Running head : CONTINGENCY AND CONFLICT ADAPTATION 1 The Parallel Episodic Processing ( PEP ) Model : Dissociating Contingency and Conflict Adaptation in the Item - Specific Proportion Congruent Paradigm

The present work introduces a computational model, the Parallel Episodic Processing (PEP) model, which demonstrates that contingency learning achieved via simple storage and retrieval of episodic memories can explain the item-specific proportion congruency effect in the colourword Stroop paradigm. The current work also presents a new experimental procedure to more directly dissociate contingency biases from conflict adaptation (i.e., proportion congruency). This was done with three different types of incongruent words that allow a comparison of: (a) high versus low contingency while keeping proportion congruency constant, and (b) high versus low proportion congruency while keeping contingency constant. Results demonstrated a significant contingency effect, but no effect of proportion congruence. It was further shown that the proportion congruency associated with the colour does not matter, either. Thus, the results quite directly demonstrate that ISPC effects are not due to conflict adaptation, but instead to contingency learning biases. CONTINGENCY AND CONFLICT ADAPTATION 3 The Parallel Episodic Processing (PEP) Model: Dissociating Contingency and Conflict Adaptation in the Item-Specific Proportion Congruent Paradigm For decades, one of the most popular ideas in the cognitive psychology literature is the idea that participants are able to adapt to conflict encountered in performance tasks such as the Stroop by adjusting attention away from the source of conflict. Perhaps the most popular instance of purported conflict adaptation is the proportion congruent effect. In the Stroop task (Stroop, 1935), participants are slower to identify the colour of a colour word when the word is incongruent (e.g., the word RED printed in blue; REDblue) relative to when it is congruent (e.g., REDred). This congruency effect is larger when the proportion of congruent trials in the task is high (e.g., 75% congruent, 25% incongruent) relative to when the proportion of congruent trials is low (e.g., 25% congruent, 75% incongruent; Lowe & Mitterer, 1982). This interaction between congruency and proportion congruency, termed the proportion congruent (PC) effect, is generally interpreted as evidence of conflict adaptation (e.g., Botvinick, Braver, Barch, Carter, & Cohen, 2001; Cheesman & Merikle, 1986; Lindsay & Jacoby, 1994). Specifically, it is argued that the congruency effect is smaller in the low PC condition because participants detect that most of the trials in the task are conflictual (i.e., incongruent) and thus direct their attention away from the distracting word to avoid further conflict. As a result, the word has less impact on performance, resulting in a smaller Stroop effect. Although the conflict adaptation idea is highly intuitive there are reasons to doubt this explanation of the proportion congruent effect. One challenge was presented by Jacoby, Lindsay, and Hessels (2003) when they introduced an item-specific version of the proportion congruency paradigm. Instead of manipulating PC between-participant or between-block, they manipulated PC across items. For example, BLUE and GREEN may have been presented most often in their CONTINGENCY AND CONFLICT ADAPTATION 4 congruent colour (high PC), whereas RED and ORANGE might have been presented most often in their incongruent colour (low PC). Participants produced a larger congruency effect for high relative to low PC items, what has been termed an item-specific proportion congruent (ISPC) effect. The ISPC effect poses some difficulty for the conflict adaptation account. If participants are detecting how much conflict they encounter in the task, then it is not clear how they would be able to adapt to conflict differently for high versus low PC items, which are intermixed in the task. Although claims have been forwarded that participants can learn the conflict associated with individual items and rapidly adjust attention accordingly (e.g., Blais, Robidoux, Risko, & Besner, 2007; Verguts & Notebaert, 2008), there is another potential explanation that does not rely on conflict adaptation at all. A drastically different interpretation of the ISPC effect (and PC effects in general) was presented by Schmidt and colleagues (Schmidt & Besner, 2008; Schmidt, Crump, Cheesman, & Besner, 2007; see also, Mordkoff, 1996). According to these authors, participants might simply be learning the contingencies between distracting words and responses to the colour. Participants then respond faster to these high contingency trials (i.e., where the word is predictive of the correct response) relative to low contingency trials (i.e., where the word is not predictive of the correct response). In non-conflict tasks, such contingency effects are found to be quite reliable (see Schmidt, 2012). For example, Miller (1987; see also Carlson & Flowers, 1996) found that when distracting letter flankers were predictive of the target letter, high contingency trials are faster than low contingency trials. Similarly, Schmidt and colleagues (2007) found a contingency effect when distracting neutral words were predictive of the colour they were printed in (e.g., MOVE most often in blue). Such contingency biases can explain the ISPC effect. For example, if GREEN is presented most often in green, then the word GREEN is accurately predictive of the CONTINGENCY AND CONFLICT ADAPTATION 5 green response. Thus, congruent trials in the high PC condition will be speeded, leading to a larger Stroop effect. Similarly, if RED is presented most often in yellow, then RED is accurately predictive of the yellow response. Thus, incongruent trials will be speeded in the low PC condition leading to a smaller Stroop effect. It can therefore be seen that contingency biases alone will produce a congruency by proportion congruency interaction (i.e., PC effect). Note that response conflict is still assumed to exist according to the contingency account, but the changes in the size of the Stroop effect with differing levels of PC has to do with the predictive relationships between words are responses and not due to variation in conflict per se. Schmidt and Besner (2008) suggested that participants learn the predictive relationships (i.e., contingencies) between words and responses to prepare for the likely (i.e., high contingency) response. In particular, they suggested that participants calculate the expected response based on the identity of the word and use this response prediction to decrease the response threshold of the predicted response. An even simpler explanation is that “contingency learning” is simply a by-product of memory storage and retrieval processes (see Schmidt, De Houwer, & Besner, 2010). Specifically, on each trial participants encode information about what stimuli (word and colour) were presented along with what response was made into an episodic memory. On subsequent trials, presentation of the word will lead to retrieval of past episodes of when this word was presented, which then directly facilitate the high contingency response associated with these episodes. The Parallel Episodic Processing (PEP) model, described in the section to follow, does exactly this. The PEP model will provide computational support for this new episodic retrieval account of the ISPC effect. In addition, the PEP model will be used to investigate an important question about additivity. Specifically, Schmidt and Besner (2008) argued that contingency and CONTINGENCY AND CONFLICT ADAPTATION 6 congruency effects are due to statistically-independent processes and should generally not interact with each other. This paper will argue that this additivity prediction is mistaken. However, the argument that Schmidt and Besner put forward is that the high contingency congruent (high PC) and incongruent (low PC) trials will both be responded to roughly equally faster than low contingency congruent (low PC) and incongruent (high PC) trials, respectively. As a result, the benefit of high contingency is equivalent for congruent and incongruent trials, meaning that contingency and congruency should not interact. Schmidt and Besner provided data consistent with this notion. These additivity predictions contrast sharply with those that would be expected from a conflict adaptation account that should anticipate all fluctuation in the size of the congruency effect to be due to changes in incongruent (and not congruent) trials, given that the Stroop effect is almost entirely an interference phenomenon (e.g., see MacLeod, 1991, for a review). Schmidt and Besner thus suggested that the interaction pattern (i.e., additive vs. interaction) could be used to distinguish between contingency learning and conflict adaptation. The additive pattern of data observed by Schmidt and Besner (2008) is indeed problematic for the conflict adaptation account of the ISPC when observed. However, there is a problem with the prediction that contingency and congruency should always be additive. Even if it is true that contingency and congruency effects are due to independent processes, it does not necessarily follow that the two effects will be perfectly additive (and, indeed, they are not in all task variants; e.g., Bugg, Jacoby, & Chanani, 2011). For example, incongruent trials take longer to respond to than congruent trials, so there is more time on an incongruent trial for contingencies to bias responding relative to a congruent trial. This would result in a larger contingency effect for incongruent relative to congruent trials, producing an overadditive interaction. Thus, even if the contingency account of ISPC effects is correct, deviation from the CONTINGENCY AND CONFLICT ADAPTATION 7 additive pattern Schmidt and Besner demonstrated is likely, particularly with higher power experiments and in situations that promote this sort of overadditive interaction (e.g., where responses to congruent trials are restricted by a floor effect). In this vein, a second goal of Simulation 1 is to see whether a model that produces an ISPC effect via contingency learning processes rather than conflict adaptation produces results that deviate from additivity. Stimulation 1 A visual representation of the PEP model is presented in Figure 1. A simplified explanation of the model is explained in the text to follow, but for interested readers a complete conceptual overview and description of the math of the model is presented in the Appendix. Fully documented source code is available online (http://users.ugent.be/~jaschmid/PEP/) or from the author. (Figure 1 about here) The primary goal of Simulation 1 is to demonstrate that a very simple episodic memory model can account for the ISPC effect. On each trial, the model creates a new episode, which is linked to activated words. Activation from word and colour Input nodes competes in Identity nodes, thus producing a congruency effect. Words also activate Episode nodes, which in turn activate Response nodes (note that colours are not linked to episodes for computational simplicity only). As the episodes associated with a particular word are most often associated with a specific (high contingency) response, these processes result in the high contingency Response node being active, thus producing a contingency effect. The model has no mechanism by which it can learn about and adapt to conflict. Response conflict does occur in the model (i.e., if two or more Identity nodes are active, then they will compete), but the model is unable to measure this conflict (conflict monitoring) or adjust attention or other processing in response to conflict CONTINGENCY AND CONFLICT ADAPTATION 8 (conflict adaptation). Method Simulation 1 was basically identical to the design of Jacoby and colleagues (2003). There were four pairs of colours. High and low PC trials were completed in one run and medium PC trials were completed in a second run (they were two separate blocks in original experiment). In the first of these two runs, two of the words were presented three of four times in their congruent colour (high PC) and once in the other (incongruent) colour, whereas the other two words were presented three of four times in a specific incongruent colour (low PC) and once in their congruent colour. In the second run, two pairs of words were presented equally often (two of four times) in both the congruent and incongruent colour (medium PC). The model was run 1000 times (i.e., 1000 “participants”), with 16 trials in each of 30 blocks, for a total of 480 trials. Results Cycle times. The results of Simulation 1 can be seen in Figure 2. The PEP produced an overall congruency effect of 89 cycles. The model also produced an ISPC effect: the congruency effect was 117 cycles in the high PC condition, 90 cycles in the medium PC condition, and 61 cycles in the low PC condition. Most importantly, deviation from additivity was apparent. When the results were plotted as a function of contingency (Figure 2b) rather than PC, the congruency effect was 68, 90, and 110 cycles in the high, medium, and low contingency conditions, respectively. Thus, an overadditive interaction was observed. (Figure 2 about here) Error percentages. The error data for Simulation 1 are presented in Figure 3. The model produced an overall congruency effect of 2.2%. The model also produced an ISPC effect: the congruency effect was 2.7% in the high PC condition, 2.2% in the medium PC condition, and CONTINGENCY AND CONFLICT ADAPTATION 9 1.7% in the low PC condition. Most importantly, deviation from additivity was again observed. When the results were plotted as a function of contingency rather than PC, the congruency effect was 1.9, 2.2, and 2.5% in the high, medium, and low contingency conditions, respectively. Thus, an overadditive interaction was again observed. (Figure 3 about here) Discussion The results of Simulation 1 demonstrate two things. First, memory encoding and retrieval processes are sufficient to produce an ISPC effect. Like conflict monitoring models (e.g., Blais et al., 2007; Verguts & Notebaert, 2008), the PEP successfully simulated the ISPC effect in both cycle times and error percentages. Thus, conflict monitoring and adaptation do not need to be assumed to simulate the ISPC effect. Second, the results were not perfectly additive. Specifically, the contingency effect was larger for incongruent relative to congruent trials. As discussed in the introduction, this is due to the fact that contingency has more time to influence responding on incongruent relative to congruent trials. The degree to which the results do or do not deviate from additivity can be altered by playing with parameters, many of which might correspond to differences between experiments (e.g., speeding target identification, similar to Bugg et al., 2011). Deviation from additivity was also found with an earlier version of the model that more closely corresponded to the response threshold idea of Schmidt and Besner (2008). Thus, the contingency account of the ISPC can tolerate such overadditive interactions, contrary to what Schmidt and Besner suggest. An interaction between contingency and congruency cannot therefore be used to argue against a contingency account, as Schmidt and Besner previously suggested. Thus, a new dissociation procedure is required to distinguish between conflict adaptation and contingency. CONTINGENCY AND CONFLICT ADAPTATION 10 Experiment 1 Schmidt and Besner (2008) previously argued that additive results support the contingency account and overadditive results support the conflict adaptation account. Simulation 1 demonstrates that this is not necessarily true. Logically, independent processes do not entail additive data and Simulation 1 clearly demonstrated that the contingency account can tolerate non-additivity. Given that overadditivity is also consistent with conflict adaptation theory, it is difficult to interpret such non-additive patterns. For example, if one finds an overadditive interaction driven solely by incongruent trials, then is this another contingency bias or legitimate conflict adaptation? A new approach is therefore needed. A more direct approach to assessing contingency biases in the ISPC task is to dissociate item-level proportion congruence from contingency. This was the goal of Experiment 1. As can be seen in Table 1, the design had four colour words, two of which were high PC (BLUE and GREEN) and two of which were low PC (RED and YELLOW). Critically, some of the low PC incongruent items were high contingency (e.g., REDyellow), whereas others were low contingency (e.g., REDblue). These manipulations allow the creation of three incongruent trial types, each shaded differently in Table 1: (1) high contingency/low PC (high/low) such as REDyellow, (2) low contingency/low PC (low/low) such as REDblue, and (3) low contingency/high PC (low/high) such as BLUEgreen. In most ISPC designs, only high/low and low/high incongruent trials are present, thus directly confounding contingency and PC. The inclusion of the low/low incongruent trials is thus critical in dissociating contingency and PC effects. Specifically, the high/low and low/low incongruent trials vary only in contingency (i.e., they are both low PC), making a difference between the two evidence for a contingency learning contribution to the ISPC effect. In contrast, low/low and low/high incongruent trials vary only in PC (i.e., they are CONTINGENCY AND CONFLICT ADAPTATION 11 both low contingency), making a difference between the two evidence for conflict adaptation. (Table 1 about here) Recently, Bugg and colleagues (2011) have suggested that sometimes the proportion congruency of the colour (rather than the word) might matter. Although the experimental setup of the current experiment is probably not ideal for matching the parameters suggested by those authors for when colour PC might matter (specifically, when the colour has a processing advantage over the word), a dissociation of colour PC independent of word PC (i.e., the typical PC measure) and contingency was provided. This was achieved by separating low/high incongruent trials into two subtypes. Of the six low/high incongruent trials in Table 1, it can be seen that two of these have a high PC colour (i.e., BLUEgreen and GREENblue), whereas the remaining four have a low PC colour (i.e., BLUEred, BLUEyellow, GREENred, and GREENyellow). Both of these trial types are low contingency and have a high PC word (i.e., BLUE or GREEN), so they vary only in the PC of the colour. Thus, these manipulations allow an assessment of contingency, word PC, and colour PC independently. Method Participants. Fifty Ghent University undergraduates participated in exchange for course credit. Apparatus. Stimulus and response timing were controlled by E-Prime software (Psychology Software Tools, 2002). Responses were made on an AZERTY keyboard. Materials and Design. Stimuli were presented on a black background. There were four Dutch colour words (blauw [blue], groen [green], rood [red], and geel [yellow]) presented in the same four display colours (blue, green, red, and yellow). Words were presented in lowercase, bold, 18 pt. Courier New font. The RGB values for the colours were 0,0,255 (blue), 0,255,0 CONTINGENCY AND CONFLICT ADAPTATION 12 (green), 255,0,0 (red), and 255,255,0 (yellow). A total of 400 stimuli were selected randomly with replacement. Two colour words were presented 70% of the time in their congruent colour (high/high congruent) and equally often in the remaining three colours (low/high incongruent). The other two colour words were presented 70% of the time in the other low PC colour (high/low incongruent) and equally often in the remaining three colours (low/low congruent and incongruent). Procedure. Participants sat approximately 60 cm from the screen. They were first presented with a white fixation (“+”) for 250 ms, followed by a blank screen for 750 ms, followed by the Stroop stimulus for 2000 ms or until a response was made. The next trial began immediately after correct responses. Trials on which an error was made or the participant failed to respond in time were followed by “XXX” in white for 500 ms before the next trial. Responses were made with the U, I, O, and P keys. Which colour was mapped to which key was randomly determined for each participant. The PC level associated with each colour was also randomized. Which keys corresponded to high or low PC colours was counterbalanced across participants. Results Correct response latencies and errors were analysed. Two participants were dropped from the analysis for failing to comply with instructions. One had almost 100% errors in the three incongruent conditions, indicating that they were responding to the word rather than the colour. The second participant that was deleted made the same mistake for the first half of the experiment and resultantly had over 50% errors in the three incongruent conditions. Response Latencies. First, the ISPC effect was assessed in the traditional way by performing a 2 congruency (congruent vs. incongruent) x 2 PC (high vs. low) ANOVA. Unsurprisingly, there was a significant main effect of congruency, F(1,47) = 147.474, MSE = CONTINGENCY AND CONFLICT ADAPTATION 13 2477, p < .001, 2 p η = .76, indicating slower overall responses to incongruent trials. There was no main effect of PC, F(1,47) = .025, MSE = 3498, p = .874, 2 p η < .001. Critically, there was a significant interaction between congruency and PC (i.e., an ISPC effect), F(1,47) = 21.444, MSE = 2612, p < .001, 2 p η = .31. Next, the three types of incongruent trials were divided up and the two critical tests were completed. Responses were significantly faster to high/low (775 ms) relative to low/low (815 ms) incongruent trials, t(47) = 3.409, SEdiff = 12, p = .001, 2 p η = .20, indicating a significant contingency effect. In contrast, no difference was found between low/low and low/high (818 ms) incongruent trials, t(47) = .319, SEdiff = 10, p = .751, 2 p η < .01, indicating no evidence for conflict adaptation. Further, this test had high power (.98) to detect an effect as large as the observed contingency effect. The potential effect of the PC of the colour was then assessed by separating low/high incongruent trials and no significant difference was found between high PC colours (815 ms) and low PC colours (820 ms), t(47) = .302, SEdiff = 17, p = .764, 2 p η < .01. Indeed the means were numerically in the wrong direction. Finally, high/high congruent trials (697 ms) were responded to significantly faster than low/low congruent trials (730 ms), t(47) = 2.437, SEdiff = 13, p = .019, 2 p η = .11, consistent with either account. Error Percentages. The 2 congruency (congruent vs. incongruent) x 2 PC (high vs. low) ANOVA for errors revealed a significant main effect of congruency, F(1,47) = 17.985, MSE = 25, p < .001, 2p η = .28, indicating more errors overall for incongruent trials. There was no main effect of PC, F(1,47) = .599, MSE = 15, p = .443, 2p η = .01. Critically, there was a significant interaction between congruency and PC (i.e., an ISPC effect), F(1,47) = 10.323, MSE = 15, p = CONTINGENCY AND CONFLICT ADAPTATION 14