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A – Analysis rationale

The rationale for our analysis relies on the following: Because S-R rules are

embedded in S-R sets, we cannot examine the influence of the interfering S-R rule in

isolation from its S-R set. Therefore, given this limitation, our ideal design would have

involved a variable with three levels. These levels differ according to what has been

suppressed in Trial N–1, but it is important to note that we always only analyze Trial N.

Level 1 represents a condition in which an interfering S-R rule, and, as a result of the above

limitation, its (competitor) S-R set, have been suppressed. Level 2 represents a condition in

which just the S-R set has been suppressed (i.e., suppression of the competitor S-R set in

isolation from suppression of the interfering S-R rule). Level 3 represents a condition in

which nothing has been suppressed. These three conditions could render three RT/PE

patterns as potentially interesting. In one of these patterns, suppression of the interfering S-R

rule (and its competitor S-R set) would result in higher cost than suppression of just the

competitor S-R set, which would, itself, result in higher cost than no suppression at all (i.e.,

Level 1 > Level 2 > Level 3). This pattern would indicate that the entire S-R set has been

suppressed (because the suppression of a component of the competing S-R set lead to higher

cost than no suppression at all, i.e., Level 2 > Level 3), but, moreover, there was additional

suppression of the interfering S-R rule (because suppression of the interfering S-R rule leads

to higher cost than suppression of the other component of the S-R set, i.e., Level 1 > Level 2).

In the second pattern, suppression of the interfering S-R rule (and its competitor S-R set)

would result in higher cost than suppression of just the competitor S-R set, but suppression of

just the competitor S-R set would not differ from no suppression at all (i.e., Level 1 > Level 2

= Level 3). This pattern would indicate that only the S-R rule has been suppressed. Finally,

in the third pattern, suppression of the interfering S-R rule would not differ from suppression

of just the competitor S-R set, but suppression of just the competitor S-R set would lead to

higher cost than no suppression at all (i.e., Level 1 = Level 2 > Level 3). The third pattern

would indicate that only the S-R set has been suppressed, and there was no extra suppression

of the interfering S-R rule.

As explained in the main text, these levels could not be directly compared, because Levels 1

and 2 (i.e., the two CbR+ conditions in our analysis) were confounded with response. This

confound was resolved by dividing level 3 (i.e., CbR– trials) into trials with response

repetition and response alternation.

Although presenting our rationale using these 3 levels may appear to indicate that a quite

simple experiment could easily manipulate these levels without a confound, the reader should

consider that such an experiment would necessitate at least four tasks with at least 3 S-R rules

for each task, thus exposing such an experiment to numerous possible confounds.

B – CbR analysis

B1. CbR- Selection criteria

The exact trial sequences that were included in the CbR analysis are presented in

Table B1. We employed strict selection criteria, based on the following phenomena: number

of competitors in Trial N, number of competitors in Trial N–1, CRP (CRP– vs. CRP+), CrC

(CrC– vs. CrC+). Specifically, we made sure that our comparison trials would be equated on

these phenomena. We also excluded trials in which all of the dimensions of the previous

stimulus (including the response) repeated (Hommel, 1998, 2004). As a result of selection, a

substantial number of trials (CbR+ and CbR– trials) were excluded from the analysis. Here,

we elaborate on these possible confounds.

Due to the fact that in CbR+ trials the relevant S-R set in Trial N was the competitor

S-R set in Trial N–1, we could only analyze trials that included either one or two competitor

S-R sets in Trial N–1 (we had to exclude trials with three competitor sets in Trial N–1

because CbR– could not materialize in these trials since one of the three competitors had to

become the relevant S-R set in Trial N).

Additionally, we could not analyze trials with three competitor S-R sets in Trial N.

Also, since we had 100% switch trials, if there are two competitor S-R sets in Trial N–1, and

if one of them becomes the relevant (to create a CbR+ trial), then the other must repeat, thus

creating repetition of one S-R set. However, if neither of them becomes the relevant S-R set

(thus creating a CbR– trial), then the two of them remain competitor S-R sets. Therefore, in

this condition, when comparing CbR+ to CbR–, in CbR+ there is lingering suppression of

one competitor S-R set, whereas in CbR– there is lingering suppression of two competitor S-

R sets. Therefore, these trials are not equated on the number of suppressed competitor trials.

Similarly, if there was one competitor S-R set in Trial N and then it became the relevant S-R

set, we would have a CbR+ trial with no S-R set repetition. On the other hand, if it does not

become the relevant S-R set (i.e., creating a CbR– trial), we would have S-R set repetition.

For similar reasons, there cannot be CbR+ if there is CrC+ and one competitor in Trial N–1,

regardless of the number of competitors in Trial N, because, in CrC+, the competitor from

Trial N–1 should remain the competitor in Trial N, whereas in CbR+ trials, the competitor in

Trial N–1 becomes the relevant in Trial N. Along these lines, there cannot be CbR– if there

is CrC– and 2 competitors in Trial N and in Trial N–1, because if none of the competitors

remains the competitor (thus creating CbR– trial), then it must become the relevant (thus

creating CbR+ trial). Moreover, there cannot be CbR– if there are 3 competitors in Trial N-1,

because one of them must become the relevant in Trial N (thus creating CbR+); and so on.

Finally, after creating the table, we carefully examined the trials, and if all of the

dimensions of the stimulus repeated in Trial N (i.e., stimulus repetition), we excluded these

trials (e.g., CbR+ trials) and their counterparts (e.g., CbR– trials). In our final sample there

were no trials in which either all of the features (including the response, a total of 5 features)

repeated, or all of the features (including the response) switched. This protects our analysis

from confounds predicted by the event coding theory (Hommel, Müsseler, Aschersleben, &

Prinz, 2001), according to which responses would be quicker when the entire event file (i.e.,

the entire stimulus and the response) repeats or when the entire event file switches. To be on

the safe side, we also equated trials according to the number of repeated stimulus features,

since one could maintain that not only relevant dimensions, but also irrelevant dimensions,

are bounded with response (Rothermund, Wentura, & De Houwer, 2005).

To conclude, the abovementioned exclusions lead to the exclusion of a substantial

number of trials. The number of trials included in the analysis are presented in Table B2.

Table B1: Examples for selected trial sequences for the CbR analysis.

# of comps

in Trial

N

# of comps

in Trial N–1

CrC CRP Feature repetition Response

# of repetitions

of the event file

CbR– CbR+

0 1 – – 3 Repeat 3Trial N–1: a1b1c2d1 Trial N–1: a1b2c1d1

Trial N: a1b1c1d1 Trial N: a1b1c1d1

0 1 – – 1 Alternate 2Trial N–1: a1b1c2d1 Trial N–1: a1b2c1d1










1 1 – + 2 Repeat 2Trial N–1: a1b1c2d1 Trial N–1: a1b2c1d1


1 1 – + 2 Alternate 3Trial N–1: a1b1c2d1 Trial N–1: a1b2c1d1






1 2 + – 3 Repeat 3Trial N–1: a1b1c2d2 Trial N–1: a1b2c1d2


1 2 + – 1 Alternate 2Trial N–1: a1b1c2d2 Trial N–1: a1b2c1d2






2 2 + + 2 Repeat 2Trial N–1: a1b1c2d2 Trial N–1: a1b2c1d2


2 2 + + 2 Alternate 3Trial N–1: a1b1c2d2 Trial N–1: a1b2c1d2

Trial N: a1b2c2d1 Trial N: a1b2c2d1CbR = Competitor becomes Relevant, CrC = Competitor remains Competitor, Comps =

Competitors, # = Number.

Without loss of generality, lowercase letters (e.g., a, b) represent stimulus dimensions (e.g., color, word), and the numbers to the right of each letter represent the dimension values (e.g., red and green for the dimension color) that go with a specific response key (Key 1, Key 2) according to the task rules. The relevant dimension is underlined. Without loss of generality, the competitor S-R set is always associated with Key 2 as the response. Thus, for the CbR phenomenon, what differentiates CbR+ trials from CbR– trials is whether the competitor S-R set in Trial N–1 became the relevant S-R set in Trial N (CbR+) or not (CbR–).

B2. Number of trials in the CbR analysis

Table B2: Number of trials in each cell in the different experiments (M, SD, min & max).

Number of Participants M SD min maxMeiran at al., 2010 24 114.07 9.62 89 136 Hsieh et al., 2012, Experiment 1 28 222.33 19.29 146 268Hsieh et al., 2012, Experiment 2 32 213.10 31.53 64 271Katzir, et al., 2015, Experiment 1A 24 107.75 13.73 68 137Katzir et al. 2015, Experiment 1B 24 106.51 14.19 70 137Katzir, Ori, Eyal, & Meiran, 2015, Experiment 1 41 107.01 13.98 60 143Katzir, Ori, Eyal, & Meiran, 2015, Experiment 2 10 212.23 25.50 161 264Katzir, Ori, & Meiran, 2017 28 211.11 21.45 140 250all 211 158.03 56.76 60 271

B3. CbR analysis – RT

In order to simplify matters, and since we were not interested in the interaction with

Experiment, we entered Experiment to the Null model. Below are the BFs from the JASP

analyses of the CbR effect in response repetition (Table B3) and switch (B4). We find

decisive evidence for a CbR effect in response alternation (Table B4), but substantial

evidence favoring the Null model when the response repeats (Table B3). Table B5 indicates

the BFs of all possible models when inspecting the interaction between CbR and Response.

The best fitting model includes the interaction, BF10 = 1.541 × 1015 and it is 409.62 more

likely than a model that does not include the interaction BF10 = 3.762 × 1012, BFcomparison =

409.62.

Table B3. CbR Effect in Response Repetition Trials (RT).

Model Comparison Models BF 10

Null model (incl. Exp, subject) 1.000 CbR-RT- Response repetition 0.128 Note. All models include Exp, subject.

Table B4. CbR Effect in Response Alternation Trials (RT).


Null model (incl. Exp, subject) 1.000

CbR-RT- Response alternation 2.389e +7

Note. All models include Exp, subject.

Table B5. Model comparison to examine the existence of an interaction between CbR and Response (RT).


Null model (incl. Exp, subject) 1.000 CbR-RT 4169.610 Response 4.314e +8 CbR-RT + Response 3.762e +12 CbR-RT + Response + CbR-RT ✻ Response 1.541e +15



Figure B1. RT as a function of Response (repetition, alternation) and CbR.

B4. CbR analysis - PE

We find decisive evidence for a CbR effect in response alternation (Table B7), but

substantial evidence favoring the Null model when the response repeats (Table B6). In

addition, the best fitting model includes the interaction, BF10 = 1.292 × 1013 but it is not more

likely than a model that does not include the interaction BF10 = 1.063 × 1013, BFcomparison = 1.26

(Table B8).

Table B6. CbR Effect in Response Repetition Trials (PE).


Null model (incl. Exp, subject) 1.000 CbR-PE-Response repetition 0.224 Note. All models include Exp, subject.

Table B7. CbR Effect in Response Alternation Trials (PE).


Null model (incl. Exp, subject) 1.000 CbR-PE-Response alternation 109510.931


Table B8. Model comparison to examine the existence of an interaction between CbR and Response

(PE).


Null model (incl. Exp, subject) 1.000 Response 5.211e +9 CbR-PE 1050.295 Response + CbR-PE 1.063e +13 Response + CbR-PE + Response ✻ CbR-PE 1.292e +13 Note. All models include Exp, subject.

Figure B2. PE as a function of Response (repetition, alternation) and CbR.

Repeat Switch-10

-505

10152025303540

A

Exp 1Exp 2Exp 3Exp 4Exp 5Exp 6Exp 7Exp 8

Response

CbR

effec

t - R

T

Repeat Switch-0.005

0

0.005

0.01

0.015

0.02

B


Response

CbR

effec

t - P

E

Figure B3. The CbR effect as a function of Response and Experiment, in A) RT and B) PE. Exp 1 = Katzir, et al., 2015, Experiment 1A; Exp 2 = Katzir, Ori, & Meiran, 2016; Exp 3 = Meiran at al., 2010; Exp 4 = Katzir, Ori, Eyal, & Meiran, 2015, Experiment 1; Exp 5 = Katzir, Ori, Eyal, & Meiran, 2015, Experiment 2; Exp 6 = Hsieh et al., 2012, Experiment 1; Exp 7 = Katzir et al. 2015, Experiment 1B; Exp 8 = Hsieh et al., 2012, Experiment 2. The Y axis shows the CbR effect which was calculated by subtracting CbR– trials from CbR+ trials, and therefore the Figure present the interaction by presenting the simple main effects at the core of our hypothesis. Error bars represent mixed-model 95% confidence interval (Jarmasz, & Hollands, 2009).

C – CrC analysis

C1. CrC - Selection criteria

The exact trial sequences that were included in the CrC analysis are presented in

Table C1. Here, too, we employed strict selection criteria, based on the following

phenomena: number of competitors in Trial N, number of competitors in Trial N–1, CRP

(CRP– vs. CRP+), and CbR (CbR– vs. CbR+). We also excluded trials in which all of the

dimensions of the previous stimulus (including the response) repeated (Hommel, 1998,

2004). The same logic for exclusion that was used in the CbR analysis was applied in the

CrC analysis. The number of trials included in the analysis are presented in Table C2.

Finally, although we excluded full repetition of stimulus’ dimensions, and assured

that our analysis does not contain full repetition or full switch of all stimulus dimensions

(including the response, Hommel, 1998, 2004; Hommel et al., 2001), number of repeated

features are not equated in the CrC analysis, leaving this analysis open to potential confounds

associated with the number of feature repetitions. Yet, since comparison trials are equated on

the CbR analysis (i.e., in CbR+ and CbR– trials that are used to examine our hypothesis), this

confound is not applicable to the CbR analysis, which rendered a similar pattern of results to

the CrC analysis. Since the two analyses (CbR & CrC) examine the same underlying process

of suppression of interfering S-R rule, we believe that number of feature repetition cannot

give an alternative explanation to the results obtained in our paper.

Table C1: Examples for selected trial sequences for the CrC analysis.

# of comps

in Trial

N

# of comps

in Trial N–1

CbR CRP Feature repetition Response

# of repetitions of

the event file

CrC– CrC+

1 2 - - 1 vs. 3 Repeat 1 vs. 3Trial N–1: a1b1c2d1 Trial N–1: a1b1c2d1


1 2 - - Trial N–1: a1b1c2d1 Trial N–1: a1b1c2d1

3 vs. 1 Alternate 4 vs. 2 Trial N: a1b2c2d1 Trial N: a1b2c1d2

2 1 + - 1 vs. 3 Repeat 1 vs. 3Trial N–1: a1b2c1d2 Trial N–1: a1b2c1d2


2 1 + - 3 vs. 1 Alternate 4 vs. 2Trial N–1: a1b2c1d2 Trial N–1: a1b2c1d2

Trial N: a2b2c1d2 Trial N: a2b2c2d1CbR = Competitor becomes Relevant, CrC = Competitor remains Competitor, Comps =

Competitors, # = Number.

The notations of this Table were the same as Table C1. Lowercase letters (e.g., a, b) represent stimulus dimensions (e.g., color, word) and the numbers to the right of each letter represent the dimension values (e.g., red and green for the dimension color) that go with a specific response key (Key 1, Key 2) according to the task rules. The relevant dimension is underlined. Without loss of generality, the competitor S-R set is always associated with Key 2 as the response. Thus, for the CrC phenomenon, what differentiates CrC+ trials from CrC– trials is whether the competitor S-R set in Trial N–1 remains the competitor S-R set in Trial N (CrC+) or not (CrC–).

C2. Number of trials in the CrC analysis

Table C2: Number of trials in each cell in the different experiments (M, SD, min & max).

Number of Participants M SD min maxMeiran at al., 2010 24 33.23 5.65 18 48Hsieh et al., 2012, Experiment 1 28 62.91 8.86 35 85Hsieh et al., 2012, Experiment 2 32 60.65 10.40 17 78Katzir, et al., 2015, Experiment 1A 24 30.97 6.70 17 47Katzir et al. 2015, Experiment 1B 24 29.74 6.44 12 44Katzir, Ori, Eyal, & Meiran, 2015, Experiment 1 41 29.93 5.87 13 44Katzir, Ori, Eyal, & Meiran, 2015, Experiment 2 10 60.68 9.82 42 86Katzir, Ori, & Meiran, 2017 28 60.41 10.01 32 84

all 211 44.94 17.21 12 86

C3. CrC analysis - RT

We find decisive evidence for a CbR effect in response repetition (Table B3), but

substantial evidence favoring the Null model when the response alternates (Table B4). In

addition, the best fitting model includes the interaction, BF10 = 1.839 × 106 and it is more

likely than a model that does not include the interaction BF10 = 38232.81, BFcomparison = 48.10

(Table C5).

Table C3. CrC Effect in Response Repetition Trials (RT).


Null model (incl. Exp, subject) 1.000

CrC-RT-response repetition 190.679 Note. All models include Exp, subject.

Table C4. CrC Effect in Response Alternation Trials (RT).


Null model (incl. Exp, subject) 1.000 CrC-RT-response alternation 0.186


Table C5. Model comparison to examine the existence of an interaction between CrC and Response

(RT).


Null model (incl. Exp, subject) 1.000 CrC-RT 0.578 Response 65764.143 CrC-RT + Response 38232.805 CrC-RT + Response + CrC-RT ✻ Response 1.839e +6 Note. All models include Exp, subject.

Figure C1. RT as a function of Response (repetition, alternation) and CrC.

C4. CrC analysis – PE

We find substantial evidence for a CbR effect in response repetition (Table B6), but

substantial evidence favoring the Null model when the response alternates (Table B7). In

addition, the best fitting model does not include the interaction, BF10 = 1118.108. The best

fitting model includes the two main effects, BF10 = 4685.336, but it is not more likely than the

next best fitting model, which includes only response as a main effect, BF10 = 4073.697. This

shows there is no evidence for the existence of the CrC effect, BFcomparison = 1.15, and there are

substantial evidence against the existence of an interaction, BFcomparison = 0.238 (Table C8).

Table C6. CrC Effect in Response Repetition Trials (PE).


Null model (incl. Exp, subject) 1.000 CrC-PE-response repetition 3.056 Note. All models include Exp, subject.

Table C7. CrC Effect in Response Alternation Trials (PE).


Null model (incl. Exp, subject) 1.000 CrC-PE-response alternation 0.141 Note. All models include Exp, subject.

Table C8. Model comparison to examine the existence of an interaction between CrC and Response

(PE).


Null model (incl. Exp, subject) 1.000 Response 4073.697 CrC-PE 1.064 Response + CrC-PE 4685.336 Response + CrC-PE + Response ✻ CrC-PE 1118.108 Note. All models include Exp, subject.

Figure C2. PE as a function of Response (repetition, alternation) and CrC.

Repeat Switch

-30-20-10

0102030405060

A


Response

CrC

effec

t - R

T

Repeat Switch

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0.025

B


Response

CrC

effec

t - P

E

Figure C3. The CrC effect as a function of Response and Experiment, in A) RT and B) PE. Exp 1 = Katzir, et al., 2015, Experiment 1A; Exp 2 = Katzir, Ori, & Meiran, 2016; Exp 3 = Meiran at al., 2010; Exp 4 = Katzir, Ori, Eyal, & Meiran, 2015, Experiment 1; Exp 5 = Katzir, Ori, Eyal, & Meiran, 2015, Experiment 2; Exp 6 = Hsieh et al., 2012, Experiment 1; Exp 7 = Katzir et al. 2015, Experiment 1B; Exp 8 = Hsieh et al., 2012, Experiment 2. The Y axis shows the CrC effect which was calculated by subtracting CrC - trials from CrC + trials, and therefore the Figure present the interaction by presenting the simple main effects at the core of our hypothesis. Error bars represent mixed-model 95% confidence interval (Jarmasz, & Hollands, 2009).

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