Differential contribution of task conflicts to task switch cost and task mixing cost in alternating...

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ORIGINAL PAPER Differential contribution of task conflicts to task switch cost and task mixing cost in alternating runs and cued task-switching: evidence from ex-Gaussian modeling of reaction time distributions Nitzan Shahar Nachshon Meiran Received: 15 December 2013 / Accepted: 8 April 2014 Ó Springer-Verlag Berlin Heidelberg 2014 Abstract Task switching involves switch cost (poorer performance switch trials than in task-repetition trials) and mixing cost (poorer performance in task-repetition trials than in trials from blocks without task switching). These are mainly studied with the alternating runs task-switching (ARTS) paradigm (in which the task changes every constant number of trials) or the cued task-switching (CTS) para- digm, in which the tasks change randomly. The authors tested the hypothesis that dealing with actual or potential conflicts regarding which task is currently required con- tribute to mixing cost in CTS more than in ARTS and contribute to switch costs more in ARTS than in CTS. This hypothesis was tested using ex-Gaussian modeling of reac- tion time (RT) distributions, in which the heaviness of the right tail marks task conflicts (Steinhauser and Hu ¨bner in J Exp Psychol Human Percept Perform 35:1398–1412 2009). As predicted, a heavier RT-distribution tail marked switch cost more strongly in ARTS than in CTS and marked mixing costs more strongly in CTS than in ARTS. These results indicate that switch cost and mixing cost reflect different processes in different task-switching paradigms. Introduction Task switching (TS) has become the method-of-choice to study the ability to flexibly change mental sets (Kiesel et al., 2010; Meiran, 2010; Monsell, 2003; Van- dierendonck, Liefooghe, & Verbruggen, 2010). Most of the task-switching studies employ one of two paradigms. In the cued task-switching (CTS) paradigm, the tasks are ordered randomly, and a cue appearing in the beginning of the trial instructs which task to execute (Shaffer, 1965; Meiran, 1996). In the alternating runs task-switching (ARTS) par- adigm, the tasks are ordered in series of trials of fixed length (called ‘‘runs’’) and the tasks alternate between runs (e.g., with Tasks A, B and run length = 2, the trial sequence would be AA-BB-AA, Rogers & Monsell, 1995). Regardless of the paradigm being used, switching often (although not always, e.g., Jersild, 1927) involves a cost. This cost is often broken down into two components (Fagot, 1994; Meiran, Chorev, & Sapir, 2000). Switching cost is the performance decrement in task switch trials relative to task-repetition trials (both taking place in blocks involving task switching), presumably reflects the influence of immediate task transition. The other component, mixing cost is based on comparing two types of task-repetition trials. It indexes the performance decrement seen in task- repetition trials coming from blocks involving task switching as compared to task-repetition trials coming from blocks without task switching (‘‘single-task’’ blocks). Mixing cost therefore reflects the contextual influence on performance, and is therefore taken to reflect more sus- tained forms of control (Braver, Reynolds, & Donaldson, 2003). Several attempts were made to offer a much more detailed process account of the costs. Regarding mixing cost, one explanation is that it reflects the higher working memory (WM) load in blocks involving task switching (especially Rogers & Monsell, 1995). Despite its intuitive appeal, this account is incompatible with several N. Shahar Á N. Meiran (&) Department of Psychology and Zlotowski Center for Neuroscience, Ben-Gurion University of the Negev, Be’er Sheva, Israel e-mail: [email protected] N. Shahar e-mail: [email protected] 123 Psychological Research DOI 10.1007/s00426-014-0569-1

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Page 1: Differential contribution of task conflicts to task switch cost and task mixing cost in alternating runs and cued task-switching: evidence from ex-Gaussian modeling of reaction time

ORIGINAL PAPER

Differential contribution of task conflicts to task switch costand task mixing cost in alternating runs and cued task-switching:evidence from ex-Gaussian modeling of reaction time distributions

Nitzan Shahar • Nachshon Meiran

Received: 15 December 2013 / Accepted: 8 April 2014

� Springer-Verlag Berlin Heidelberg 2014

Abstract Task switching involves switch cost (poorer

performance switch trials than in task-repetition trials) and

mixing cost (poorer performance in task-repetition trials

than in trials from blocks without task switching). These are

mainly studied with the alternating runs task-switching

(ARTS) paradigm (in which the task changes every constant

number of trials) or the cued task-switching (CTS) para-

digm, in which the tasks change randomly. The authors

tested the hypothesis that dealing with actual or potential

conflicts regarding which task is currently required con-

tribute to mixing cost in CTS more than in ARTS and

contribute to switch costs more in ARTS than in CTS. This

hypothesis was tested using ex-Gaussian modeling of reac-

tion time (RT) distributions, in which the heaviness of the

right tail marks task conflicts (Steinhauser and Hubner in J

Exp Psychol Human Percept Perform 35:1398–1412 2009).

As predicted, a heavier RT-distribution tail marked switch

cost more strongly in ARTS than in CTS and marked mixing

costs more strongly in CTS than in ARTS. These results

indicate that switch cost and mixing cost reflect different

processes in different task-switching paradigms.

Introduction

Task switching (TS) has become the method-of-choice to

study the ability to flexibly change mental sets (Kiesel

et al., 2010; Meiran, 2010; Monsell, 2003; Van-

dierendonck, Liefooghe, & Verbruggen, 2010). Most of the

task-switching studies employ one of two paradigms. In the

cued task-switching (CTS) paradigm, the tasks are ordered

randomly, and a cue appearing in the beginning of the trial

instructs which task to execute (Shaffer, 1965; Meiran,

1996). In the alternating runs task-switching (ARTS) par-

adigm, the tasks are ordered in series of trials of fixed

length (called ‘‘runs’’) and the tasks alternate between runs

(e.g., with Tasks A, B and run length = 2, the trial

sequence would be AA-BB-AA…, Rogers & Monsell,

1995).

Regardless of the paradigm being used, switching often

(although not always, e.g., Jersild, 1927) involves a cost.

This cost is often broken down into two components

(Fagot, 1994; Meiran, Chorev, & Sapir, 2000). Switching

cost is the performance decrement in task switch trials

relative to task-repetition trials (both taking place in blocks

involving task switching), presumably reflects the influence

of immediate task transition. The other component, mixing

cost is based on comparing two types of task-repetition

trials. It indexes the performance decrement seen in task-

repetition trials coming from blocks involving task

switching as compared to task-repetition trials coming

from blocks without task switching (‘‘single-task’’ blocks).

Mixing cost therefore reflects the contextual influence on

performance, and is therefore taken to reflect more sus-

tained forms of control (Braver, Reynolds, & Donaldson,

2003).

Several attempts were made to offer a much more

detailed process account of the costs. Regarding mixing

cost, one explanation is that it reflects the higher working

memory (WM) load in blocks involving task switching

(especially Rogers & Monsell, 1995). Despite its intuitive

appeal, this account is incompatible with several

N. Shahar � N. Meiran (&)

Department of Psychology and Zlotowski Center for

Neuroscience, Ben-Gurion University of the Negev,

Be’er Sheva, Israel

e-mail: [email protected]

N. Shahar

e-mail: [email protected]

123

Psychological Research

DOI 10.1007/s00426-014-0569-1

Page 2: Differential contribution of task conflicts to task switch cost and task mixing cost in alternating runs and cued task-switching: evidence from ex-Gaussian modeling of reaction time

observations. One comes from Experiment 2 in Rubin and

Meiran’s (2005) paper. These authors used a CTS para-

digm and required participants to switch between four

tasks. Two of the four tasks, the color task and the shape

task, were executed on colored shapes. The two other tasks,

vertical (up vs. down) and horizontal (right vs. left) were

executed on a stimulus presented inside a 2 9 2 grid. Thus,

the objective WM load involved four task rules. None-

theless, performance in the 4-tasks condition was similar to

that seen when participants switched between two tasks:

the color task and the shape task (or between the vertical

task and the horizontal task). Hence, the results suggest that

WM load (4 tasks vs. 2 tasks) did not contribute to mixing

cost. Similar conclusions regarding the lack of influence of

WM load on behavior in the CTS paradigm were reached

by other investigators (see also Kessler & Meiran, 2010;

Kiesel, Wendt, & Peters, 2007; van ‘t Wout, Lavric, &

Monsell, 2013).

Another account of mixing cost refers to task uncertainty.

Namely, when task switching takes place, the probability

that a given task will be required is lower (say 50 %) than

when the task is executed in isolation (100 %). Nonetheless,

the aforementioned results of Rubin and Meiran (2005) seem

to also rule out task uncertainty as an explanation since the

likelihood of each task to appear was 50 % in the 2-task

condition as compared to 25 % when all four tasks were

intermixed. Thus, despite the large uncertainty difference,

performance remained roughly unchanged.

Of greatest relevance in the present work is Koch, Prinz,

& Allport, (2005) as well as Rubin and Meiran’s (2005; cf.

Steinhauser & Hubner, 2009) suggestion that task mixing

costs involve task conflict. The term ‘‘task conflict’’ has

been distinguished from ‘‘response conflict’’ (or ‘‘infor-

mation conflict’’, e.g., Goldfarb & Henik, 2007). It refers to

a conflict between abstract task rules (each rule referring to

more than one response, such as the rule ‘‘respond to color

by pressing the right key in response to green color and

pressing the left key in response to red color’’). Basically,

Koch et al.’s and Rubin and Meiran’s findings indicate

greater mixing costs when the stimuli cued the competing

task and the account is therefore in terms of the resultant

conflict between task rules. In other words, when two (or

more) tasks are executed on the same stimuli, the stimulus

leads to the retrieval of the wrong task rule and generates a

conflict regarding which task rule is currently required

(Waszak, Hommel, & Allport, 2003; cf. Gilbert & Shallice,

2002). Notably, mixing costs are observed even with uni-

valent trials that afford only one task, as long as bivalent

trials (affording both tasks) are also included (Woodward,

Meier, Tipper, & Graf, 2003) suggesting that mixing costs

may also reflect dealing with the potential task conflict, not

only with an actual conflict.

Nonetheless, Koch et al. (2005) and Rubin and Meiran’s

hypothesis is based on results coming from the CTS par-

adigm, and the causes for mixing cost may depend on the

paradigm, especially given the known processing differ-

ences between the ARTS and CTS paradigms (Altmann,

2007, 2013; Andreadis & Quinlan, 2010; Koch, 2003,

2005; Monsell, Sumner, & Waters, 2003; Pereg, Shahar, &

Meiran, 2013; Schmitz & Voss, 2012; Tornay & Milan

2001). More specifically, Altmann (2007) referred to a

process in which participants activate the abstract task

representation. He suggested that, given the task uncer-

tainty that characterizes the CTS paradigm, participants

employ this process (activate the abstract task representa-

tion) in each and every trial. However, in the ARTS par-

adigm, participants make use of task predictability. What

they appear to do is to activate the abstract task represen-

tation only in the first trial of the run, and then skip this

process in the remaining trials of the run (see also Meiran,

Kessler, & Adi-Japha, 2008). So, for example, if the run

length is 4, participants know that once the run has begun,

the task will remain unchanged in the next three trials.

Therefore, they activate the abstract task representation

only in the first trial in the run (which is the switch trial)

and do not activate it in the second through fourth trial of

the run (which are task-repetition trials).

This strategy which differentiates ARTS from CTS has

specific implications to the processes which are responsible

for switch costs and mixing costs in the two paradigms.

Because switch costs are computed as the difference

between task switch trials (which is the first task in the run

in ARTS) and task-repetition trials (subsequent trials in the

run), switch cost in the ARTS paradigm is influenced by

the need to activate task representation (present only in

switch trials, and absent in task-repetition trials, hence

contributing to their difference). In contrast, in CTS, par-

ticipants activate the abstract task representation in each

and every trial. Consequently, both switch trials and task-

repetition trials involve the process of task-representation

activation and the difference between them does not reflect

this process. For that reason, this process of activating

abstract task representation does not contribute (as much)

to switch costs in the CTS paradigm.

The opposite applies to mixing costs, defined as the

difference between task-repetition trials and single-task

trials. Task-repetition trials in CTS involve the activation

of task representation. In single-task trials this is not the

case, given the perfect task certainty in these blocks. Thus,

mixing cost in CTS reflects this process (see Altmann &

Gray, 2008). In contrast, in ARTS, task-repetition trials

like single-task trials do not involve the activation of task

representation. Thus, mixing costs in ARTS do not reflect

this process (as much).

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Altmann’s (2007) hypothesis can be combined with

Koch et al.’s (2005) and Rubin and Meiran’s (2005)

hypothesis as follows. On trials in which task representa-

tion is activated, greater interference from competing task

representations (task conflict) is expected, and/or greater

effort associated with potential task conflicts is expected.

Thus, the two hypotheses, combined, predict that processes

dealing with actual or potential task conflicts will differ-

entially influence mixing cost and switch cost in CTS and

ARTS, depending on which cost-component mostly

reflects the activation of task representation. Accordingly,

in CTS, mixing cost is predicted to demonstrate larger task

conflict-related processing; whereas, in ARTS task con-

flict-related processing is predicted to primarily influence

switch cost. One line of evidence supporting the afore-

mentioned hypothesis comes from a study comparing

bivalent trials (affording both tasks) with univalent trials

(affording just one task). Usually, performance is poorer in

bivalent trials than in univalent trials (e.g., see Rogers &

Monsell’s, 1995, ‘‘task cuing effect’’, cf. Woodward et al.

2003, for a related finding), a finding that is interpreted as

evidence for a conflict taking place at the level of the

abstract task representations (e.g., Goldfarb & Henik,

2007). Accordingly, Andreadis and Quinlan (2010) found

greater involvement of bivalent vs. univalent costs in task-

repetition trials in conditions in which the task was

unpredictable (CTS) than in conditions when the task was

predictable (ARTS).

Another very relevant study has been reported by Ste-

inhauser and Hubner (2009), who used a CTS paradigm in

which there were bivalent and univalent trials and mixing

costs were also assessed. Importantly, the authors modeled

the shape of the RT distributions with the ex-Gaussian

distribution (e.g., Ratcliff, 1993). This distribution is a

combination of two distributions: Gaussian, described by

the parameters l (mu) and r (sigma), and exponential,

described by the parameter s (tau). In this distribution, the sparameter is mostly responsible for the typical heavy right

tail, so that when s = 0, the distribution no longer has such

a tail and becomes Gaussian, and when s increases, so does

the heaviness of the right tail. Two important additional

characteristics of this distribution are: (1) that

RTmean = l ? s, and (2) RTvar = r2 ? s2.

Steinhauser and Hubner’s (2009) results show (a) that

the difference between bivalent and univalent trials is

mostly seen in s; and, (b) that the same holds true for

mixing costs. This has led the authors to conclude that

increased s characterizes task conflicts. We therefore have

decided to use this index to test our hypothesis concerning

differential contribution of task conflicts to mixing costs

and switch costs in CTS vs. ARTS.

Accordingly, the present work was based on ex-Gauss-

ian analysis of RT distributions taken from an experiment

in which the participants performed in comparable ARTS

and CTS paradigms. We predicted that, for switch costs, swill be influential mostly in ARTS whereas for mixing

costs, s will be mostly influential in CTS.

Method

Participants

A total of 16 healthy undergraduate students

(Mage = 23.25, SD = 1.81, 10 females, 6 males) took part

in the experiment in return for 25 NIS per hour (*6$).

Participants were pre-screened based on self-reported for

not previously suffering from head injury, psychiatric dis-

orders, drug/alcohol use, color blindness or diag-

nosed learning disabilities.

Stimuli and apparatus

Four stimuli were used as targets including a circle or a

triangle, either in red or green printed with a 2-mm outline.

Task cues in the CTS conditions included the Hebrew word

‘‘ ’’ or ‘‘ ’’ (i.e., ‘‘shape’’ or ‘‘color’’). Each shape

stimulus was 40 9 40 mm in size. Text was presented in a

white 18-point Courier New font in the center of the

screen. The experiment was programmed using E-Prime

2.0 (Psychology Software Tools, Pittsburgh, PA, USA). All

stimuli were presented in the center of a black 19-in.

computer screen.

Procedure

Participants were seated in front of the computer screen in

a small room in the lab. After a short instruction screen,

participants performed four trials of each condition

including the shape as a single task, color as a single task,

and two mixed blocks (i.e., either ARTS followed by CTS

or vice versa, counterbalanced between participants). The

test phase included the same sequence of conditions,

repeated twice. Each single-task block in the test phase

included two mini-blocks of 24 trials, and each mixed

block included four mini-blocks of 24 trials, with a short

recess after each mini-block. Thus, each participant per-

formed in the test phase 96 trials of each single task (i.e.,

shape or color) and 192 trials for each mixed block (i.e.,

CTS or ARTS).

In shape or color single-task blocks, the participants

were asked to perform the same task without switching

until the end of the block. In CTS blocks, the participants

were asked to perform either the shape task or the color

task according to a cue presented before the target. In

ARTS blocks, the participants were asked to switch tasks

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after every second trial, beginning with the shape task (i.e.,

shape, shape, color, color, etc.).

In shape trials, participants were asked to decide whe-

ther the shape is a circle or a triangle. In the color trials

participants were asked to report whether the color of the

outline of the shape is green or red. In the single-task

blocks and ARTS mixed blocks, each trial included a fix-

ation screen (1,000 ms) followed by the target that was

presented until the response was given or until 6 s had

elapsed. In CTS blocks, each trial included a fixation

screen (500 ms), a randomly chosen cue screen (switch

probability = 50 %, as in ARTS; 500 ms), followed by the

target. Participants reacted by pressing the ‘‘s’’ (left) or the

‘‘k’’ (right) key. A 400-ms beep signaled errors.

Results

For RT analyses, error and post-error trials, ten first trials in

each condition and the first trial after each recess were

discarded. RTs below 200 ms or above 4 SDs from the

participant’s mean in the respective condition were con-

sidered as outliers and thus omitted. We re-calculated the

RT mean in each condition and repeated trimming until all

outliers were removed (resulting in 0–4 trials omitted in

each conditions; Schmiedek, Oberauer, Wilhelm, Suss, &

Wittmann, 2007). The ex-Gaussian distribution fitting was

performed using the DISTRIB toolbox in MATLABTM

(Lacouture & Cousineau, 2008). In order to ensure that the

ex-Gaussian distribution fits the data, we simulated 10,000

data points from each set of the ex-Gaussian parameters in

each condition. We then calculated four quantile means

(e.g., 0.20 0.40 0.60 0.80) for both the simulated and the

empirical data. A quantile–quantile plot was generated to

allow a visual comparison between the simulated and

empirical data (e.g., Steinhauser & Hubner, 2009). A good

fit between the theoretical ex-Gaussian distributions and

the empirical data was demonstrated (see Fig. 1).

Summary of the means in all conditions is presented in

Table 1. Because the same single-task condition served as

baseline for both ARTS and CTS, the conditions did not

form a factorial design. We therefore conducted the anal-

yses on costs by calculating switch cost (i.e., subtracting

switch from repeat trials) and mixing cost (i.e., subtracting

repeat trials from single-task trials). A series of repeated

measures analyses of variance (ANOVAs) were conducted

with Cost-Type (switch cost vs. mixing cost), Paradigm

(CTS vs. ARTS) and Task (Shape vs. Color) as indepen-

dent variables (see Fig. 2). The first ANOVA was per-

formed on the mean RTs. It revealed a significant

interaction between cost-type and block-type

[F(1,15) = 17.35, p \ 0.001., g2p = 0.54] showing a larger

mixing cost in the CTS than in ARTS and a larger

switching cost for ARTS than for CTS (see Fig. 2).

Similar ANOVAs were performed on each one of the three

ex-Gaussian parameters (l, r, s, see Fig. 2). A significant

main effects for Cost-Type was found in l [F(1, 15) = 5.80,

p \ 0.05, g2p = 0.29] and r [F(1,15) = 5.16, p \ 0.05,

g2p = 0.25], but not in s [F(1,15) = 0.98, n.s., g2

p = 0.06].

Most importantly, there was a significant interaction between

Paradigm and Cost-Type only for s [F(1, 15) = 16.50,

p \ 0.001, g2p = 0.52].

The significant interaction found for s was probed by

planned contrasts comparing between paradigms. The dif-

ference between paradigms was significant for mixing cost

[t(15) = 2.78, p \ 0.01, g2p = 0.34] and switch cost

[t(15) = 3.48, p \ 0.001, g2p = 0.44].

A similar ANOVA on accuracy demonstrated a signifi-

cant main effect for Paradigm [F(1,15) = 8.66, n.s.,

g2p = 0.37], Cost-Type [F(1, 15) = 29.54, p \ 0.001,

g2p = 0.66], and Task. The latter effect indicates lower,

negative costs for the shape task as compared with positive

costs in the color task (see Fig. 2).

Task-rule congruency effect (TRCE)

TRCE results from the competition between response

tendencies generated by the required (relevant) task rule

and the irrelevant task rule (see Meiran & Kessler, 2008).

For example, the task rule in the current trial may be

Fig. 1 To obtain an estimation of how well the ex-Gaussian

distribution fits the data, we first simulated a set of 10,000 data

points using the previously extracted ex-Gaussian parameters. We

then calculated the mean RT for four bins (0.2 0.4 0.6 0.8), once for

the empirical and once for simulated data sets. A quantile–quantile

plot was created. Each data point describes the mean RT for the

relevant bin in the empirical data (i.e., x axis) and simulated data (i.e.,

y axis). A poor fit between the data and the ex-Gaussian should be

observed by a discrepancy from the diagonal line. As can be seen, an

excellent fit was observed

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SHAPE and this rule may indicate the right key as the

correct response. The currently irrelevant rule (COLOR)

may indicate the same key as the correct response (in

congruent trials) or the opposite key (in incongruent trials).

The performance difference between congruent and

incongruent trials (the TRCE) thus reflects the aforemen-

tioned competition. Note, however, that the TRCE con-

founds task conflict and response conflict, since the

response competition takes place between responses that

were generated by two competing task rules (see Braver-

man & Meiran, 2010).

We analyzed the TRCE in the mixed blocks despite the

fact that participants were not reminded of the required task

in ARTS. This fact makes it conceivable that they may

have lost track of the task sequence, something that could

not have occurred in CTS. To ameliorate this problem, we

used very short blocks, but this may have been only a

partial solution. Therefore, one could argue that the para-

digms were not equated in this regard (namely, the chance

of committing the wrong task). Fortunately, it is possible to

estimate the rate of task errors by comparing error rates

between incongruent and congruent trials. While making a

task error in incongruent trials would lead to an error, it

would not lead to an error in congruent trials (assuming

that making the color or shape judgment is trivial, see

Meiran & Daichman, 2005). An analysis of the mixed-tasks

blocks revealed a robust TRCE in errors, F(1, 15) = 73.38,

MSE = 0.0019, g2p = 0.83, but the interaction with Para-

digm was clearly non-significant, F(1,15) = 1.44,

p = 0.25, g2p = 0.09. PE-TRCE was 0.07 in CTS and 0.06

in ARTS. Note that the direction of this (non-significant)

interaction is opposite to that predicted by the alternate

account (more task errors in ARTS).

We began by an analysis of raw RT, which indicated a

significant main effect for TRCE, F(1, 15) = 33.52,

MSE = 1,235.72, p \ 0.0001, g2p = 0.69, but a clearly

non-significant interaction between TRCE and Paradigm,

F(1, 15) = 0.87, MSE = 1,155.36, p = 0.36, g2p = 0.05

(42 and 30 ms in CTS and ARTS, respectively). We have

also fitted the ex-Gaussian model to RT distributions in the

mixed-tasks blocks, this time classifying the trials

according to Congruency (and ignoring the Switch vari-

able). The TRCE was neither significant in l (-2 and 3 ms

in CTS and ARTS, respectively) nor in r (-4 and 0 ms,

respectively), but has reached significance in s, F(1,

15) = 17.16, MSE = 2,149.14, p \ 0.001, g2p = 0.53.

However, the s-TRCE did not differ significantly between

paradigms, F(1, 15) = 1.12, p = 0.30, g2p = 0.07. It was

40 ms in CTS and 27 ms in ARTS.

The present results differ somewhat from Steinhauser

and Hubner’s (2009) results showing a significant Stroop

congruency effect (that resembles the TRCE in a sense) in

all the three ex-Gaussian parameters. Nonetheless, even in

their experiments, it was numerically larger in s than in the

Gaussian parameters. Moreover, Meiran and Kessler

(2008) found that the TRCE increases with response

slowness, a result that seems compatible with the current

trend.

In summary, the TRCE analyses do not suggest any

differential contribution of this variable to the paradigm

differences that we observed in the preceding analyses.

Discussion

The present work tested the hypothesis that, in the ARTS,

processes associated with dealing with actual or potential

task conflicts influence switch costs, mostly; whereas, for

CTS these processes influence mixing costs, mostly. This

hypothesis was based on Altmann’s (2007) hypothesized

Table 1 Means (and standard deviations) in ms

Trial-type Task RT Mean l r s Accuracy

(proportion)

Single tasks Shape 418 (49) 345 (30) 34 (8) 74 (35) 0.96 (0.03)

Color 420 (75) 329 (32) 30 (19) 91 (66) 0.98 (0.02)

Cued task

switching

Repeat Shape 560 (127) 357 (35) 34 (13) 202 (129) 0.96 (0.03)

Color 569 (158) 344 (45) 32 (19) 230 (157) 0.95 (0.03)

Switch Shape 656 (172) 409 (69) 60 (55) 246 (158) 0.91 (0.05)

Color 688 (216) 402 (118) 57 (58) 286 (148) 0.91 (0.04)

Alternating runs

task switching

Repeat Shape 515 (104) 348 (34) 31 (15) 166 (92) 0.97 (0.02)

Color 512 (103) 344 (50) 29 (14) 168 (92) 0.97 (0.02)

Switch Shape 702 (194) 420 (89) 67 (35) 283 (154) 0.95 (0.04)

Color 690 (184) 382 (116) 41 (50) 308 (135) 0.91 (0.05)

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strategic difference between the two paradigms, whereby

the abstract task representation of the task is encoded only

in the first trial of the run, whereas it is encoded in each and

every CTS trial. We additionally hypothesized that task

conflicts will influence performance in trials in which the

abstract task identity is encoded (Koch et al., 2005; Rubin

& Meiran, 2005). With these two hypotheses, combined,

we predicted that task conflicts will be seen in switch costs

in the ARTS and in mixing costs in CTS. Finally, following

Steinhauser and Hubner (2009), we used the s parameter

from the ex-Gaussian RT distribution (describing the

heaviness of the right RT-distribution tail) as an empirical

marker of task conflicts. As predicted, we found that s

contributed to mixing cost more in the CTS than in the

ARTS and it contributed more to switch cost in ARTS than

in CTS.

In addition to supporting the hypothesis (and the

hypotheses on which it was based), our results provide an

important replication to Steinhauser and Hubner’s (2009)

results. Their results were based on Stroop task switching,

which is a less commonly used version of the CTS para-

digm, and we showed similar results in a much more

standard CTS paradigm. More importantly, we found the

exact opposite pattern in the ARTS paradigm. This aspect

of our results, in fact, provides important support to Ste-

inhauser and Hubner given that our hypothesis was partly

Fig. 2 Mean cost as a function of cost-type and paradigm: a in reaction time (ms); b in proportion of errors; c in g (ms); d in r (ms); e in s (ms).

Error bars represent within-subject confidence intervals (Hollands & Jarmasz, 2010; Jarmasz & Hollands, 2009)

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based on their conclusions that the s parameter signals

processes associated with task conflict.

Importantly, the literature often refers to switch cost and

mixing cost as indications of specific processes. The

present results show that these processes change as a

function of the constraints afforded by the experimental

paradigm. Thus, for example, the fact that a given popu-

lation such as normally aged adults show enlarged mixing

costs, may tell us quite different things when the finding

comes from ARTS (e.g., Kray & Lindenberger, 2000) or

from CTS (e.g., Meiran, Gotler, & Perlman, 2001).

Two noteworthy limitations of this study should be

acknowledged. One is that, although we tried to match the

paradigms as closely as possible, some differences

remained, nonetheless. The other limitation is that we used

a particular combination of tasks, and given the large dif-

ferences between tasks, any general conclusion should be

treated as a conjecture. Nonetheless, the critical interaction

was not modulated by Task and included an element which

replicated a previous study (Steinhauser & Hubner, 2009)

with very different tasks, two facts that suggest that a

generalization may be warranted.

In conclusion, the present experiment provides impor-

tant converging evidence for two hypotheses. The first

hypothesis is that processes dealing with actual or potential

task conflicts contribute differentially to mixing cost and

switch cost, depending on the paradigm. The second

hypothesis is that the s parameter from the ex-Gaussian

model of the RT distribution, which indexes the heaviness

of the right RT-distribution tail, apparently marks pro-

cessing related to task conflicts.

Acknowledgments We wish to thank Maayan Pereg for her help in

designing the experiment, Miriam Gade and an anonymous reviewer

for helpful comments. This research was supported by a research

grant from the Israel Science Foundation to N. Meiran.

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