Journal of Experimental Psychology:
Learning, Memory, and Cognition
2007, Vol. 33, No. 3, 475– 483
Copyright 2007 by the American Psychological Association
0278-7393/07/$12.00 DOI: 10.1037/0278-7393.33.3.475
Comparing Switch Costs: Alternating Runs and Explicit Cuing
Erik M. Altmann
Michigan State University
The task-switching literature routinely conflates different operational definitions of switch cost, its
predominant behavioral measure. This article is an attempt to draw attention to differences between the
two most common definitions, alternating-runs switch cost (ARS) and explicit-cuing switch cost (ECS).
ARS appears to include both the costs of switching tasks and the switch-independent costs specific to the
first trial of a run, with the implication that it should generally be larger than ECS, but worse is that the
alternating-runs procedure does not allow these costs to be separated. New data are presented to make
these issues concrete, existing data are surveyed for evidence that ARS is larger than ECS, and
implications of conflating these measures are examined for existing theoretical constructs.
Keywords: cognitive control, task switching, alternating-runs procedure, explicit cuing procedure
directly separate their effects. The aim here is to ground these
issues in a study to make them concrete, survey published data for
indirect evidence that the two measures really are different, and
finally, illustrate the relevance to some existing control-related
theoretical constructs.
Questions about how people set, focus on, and switch among the
short-term goals that govern everyday behavior are central in the
study of cognitive control. One experimental domain in which
these questions are addressed is task switching (for surveys, see
Logan, 2003; Monsell, 2003). In a typical task-switching experiment, the participant performs one of two simple tasks on each of
a (usually large) number of trials. The stimulus presented on each
trial, at least in the study reported shortly here, is a randomly
selected digit, and the task is either to judge the digit’s parity (even
or odd) or to judge its magnitude (higher or lower than 5). The
correct task for a given trial, or run of consecutive trials depending
on the procedural variant, is signaled by a task cue of some kind.
The usual empirical finding of interest, generally modulated by
some experimental manipulation, is switch cost: Performance on
switch trials, in which the task differs from the previous trial, is
worse than performance on repeat trials, in which the task is the
same as on the previous trial. Switch cost is often taken to reflect
the operation of processes involved in cognitive control (e.g.,
Monsell, 2003) but in any case is richly documented enough to call
for some sort of theoretical explanation.
Good explanations depend on good construct validity, and there
are two validity problems with how the construct of switch cost
has been reported and discussed in the literature. First, although
the two most common task-switching procedures measure switch
cost differently, this distinction has not been raised in comparative
surveys of task-switching data (e.g., Logan, 2003; Monsell, 2003).
This lack of qualification may explain some of the heterogeneity
that can be found across different studies of what is nominally the
same quantity. Second, one of the two measures is structurally
confounded, meaning that (a) its variance could be attributed to
either of two independent variables and (b) there is no way to
The Problem: Two Different Operational Definitions
The two most common task-switching procedures are explicit
cuing and alternating runs. In the explicit-cuing procedure, a task
cue is presented on every trial to indicate what task to perform on
that trial. Cue selection is randomized, such that the task could
switch from one trial to the next but could also repeat. Switch
cost— explicit-cuing switch cost (ECS)—is measured simply by
comparing switch trials with repeat trials.
In the alternating-runs procedure, in contrast, trials are grouped
into predictable-length runs that alternate between tasks (e.g.,
AABBAABB . . .). The task (A or B) is cued by the position of the
current trial within a run and usually also by the spatial location of
the trial stimulus (e.g., Rogers & Monsell, 1995) or other perceptual cue (Koch, 2003; Waszak, Hommel, & Allport, 2003). Switch
cost—alternating-runs switch cost (ARS)—is measured by comparing the trial in Position 1 of a run to the trial in Position 2. By
design, this position variable (levels 1 and 2) correlates perfectly
with the switching variable (levels switch and repeat) in that the
Position 1 trial is the switch trial and the Position 2 trial is the
repeat trial. Thus, whereas explicit cuing compares switch and
repeat within Position 1 (there being no Position 2), alternating
runs compares switch and repeat between Positions 1 and 2. A
critical issue, of course, is whether this confounding of position and
switching in the alternating-runs procedure is a mere technicality or
whether there is reason to believe that position and switching both
contribute to variance in this measure of switch cost.
For illustration of these two different switch-cost measures, an
experiment was conducted by use of a hybrid design that combines
central characteristics of the two procedures at issue. In this
experiment, trials were grouped by task into predictable-length
runs, as in alternating runs. However, a randomly selected task cue
was presented just before the Position 1 trial, as in explicit cuing.
This work was supported by ONR Grant N00014-06-1-0077. I thank
Rich Carlson, Tim Gamble, and Stephen Monsell for their comments and
suggestions for improvement.
Correspondence concerning this article should be addressed to Erik M.
Altmann, Department of Psychology, Michigan State University, East
Lansing, MI 48824. E-mail: [email protected]
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Thus, this design affords two measures of switch cost: One derived
by comparing switch and repeat trials on Position 1 (comparable
with ECS) and one derived by comparing Positions 1 and 2 on
switch runs (comparable with ARS). This procedure also affords a
measure of first-trial cost, which is the difference in performance
between Positions 1 and 2 of repeat runs. First-trial cost is an index
of processes that are deployed only on the first trial of a run and
that are independent of whether the task switches. With respect to
the alternating-runs procedure, the issue developed here is that
ARS may well include first-trial cost as well as switch cost.
The present design also preserves a feature of many alternatingruns studies, which is a constant response–stimulus interval (RSI)
between trials. A number of previous studies have demonstrated
first-trial cost in a situation in which the RSI differs for Positions
1 and 2 (Allport & Wylie, 1999, 2000; Altmann, 2004a; Altmann
& Gray, 2002; Gopher, Armony, & Greenshpan, 2000; Kramer,
Hahn, & Gopher, 1999; Waszak et al., 2003). For example, in
Experiment 4 of Allport and Wylie’s (2000) study, which was
designed to probe first-trial cost, RSI before Position 1 was 2 s,
whereas RSI between positions of a run was only 300 ms. Similarly, in Altmann’s (2004a) study, RSI before Position 1 was 1 s,
and RSI between positions within a run was zero. In these situations, first-trial effects could have emerged from the change in
event timing between Positions 1 and 2 (Gopher et al., 2000).
Indeed, the term restart cost has been used to describe these
effects, reflecting a hypothetical role for the pause coming before
Position 1, which, although brief, could have put the system into
some state from which it needs to be restarted. There is no such
pause in many alternating-runs studies (e.g., Koch, 2005; Rogers
& Monsell, 1995), so to help make the case that ARS may include
first-trial cost in these situations also, it was useful to show that
first-trial cost can arise in a situation in which RSI is uniform
between all trials.
block with the experimenter present to answer questions and
continued with 10 regular blocks. Each block contained 60 trials
and was followed by online feedback and a chance to rest. The
feedback asked participants to be more accurate if the block score
was below 90% and to be faster if the block score was 100%.
A trial began with onset of a trial stimulus and ended with the
participant’s response. A task cue appeared every other trial and
remained visible until the response for that trial. The subsequent
uncued trial was governed by the same task, meaning that trials
were grouped by task into runs of two. The RSI was 1,000 ms, and
the cue–stimulus interval (CSI) was 100 ms, also as in Koch’s
(2005, Experiments 2 and 3) study. The screen flashed after an
error, adding 400 ms after error trials.
Task cues were randomly selected subject to the constraint that
at most three repeat cues could occur in a row (as in Koch, 2005).
Trial stimuli were randomly selected subject to the constraint that
immediate and lag-two repetitions were not allowed.
Design and Analysis
The practice block and the first trial of remaining blocks were
excluded from analysis. Error trials and trials following error trials
were excluded from latency analysis. Latencies were trimmed by
taking medians. Latencies and errors were examined with a 2 (run
type: switch, repeat) ⫻ 2 (position in run: 1, 2) analysis of
variance. Task (parity, magnitude) was included in the analysis,
but its effects are not reported. Various simple-effects analyses of
variance were used to examine the costs labeled in Figure 1.
Results
The latency results appear in Figure 1, separated by run type
(switch, repeat) and position (1, 2). Latency on switch runs (1,007
Method
Switch run
Participants
Task cues and trial stimuli were taken from a recent alternatingruns study (Koch, 2005). A task cue was a square (indicating the
parity task) or diamond (indicating the magnitude task), unfilled
and 3.8 cm on a side, presented in white in the center of a dark
computer display. A trial stimulus was a digit from the set 1 to 9
excluding 5, presented with a height of 0.8 cm, also in white in the
center of the display (surrounded by the task cue). The parity task
was to judge whether the trial stimulus was even or odd, and the
magnitude task was to judge whether the trial stimulus was higher
or lower than 5. The Z and ?/ keys of a QWERTY keyboard were
used to respond to both tasks. Response-to-key mapping was
randomized between participants.
Procedure
Participants were tested individually in sessions lasting roughly
30 min. A session began with online instructions and a practice
1100
Response latency (ms)
Materials
Repeat run
1200
Fifteen Michigan State University undergraduate students participated in exchange for credit toward a course requirement. Two
additional participants were excluded from analysis because their
overall accuracy was below 90%.
ECS analog
ARS analog
1000
First-trial cost
900
800
1
2
Position in run
Figure 1. Response latencies from the experiment, showing measures
analogous to alternating-runs switch cost (ARS) and explicit-cuing switch
cost (ECS) as well as a measure of first-trial cost.
COMPARING SWITCH COSTS
ms) was marginally slower than on repeat runs (957 ms), F(1,
14) ⫽ 4.5, p ⫽ .052, MSE ⫽ 16,625. Latency on Position 1 (1,096
ms) was slower than on Position 2 (867 ms), F(1, 14) ⫽ 21.5, p ⬍
.001, MSE ⫽ 73,075. Run type and position interacted, F(1, 14) ⫽
7.9, p ⫽ .014, MSE ⫽ 8,391.
In terms of the costs labeled in Figure 1, the ARS analog was
reliable, as reflected in a simple effect of position on switch runs,
F(1, 14) ⫽ 24.5, p ⬍ .001, MSE ⫽ 46,517. The ECS analog was
also reliable, as reflected in a simple effect of run type on Position
1, F(1, 14) ⫽ 10.1, p ⫽ .007, MSE ⫽ 13,955. Finally, first-trial
cost was reliable, as reflected as a simple effect of position on
repeat runs, F(1, 14) ⫽ 14.2, p ⫽ .002, MSE ⫽ 34,949.
Error rates were 2.47% on Position 1 switch, 2.78% on Position
1 repeat, 2.01% on Position 2 switch, and 2.29% on Position 2
repeat. There were no main effects of run type or position on error
rates, and there was no interaction ( ps ⬎ .182).
Discussion
The data in Figure 1 illustrate, in the context of this hybrid
procedure, the distinctions raised above between ARS and ECS.
Of particular interest is the first-trial cost incurred on Position 1 of
a repeat run, which is almost exactly the difference between the
quantities representing analogs of ARS and ECS. This first-trial
cost represents a measure of whatever processes are triggered on
the first trial of a run but are not related to switching tasks. Any
such cost incurred in an alternating-runs study will be included
when Position 2 is subtracted from Position 1 to compute ARS.
These results also show that first-trial cost can arise in a situation in which event timing, in particular the RSI, is equal for all
trials, which is often the case in alternating-runs studies (e.g.,
Koch, 2005; Rogers & Monsell, 1995). Thus, it now seems difficult to argue that first-trial costs will be absent from ARS as long
as the particular implementation of alternating runs uses uniform
event timing.
Although these results suggest that first-trial cost contributes to
ARS, they are only indirect evidence that it does, because this
procedure is not actually alternating runs. This lack of direct
evidence reflects not so much a deficit in the present hybrid
procedure but a deeper structural limitation of the alternating-runs
procedure, which is that it has no repeat run that would allow such
evidence to be developed, one way or the other. Without a repeat
run, there is no way to estimate first-trial cost as in Figure 1 and
no way to compute switch cost net of first-trial cost by comparing
a Position 1 repeat trial with a Position 1 switch trial. The implication is that if a given manipulation in an alternating-runs study
affects ARS in some way, it is impossible to know whether this
manipulation is having its effect on first-trial processes, on switchrelated processes, or on both. The further and perhaps surprising
implication is that despite the deep roots of the alternating-runs
procedure in the task-switching domain (Fagot, 1994; Rogers &
Monsell, 1995), it offers little leverage on the question of what
processes cause switch cost, which from the outset has been the
predominant question in this literature. The explicit-cuing procedure does not have this problem, because ECS is computed within
position, which, as operationalized here in terms of predictablelength runs, is always simply 1.
That said, any procedure will have its drawbacks, and explicitcuing is no exception. Indeed, there is a line of work premised on
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the notion that ECS itself is confounded because the cost of
switching tasks is entangled with the cost of switching task cues,
with an attendant theoretical proposal that task-switch cost reduces
simply to cue-switch cost (Logan & Bundesen, 2003, 2004). This
theoretical proposal itself is weak (Altmann, in press; Mayr, 2006;
Monsell & Mizon, 2006; see also Forstmann, Brass, & Koch, in
press), and the confounding of task switching and cue switching is
actually present in any task-switching procedure that involves task
cues, including alternating runs. However, a more easily detectable
problem with explicit cuing, which is not necessarily shared by
alternating runs, is that it does not allow cue-related processing to
be separated from processing that starts with onset of the trial
stimulus. Thus, for example, explicit-cuing studies alone cannot
tell us whether manipulations of the CSI before a trial affect only
cue-related processing, as at least one model implies (Logan &
Bundesen, 2003, 2004) or whether they also affect later stages like
stimulus encoding or response selection. To develop evidence on
this point, uncued trials need to be included in the procedure,
implying a run structure of some sort, and indeed, in an experiment
similar to the one reported here in which CSI before Position 1 was
manipulated, both Position 2 and Position 1 were affected, suggesting that cue encoding was not the only process that changed
(Altmann, in press). The larger point is that these and any similar
issues that might emerge as we refine our understanding of procedures for studying cognitive control are important but separate
from the issue addressed here, which is an under-appreciated
problem with the alternating-runs procedure that the explicit-cuing
procedure does not share.
Evidence That One Switch Cost Is Larger Than the Other
Even if the alternating-runs procedure, lacking repeat runs, does
not afford a direct test of whether ARS includes a first-trial
component, one can still approach the question indirectly. This
section first develops a theoretical case that a functional adaptation
could produce first-trial cost in the alternating-runs procedure, then
reviews empirical data at two different levels— closely-matched
comparisons of the two procedures and unmatched comparisons—
suggesting that ARS is in fact larger than ECS, which is the
prediction if ARS spans a process that ECS does not.
A Theoretical Perspective
Given a situation in which trials are predictably grouped into
runs, consider the possibility that the cognitive system exploits this
regularity by opting to process the task cue on the first trial of a
run—whatever the cue, switch or repeat—in some way that it does
not process task cues on later trials of the run. The function of this
first-trial process might be to encode (Altmann, 2002) or retrieve
(Mayr & Kliegl, 2000, 2003) a mental representation of the current
task, which could then serve the system for the duration of that run,
until the next run starts. Such a first-trial strategy, whatever its
specific processing details, could have benefits even if, as assumed
here, all trials, and not just the first of a run, are accompanied by
task cues. For example, it would save having to establish the
relevant mental representation anew on every trial. It would also,
by virtue of applying to switch cues and repeat cues alike, spare the
system a decision process that would otherwise be necessary to
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distinguish whether the current cue represents a different task than
the one performed on the previous trial.
If a first-trial strategy like this were deployed when trials are
grouped into alternating runs, not just when trials are grouped into
randomized runs, then at least some of ARS would reflect first-trial
cost, plus any additional cost arising because Position 1 happens to
be a switch trial. This would be true even if a first-trial strategy
was deployed only stochastically within a given study, by some
participants on all trials, all participants on some trials, or some
other combination. (As hinted above, an alternate strategy available in the typical alternating-runs procedure, in which every trial
is accompanied by an external cue, would be to acquire task
information anew from the cue on every trial.) If the aggregate data
from a given study include any meaningful proportion of runs on
which the system deployed a first-trial strategy, then ARS for that
study will include some first-trial cost, as well as the cost of
switching tasks (the Position 1 trial also being a switch trial). Thus,
to have confidence that ARS contains no first-trial cost, one would
need to develop evidence that such a strategy was, in effect, never
used. This is a high burden that no extant alternating-runs study
can be said to have met. A conservative conclusion would therefore be that ARS, as commonly reported in alternating-runs studies, includes some amount of first-trial cost linked to at least
stochastic use of a first-trial strategy.
This analysis suggests that a cleaner implementation of the
alternating-runs procedure would be to present a task cue only on
the first trial of a run, as in the experiment reported earlier, rather
than cuing every trial. The original motivation for cuing every trial
was to helpfully relieve the experimental participant of the need to
carry the task in memory (Rogers & Monsell, 1995), but of course
this does not prevent the system from carrying the task in memory,
if this happens to be the more efficient strategy (e.g., Gray, Sims,
Fu, & Schoelles, 2006). In general, there is no way to prevent use
of memory short of inducing appropriate lesions, and indeed a fact
of life is that we often use memory to store information (like
access codes or phone numbers) because this affords fast access. In
effect, then, helpfully relieving the participant of the need to carry
a memory load unhelpfully relieves the analyst of any control over
where the participant stores information about the current task.
Cuing only the first trial of a run would limit the strategic choices
available to participants and thus make at least Position 2 latencies,
for example, interpretable in terms net of perceptual task-related
operations.
trials in the alternating-runs procedure. Despite these procedural
differences, however, there is no harm in probing performance
differences between alternating-runs and explicit-cuing procedures, and four studies to date have done so.
In the first study, Tornay and Milan (2001) reported three
experiments comparing the two procedures. In their Experiments 1
and 2, there appears to have been no interaction of the procedure
variable (alternating runs vs. explicit cuing) with switching (switch
vs. repeat). However, in their Experiment 3, in which slightly
longer runs were used in the alternating-runs procedure, ARS did
in fact seem to be larger than ECS. Figure 2 shows these results.
The solid line shows the alternating-runs (predictable) condition,
and the dashed line shows the explicit-cuing (random) condition.
The abscissa shows a generalized position variable that drops the
predictability constraint to accommodate a comparison between
predictable runs in the alternating-runs procedure and randomly
occurring runs in the explicit-cuing procedure (the relevance of
distinguishing these two kinds of runs is addressed later in this
section). ARS is simply the difference, along the solid line, between shift trials and first repetition. ECS is the difference, along
the dashed line, between shift trials and an average of first repetition and second repetition, weighted toward the former because
of the lower binomial probability of reaching two repeat trials in a
row. Comparing these representations of ARS and ECS, it seems
reasonably clear that ARS is larger, and although no statistics
involving the switching variable (switch vs. repeat) were reported
for this experiment, the interaction of the procedure and general-
Empirical Evidence From Closely Matched Experiments
From an empirical angle, there is in fact a circumstantial case
that ARS is generally larger than ECS, consistent with the proposal
that ARS includes some amount of first-trial cost. The case can
only be circumstantial because the two procedures are fundamentally different in ways that may affect the cost of switching tasks.
The most salient difference may be the predictability of tasks in the
alternating-runs procedure, which should largely eliminate any
effects of task uncertainty from trial to trial and may facilitate
anticipatory processing for pending trials in a way that the explicitcuing procedure cannot. Certainly the probability of a task switch
is known to affect performance (e.g., Dreisbach, Haider, & Kluwe,
2002; Monsell & Mizon, 2006), and this is roughly one half in the
typical explicit-cuing procedure but either zero or one on different
Figure 2. Response times (RTs) for alternating runs (predictable condition) compared with explicit cuing (random condition), from Experiment 3
of Tornay and Milan’s (2001) study. The abscissa represents a generalized
definition of the position variable (shift trials ⫽ Position 1, first repetition ⫽ Position 2, second repetition ⫽ Position 3) that accommodates both
predictable-length and randomly occurring runs. Reprinted, with permission, from “A More Complete Task-Set Reconfiguration in Random Than
in Predictable Task Switch,” by F. J. Tornay and E. G. Milan, 2001,
Quarterly Journal of Experimental Psychology, Human Experimental Psychology, 54(A), 785– 803, Figure 3. Copyright 2001 by Experimental
Psychology Society.
COMPARING SWITCH COSTS
ized position variables—the two variables shown in Figure 2—was
reliable, F(2, 34) ⫽ 3.51, p ⬍ .05.
In a second study, Monsell, Sumner, and Waters (2003) reported
one experiment that compared alternating runs with explicit cuing.
The results of their Experiment 2 appear in Figure 3. Here, the
alternating-runs (predictable) condition appears in the left panels,
and the explicit-cuing (random) condition appears in the right
panels. The different lines represent different intervals (in milliseconds) separating the response on one trial from onset of the
stimulus for the next trial (this is the RSI). The abscissa again
shows the generalized position variable that drops the predictability constraint to accommodate explicit-cuing runs. ARS is the
difference, along each line in the upper left panel, between the 1
and 2 bins on the abscissa. ECS is the difference, along each line
in the upper right panel, between the 1 bin on the abscissa and an
average of the 2, 3, and 4 bins, weighted toward the 2 bin. Within
each RSI, but most dramatically for the 50 condition, ARS was
again larger than ECS. Statistics involving the switching variable
(switch vs. repeat) were not reported, but the interaction between
the procedure (alternating runs vs. explicit cuing) and position in
run variables was again reliable, F(3, 33) ⫽ 9.77, p ⬍ .001.
In a third study, Milan, Sanabria, Tornay, and Gonzalez (2005)
also reported one experiment that compared alternating runs with
explicit cuing. The results of their Experiment 1 appear in Figure
4, in a format similar to Figure 2. ARS is the difference, along the
Figure 3. Response times (RTs) for alternating runs (predictable condition) compared with explicit cuing (random condition), from Experiment 2
of Monsell et al.’s (2003) study. The abscissa again represents a generalized definition of the position variable that accommodates both
predictable-length and randomly occurring runs. Reprinted, with permission, from “Task-Set Reconfiguration With Predictable and Unpredictable
Task Switches,” by S. Monsell, P. Sumner, and H. Waters, 2003, Memory
& Cognition, 31, 327–342, Figure 6. Copyright 2003 by Psychonomic
Society.
479
solid (predictable) line, between the 0 and 1 bins on the abscissa.
ECS is the difference, along the dotted (random) line, between the
0 bin on the abscissa and an average of the 1 and 2 bins, weighted
toward the 1 bin. ARS was larger than ECS, and although statistics
involving switching (switch vs. repeat) were not reported, the
interaction between the variables shown in Figure 4 was again
reliable, F(2, 34) ⫽ 7.96, p ⬍ .01.
In all three studies discussed above, the original aim was to
compare predictable runs in an alternating-runs condition with
randomly-occurring runs in an explicit-cuing condition, the latter
collected by finding unpredicted runs in the data post hoc. For
present purposes, the relevance of this difference between conditions lies in the difference in opportunities afforded the cognitive
system. Under the theoretical perspective developed earlier,
predictable-length runs should allow the system to save itself some
processing on later trials of a run by setting up a functional
representation of the current task on the first trial and then using
this for the duration of the run. Such a strategy would produce
confounds in ARS, as developed earlier. In explicit cuing, however, there are no predictable runs to exploit, so one might expect
the system to treat every trial somewhat like a first trial. This in
turn predicts that Positions 2 and later in an explicit-cuing run
should incur longer latencies than Positions 2 and later in an
alternating-runs run. This is empirically the case in at least Figures
3 and 4 (with little difference between the conditions in Figure 2).
The story may be more complicated, however, given the trend for
latencies to decrease across an explicit-cuing run, as seen particularly in Figure 3 (right panel; see also Meiran, Chorev, & Sapir,
2000). This trend could reflect facilitation of cue-related processing by repetition priming (e.g., Altmann, 2005; Sohn & Anderson,
2001), if this happens to build up over successive cue repetitions,
or conceivably an effect of a lengthening streak of repeated events
within a randomized event stream (Altmann & Burns, 2005), or
some other mechanism. The details of whatever explanation
emerges may suggest that the repeat trial in some particular position of a randomly occurring run is the best estimate of the offset
of switch-related processes in explicit cuing, which in turn would
make it important, for present purposes, to check whether differences between ARS and a revised ECS still stand. In purely
procedural terms, however, the best match for the Position 2 trial
used to compute ARS is the Position 2 trial of an explicit-cuing
run, which would produce the smallest ECS (see Figure 3) and thus
the largest difference between ARS and ECS.
Finally, in a fourth study that undertook a different kind of
comparison between the two procedures, Koch (2005) reported
three experiments in each of which participants performed the first
five blocks under one procedure, switched to the other procedure
for the sixth block, then switched back to the original procedure for
a seventh block. In his Experiments 1 and 2, in which the first and
last procedure was alternating runs, the switch in between to
explicit cuing produced no reliable change in switch cost. However, in his Experiment 3, in which the first and last procedure was
explicit cuing, the switch in between to alternating runs did in fact
produce an increase in switch cost, F(1, 15) ⫽ 11.8, p ⬍ .05.
The generalization across these four studies is that, in all cases
in which ARS and ECS differed reliably, ARS was larger, supporting the notion that ARS includes components that ECS does
not.
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Figure 4. Response times for alternating runs (predictable condition) compared with explicit cuing (random
condition), from Experiment 1 of Milan, Sanabria, Tornay, and Gonzalez’s (2005) study. The abscissa again
represents a generalized definition of the position variable (0 ⫽ Position 1, 1 ⫽ Position 2, 2 ⫽ Position 3) that
accommodates both predictable-length and randomly occurring runs. Reprinted from Acta Psychologica, 118,
E. G. Milan, D. Sanabria, F. J. Tornay, and A. Gonzalez, “Exploring Task-Set Reconfiguration With Random
Task Sequences,” 319 –331, Copyright 2005, with permission from Elsevier.
Empirical Evidence From Unmatched Experiments
Apart from these few closely-matched comparisons of alternating runs and explicit cuing, both procedures are popular, and many
studies have been published using one or the other. Therefore, if
ARS is on balance larger than ECS, this difference should manifest
in a sufficiently large unmatched-samples comparison. Table 1
shows the results of such an analysis. Studies selected for inclusion
were those involving healthy adults, in which cues were mapped
one-to-one to tasks (see Altmann, in press) and in which there was
a manipulation of the CSI between onset of the task cue and onset
of the subsequent trial stimulus. This last criterion was adopted
from another meta-analysis (Altmann, 2004b) simply to produce a
tractable sample size here, but it also happens to control nicely for CSI
duration, which was nearly equal for the two sets of studies (608 vs.
605 ms). (This control is relevant because CSI is often cited as
modulating switch cost, at least as switch cost is construed in, e.g.,
Logan, 2003; Monsell, 2003; see Altmann, 2004b, for a review of
contrary evidence.) Mean ARS across studies was 172 ms, and mean
ECS was 94 ms, F(1, 32) ⫽ 14.2, p ⫽ .001, MSE ⫽ 3,486.
Available empirical evidence, then, both from studies that match
the two procedures as closely as possible and from a broader
survey of studies that each use one procedure or the other, suggests
that ECS spans less processing than ARS—that subtracting repeat
trials from switch trials in explicit cuing cancels processing costs
that subtracting Position 2 trials from Position 1 trials in alternating runs does not. The remaining question is whether this matters—whether, after a dozen years of task switching (in the modern
era) and hundreds of studies, it may nonetheless be worthwhile
now to adopt a greater degree of precision in discussing switch
costs.
Implications: Failure-to-Engage and Stimulus Priming
Accounts of . . . What?
To summarize, the basic issue is that ARS and ECS have
different operational definitions, with the contrast sharpened by
conceptualizing ARS as ECS plus any first-trial costs (see Figure
1). The deeper methodological problem for ARS is that the
alternating-runs procedure affords no way to disentangle switchrelated processes from switch-independent, first-trial related processes. The reaction to these issues in the task-switching community will surely range from boredom to irritation. On one hand,
much of the procedural detail is in some sense obvious, and studies
have been published comparing the two procedures, so some
attention has been paid. On the other hand, everyone in the
community (myself included) has at one point or another referred
to these two measures interchangeably in framing research questions or results or in captioning existing findings, so we all stand
accused of some methodological sloppiness. Is it possible, therefore, to point to specific examples where such conflation has cost
us something, to illustrate the common interest in greater precision?
Three examples are offered here, the first two involving important constructs that are difficult to interpret because almost all the
relevant data were collected with the alternating-runs procedure.
The first line of work involves the failure-to-engage hypothesis
and its predictions concerning variance in response latencies (De
Jong, 2000; De Jong, Berendsen, & Cools, 1999; Lien, Ruthruff,
Remington, & Johnston, 2005; Nieuwenhuis & Monsell, 2002).
The empirical finding is that, at long CSIs, fast responses on
switch trials are as fast as the fastest responses on repeat trials, but
slow responses on switch trials are much slower than the slowest
responses on repeat trials. This pattern is consistent with a reconfiguration process that has work to do on switch trials (Monsell,
2003; Rogers & Monsell, 1995) and either completes this work
during a long CSI, if it can engage in a timely fashion, or engages
only after stimulus onset, in which case the time to do the work is
charged to response latency. Mixing the two types of trials—those
in which reconfiguration completes during the CSI and those in
which reconfiguration only starts after stimulus onset— explains
the empirical pattern in terms of some switches costing no extra
response latency and others costing the full amount of reconfigu-
COMPARING SWITCH COSTS
Table 1
Comparison of Alternating-Runs and Explicit-Cuing Switch
Costs
Study author(s)
Alternating-runs studies
De Jong (2000)
De Jong et al. (1999)
De Jong (2001)
Fagot (1994)
Kleinsorge (1999)
Koch (2003)
Koch (2005)
Kramer et al. (1999)
Kray & Lindenberger (2000)
Monsell et al. (2003)
Nieuwenhuis & Monsell (2002)
Oriet & Jolicoeur (2003)
Rogers & Monsell (1995)
Yeung & Monsell (2003)
Mean across studies
Explicit-cuing studies
Altmann (2004a)
Altmann (2004b)
Arrington (2002)
Besner & Care (2003)
Bojko et al. (2004)
Garavan (1998)
Hahn et al. (2003)
Hubner et al. (2004)
Kleinsorge et al. (2005)
Kleinsorge & Gajewski (2004)
Koch (2001)
Mayr (2002)
Mayr & Keele (2000)
Meiran (1996)
Meiran (2000a)
Meiran (2000b)
Meiran et al. (2000)
Meiran & Marciano (2002)
Schuch & Koch (2003)
Tornay & Milan (2001)
Mean across studies
Experiment
Mean
CSI
Mean
switch
cost
1, 2
2
2a
3
1–3
1
1 vs. 2
2, 3a
1a
1, 2
1
1, 2
2, 3
4
750
733
900
200
450
600
500
750
700
600
563
520
540
700
608
160
105
170
197
30
272
199
308
143
137
105
278
175
128
172
1, 2
1–3
2
1
1a
2
1
1–4
2b
1
1 vs. 3, 4
1
4
1–5
1, 2
1
2–4
1
1–4c
1, 2
500
500
700
375
300
305
450
675
675
550
500
317
400
982
891
516
785
1270
550
850
605
100
100
129
59
6
201
120
89
101
116
180
33
98
75
70
67
73
94
110
67
94
Note. Mean cue–stimulus interval (CSI) and mean switch cost are simple,
unweighted averages of CSIs and switch costs, respectively, in all conditions of all listed experiments in a given study, excluding any general
switch (or mixing) costs.
a
Young conditions only. b Correctly cued trials only. c Go conditions
only.
ration time. These studies were all framed in terms of a reconfiguration perspective on cognitive control. Yet, because they all used
alternating runs, their switch trials were also Position 1 trials, and
their repeat trials were also Position 2 trials, so they equally well
support a model in which the functional processes that engage
during some CSIs but not others are those that execute on the first
trial of a run—any run, switch or repeat. Thus, despite how it has
been framed, the failure-to-engage hypothesis may well turn out to
be an important element of a model in which the processes that
implement cognitive control have nothing to do with switching
tasks.
The second example is a line of work that characterizes switch
cost as a consequence of negative effects of stimulus priming. The
481
basic finding is that performance in response to new stimuli,
namely those that have never been used together with the competing task, is better than performance in response to old stimuli,
namely those that have been used together with the competing task
(Allport & Wylie, 2000, Experiment 5; Waszak et al., 2003;
Waszak, Hommel, & Allport, 2005). In these studies, a stimuluspriming effect registered on Position 1 of a switch run when
switching was from a picture-naming task to a word-reading task
(and registered on all positions when switching was in the other
direction). However, because these results were gathered by use of
alternating runs, with no repeat runs interleaved, they are silent on
whether this effect on Position 1 reflected changes in switching
processes or changes in first-trial processes. More recently, one
explicit-cuing study has linked stimulus priming to an increase in
ECS (Koch & Allport, 2006) but also reported a main effect on
response latency. To know whether this main effect reflected a
change in first-trial processes, one would need to reproduce it
using randomized runs, which would allow a test of the effect on
first-trial cost (see Figure 1).
The third example concerns the four aging studies included in
Table 1. In the three that used alternating runs (De Jong, 2001;
Kramer et al., 1999; Kray & Lindenberger, 2000), differences in
ARS between young and older adults were 159 ms, 282 ms, and (a
nonsignificant) 80 ms, respectively. In the one that used explicit
cuing (Bojko, Kramer, & Peterson, 2004), the difference in ECS
was a smaller (also nonsignificant) 33 ms. Were it not for the
“switching” terminology used in the first three studies, they might
suggest that first-trial costs, not task-switch costs, were what
increased with age, which could lead to very different guidance
from these studies about which mechanisms to target in future
cognitive-aging studies.
These three examples do not reflect an exhaustive search, so
there may be others, given that the alternating-runs procedure was
present at the inception of the modern task-switching era (Fagot,
1994; Rogers & Monsell, 1995) and remains in use today (e.g.,
Lien et al., 2005; Taube-Schiff & Segalowitz, 2005; Waszak et al.,
2005). However, what they may suffice to show is that precision in
reporting and discussion of switch cost is not just good in principle, in a domain broadly concerned with this construct, but is a
prerequisite for developing empirical results like those sketched
above into diagnostically useful constraints on models of cognitive
control.
Summary
The aim here has been to draw attention to a difference in how
switch cost is operationally defined in the two most common
task-switching procedures—a difference that in the literature is
generally ignored, even in integrative surveys (e.g., Logan, 2003;
Monsell, 2003). ARS is derived through comparison of Positions 1
and 2 of switch runs and thus may include costs specific to the first
trial of a run as well as costs of switching tasks. Whether it does
or not cannot be tested directly, because the alternating-runs procedure affords no Position 1 repeat trial that would cancel such
costs when used as a baseline. Nonetheless, if there is a realistic
possibility that performance in a context of predictable-length runs
involves a first-trial strategy of some kind, in which whatever cue
is presented at the start of a run is generically transformed into an
internal task representation that governs until its relevance expires,
ALTMANN
482
then first-trial costs cannot be ruled out, and ARS should be treated
with caution, as a confounded measure. In contrast, ECS is derived
by comparing switch trials and repeat trials with no position confound, such that any costs specific to the first trial of a predictablelength run—a run of length 1, in this instance— cancel in the comparison; explicit-cuing has shortcomings of its own, but at least it does
not suffer a structural confound between effects of switching tasks and
effects of position within a predictable-length run.
This analysis makes a prediction—that ARS should in general
be larger than ECS—that is supported by available empirical
evidence from the few studies that have compared the two procedures under relatively controlled circumstances and from a broader
survey of unmatched studies. It also suggests that one would need
to elaborate at least two lines of work in the task-switching
domain, one on the failure-to-engage hypothesis and the other on
the negative effects of stimulus priming, using a randomized-runs
procedure to identify whether effects reported in the original
studies were switch-related or first-trial related. More generally,
this analysis suggests that it would be useful to start acknowledging that ARS and ECS have different operational definitions, rather
than citing them together as if they are identical measures, as is
currently the standard (e.g., Logan, 2003; Monsell, 2003).
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Received July 7, 2006
Revision received September 30, 2006
Accepted December 11, 2006 䡲