Everything We Know About Aging

Everything We Know About Aging and Response Times:
A Meta-Analytic Integration

Paul Verhaeghen and John Cerella
Syracuse University

Hofer, S. M., & Alwin, D. F. (Eds.). The Handbook of Cognitive Aging: Interdisciplinary Perspectives. Thousand Oaks: Sage Publications.
Acknowledgments
This research was supported in part by a grant from the National Institute on Aging (AG-16201). We thank Lieve De Meersman, Martin Sliwinski, David Steitz, and Christina Wasylyshyn for their contributions to the original research.

Older adults take longer to process information than younger adults. It has long been known that the increase in response time (RT) is monotonic with adult age. In a large meta-analysis of studies using continuous age samples, Verhaeghen and Salthouse (1997) reported an age-speed correlation of -.52, and Welford (1977) estimated that each additional year of adult age increases choice reaction time by 1.5 ms. Cerella & Hale (1994) estimated that the average 70-year old functions at the speed of the average 8-year old – a large effect.
It also appears that this age-related slowing occurs in a wide variety of tasks, implicating a wide variety of cognitive systems: Memory search, visual search, lexical decision, mental rotation, speech discrimination, digit-symbol substitution, are but a few of the tasks that have consistently been found to yield age-related deficits in response times (see Kausler, 1991, and Salthouse, 1991, for excellent reviews of the deficits observed in the literature). A key and still unsettled question in the field of cognitive aging is: How many explanatory mechanisms or dimensions are necessary for an adequate description of age-related slowing?
A first school of thought tends towards strong reductionism. A monograph that best exemplifies this tendency is Salthouse’s 1991 Theoretical perspectives on cognitive aging. This research program seeks to establish a single mechanism as governing aging, identified as either processing speed (e.g., Salthouse, 1996), the neuromodulation effects underlying it (Braver & Barch, 2002; Li, Lindenberger, & French, 2000), or even a common cause linking cognitive change to perceptual/motor processes (e.g., Lindenberger & Baltes, 1997). Researchers working in this framework have favored a correlational, individual-differences approach in which a set of antecedent variables – often measured by a small set of tasks assumed to tap a relatively broad psychometric factor – is used to predict age differences (in a cross-sectional design) or age changes (in a longitudinal design) in some aspect of cognition. The current aspiration among reductionists is of cross-level unification, building explanations for cognitive aging from the bottom up, starting with gross changes in brain structure or neuronal functioning (see, e.g., the strong claims in Li, Lindenberger, & Frensch, 2000, and Park, Polk, Mikels, Taylor, & Marshuetz, 2001).
A second school of thought is well represented by Kausler’s 1991 monograph Experimental psychology, cognition, and human aging. The explanatory preference here is towards high precision, leading researchers to measure aging at the level of information-processing components. The emergent current in this process-oriented camp is computational -starting with mathematical models from cognitive psychology, the goal is to isolate those parameters whose modification reproduces the observed pattern of age effects (see, e.g., the strong positions taken by Byrne, 1998; Kahana, Howard, Zaromb, & Wingfield, 2002; Meyer, Glass, Mueller, Seymour, & Kieras, 2001; and Ratcliff, Spieler, & McKoon, 2000). The preferred data are experimental, comparing performance (latency or accuracy) between a baseline task and a version in which the process of interest is manipulated.
These two approaches to cognitive aging are opposite in many ways. One broadcasts its effects at a macro-level and aims at breath; the other focuses its effects at a micro-level, and aims at depth. The first engenders the impression that cognitive aging is orderly and simple; the second that it is diverse and messy. A third orientation has evolved at a meso-level: Aging is conceptualized in more detail than in macro-research, but at a resolution coarser than obtained in micro-research (e.g., Hale & Myerson, 1996; Verhaeghen et al., 2002). The approach here has been to examine large data sets for communalities in the age effects from tasks thought to represent similar kinds of processes, and for dissimilarities in the age effects from tasks differing in kind. Communalities are expressed as common “slowing factors” for related tasks; dissimilarities are seen in distinct slowing factors for dissimilar tasks; outcomes of the latter sort are often called dissociations (e.g., Perfect & Maylor, 2000). Dissociation research grew out of early attempts to expose regularities in young-old reaction-time data through the use of Brinley plots (e.g., Brinley, 1965; Cerella, Poon, & Williams, 1980). Historically, such plots were a primary impetus for reductionist theories. Their refinement led directly from the extreme reductionism noted above to the moderate reductionism of our own views. Given its central role in our argument, this unique way of portraying age outcomes must be understood by the reader.
The tools: Brinley plots and dissociations
Figure 1 (upper left panel) shows data from an experiment conducted in our lab (Verhaeghen, Cerella, and Basak, 2006). The task was mental arithmetic (We will show data from several other tasks in this experiment as we go along): Addition problems consisting of 4, 5, 6, or 7 signed digits were displayed on a screen, and participants had to determine whether the indicated sum was correct or off by one unit (e.g., 5 + 2 – 3 – 2 + 6 – 3 = 5). The figure shows the mean RTs for both age groups as a function of problem size or load. Not surprisingly, solution times increased as a linear function of problem size. This is characteristic of iterative tasks, in which difficulty is manipulated by varying the number of processing steps. The slopes of linear load functions offer a precise measurement of the mental-processing rate of the iterated operation – single-digit addition in this case. The load function for the old is slightly steeper than the load function for the young, with slopes of 1533 ms/digit and 1320 ms/digit respectively. These measures allow a conclusion as precise as any micro-research: the addition rate in elderly participants was slowed by a factor of 1533/1320 = 1.16, or 16%.
Figure 1 (upper right panel) shows the same data reconfigured as a Brinley plot. Where there are eight points in the load functions (four points for the old, and four points for the young), the Brinley function has only four points, one point for each load level. The data for each level can be construed as an (X, Y) pair, defined by (RT(young), RT(old)). These pairs are entered in a scatter-plot, with RT(young) values composed along the abscissa, and RT(old) values along the ordinate. It can be demonstrated both analytically and empirically that when the load functions are linear, the Brinley function will also be linear (as can be seen in the right panel), and further, that the slope of the Brinley function will be equal to the ratio of the slopes of the component load functions (1.16 in this case) (Myerson, Adams, Hale, & Jenkins, 2003). Thus the slowing factor for mental arithmetic can be read off the slope of the Brinley function.
In the case of mental arithmetic, this exercise gains us nothing – the aging outcome is given in a more insightful form in the load functions themselves. In the fields of cognitive aging, however, and of cognition itself, iterative tasks are rare. Most experiments involve comparisons between conditions unrelated by any quantitative parameter from which load functions might be constructed. These data can still, however, be plotted as a Brinley function. The value of the Brinley plot then arises from the fact that it can be constructed from any ensemble of conditions that yield paired young-old data points. Indeed, data sets need not be restricted to individual experiments. A Brinley plot provides a convenient format for combining data across studies; from the onset, meta-analyses of age and response times have adopted this methodology.
The first of those meta-analyses was published by Cerella, Poon, & Williams (1980), based on a 99 data points taken from 18 studies. Their result was striking – the locus of points was highly linear, described by the regression equation RT(old) = 1.36 RT(young) – 70 ms with an R2 of .95. (We note that this R2 value reflects the amount of variance in condition means of older adults that can be explained from condition means of younger adults; this obviously neglects a large portion of the total variance in RT. In other words, we can explain the condition means of older adults very well, but that does not necessarily imply high predictability at the individual level.) Subsequent data sets showed a similar pattern (e.g., Cerella, 1985, 1990; Myerson, Hale, Wagstaff, Poon, & Smith, 1990). The regularity of this outcome gave rise to the idea that, from the perspective of cognitive aging, performance on a wide variety of tasks could be viewed as the outcome of a single processing stream. The stream differs in content from task to task, and in duration from condition to condition – differences of a sort that may be exposed by micro-theories, but are irrelevant to a macro-theory. A linear Brinley function puts strong constraints on the processing stream of older adults: First, it must correspond, step-by-step, to the young-adult stream; and second, the stream rate, whatever its value in the young adult for a particular task, is slowed by a constant proportion in older adults (Cerella, 1994). The claim that all computational processes in older adults are slowed to the same degree, indexed by the slope of the Brinley function (the slope of 1.36 from the Cerella et al. meta indicates 36% slowing), is known as the ‘generalized slowing’ hypothesis.
Aging in three dimensions: Age-related dissociations by task domain
Verhaeghen (2006) offers a recent update of the classical meta-analyses just cited, including a total of 1,354 young-old RT pairs from 190 studies (with the stipulation that RT(young) = 2000ms; this meta-analysis also investigated accuracy, but this aspect of the analysis will not be summarized here). The RT results (which we will revisit in more detail below) are shown in Figure 2. A single linear function fitted the full data set well (RT(old) = 1.46 RT(young) – 74 ms , R2 = .79), with values that replicated the 1980 Cerella et al. result closely (46% slowing).
Despite the fact that a single line describes the data fairly well, the scatter in Figure 2 is conspicuous, and raises the possibility that the degree of slowing may be less than uniform from task to task. This impression was reinforced by a multi-level regression (Sliwinski & Hall, 1998) that assessed the linear trend within each of the 190 studies. This analysis exposed significant heterogeneity in slope values. In such a broad database the causes of heterogeneity may be uninteresting: differences in the absolute age of the subject samples (sexagenarians, octogenarians), in the populations sampled (in college, out of college; independently living, institutionalized), in the experimental methodology (paper-and-pencil, computer), in modality (visual, auditory), in the amount of practice (disuse effects, Barron and Cerella, 1993), etc. Beginning with the first meta-analysis of Cerella et al. (1980), heterogeneity has been attributed to far more interesting differences, those of task domain.
Figure 1 (lower left panel, square symbols) shows data from another task in the Verhaeghen and Cerella (2002) experiment that illustrates heterogeneity in slowing due to task domain. Participants performed a pattern-detection task; 4, 7, 9, or 11 dots were scattered over the screen, and participants had to determine if four of the dots occupied the corners of a possible square. Like the arithmetic data (which are lifted from the upper panel and duplicated in the lower panel, round symbols), detection RTs were a linear function of the load parameter (the number of foils in the display, 0, 3, 5, or 7). This task was easier than mental arithmetic – the load functions were considerably shallower, with slopes of 392 ms/foil (young) and 679 ms/foil (old). But the slowing factor defined by these processing rates, 679/392 = 1.73, was considerably greater than arithmetic slowing (73% versus 16%). Here then is a difference in age outcome due to a difference in task domain, with other variables such as subject sample and amount of practice, etc., held constant. In the lower right panel, data from both tasks are combined in a Brinley plot – two lines are needed for an adequate description of this dataset, one line is not sufficient. This is a direct consequence of the fact that processing in the two tasks is slowed by different factors. These data echo similar data obtained from meta-analytic Brinley plots that suggest that verbally- or semantically-based tasks are bound by a common slowing factor which is less than the factor that governs spatially-based tasks (Lima, Hale, & Myerson, 1991; Myerson & Hale, 1993), with a slope around 1.5 for the verbal trend, and around 2.0 for the spatial trend.
The verbal-spatial distinction is one of two that have arisen in meso-research. The other is the distinction between peripheral (i.e., perceptual and motor processes), and central (i.e., computational and decision) processes (Cerella, Poon, & Williams, 1980; Cerella, 1985). This distinction followed experimental findings that tasks with minimal computational demands show lesser deficits than heavily computational tasks, with a slope around 1.2 for the sensory-motor trend, and around 1.5 for the computational trend.
Guided by these meso-theories, tasks in the Verhaeghen (2006) survey were divided into four classes as follows:
1. Simple Decisions (104 observations): single reaction times, choice reaction times, saccadic reaction times, digit-digit reaction times, vocal reaction times, initiation time for single reaction times, preparation times for target detection, attentional capture, and mouse movement times (this class comes closest to a peripheral or sensory-motor class);
2. Lexical (252 observations): letter reading, lexical decision, word naming, picture naming, semantic category judgment, semantic matching, semanticity judgment, synonym matching, synonym-antonym production, reading rates, speech discrimination, spoken word identification, grammatical judgment, and generating an appropriate verb for a noun;
3. Spatial (646 observations): visual search, visual marking, location discrimination or detection, line length discrimination, orientation detection, shape classification, pattern detection, shape identity judgment, distance judgment, matrix scanning, pro-saccade tasks and the Simon task;
4. All Other (352 observations): enumeration, arithmetic, alphabet arithmetic, memory retrieval, letter cancellation, digit-symbol substitution, auditory classification of consonants, color naming, odd/even judgments on digits, Stroop or other kinds of response-inhibition, and the like (Note that some tasks examined below under the heading of ‘executive control’ are grouped here).
A multilevel regression analysis was applied to the dataset to determine which, if any, classes were governed by distinct slowing factors. Its outcome defines the ‘dimensionality’ of simple tasks from the perspective of cognitive aging (conditional, of course, on the classification scheme in force).
The outcome is presented in Figure 2. Three distinct slowing factors were obtained, with the trifurcation emanating from a common origin at (470, 640). The lowest limb of the trifurcation was defined by lexical tasks, which exhibited not age-related slowing, but an age-related speed-up, by a factor of 0.8. This striking result is in line with the finding that older adults in modern aging studies typically show an age advantage in standardized tasks that require active or passive retrieval from the lexicon (Verhaeghen, 2003). Simple-decision tasks and unclassified tasks clustered together on the middle limb of the trifurcation, with a slowing factor of 1.5. Spatial tasks occupied the highest limb, with a slowing factor of 2.0. Altogether the trifurcation explained 92% of the within-study variance in condition means, compared to 83% when only RT(young) was used as a predictor.
The cause of these dissociations is as yet unclear. We cite one small observation: Bopp (2003) found that processing times for verbal items in working memory showed less slowing than processing times for visuospatial items cast as exact analogues to the verbal items. Thus the stimulus type seemed to force a dissociation while the task remained the same: The type of material (verbal versus visual) may be more important than the type of processing.
One unanticipated result was that many cognitive tasks – those falling under the ill-defined category of other – displayed no more slowing than was observed for simple decisions. Thus many tasks that are commonly assumed to demonstrate age-related ‘cognitive’ slowing may in fact be affected no more than any simple decision – slowing in sensory-motor and response selection processes. In this light, researchers would do well to include a simple decision of some sort as a control in their aging designs. We would argue that aging effects in cognitive tasks are truly interesting only if they exceed the simple-decision deficit.
We would like to point out another methodological consequence of these findings, namely its implications for the analysis of age by condition interactions (see Cerella, 1995, Faust, Balota, Ferraro, & Spieler, 1999, for earlier and more exhaustive treatments of this problem). The relationship between RTs of younger and older adults is near-multiplicative. This implies that with increasing task duration, even within each of the domains proposed here, the absolute difference between RTs of younger and older will increase as well (with the exception of lexical tasks). Conventional techniques for assessing age by condition interactions (analysis of variance, first and foremost) test for this absolute difference, and can therefore be expected to generate false positives. An example illustrates this. Our best estimate of the equation relating the RTs of young and old adults in spatial tasks is RT(older) = 2*RT(young) – 270 (Verhaeghen, 2006). Assume that groups of young and old adults perform a task such as visual search with five distractors. Young adults take 1,000 ms in this condition; then we would expect older adults to take (2*1000 – 270) ms, or 1,730 ms. The absolute age difference is 730 ms. We then make the task more difficult by increasing the number of distractors, so that the young adults now take 2000 ms. The expected value for older adults in the harder condition is (2*2000 – 270) ms, or 3730 ms. The absolute age difference is now 1730 ms, much larger than in the easier condition. If the data are at all reliable, an ANOVA will flag the age by condition interaction as significant, and the researcher might conclude that older adults have particular difficulty with larger displays. From the perspective of a macro- or meso-theory, however, the same slowing factor is operating in the two conditions; no additional mechanism needs to be invoked to explain the increase in the absolute age difference between conditions.
Aging in one additional dimension:
Age-related dissociations in tasks requiring executive control
We turn now from tasks that can be defined by a single processing stream to tasks involving multiple processing streams. Let us call single-stream tasks ‘simple’; multiple-stream tasks will be referred to as ‘compound’. Interest in compound tasks arises from the control processes they are thought to necessitate: the need either to suppress (as with the Stroop) or else to maintain and coordinate (as with dual- and switching-tasks) two processing streams.
Control processes are measured indirectly, by means of experimental designs that contrast the duration of a task component executed in two contexts, the simple-task context or baseline, and the compound-task context. For example ink-color naming latencies may be measured with the neutral stimulus XXXX, and with conflicting color words, BLUE, RED, etc.; or parity judgments (“Is the digit 7 odd or even?”) may be measured in same-task blocks of trials, and in mixed-task blocks alternated with magnitude judgments (“Is the digit 7 greater than or less than 5?”). We will refer to the context manipulation as the ‘compounding’ of a task or component. In most cases compounding leads to an increase in RT over the baseline. The primary literature is predicated on the assumption that the RT increase reflects the intrusion of control processes. Theories of control processes stand or fall dependent on the magnitude of the increase in various situations.
This somewhat elaborate data structure, the contrast between a set of compound tasks and the corresponding simple tasks, is complicated further in an aging study. We are then seeking to compare the age deficit in the compound tasks with the age deficit in the simple tasks. The comparison will expose a deficit specific to the control process, if any exists. In the meso-theoretic framework this maps neatly onto a test for dissociation between the compound tasks and the simple tasks in a Brinley analysis. This is the methodology we bring to bear in what follows. As noted earlier, this approach avoids the hazard of false positives arising from the use of an analysis of variance on raw RTs, a hazard that pervades the aging literature.
Control Costs
A complicating factor is that the effects of executive control are themselves not well understood. The common (often implicit) assumption is that compounding adds an extra stage to the processing stream (task-switching studies provide the clearest examples of this interpretation; e.g., Allport, Styles, & Hsieh, 1994; Pashler, 2000). In that case, the cost of executive intervention can be calculated by subtracting the simple RTs from the compound RTs. An often unrecognized possibility is that the control cost may be expressed non-additively. For instance, executive oversight may prolong each step of a processing stream by a constant multiple. An astute test for age deficits in control must first resolve the form of its influence on the processing stream, and explore the consequences for a Brinley analysis.
To quantify the influence of control processes an adjunct to the Brinley plot is useful, called a state-space plot (Mayr, Kliegl, & Krampe, 1996). In state space, performance on a set of compound tasks is plotted as a function of performance on the corresponding simple tasks. The resulting locus of points is the state trace. Thus the state trace follows the performance of a single subject group across conditions. In an aging study, data from the young will define one trace, and data from the old will define another trace.
Endless configurations of Brinley functions and state traces are possible. Here we present a framework within which a number of canonical configurations are open to straightforward interpretation (see Verhaeghen, Steitz, Cerella, & Sliwinski, 2002, Appendix A, for a formal mathematical treatment), namely the cases of additive and multiplicative complexity.
One effect of compounding may be to add an extra processing stage to a task, perhaps by imposing a fixed overhead cost or ‘set-up charge’. We call this type of compounding additive, because its effect is to add a constant interval to the simple RT. This outcome is illustrated in the top row of Figure 3, which shows data from another task from Verhaeghen, Cerella, and Basak (2006). In the simple conditions, 6, 7, 8, or 9 Xs were scattered over the screen; the task was to count the Xs. In the compound conditions, several Os appeared as distractors among the Xs. As seen in the left panel, the effect of this manipulation was to elevate the compound load function above the simple load function – bypassing the distractors apparently added a step to the processing stream but did not reduce the counting rate. As seen in the center panel, the resulting state trace is a line elevated above and parallel to the diagonal. This figure also shows that the state trace for the old is elevated above and parallel to that of the young. This will be true regardless of the age-related slowing factors. The corresponding Brinley plot, however, can have two parallel lines or one, depending on whether or not age-related slowing is larger in the compounded condition than in the baseline condition. The obtained Brinley function from our experiment is given in the right panel. It shows two lines rather than one; thus compounding induces a dissociation in the Brinley plot for this task. This two-part analysis allows us to conclude that (a) counting-with-distractors leads to an additive cost in RT, and that (b) the age difference in counting-with-distractors was proportionally larger than that observed in counting per se.
Alternately in our framework, compounding may prolong each step in the original processing stream. We call this type of compounding multiplicative, because it induces multiplicative effects in the state trace. This outcome is illustrated in the bottom row of Figure 3. The round symbols in the left panel repeat data from the mental arithmetic task already seen in Figure 1. The square symbols show data from a ‘bracketed’ version of the task (e.g., [5 – (1 + 2)] + [(2 + 6) – 3] = 7). This kind of compounding forced participants to store intermediate results and to reorder operations. As can be seen in the lower left panel, the compounded load functions were steeper than the simple load functions – negotiating the brackets slowed the rate of the addition process itself. The state trace in the lower center panel is a line steeper than the diagonal; the multiplicative cost is given directly by the slope of this line. The state trace of old adults will either overlay the state trace of the young adults or else will diverge from it, depending on whether the multiplicative cost in the old is equal to or greater than the multiplicative cost in the young. The Brinley functions follow the state traces, and will dissociate or not depending on whether the control cost in the old is equal to or greater than the control cost in the young. In the case of mental arithmetic, both the state-traces and the Brinley functions point to an age deficit in the multiplicative cost associated with bracketed arithmetic.
In our view, then, an answer to two questions is critical to establishing an age-related deficit specific to executive-control manipulations: (a) Is the control manipulation associated with an additive compounding effect, a multiplicative compounding effect, or both?; and (b) Can an age deficit specific to this effect be reliably observed?
Age claims
The three ‘compounding’ paradigms mentioned at the outset, Stroop, dual-task and task-switching, have been studied intensively in cognitive aging. Results have lead to claims of age declines in executive processes in all three cases (for a recent overview, see McDowd & Shaw, 2000; for our classification of control processes, we used Miyake, Friedman, Emerson, Witzki, & Howerter, 2000):
1. Resistance to interference, also known as inhibitory control, has been a central explanatory construct in aging theories throughout the 1990s (e.g., Hasher & Zacks, 1988; Hasher, Zacks, & May, 1999; for a computational approach, see Braver & Barch, 2002). A loss of inhibitory control would lead to mental clutter in older adults’ working memory, thereby limiting its functional capacity, and perhaps also its speed of operation;
2. Age-related deficits have been posited in the ability to coordinate multiple tasks or processing streams. Much of the relevant literature pertains to dual-task performance (e.g., Hartley & Little, 1999; McDowd & Shaw, 2000), but this type of deficit has also been raised in the working memory literature (e.g., Mayr & Kliegl, 1993). Losses in coordination appear to be necessary to explain age differences in compound contexts in excess of those projected on the basis of mere slowing;
3. Age and task-switching deficiencies have been targeted in a surge of publications from the late 1990s and early 2000s (e.g., Mayr, Spieler, & Kliegl, 2001). Much like the coordination theories, this work considers age declines in task-switching efficiency as additional to other deficits that may exist in the cognitive system;
4. A fourth control process, working memory updating has been investigated relatively rarely in cognitive aging (e.g., Van der Linden, Brédart, & Beerten, 1994); the sparsity of data does not allow for its inclusion in our analyses.
In the sections that follow we assess these several claims, reviewing the conclusions of a number of meta-analyses conducted in our lab (We draw heavily on a previous review paper; Verhaeghen & Cerella, 2002). If any or all of these control deficits are sustained, they will add to the dimensionality or explanatory mechanisms necessary for a full account of age changes in RTs.
Aging and resistance to interference
The Stroop task and negative priming are the procedures most often used to test for age differences in resistance to interference. In the Stroop task, participants are presented with colored stimuli, and have to report the color. RTs from a baseline condition where the stimulus is neutral, for instance a series of colored Xs, are compared with RTs from a critical condition in which the stimulus is itself a word denoting a color (e.g., the word ‘yellow’ printed in red). Response times are slower in that case, due to interference from the meaning of the word. In the negative priming task, participants are shown two stimuli simultaneously, one of which is the stimulus to be evaluated (the target), the other is the stimulus to be ignored (the distractor). For instance, the participant can be asked to name a red letter in a display that also contains a superimposed green letter. If the distractor on one trial becomes the target on the next (the critical, negative priming condition), reaction time is slower than in a neutral condition where none of the stimuli are repeated (the baseline condition). Note that this effect is counterintuitive: higher levels of inhibition are associated with larger costs.
Results from two meta-analyses (Verhaeghen & De Meersman, 1998a, 1998b) are presented in Figure 4 (surveying 20 studies for Stroop and 21 studies for negative priming). Each data point represents a result from an independent subject sample. Gamboz, Russo, and Fox (2002) updated the negative-priming analysis by adding more recent studies; Verhaeghen (2006) updated both the Stroop and the negative-priming analyses by adding more recent studies and by applying multilevel modeling to the data (i.e., by taking into account that conditions are nested within studies). The pattern of results from these recent updates was unchanged from that showing in the figure.
Both Stroop interference and negative priming induced multiplicative control effects, signaled by slopes greater than unity in the state traces. This indicates that in these two tasks, the need to resist interference inflates central processing. Although both effects were multiplicative, they differed in magnitude. The inflation factor in the Stroop tasks (a slope of 1.9, indicating 90% inflation) was much larger than in the negative priming tasks (a slope of 1.1, indicating 10% inflation). The difference may be due to the temporal dynamics of the two tasks. The Stroop task involves selection of one of two information sources that are present simultaneously; negative priming involves reactivating a stimulus that was deactivated on the previous trial. The time delay alone may explain the smaller effect in negative priming.
The second result to observe in Figure 4 is the absence of age deficits specific to the interference effects in either task. A single line sufficed to capture the inflation of central processes in both young and old state traces; so too, a single line was sufficient to capture both baseline and critical conditions in the Brinley plot.
Like the inflation factor, the age-related slowing factor was larger for color naming (with or without interference, the slope of the Brinley function was 1.8) than for negative priming (with or without priming, the slope of the Brinley function was 1.04). This difference most likely reflects the nature of the baseline tasks. The typical task involved in baseline negative priming conditions is the sounding of letters or of the naming of depicted objects; both of these are lexical tasks, and so little or no slowing is expected. The baseline Stroop task involves color naming; it is possible that the large slope indicates that color naming is by nature a spatial-type task.
Aging and coordination
Coordinative ability is typically appraised in a dual-task paradigm in which performance on a single task is compared to performance on the same task when a second task has to be performed concurrently (e.g., a visual reaction time task with or without a concurrent auditory reaction time task). Verhaeghen et al. (2003) reported a meta-analysis of 33 dual-task studies that included age as a design factor. The results of their multi-level analysis are given in the top row of Figure 5.
The pattern in Figure 5 differs markedly from that in Figure 4. First, the state traces, having positive intercepts and slopes of unity, show an additive effect. This indicates that dual-tasking involves a set-up cost that does not permeate the computational processes involved in the baseline task. Second, the lines for single and dual separate out in the Brinley plot, indicating that the coordination process is slowed by a larger amount than the central computational process.
Several moderators of the dual-task effect were examined by Verhaeghen et al. (2003): the peripheral versus central locus of the primary task; the lexical versus non-lexical status of the task; its modality, visual versus auditory; and the match in modality between the primary and the secondary task. None of the moderators interacted reliably with age. Therefore, the age-sensitivity of coordination seems to arise from the control process itself, and not to how it happens to be implemented under different task conditions. Note, however, that the age effect is a small one. The slowing factor in the baseline task was 1.6 (this is the slope of the baseline Brinley function). The degree of slowing in the dual-task effect was estimated by the old/young ratio of the difference in intercepts. This factor had a value of 1.8, an increase of 20% over baseline slowing (80% – 60%).
Aging and task switching.
A more recent paradigm, called task switching (e.g., Allport, Styles, & Hsieh, 1994), studies the maintenance and scheduling of two mental task sets performed in succession. In task-switching research, the participant is shown a series of stimuli, and has to perform one of two possible tasks on each, the required task being indicated by the experimenter. For example a series of digits may be shown: if the number is printed in red, the participant must report its parity; if the number is printed in blue, the participant must report its relative magnitude. The switch in task can be predictable or not; in the former case, it can be explicitly cued (e.g., by the color coding just described) or not.
Two types of task-switching costs can be calculated. First, one can compare RTs from pure, single-task blocks, with RTs from mixed, multiple-task blocks. This is the global task-switching cost; it is thought to indicate the set-up cost associated with maintaining and scheduling two mental task sets. This cost is similar to a dual-task cost, where performance on a block of dual-task trials is compared to performance on a block of single-task trials. The two paradigms – dual-task performance and global task switching – differ mainly in their temporal dynamics: In task switching, task A and task B are performed in succession, in dual tasking, they are performed concurrently.
A second type of task-switching cost involves the comparison, within a mixed block, between trials in which a switch is actually required, with non-switch or repeat trials. This local task-switching cost is an indication of the control process associated with the actual switching.
Wasylyshyn et al. (2003) reported a multilevel meta-analysis of age and task switching based on 10 studies for global switching, and 15 studies for local switching. Their results are presented in Figure 5, middle and bottom rows. For global task switching, the compounding effect was additive; for local task switching, the compounding effect was multiplicative. Global task switching was clearly age-sensitive: In state space, the lines for younger and older adults separate out reliably, as do the lines for switch and non-switch blocks in the Brinley plot. The degree of slowing in the global task-switching cost was 2.2 (the old/young ratio of the intercept difference between mixed blocks and pure blocks), compared to a slowing factor of 1.6 in the baseline task. Local task switching was found to be age-constant: One line described the data adequately in both the state space and the Brinley plot. Again, several moderator variables were examined, but none yielded reliable interactions with age.
Aging and executive control: Summary and outlook
Two kinds of outcomes arise from our meta-analyses of aging and executive control. Tasks involving resistance to interference (Stroop and negative priming) showed a multiplicative compounding effect of the same magnitude in young and old. This was also true of local task-switching. On the other hand, global task-switching yielded an additive compounding effect, and the effect was larger for older adults than would be projected from their baseline slowing. The latter pattern was also observed for coordination (dual-task performance).
Accepting our mathematical framework, these findings can be summarized as follows. Age deficits in control were never observed when compounding costs were multiplicative, that is, when the central-processing rate was reduced. When compounding costs were additive, that is, when the processing stream was extended by an additional step but unchanged in rate, age deficits in the inserted step were found, and those deficits were larger than those extrapolated from the baseline tasks.
The same findings can be re-stated closer to the psychology of the tasks. We found that control-specific deficits did not emerge in tasks that involved active selection of relevant information, such as determining the ink color of words (Stroop), in actively ignoring or inhibiting a stimulus (negative priming), or in relinquishing attention from one aspect of the stimulus to reattach it to a different aspect (local task-switching). In those cases the selection requirement rescaled the entire processing sequence, but the rescaling was no greater in older adults than in younger adults. On the other hand, age differences emerged in tasks that involved the maintenance of two distinct mental task sets, as in dual-task performance or global task-switching. The costs of maintaining such dual states of mind were additive – some step was added or prolonged. The duration of the added step was greater for older adults than that extrapolated from the surrounding steps.
From these meta-analyses we conclude that, contrary to many claims in the literature, there is no age-related deficit specific to inhibitory control. Multiple task-set maintenance, on the other hand, does lead to an age-related deficit over and beyond the effects of general slowing in the relevant task domain. Multiple task-set maintenance could challenge the control system in several ways. The deficit could arise from the logic implemented in the coordination step itself (the most natural interpretation). But it is also possible that an age-related deficit in the capacity of working memory may be responsible for the difficulty in maintaining multiple sets (for a meta-analysis of age and working-memory, see Bopp & Verhaeghen, 2005). In that case, the underlying problem would arise from a structural limit rather than from a specific control process (Verhaeghen, Cerella, Bopp, & Basak, 2005, expand on this point).
From our meso-theoretic perspective, control-processes are not all of a kind. Some are spared by age, and others are disproportionately damaged. The identification of such differential effects in this set of basic control processes is an important step forward in our understanding of cognitive aging deficits; a step that may have implications for a broader class of more complex tasks.
General Conclusion.
Reviewing all the meta-analyses presented here, we are led to offer a modest proposal: The aging of response times unfolds in three-plus-one dimensions. Lexical tasks are largely spared from the ill effects of aging; simple decisions show modest age-related slowing; spatial tasks are slowed to a greater degree. Dual task-set maintenance adds another dimension, orthogonal to the three content-based domains, a degree of slowing that exceeds the baseline domain. Contrary to received opinion, other control processes (resistance to interference, local task switching) appear to be age-constant – the deficits reported in the primary literature may be due to insufficient statistical control for baseline slowing. The picture of cognitive aging that emerges from our analyses is both simpler and more positive than that painted in typical review articles: apart from spatial processes and tasks demanding dual task-set maintenance, no cognitive tasks appear to show deficits beyond those seen in simple decisions.
More work needs to be done. We do not know what drives the trifurcation into three dimensions; we do not know how lexical tasks apparently circumvent the restrictions on simple decisions; we know hardly anything at all about the process of working memory updating. We trust that our simple three-plus-one scheme will soon prove naïve, and are looking forward to more astute theorizing. To that end, we advocate that researchers in the field include simple-decision control conditions in their experiments, and carefully control for the effects of general slowing in their baseline measures.
References
Allport, A., Styles, E. A., & Hsieh, S. (1994). Shifting intentional set: Exploring the dynamic control of tasks. In C. Umilta & M. Moscovitch (Eds.), Attention and Performance IV (pp. 421-452). Cambridge, MA: MIT Press.
Baron, J. A., & Cerella, J. (1993). Laboratory tests of the disuse account of cognitive decline. In J. Cerella, J. M. Rybash, W. J. Hoyer, & M. Commons (1993). Adult information processing: Limits on loss (pp. 175-203). San Diego: Academic Press.
Bopp, K. L. (2003). Exploration of age-related differences in executive control processes of verbal and visuo-spatial working memory: Evidence from the repetition detection paradigm. Unpublished doctoral dissertation, Syracuse University, Syracuse.
Bopp, K. L., & Verhaeghen, P. (2005). Aging and verbal memory span: A meta-analysis. Journal of Gerontology: Psychological Sciences, 60B, 223-233.
Braver, T. S., Barch, D. M. (2002). A theory of cognitive control, aging cognition, and neuromodulation. Neuroscience and Biobehavioral Reviews, 26, 809-817.
Brinley, J. F. (1965). Cognitive sets, speed and accuracy of performance in the elderly. In A. T. Welford & J. E. Birren (Eds.), Behavior, aging and the nervous system (pp. 114-149). Springfield, IL: Thomas.
Byrne, M. D. (1998). Taking a computational approach to aging: The SPAN theory of working memory. Psychology and Aging, 13, 309-322.
Cerella, J. (1985). Information processing rates in the elderly. Psychological Bulletin, 98, 67-83.
Cerella, J. (1990). Aging and information processing rate. In J. E. Birren & K. W. Schaie (Eds.), Handbook of the psychology of aging (3rd. ed., pp. 201-221). San Diego, CA: Academic Press.
Cerella, J. (1994). Generalized slowing in Brinley plots. Journal of Gerontology: Psychological Sciences, 49, P65-P71.
Cerella, J., & Hale, S. (1994). The rise and fall in information-processing rates over the life span. Acta Psychologica, 86, 109-197.
Cerella, J., Poon, L. W., & Williams, D. H. (1980). Age and the complexity hypothesis. In L. W. Poon (Ed.), Aging in the 1980’s (pp. 332-340). Washington, DC: American Psychological Association.
Faust, M. E., Balota, D. A., Spieler, D. H., & Ferraro, F. R. (1999). Individual differences in information-processing rate and amount: Implications for group differences in response latency. Psychological Bulletin, 125, 777-799.
Gamboz, N., Russo, R., Fox, E. (2002). Age differences and the negative priming effect: An updated meta-analysis. Psychology and Aging. 17, 525-531.
Hale, S., & Myerson, J. (1996). Experimental evidence for differential slowing in the lexical and nonlexical domains. Aging, Neuropsychology, and Cognition, 3, 154-165.
Hartley, A. A., & Little, D. M. (1999). Age-related differences and similarities in dual task interference. Journal of Experimental Psychology: General, 128, 416-449.
Hasher, L., & Zacks, R. T. (1988). Working memory, comprehension, and aging: a review and a new view. In G. H. Bower (Ed.), The psychology of learning and motivation (Vol. 22, pp. 193-225). San Diego, CA: Academic Press.
Hasher, L., Zacks, R. T., & May, C. P. (1999). Inhibitory control, circadian arousal, and age. In D. Gopher & A. Koriat (Eds.), Attention & Performance, XVII, Cognitive Regulation of Performance: Interaction of Theory and Application (pp. 653-675). Cambridge, MA: MIT Press.
Kahana, M. J., Howard, M. W., Zaromb, F., & Wingfield, A. (2002). Age dissociates recency and lag recency effects in free recall. Journal of Experimental Research: Learning, Memory, and Cognition, 28, 530-540.
Kausler, D. H. (1991). Experimental psychology, cognition, and human aging (2nd ed.). New York: Springer-Verlag.
Kliegl, R., Mayr, U., & Krampe, R. T. (1994). Time-accuracy functions for determining process and person differences: An application to cognitive aging. Cognitive Psychology, 26, 134-164.
Li, S.-C., Lindenberger, U., & Frensch, P. (2000). Unifying cognitive aging: From neuromodulation to representation to cognition. Neurocomputing, 32-33, 879-890.
Lima, S. D, Hale, S., Myerson, J. (1991). How general is general slowing? Evidence from the lexical domain. Psychology and Aging, 6, 416-425.
Lindenberger, U., & Baltes, P. B. (1997). Intellectual functioning in old and very old age: Cross-sectional results from the Berlin Aging Study. Psychology and Aging, 12, 410-432.
Luce, R.D. (186). Response times. Oxford UK: Oxford University Press
Mayr, U., & Kliegl, R. (1993). Sequential and coordinative complexity: Age-based processing limitations in figural transformations. Journal of Experimental Psychology: Learning, Memory, and Cognition, 19, 1297-1320.
Mayr, U., Kliegl, R., & Krampe, R. (1996). Sequential and coordinative processing dynamics in figural transformation across the life span. Cognition, 59, 61-90.
Mayr, U., Spieler, D. H., & Kliegl, R. (2001). Aging and executive control. New York: Routledge.
McDowd, J. M., & Shaw, R. J. (2000). Attention and aging: A functional perspective. In F. I. M. Craik & T. A. Salthouse (Eds.), The Handbook of Aging and Cognition (2nd ed., pp.221-292). Mahwah, N. J.: Erlbaum.
Meyer, D. E., Glass, J. M., Mueller, S. T., Seymour, T. L., & Kieras, D. E. (2001). Executive-process interactive control: A unified computational theory for answering 20 questions (and more) about cognitive aging. European Journal of Cognitive Psychology, 13, 123-164.
Miyake, A., Friedman, N. P., Emerson, M. J., Witzki, A. H., & Howerter, A. (2000). The unity and diversity of executive functions and their contributions to complex “frontal lobe” tasks: A latent variable analysis. Cognitive Psychology, 41, 49-100.
Myerson, J., Adams, D. R., Hale, S., & Jenkins, L. (2003). Analysis of group differences in processing speed: Brinley plots, Q-Q plots, and other conspiracies. Psychonomic Bulletin and Review, 10, 224-237.
Myerson, J., & Hale, S. (1993). General slowing and age invariance in cognitive processing: The other side of the coin. In J. Cerella, J. Rybash, W. Hoyer, & M. L. Commons (Eds.), Adult information processing: Limits on loss (pp. 115-141). San Diego, CA: Academic Press.
Myerson, J., Hale, S., Wagstaff, D., Poon, L. W., & Smith, G. A. (1990). The information-loss model: A mathematical theory of age-related cognitive slowing. Psychological Review, 97, 475-487.
Park, D. C., Polk, T. A., Mikels, J. A., Taylor, S. F., & Marshuetz, C. (2001). Cerebral aging: Integration of brain and behavioral models of cognitive function. Dialogues in Clinical Neuroscience, 3, 151-165.
Pashler, H. (2000). Task switching and multitask performance. In Monsell, S., and Driver, J. (editors). Attention and Performance XVIII: Control of mental processes. Cambridge, MA: MIT Press.
Ratcliff, R., Spieler, D., & McKoon, G. (2000). Explicitly modeling the effects of aging on response time. Psychonomic Bulletin and Review, 7, 1-25.
Raz, N. (2000). Aging of the brain and its impact on cognitive performance: Integration of structural and functional findings. In: F.I.M. Craik and T.A. Salthouse (Eds.) Handbook of Aging and Cognition (Second edition, pp. 1-90). Mahwah, NJ : Erlbaum.
Salthouse, T. A. (1991). Theoretical perspectives on cognitive aging. Hillsdale, NJ: Erlbaum.
Salthouse, T. A. (1996). The processing-speed theory of adult age differences in cognition. Psychological Review, 103, 403-428.
Sliwinski, M., & Hall, C. B. (1998). Constraints on general slowing: A meta-analysis using hierarchical linear models with random coefficients. Psychology and Aging, 13, 164-175.
Van der Linden, M., Brédart, S., & Beerten, A. (1994). Age-related differences in updating working memory. British Journal of Psychology, 85, 145-152.
Verhaeghen, P. (2006). Cognitive aging in three-plus-one dimensions: A meta-analysis of age-related dissociations in response times. Manuscript under review.
Verhaeghen, P., & Cerella, J. (2002). Aging, executive control, and attention: A review of meta-analyses. Neuroscience and Biobehavioral Reviews, 26, 849-857.
Verhaeghen, P., Cerella, J, & Basak, C. (2006). Aging, task complexity, and efficiency modes: The influence of working memory involvement on age differences in response times for verbal and visuospatial tasks. Aging, Neuropsychology, and Cognition, 13, 254-280.
Verhaeghen, P., Cerella, J., Bopp, K. L., & Basak, C. (2005). Aging and varieties of cognitive control: A review of meta-analyses on resistance to interference, coordination and task switching, and an experimental exploration of age-sensitivity in the newly identified process of focus switching. In R. W. Engle, G. Sedek, U. von Hecker, & D. N. McIntosh (Eds.), Cognitive Limitations in Aging and Psychopathology: Attention, Working Memory, and Executive Functions (pp.160-189). Cambridge, MA: Cambridge University Press.
Verhaeghen, P., Cerella, J., Semenec, S. C.; Leo, M. E., Bopp, K. L., &. Steitz, D. W. (2002). Cognitive efficiency modes in old age: Performance on sequential and coordinative verbal and visuo-spatial tasks. Psychology and Aging, 17, 558-570.
Verhaeghen, P., & De Meersman, L. (1998a). Aging and negative priming: A meta-analysis. Psychology and Aging, 13, 435-444.
Verhaeghen, P., & De Meersman, L. (1998b). Aging and the Stroop effect: A meta-analysis. Psychology and Aging, 13, 120-126.
Verhaeghen, P., & Salthouse, T. A. (1997). Meta-analyses of age-cognition relations in adulthood: Estimates of linear and non-linear age effects and structural models. Psychological Bulletin, 122, 231-249.
Verhaeghen, P., Steitz, D. W., Sliwinski, M. J., & Cerella, J. (2003). Aging and dual-task performance: A meta-analysis. Psychology and Aging, 18, 443-460.
Washylyshyn, C., Verhaeghen, P., & Sliwinski, M. J. (2003). Aging and task switching: A meta-analysis. Manuscript submitted for publication.
Welford, A. T. (1977). Motor performance. In J. E. Birren and K. W. Schaie (Eds.), Handbook of the Psychology of Aging (p. 450-496). New York: Van Nostrand Reinhold.

Figure captions
Figure 1. From load functions (left panels) to Brinley functions (right panels) in an arithmetic task (top panels) and an arithmetic and a pattern detection task (bottom panels) (data from Verhaeghen, Cerella, & Basak, 2006).
Figure 2. Brinley plot from 1,354 data points from 190 studies, as a function of task type (from Verhaeghen, 2006).
Figure 3. Illustration of additive and multiplicative complexity effects in two experimental tasks: reaction time as a function of difficulty, Brinley plots and state traces. In the latter two graphs, the diagonal is indicated by a full line (from Verhaeghen & Cerella, 2002).
Figure 4. Brinley plots and state traces for two tasks for resistance to interference (Stroop and negative priming). The diagonal is indicated by a full line (from Verhaeghen & Cerella, 2002).
Figure 5. Brinley plots and state traces for dual-task performance and global and local task-switching. The diagonal is indicated by a full line (from Verhaeghen & Cerella, 2002).

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