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Aging, Focus Switching, Task Switching p. 3

Aging, focus switching and task switching in a continuous calculation task:

Evidence toward a new working memory control process

Age-related deficits in cognitive functioning have been observed in a large variety of

tasks, such as simple and choice reaction times, working memory tasks, tests of episodic

memory, tests of spatial and reasoning abilities, mental rotation, and visual search (for

reviews, see e.g., Kausler, 1991; Salthouse, 1985, 1991). It has also been noted that many

of the observed declines are correlated across tasks (Lindenberger & Baltes, 1994;

Salthouse & Ferrer-Caja, 2003;Verhaeghen & Salthouse, 1997), suggesting that a small

number of factors may account for the majority of age differences. Many researchers

have claimed that the fundamental factors may well be relatively general processes or

general aspects of cognition (e.g., Cerella, 1990; Hasher & Zacks, 1988; Li,

Lindenberger, & Frensch, 2000; Salthouse, 1996).

Early accounts of cognitive aging pointed to deficits in elementary processing

resources, such as speed (Birren, 1965; Salthouse, 1996), but recently, attention has

turned to processes of executive control as a basic mechanism to explain age differences

in relatively complex aspects of cognition. Age effects in several aspects of cognitive

control have already been investigated; notably, task coordination (e.g., Mayr & Kliegl,

1993; for a meta-analysis, see Verhaeghen, Steitz, Sliwinski, & Cerella, 2003), task

switching (e.g., Mayr, Spieler, & Kliegl, 2001; for a meta-analysis, see Wasylyshyn,

Verhaeghen, & Sliwinski, 2004), and inhibition (e.g., Hasher & Zacks, 1988; Hasher,

Zacks, & May, 1999; for a computational approach, see Braver & Barch, 2002; for meta-

analyses, see Verhaeghen & De Meersman, 1998a, 1998b). Recently, we (Verhaeghen &

Basak, in press; Verhaeghen, Cerella, Bopp, & Basak, in press) have argued for the


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Another possibility is that in old age items decay more rapidly when stored outside the

focus of attention.

An important question is whether focus switching is indeed a cognitive primitive.

In the Verhaeghen and Basak (in press) study, we compared focus-switching with two

other control processes that might be related to or implicated in focus switching. The first

was updating, that is, the requirement to change the identity of an item that is stored in

working memory. In focus switching, updating the content of the focus, and potentially of

items outside the focus, seems to be one of the constituent processes. The second

comparison process was (global) task switching. Task switching and focus switching

obviously share a switching requirement. In focus switching, the task remains the same

across trials, but items have to be swapped in and out of the focus of attention. In task

switching, the task changes from trial to trial, but no storage (and therefore no swapping)

of items is necessary. Switching between tasks, like focus switching, increases response

times (e.g., Jersild, 1927; Rogers & Monsell, 1995). (Note that in this study, as in the

present experiment, we compared alternating sequences with pure sequences for task

switching, thereby including local, or specific, task switching costs, due to selection

between task sets, in the global task switching cost.) Our study suggested quite clearly

that focus switching is largely independent from both updating and task switching. First,

focus-switch costs did not interact with either updating costs (Experiments 1 and 2) or

global task-switching costs (Experiment 2). Second, two age-related dissociations were

found: Focus switching was age-sensitive in accuracy, but no age-sensitivity was found

for the either updating or task switching. Such dissociations can be taken as evidence for

the modular independence of processes (Perfect & Maylor, 2000; Sternberg, 2001).


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Taken together, our earlier findings suggest (a) that focus switching is a control process

in its own right, distinct from task switching and updating, and (b) that focus switching

shows a specific age-related deficit, but only in the accuracy domain.

The current experiment

The aim of the present study is to provide additional evidence regarding the

particulars of this process of focus switching. More specifically, we examined three main

questions. First and foremost, we investigated whether focus-switching costs in both

response times and accuracy could be observed in a new task, namely a continuous-

calculation task. This would indicate that the process is not task-specific, but rather

operates whenever a focus switch is necessary. Second, we investigated whether this

focus-switching cost was larger in older adults than in younger adults in the accuracy

domain, but not the response time domain, as could be predicted from the N-Back study.

Third, we tested whether further evidence could be found for the independence of the

focus-switching process from the processes involved in global task switching. To assess

independence, we used the dissociation method described above, that is, we examined

whether both processes were equally sensitive to aging, or not. If they were not, this

would be evidence for independence. Additionally, we examined the response time

distributions using ex-Gaussian decomposition (see Methods), and examined whether the

two types of switching yielded identical effects on all three parameters. If they did not,

this would indicate independence.

Our paradigm of choice was a continuous calculation task. The task was modeled

after a number reduction task used by Woltz, Bell, Kyllonen, and Gardner (1996) and

Woltz, Gardner, and Bell (2000). In the continuous calculation task, participants are


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the next number shown on the screen (midpoint rule). When the numbers differed by

one, the participant reported the next number in the up or down sequence, and used that

number to be combined with the next number shown on the screen (up-and-down rule).

To aid participants, all items for which the midpoint rule had to be used were shown in

yellow on a black background; all up-and-down items were shown in light blue on the

same black background.

Focus switching was manipulated by having the participant work on one

continuous series (single condition, no focus switching) versus having the participant

work on two series, each one shown in a different column on the screen (dual condition,

focus switching). Task switching was manipulated orthogonally by either having the

participant work according to a single rule throughout a trial (pure condition) or by

mixing the two rules according to a predictable ABAB schema, always starting with

the midpoint rule (mixed condition). Note that this implies that in the combination of

focus switching and task switching (a mixed dual trial), the right-hand column always

contained only midpoint items, the left-hand column only up-and-down items. Table 1

shows an example for each of the four conditions.

Each stimulus set (a trial) contained 10 to-be-responded to items. After each

trial, the subject received feedback about accuracy and average response time. An online

algorithm that used a random seed determined the exact composition of a trial; after the

second item was presented, the participants response was used to construct the next item.

This was done to spare the participants confusion after they made an error we simply

took the erroneous answer as the basis for the next item. Note that the number of errors in

the pure, single condition was extremely low. Therefore, we can assume that there were


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97.5th

percentile; in practice, this amounted to discarding response times longer than 7 s.

This concerned 1.11% of the data of the young and 4.25% of the data of the old.

Alpha level for all statistical testing was set at p = .05.

Results

Response time analysis

The response time results are presented in Figure 2. We conducted an ANOVA

with focus switching (single vs. dual), and task switching (pure vs. mixed) as within-

subject factors, and age category (younger vs. older) as the between-subject factor. Only

the main effects were significant: single trials were executed faster than dual trials, F (1,

47) = 75.71, MSE = 118,362.33; pure trials were executed faster than mixed trials, F (1,

47) = 65.92, MSE = 39,470.27, and older adults were slower than younger adults, F (1,

47) = 34.19, MSE = 1,600,682.37. None of the interaction terms reached significance, all

Fs < 1.

Ex-Gaussian decomposition of response times

Results of the ex-Gaussian decomposition are depicted in Figure 3. The parameter

estimates were not independent: The two Gaussian components (mu and sigma) were

highly positively correlated (median r = .87), mu and tau tended to have a moderately

negative correlation (median r = -.21).

For the mu parameter (the mean of the Gaussian component), all three main

effects were significant. Single trials yielded lower values of mu than dual trials, F (1, 47)

= 36.92, MSE = 284,349.01. Pure trials yielded lower values of mu than mixed trials.

Older adults had higher mu values than younger adults, F (1, 47) = 27.18, MSE =

1,160,573.06. None of the interactions terms reached significance, all Fs < 2.03.


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For the sigma parameter (the standard deviation of the Gaussian component), only

the main effects of focus switching and age were significant in the expected direction.

Single trials yielded lower values of sigma than dual trials, F (1, 47) = 31.30, MSE =

66,576.83, and older adults had higher values of sigma than younger adults, F (1, 47) =

4.95, MSE = 153,509.86. There was a significant main effect of task switching, F (1, 47)

= 9.52, MSE = 13,751.78, but this went in the opposite direction from what would be

expected: Mixed trials yielded smaller values of sigma than pure trials. This effect was

rather small (367 ms vs. 315 ms). None of the interaction terms reached significance, all

Fs < 1.

For the tau parameter (the mean of the exponential component), the main effects

of focus switching and age reached significance. Dual trials yielded higher values of tau

than single trials, F (1, 47) = 15.66, MSE = 71,298.50, and older adults had higher values

of tau than younger adults, F (1, 47) = 26.09, MSE = 91,451.45. Task switching

interacted with focus switching; the increase in tau due to focus switching was larger in

pure trials (206 ms) than in mixed trials (96 ms). All other effects failed to reach

significance, all Fs < 1.58.

Accuracy analysis

The accuracy results are presented in Figure 2. We conducted an ANOVA with

focus switching (single vs. dual), and task switching (pure vs. mixed) as within-subject

factors, and age category (younger vs. older) as the between-subject factor. All main

effects were significant: single trials yielded higher accuracy than dual trials, F (1, 47) =

68.49, MSE = 0.003; pure trials yielded higher accuracy than mixed trials, F (1, 47) =

5.98, MSE = 0.001, and older adults had lower accuracy overall than younger adults, F


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increase. The focus-switching effect is therefore almost three times as large as the already

large global task-switching effect. Focus switching decreased accuracy from 98% to

93%, or by 5%; in comparison, task switching decreased accuracy by 0.5%. These results

confirm both the existence of the focus-switching process and its importance.

We should point out that alternative accounts of these data are possible. One is

that the focus-switch cost is not related to retrieval, but that it is a function of working

memory load. Previous research (Verhaeghen & Basak, in press; Voigt & Hagendorf,

2002), however, casts serious doubt on this alternative hypothesis. In the Verhaeghen and

Basak study, increases in working load beyond two items did not produce further RT

costs in younger adults, and only slight costs in older adults. Voigt and Hagendorf clearly

showed that focus-switching costs are sensitive to the retrieval demands of the task.

Another possibility is that the RT cost is due to a speed-accuracy trade-off, that is,

participants slow down their responses in order to retain an acceptable level of accuracy.

Correlational analysis shows that this is unlikely. The correlation between the cost in RT

and the costs in accuracy is negative (-.31), indicating that individuals who slow down

most due to the focus switch are also more likely to have the largest decreases in

accuracy.

Second, we found, as predicted, that the focus-switching cost was larger for older

adults than for younger adults in the accuracy domain, but not the response time domain.

This result replicates earlier findings with the identity judgment N-Back task

(Verhaeghen & Basak, in press, Experiment 1 and Experiment 2). The previous results

were obtained with a much easier task, namely identity judgment, and were ascribed to

item interference in the zone of working memory outside the focus of attention. The


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findings of the present study are consistent with this interpretation. It is important to note,

however, that accuracy was high for both older and younger adults throughout, and it is

possible that the interaction was entirely due to a ceiling effect for the single trials. Three

arguments plead against this interpretation. First, in our opinion, the ceiling effect is not a

psychometric artifact, but it is theoretically meaningful. That is, in the pure, single

condition, we basically ask our participants if they can retrieve an item just seen on the

screen. Performance on this task should be errorless. Therefore, very high accuracy in the

pure, single condition is not an indication of failings of the experimenter to elicit a range

of performance; it is simply a characteristic of the cognitive system. Additionally, there

are two empirical reasons to trust the findings as useful rather than artifactual. First, we

conducted an exploratory analysis in which we deleted participants who performed at

ceiling, that is, with scores of 99% correct or more in the single, pure trials. We were left

with 6 younger adults and 13 older adults; the 6 selected younger adults scored 97%

correct on single, pure trials and 93% on dual, pure trials; the 13 selected older adults

scored 96% and 86%, respectively. Consequently, this selected sample yielded the same

result as the full sample: a larger focus-switch-related drop in accuracy in older adults

than in younger adults. Second, the correlation between the drop in accuracy due to task

switching and the drop in accuracy due to focus switching was relatively high (.56). If the

very high accuracy in the single, pure trials masked a higher level of true performance,

neither the focus-switch switch cost nor the task-switch cost would be meaningful

quantities, and they would not correlate.

Third, we indeed found evidence for the independence of focus switching from

global task switching. The evidence we uncovered is threefold. First, the costs in


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Third, there were differential effects of focus switching and task switching in the

parameters of the ex-Gaussian distribution. Focus switching produced a substantial

increase in each of the parameters, indicating that both the leading edge and the

dispersion (including the skew) of the distribution was affected. This can be contrasted

with the effect of task switching, which produced an increase in mu, or the leading edge

of the distribution, only. Sigma decreased slightly (by about 50 ms) when the task

switching requirement was added, and tau remained stable. Thus, task switching has the

effect of shifting the distribution along the horizontal axis, without changing its

dispersion, including the skew. As stated earlier, one-on-one correspondences between

ex-Gaussian parameters and cognitive processes are seldom obtained, and we were using

the decomposition primarily for the purpose of examining possible dissociations. Some

tentative conclusions can be drawn, however. The global task-switching results suggest

that global task switching works additively (see also Wasylyshyn, Verhaeghen &

Sliwinski, 2004), that is, the result can be explained by the insertion of a set of normally

distributed processes that do not interfere with the computational requirements of the

continuous calculation task itself. Such an insertion only affects the leading edge of the

distribution, and not its shape. The focus-switching results cannot be explained through

such a mechanism. Rather, the results suggest either that an additional ex-Gaussian

process is added to the original distribution, or that several of the main component

processes of the original distribution are slowed by a multiplicative factor. Given that the

increase in mu seems to be proportionally larger than the increase in tau, the effects are

larger for the normally distributed processes than for the exponentially distributed

component processes. The underadditive interaction between focus switching and task


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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.

Voigt, S. & Hagendorf, H. (2002). The role of task context for component

processes in focus switching. Psychologische Beitrge, 44, 248-274.

Washylyshyn, C., Verhaeghen, P., & Sliwinski, M. J. (2003). Aging and task

switching: A meta-analysis. Manuscript submitted for publication.

Woltz, D. J., Bell, B. G., Kyllonen, P. C., & Gardner, M. K. (1996). Memory for

order of operations in the acquisition and transfer of sequential cognitive skills. Journal of

Experimental Psychology: Learning, Memory, and Cognition, 22, 438-457.

Woltz, D. J., Gardner, M. K., & Bell, B. G. (2000). Negative transfer errors in

sequential cognitive skills: Strong but wrong sequence application. Journal of

Experimental Psychology: Learning, Memory, and Cognition, 26, 601-625.


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