso ll specific vrince ssocited with methods, mterils, nd mesures, ws shred cross the controlled nd criterion vribles (Slthouse, 1992). A potentilly more meningful bsis for evluting sttisticl control outcomes is in terms of the percentge reduction of gerelted vrince. For exmple, I ( Slthouse, 1992, p. 26) hve suggested tht percentge reductions of less thn 20% re smll, vlues between 20% nd 40% re interesting, vlues between 40% nd 60% re importnt, nd vlues greter thn 60% should be considered mjor becuse in tht cse ll other determinnts together would be responsible for less thn hlf of the totl ge-relted vrince. These vlues re dmittedly rbitrry, but even tenttive guidelines my be useful in interpreting the results of sttisticl control nlyses. Percentge reduction in ge-relted vrince is not the only possible metric of the importnce of hypothesized meditor, but if the vrible is found to be ssocited with very smll reduction in ge-relted vrince, then dditionl justifiction is probbly needed to estblish its importnce. If the vrible is ssocited with lrge reduction in ge-relted vrince, however, it cn be considered importnt s potentil meditor for this reson lone. Some of the erliest results from sttisticl control nlyses with speed mesures were described in Slthouse ( 1985b). Although the results of those initil nlyses were generlly consistent with the predictions from the processing-speed theory, the nlyses were not optiml becuse the smples were often smll, the speed nd cognition constructs were ssessed with single mesures, nd prtil correltion rther thn semiprtil (i.e., hierrchicl regression) correltion nlyses were used. Numerous other studies shring mny of these chrcteristics hve lso been reported with mixed results (e.g., Biemn-Coplnd & Chrness, 1994; Bors & Forrin, 1995; Bryn & Luszcz, 1996; Chrness, 1987; Grf& Uttl, 1995; Hrtley, 1986, 1993; Kwong See & Ryn, 1995; Nettelbeck & Rbbitt, 1992). As reported lter, stronger evidence for meditionl role of processing speed hs been obtined with lrger smples nd multiple indictors of both the speed nd cognition constructs. A grphicl illustrtion of the effects of sttisticl control of mesures of speed, nd of mtching individuls on speed, is presented in Figure 7. The dt in this figure were obtined from smple of 221 dults who were dministered the Rven's Progressive Mtrices Test with 20-min time limit, long with the Letter Comprison nd Pttern Comprison tests of perceptul speed (the smple, the sme s tht used in Figure 1, ws reported s Study 1 in Slthouse, 1993b). The verticl xis represents performnce on the Rven's test expressed in z-score units. Pnels in the figure illustrte the initil ge reltions in the totl smple (A); the ge reltions in the totl smple fter use of sttisticl djustment to eliminte the vrince in the composite speed mesure, derived by verging z scores for the Letter Comprison nd Pttern Comprison mesures (B); nd the ge reltions in subsmple (n = 90) whose composite speed scores were within 0.5 stndrd devitions of zero (C). It is pprent tht there ws lrge ttenution of the ge reltions with the sttisticl control procedure (82%) nd somewht less (61%) ttenution when the smple ws restricted to prticipnts with nrrow rnge of speed. However, it is noteworthy tht despite the substntil decrese in smple size from 221 to 90, there ws still significnt correltion between ge nd speed (-.35) in the subsmple. This is one of the resons why mtching is not the optimum method for these types of nlyses. Sttisticl control results resembling those portryed in Pnels A nd B of Figure 7 hve been obtined in n independent smple of dults by Bbcock (1994), who found 61% reduction (i.e., from n R 2 vlue of.212 to vlue of.083) in the gerelted vrince in the Rven's score fter control of perceptul speed mesures. Similr results hve lso been reported with computer-dministered, self-pced, mtrix resoning tsk (Slthouse, 1993b, 1994d). In the ltter study, the R 2 in decision ccurcy ssocited with ge in smple of 246 dults from wide rnge of ges ws. 149, nd this ws reduced to.014 (91% ttenution ) fter control of composite mesure of rection time speed nd to.015 (90% ttenution) fter control of composite mesure of pper-nd-pencil perceptul speed. Mny published studies now exist in which some index of processing speed hs been controlled in exmintions of gerelted influences on vriety of cognitive mesures rnging from resoning nd sptil bilities to working memory, ssocitive memory, nd free recll. To illustrte, totl of 44 comprisons with mesures from individul cognitive tests were summrized by Slthouse (1993d). These comprisons were extrcted from studies by Hertzog (1989) nd Schie (1989, 1990), s well s severl studies by Slthouse nd collegues. Age ws initilly ssocited with men of 16.2% of the vrince in these nlyses, but the ge-relted vrince ws reduced to only 3.6% fter mesures of perceptul speed hd been controlled. The verge ttenution in the comprisons summrized in Slthouse (1993d) ws therefore nerly 78%. Comprisons with composite (i.e., verge of z scores) cognition mesures were summrized in Slthouse ( 1992b; e.g., see Fig. 3.6). Age ws initilly ssocited with men of 25.2% of the vrince in these nlyses, but the ge-relted vrince ws reduced to men of only 4.3% fter control of speed. The

18 420 SALTHOUSE A 3 z = oo (Age), r '::.--,.,,..: : ~ ~ '. ',.. r s ".." o ~ ~ ~ - i ; ~ ;...: ".. ee ee-j.. "G~P'~-o~ o. I.'. e -2 oo Oo~ B ~o~og~ ~e C 3 3 z : o.s2 -.oi (Age), r l ,. z = (Age), r 2= '..e OO~o o. "~ %;- 1 ~ f,.~ee.o.o~.~. i, o... "..:... ;~.s ---~... ~e "..: -2-2 Chronologicl Age I I I Chronologicl Age Figure 7. Reltions between ge nd Rven's Progressive Mtrices Test performnce in the totl smple (A), in the totl smple fter control of mesure of speed (B), nd in smple of prticipnts within nrrow speed rnge (C; dt from Slthouse, 1993b, Study l ). verge reduction of the ge-relted vrince in these comprisons ws therefore pproximtely 83%. Similr mgnitudes of ttenution hve been found when the criterion cognitive tsks were self-pced nd when seprte mesures of decision ccurcy nd decision time were obtined (i.e., Slthouse, 1993b, 1994d). In fct, the percentge ttenution of the ge-relted vrince in the Slthouse (1994d) studies ws ctully greter for criterion mesure of decision ccurcy (81.3% in Study 1 nd 70.0% in Study 2) thn for criterion mesure of decision time (74.5% in Study 1 nd 54.8% in Study 2). Substntil reduction of the ge-relted vrince fter control of reltively simple mesures of processing speed hs lso been found when vriety of memory mesures served s the criterion cognitive vrible. To illustrte, results from severl recent projects conducted in my lbortory re summrized in Tble 6. The speed mesures in these studies were composites formed by verging z scores for the Digit Symbol nd Digit Digit rection time mesures to crete rection time speed composite mesure or by verging z scores for the Letter Comprison nd Pttern Comprison mesures to crete perceptul speed composite mesure. Severl of the memory mesures were bsed on single score (e.g., percentge correct recll in 12- word lists for free recll nd percentge correct in study-test pired-ssocites trils). However, in the continuous ssocitive memory tsks, the ssocitive memory mesures were ggregted cross ll presenttion times to form composite mesure of ssocitive memory performnce. The working memory mesures were lso composites formed by verging z scores from the spns obtined in the Reding Spn nd Computtion Spn working memory tsks. Across ll memory mesures in Tble 6, the ge-relted vrince ws reduced n verge of 77.6% fter control of the rection time speed mesure nd ws reduced n verge of 85.1% fter control of the pper-nd-pencil perceptul speed mesure. All of the vlues in Tble 6 re thus in the importnt-to-mjor rnge ccording to the guidelines mentioned erlier, becuse more thn 50% of the ge-relted vrince in the mesures of memory is shred with the vrince in reltively simple mesures of processing speed. It should lso be noted tht, in severl studies, the proportionl ttenution of the ge-relted vrince ws greter with speed mesures from tsks involving perceptul or cognitive opertions, such s substitution, trnsformtion, or comprison, thn with tsks merely requiring copying or line drwing responses (Slthouse, 1992b, 1993d, 1994, 1994d; Slthouse & Kersten, 1993; Slthouse et l., 1995 ). As suggested by the pth nlysis results illustrted in Figure 5, the speed most relevnt to the medition of dult ge differences in cognition therefore ppers to reflect the durtion of cognitive opertions rther thn simply the speed of sensory nd motor processes. The results just described revel tht n verge of 75% or more of the ge-relted vrince in wide rnge of memory nd cognitive vribles is shred with mesures of processing speed. Moreover, this is true for different combintions of speed nd cognitive mesures, with both pper-nd-pencil nd computer-

19 PROCESSING-SPEED THEORY 421 Tble 6 Age-Relted Vrince in Mesures of Memory Performnce Age-relted vrince Age Mesure nd study N lone Free recll Slthouse (1993d) Slthouse (1993e) Slthouse (1995b) Pired ssocites Slthouse (1993d) Slthouse (1993e) Long-term memory for ctivities Erles & Coon (1994) Associtive lerning Slthouse & Kersten (1993) Slthouse (1994) Study Study Continuous ssocitive memory Letters nd Digits Sithouse (1994) Study Study Kersten & Slthousc (1993) Words nd Digits Slthouse (1994d) Study l l Study l Slthouse (1995d) 100 ~.369 Working memory Pper-nd-pencil procedures Sithouse & Bbcock ( 199 l), Study Slthouse ( 1991 b) Study l Study Study Computer-dministered procedures Slthouse (1992) Study l 180 ~.279 Study Slthouse (1995b) I Slthouse & Meinz (1995) Combined smples from severl studies Miscellneous (Slthouse, 1995) Mtrix memory Verbl Sptil Element memory Verbl Sptil Keeping trck Verbl Sptil After rection After perceptul Proportion of time speed speed shred vrince / / / / / / / / / / / / / / / / / / / / / / / / / / / / / /.75 Note. Dshes indicte tht mesures were not vilble. Only young nd old dults. dministered tests, nd cross different types of tests (e.g., those requiring resoning, sptil, nd memory bilities). The sttisticl control results therefore provide strong evidence for mjor role of processing speed in the reltions between ge nd mesures of cognitive performnce. In summry, reserch exmining the reltionl prediction of the processing-speed theory hs provided impressive support for tht prediction. Not only hve the pth nlyses reveled ptterns consistent with the expecttions, but the sttisticl control nlyses indicted tht nerly 75% of the ge-relted vrince in mny cognitive mesures is shred with mesures of processing speed. Becuse similr estimtes of shred ge-relted vrince hve been obtined cross timed nd self-pced mesures of resoning nd sptil bilities, cross wide rnge

20 422 SALTHOUSE 90 Lg 1 --e... o-- 2 L.. 0 o t9 0) r" ) 2 t~ Q. oo," 80,o'" tp ~" o0o 2500 Presenttion Durtion (msec) Figure 8. Accurcy s function of stimulus presenttion time with zero items nd one item intervening between presenttion nd test of digit-letter pirs (unpublished dt from Kersten & Slthouse, 1993). of memory mesures, nd with different types of speed mesures, it seems indisputble tht processing speed is involved in the reltions between ge nd cognitive performnce. Hypothesis 3." The limited time mechnism nd the simultneity mechnism re primrily responsible for the reltions between processing speed nd mesures of cognitive functioning. Limited Time Mechnism The bsic ide underlying the limited time mechnism is tht slower speed of executing mny processing opertions mens tht less processing cn be completed in given mount of time. One method of illustrting the hypothesized reltions involves mnipulting the mount of time vilble to process the stimulus. Although it is unlikely tht vritions in stimulus presenttion time will ffect the speed of internl processing opertions (Slthouse, 199 lc, 1992b), this mnipultion cn still be informtive bout how level of cognitive performnce is relted to time vilble for processing. Results from mnipultions of stimulus presenttion time cn be portryed in time-ccurcy functions in which ccurcy is represented long the verticl xis nd time is represented long the horizontl xis. Verticl contrsts in this type of representtion reflect the level of ccurcy t given time, nd horizontl contrsts reflect the mount of time needed to chieve given level of ccurcy. If the complete function is vilble, then prmeters of the mthemticl function cn be exmined nd compred cross experimentl conditions or ge groups (e.g., Kliegl et l., 1994; Myr & Kliegl, 1993; Slthouse & Coon, 1993 ). Figure 8, bsed on results of n unpublished study by Kersten nd Slthouse (1993), illustrtes typicl pttern from mnipultions of stimulus presenttion time in dults of different ges. 5 The tsk in this study, which ws performed by 39 young dults (Mge = 20.5 yers) nd 39 older dults (Mge = 67.9 yers), ws continuous ssocitive memory tsk involving letter-digit pirs. Probes, requiring decision of whether the items in the test pir hd been pired with one nother when either item lst occurred, were presented either immeditely fter the letter-digit pir (Lg 0) or fter one intervening pir (Lg l ). This tsk is interesting becuse it llows the influence of stimulus presenttion time to be exmined not only on reltively simple mesure (i.e., ccurcy t Lg 0) but lso with nother mesure tht presumbly requires processing beyond tht needed for the first mesure (i.e., ccurcy t Lg i ). Tht is, in ddition to the registrtion nd encoding required for the Lg 0 mesure, relevnt informtion needs to be preserved during the presenttion nd processing of dditionl items in the Lg 1 mesure. Three points should be noted bout the results portryed in Figure 8. First, ll of the functions pper to hve similr negtively ccelerted reltion between ccurcy nd presenttion time, but with symptotes of less thn 100%. The finding of symptotes below 100% suggests tht fctors other thn the durtion of the stimulus contribute to performnce on this tsk. Second, the functions for the Lg 0 mesure (solid lines) re consistently bove nd to the left of those for the Lg 1 mesure (dshed lines), indicting tht, s expected, more time ws needed for the processing ssocited with Lg 1 decisions thn for tht ssocited with Lg 0 decisions. This indictes tht the effects of restricted processing time propgte to more complex forms of processing nd re not simply confined to the simplest type of processing. The third point to be noted bout Figure 8 is tht the functions for older dults (open circles) re consis- 5 The functions in this figure hve symptotes below 100%, indicting tht perfect performnce ws not chieved even t the longest vilble durtion. A similr finding hs been reported by Slthouse nd Coon (1993), nd this my be chrcteristic of reltively difficult tsks in which only limited mounts of prctice re provided (cf. Kliegl et l., 1994).