Assessing the Time Course of Stroop and Simon Effects. Michael S. Pratte, Jeffrey N. Rouder, Richard D. Morey, Kathleen E. Wenzlick, and.

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1 Stroop vs. Simon 1 Running head: STROOP VS. SIMON Assessing the Time Course of Stroop and Simon Effects Michael S. Pratte, Jeffrey N. Rouder, Richard D. Morey, Kathleen E. Wenzlick, and Chuning Feng University of Missouri-Columbia Michael S. Pratte 210 McAlester Hall University of Missouri Columbia, MO mspn69@missouri.edu

2 Stroop vs. Simon 2 Abstract Stroop and Simon tasks are logically similar and are often used to investigate cognitive control and inhibition processes. We compare the time course of Stroop and Simon effects with delta plots and find different though stable patterns. Stroop effects across a variety of conditions are smallest for fast responses and increase as responses slow. Simon effects across a variety of conditions, however, are largest for fast responses, decrease, and even reverse as responses slow. We show in two experiments that these diverging patters hold within participants and even when the stimulus materials are identical across the tasks. These stable differences in time course serve as bedrock phenomena for building and testing theories of cognitive control and inhibition. The results of two additional experiments suggest that the determinant of time course is whether the task-irrelevant information is represented in a manner that preserves spatial left-right laterality.

3 Stroop vs. Simon 3 Assessing the Time Course of Stroop and Simon Effects Psychologists have long known that judgments about target stimuli are affected by the surrounding context. A classic example is the Stroop task in which judgments about the ink color of a color term is affected by the identity of the color term (Stroop, 1935). In this case, word identity serves as task-irrelevant context information. Other examples include Simon tasks (Simon, 1969), priming tasks (Scarborough, Cortese, & Scarborough, 1977) flanker tasks (Eriksen & Eriksen, 1974), and identification tasks with nested letters (Navon, 1977). Because these and similar tasks can be described as assessing the effects of a task-irrelevant context information on judgments about a target, we refer to them generically as context tasks (see also Kornblum & Lee, 1995). The main result in all of these contexts tasks is that judgments about targets are made more quickly and more accurately when targets are congruent than incongruent with the context. In the Stroop task, for example, naming the ink color is speeded when it is the same as the meaning of the color word (e.g., when the word RED is presented in red) than when it is different (e.g., when the word GREEN is presented in red). Another example of a congruency effect occurs in the Simon task, in which participants judge the color of a target square by pressing left- and right-hand response keys. Responses are speeded when the stimulus is displayed on the same side as the response compared to when it is displayed on the opposite side. Congruency effects have been interpreted as evidence for cognitive control (Botvinick, Braver, Barch, Carter, & Cohen, 2001), selective attention (Spieler, Balota, & Faust, 2000), response inhibition (Ridderinkhof, 1997), and spreading activation (Neely, 1991), depending on the task and specifics of the experimental conditions. Differences in congruency effects across populations have been used to make claims about the affects of aging (Spieler, Balota, & Faust, 1996), schizophrenia (Baving, Wagner, Cohen, &

4 Stroop vs. Simon 4 Rockstroh, 2001), autism (Christ, Holt, White, & Green, 2007), and attention deficit disorder (Ridderinkhof, Scheres, Oosterlaan, & Sergeant, 2005) on cognitive control, selective attention, and inhibition. In fact, the robustness of this congruency effect across several tasks, as well as the logical similarity of these tasks has led to general perception that these tasks are more or less interchangeable in measuring cognitive control, selective attention, or inhibition. In this paper, we examine the time course of context effects in Simon, Stroop, and priming tasks. Based on the robustness of the congruency effect as well as the logical similarity of the tasks, it might be expected that the time courses follow the same qualitative patterns. In fact, we report here dramatic differences. In Stroop tasks, the congruency effect is minimal for the fastest responses and increases as responses slow. The opposite pattern is found for Simon tasks: the congruency effect is maximal for the fastest responses and decreases as responses slow, and may even reverse for the slowest responses. In this paper we explore some of the factors that lead to these opposing Simon-like and Stroop-like time courses. Distributions and Delta Plots Although it may not be immediately obvious, the dynamics of the time course of an effect is determined by the underlying response time distributions. Figure 1A shows two hypothetical distributions for congruent and incongruent conditions. Many appropriate verbal statements may be made about this effect, for example, the mean and variance both increase with incongruency. One appealing statement from a theoretical perspective is that the effect is minimal for the fastest responses and grows as RT slows. This statement is captured by the plot in Figure 1B. This plot, the delta plot (De Jong, Liang, & Lauber, 1994), is drawn from RT percentiles. The filled circles in Figures 1A and 1B show the 10th percentile for the distributions. The y-axis of the delta plot (Figure 1B)

5 Stroop vs. Simon 5 shows the difference of these percentiles, or the size of the congruency effect, at a particular percentile. In the figure, the effect is 66 ms at the 10th percentile. The x-axis of the delta plot is an average of the congruent and incongruent conditions at a given percentile. For example, the average RT for the 10th percentile is 414 ms. The set of open squares in Figures 1A and 1B show the same construction for the 65th percentile. The remaining rows of Figure 1 show alternative distributional relationships which may underlie the congruency effect. The center row shows the case in which the slowing from incongruency is constant across the distribution. This pattern occurs if the cost of incongruency does not depend on the speed of response. As seen, the distributions are shifted and the corresponding delta plot is a horizontal line with an intercept reflecting the cost. The bottom row shows two distributions that have a complex relationship. The incongruent distribution starts later than the congruent one, however it has smaller variance. The corresponding delta plot is a negatively sloped straight line. From the delta plot, it is clear that there is a large congruency effect for the fastest responses that diminishes and even reverses as response slow (i.e., there is an advantage of incongruency for these slowest responses). Although the relationship in the bottom row seems unlikely, it is implicated in some of the data we present here. Delta plots do not capture all of the information in the underlying RT distribution. In fact, they miss many aspects such as the overall shape of the distributions. They do, however, bring into sharp focus the differences among distributions, and in this regard, they are exceptionally useful. Figure 1 provides an intuitive guide about how delta plots capture relations among distributions. More formal characterizations of the relationship between delta plots and underlying distributions is provided in Speckman, Rouder, Morey, & Pratte (in press) and Zhang & Kornblum (1997).

6 Stroop vs. Simon 6 The Time Course of Effects In this section, we review the time course of a few previously published context-effect experiments. Before doing so, it is worthwhile to consider the time course of strength effects for comparison. Examples of strength variables include obvious manipulations such as the intensity or duration of a to-be-detected light source. Other examples include the frequency of a word in lexical decision (Meyer, Schvaneveldt, & Ruddy, 1975), or even numeric distance effects (Moyer & Landauer, 1967). Strength effects have been well studied though not typically with delta plots. Figure 2A shows the patterns resulting from strength manipulations. The data in this case are from some of our previously published work. All of these delta plots are positive and positively increasing. This pattern implies three RT properties: first, distributions obey stochastic dominance in that no part of the slower distribution is faster than than the faster distribution. Second, the slowing increases throughout the distribution. Third, the mean and standard deviation of RT increase together. This last property is so ubiquitous that Wagenmakers & Brown (2007) have proposed, as a law, that standard deviation is proportional to mean and show this relationship holds across a surprisingly wide range of strength manipulations. Consideration of these plots and of previously published RT distributions leads to the following generalization: delta plots of strength manipulations (low strength minus high strength) are positive with positive slope. The delta plot pattern in Figure 2A is concordant with many processing theories and explanations. For example, all positive and increasing delta plots are compatible with either drift rate or bound changes in the diffusion model of perception (Ratcliff, 1978); with changes in the τ parameter in the ex-gaussian (Andrews & Heathcote, 2001); or with the insertion of stages in processes (Ashby & Townsend, 1980; Balota & Chumbley, 1984). In sum, the delta plots in Figure 2A serve as a default expectation that are often observed and broadly consistent with several different existing theories.

7 Stroop vs. Simon 7 Figure 2B shows delta plots from a few previously published Stroop task studies. Although there is a fair amount of variation in the methods, populations, and stimuli used, the overall pattern is clear the Stroop manipulation acts like a strength manipulation. Delta plots are positive and increasing; that is, the effect is minimal for the fastest responses and increases thereafter. Figure 2C shows delta plots from two previously-published studies of the Simon effect. These are shockingly different than the Stroop and strength-effect delta plots. The congruency effect is greatest early on and decreases thereafter, and even becomes negative for the slowest responses in Burle, van den Wildenberg, & Ridderinkhof (2005). These patterns violate the Wagenmakers & Brown (2007) law that mean and standard deviation vary together. Instead, the negative delta plot slope indicates the reverse pattern: Increases in mean are accompanied by decreases in standard deviation. The opposing patterns in the Stroop and Simon congruity effects are surprising given the logical similarity of the tasks. At a minimum, they indicate that Stroop and Simon interference should not be considered equivalent. From a theoretical perspective, Stroop interference is broadly consistent with a host of information-processing explanations including slower accumulation of information from lateral inhibition or the insertion of recheck stages. These explanations, however, cannot explain the negative slope in the Simon congruency effect. A converse statement holds as well theories of Simon interference cannot explain Stroop interference. One explanation of the negatively-sloped delta plot is Ridderinkhof s (1997) two-process model. Initially, there is a quick and automatic facilitory effect of the response initiated by the context. This facilitation is then countered by inhibition of the activated response. This inhibition is slowly deployed resulting in the observed negatively-sloped time course. Similar ideas are present in the Huber, Shiffrin, Quash, & Lyle (2002) concept of prime discounting and Eimer s model of response overcompensation

8 Stroop vs. Simon 8 (Eimer, 1999). Because each of these models explains negatively-sloped delta plots, however, they cannot account for the Stroop congruency effect in which there is a positively-sloped delta-plot pattern. This theoretical state is problematic because underlying mechanisms are pitched rather generally. For example, consider Ridderinkhof and colleague s claim that the slope of the delta plot reflects the strength of inhibition. This interpretation would imply that the Stroop task entails very weak or nonexistent inhibition compared to the Simon task. We find this implication troubling because it seems like participants should employ at least as much inhibition in the Stroop task as in the Simon task. Therefore, general concepts such as inhibition, selective attention, or overcompensation seem ill-suited to describe the fundamental difference in time course between Stroop and Simon interference. The key question addressed here is what constellation of conditions give rise to Stroop- and Simon-like patterns. To foreshadow, we present here our working hypothesis (even though it was formulated after the following experiments were analyzed). By default, most context effects are like strength effects and give rise to positively-sloped delta plots. Exceptions occur when the distracting information has a lateralized representation and the responses are also lateralized. In the Simon task, for instance, the side of presentation serves as the distracting information and it has a left-right lateralized representation. Given the lateral organization of brain structures, it is plausible that the connections from the brain regions representing one side of space are stronger to brain areas representing ipsilateral action than to those representing contralateral action. This explanation is similar to several proposed explanations of the Simon effect (Hommel, 1998; Wiegand & Wascher, 2005, 2007). In the Stroop task, in contrast, the distracting information is the meaning of the word, which does not have a left-right lateralized representation. The patterns of results shown in Figure 2 come from different experiments with different participants. In Experiment 1, we assessed whether the different delta-plot slopes

9 Stroop vs. Simon 9 hold when the same set of participants perform both tasks. Participants first performed a Simon task in which they identified the color of squares presented to the left and right side of fixation. Then they performed a Stroop task in which they identified the color of color words. Experiment 1 Method Participants. Thirty-eight University of Missouri students participated in Experiment 1 in return for credit toward a course requirement. Apparatus & Stimuli. For all experiments participants were tested in individual cubicles and the experiments were run on Pentium 4 PCs running MS-DOS. Stimulus display and response collection was controlled by a custom-written set of C routines. Monitors were 17-inch Dell CRTs with resolutions of 800 pixels by 600 pixels refreshing with a frequency of 60 hz (except for Experiment 4 in which the frequency was 85 hz). Stimuli in the Simon task were red and green squares subtending 2 of arc and presented 4 to the left or right of fixation. Stimuli in the Stroop task were the words red, green, blue, and XXXX presented in colors of red, green, and blue in the center of the screen. Design. The Simon task was a 2X2 within-subject balanced factorial design with stimulus color and side of presentation serving as factors. All combinations of factors occurred equally often across each block of 72 trials. The Stroop task was a 4X3 within-subject factorial design with word identity and word color serving as factors. Combinations that were congruent, incongruent, and with the neural word XXXX were presented equally often in blocks of 72 trials. Procedure. Participants first performed 7 blocks of the Simon task. Each trial began with a fixation cross presented for 700 ms in the center of the screen. Following fixation

10 Stroop vs. Simon 10 the target appeared and was displayed until a response was made. Following the response, a blank screen presented for 700 ms preceded the beginning of the next trial. Participants were instructed to press the key labeled Green ( / ) with their right hand if the target was green, and to press the key labeled red ( z ) with their left hand if the target was red. Upon completing the Simon task, participants were given instructions for, and then completed 7 blocks of the Stroop task. The procedure of the Stroop task was identical to that of the Simon task with the following exceptions. After 700 ms of fixation, the fixation cross was replaced with a target word. Participants were instructed to press the key labeled Green ( / ) with their right index finger if the word was colored green, to press that labeled Blue (space) with their thumb if it was colored blue, and to press the key labeled red ( z ) with their left index finger if it was colored red. Results Response time served as the main dependent variable and there was a reliable 13.7 ms congruency effect in the Simon task (541.2 ms vs ms, t(37) = 3.66, p <.05) and a reliable 90.0 ms congruency effect in the Stroop task (705.5 ms vs ms, t(37) = 9.52, p <.05). Additionally, although performance was highly accurate in both tasks, there were reliable congruency effects in accuracy as well (Simon: 98.5% vs. 96.9%, t(37) = 4.15, p <.05; Stroop: 97.2% vs. 95.0%, t(37) = 4.19, p <.05) indicating that the observed RT effects do not reflect a speed-accuracy trade off. Delta plots of the Stroop and Simon effects are shown in Figure 3A. These plots were constructed by calculating the deciles (that is, the 10th,..., 90th percentiles) for each participant in congruent and incongruent conditions for each task. The deciles were then averaged across participants. Averaging percentiles is accurate when the underlying distributions across people have the same shape and vary only in shift and scale (Jiang,

11 Stroop vs. Simon 11 Rouder, & Speckman, 2004; Thomas & Ross, 1980). 1 For instance, all of the distributions in Figure 1 have the same shape. Rouder & Speckman (2004) show that percentile averaging is accurate for unimodal distributions even when the same-shape assumption is modestly violated; hence the method is defensible here as a means of inspecting distributional properties. Delta plots were constructed from these decile averages as discussed previously. The trend follows the previous results: the curves are sloped positively and negatively for Stroop and Simon effects, respectively. Slope in delta plots are ratios that describe the milliseconds of effect change for each millisecond that RT increases. For the Stroop task, the slope is.26 which indicates about a 1 ms increase in effect for every 4 ms increase in RT. For the Simon effect, the slope is -.19 which indicates about 1 ms decrease in effect for every 5 ms increase in RT. We do not know of any statistical test of the trends in delta-plot slopes without assuming that the shape of RT distribution does not vary across conditions or people. This assumption is equivalent to modeling the underlying delta plots as straight lines. In this case, the slope reflects the ratio of standard deviations in the congruent and incongruent conditions (Zhang & Kornblum, 1997). This fact suggests that the ratio of standard deviations may be used to asses the statistical significance of delta-plot slopes. Alternatively, De Jong et al. (1994) fit straight lines to individuals delta plots directly with ordinary linear regression. They then constructed contrasts across conditions on the resulting slope estimates. It would seem that contrasts on standard deviations are more appropriate than contrasts on estimated slope because fitting lines to delta plots violates several assumptions of OLS. Specifically, independence is violated because percentiles are correlated across nearby percentiles; homogeneity of variance is violated as the sample variance in a percentile varies across the distribution. Moreover, there is sample noise in both axes leading to an errors-in-measurements problem (Klauer, Draine, & Greenwald, 1998).

12 Stroop vs. Simon 12 Given the lack of standard for assessing slope, we explored the properties of a few methods with Monte Carlo simulation. In one simulation, RT distributions were distributed as a Weibull with a shape of 1.7; in a second simulation, they were distributed as a log-normal with a shape of log σ =.5. We found that the method based on OLS estimation of individuals slopes was very reasonable (real Type I error rates ranged from.04 to.06 at the nominal.05 level) even though the underlying assumptions were violated. Moreover, the power of this test was substantially greater than other methods including contrasts on individuals standard deviation. Hence, we use OLS regression to estimate delta plot slopes throughout this paper with reasonable confidence that nominal Type I error rates are accurate. For Experiment 1, the OLS slope estimate method reveals that the slope of the Stroop effect is significantly positive (M =.26, t(37) = 7.66, p <.05) while that of the Simon effect is significantly negative (M =.19, t(37) = 7.82, p <.05). Discussion The delta-plot analyses of Experiment 1 replicate the qualitative difference in the nature of Stroop and Simon effects: The Stroop effect is small for fast responses and increases as responses slow; the Simon effect is largest for fast responses and decreases as responses slow. These diverging patterns hold when the task is manipulated within-subject. There are several procedural differences between Stroop and Simon tasks that may account for their different patterns of effects. Among these are that the stimulus materials differ (words vs. squares) and that the number of response options differ. It is important to understand whether the delta-plot patterns reflect underlying processing differences in Stroop and Simon tasks or differences in these procedural elements. Our approach in Experiment 2 was to control these procedural differences and assess whether the delta-plot differences remain.

13 Stroop vs. Simon 13 Experiment 2 O Leary & Barber (1993) introduced a task similar to Simon s early work (Simon, 1968) that is ideal for controlling procedural differences in Stroop and Simon tasks. O Leary & Barber used the words LEFT and RIGHT as stimuli and these words were presented either to the left or right of fixation. Congruent stimuli are those in which the word meaning and side of presentation match; incongruent stimuli are those in which they mismatch. There are two sets of instructions: in the Simon instruction condition, participants identify the identity of the word with the words LEFT and RIGHT mapped to left- and right-hand responses, respectively. The instructions reflect Simon interference because the incongruency occurs when the target word is presented contralateral to the correct response. In the Stroop instruction condition, participants identify the side of target presentation with the left and right side mapped to left- and right-hand responses, respectively. The instructions reflect Stroop interference because incongruency occurs when the target s meaning is in opposition with the to-be-judged feature of the target. If the delta plot patterns show the robust differences of Experiment 1 and the previous work, these differences reflect deep processing differences rather than procedural ones. We refer to this task as the integrated Stroop Simon task. As an aside, O Leary & Barber found modest congruency effects for both instruction conditions. Their research, however, was performed before delta plots were introduced and they did not perform any distributional analyses. Hence, their results provide no expectations about the delta plot patterns. Method Participants. Thirty-eight University of Missouri students that did not participate in Experiment 1 participated in Experiment 2 in return for credit toward a course requirement.

14 Stroop vs. Simon 14 Stimuli. Across the entire experiment, stimuli consisted of the words LEFT and RIGHT presented approximately 5 to the left or right of a central fixation cross. Design. Experiment 2 was a 2X2X2 within-subject balanced factorial design with side of presentation, word identity, and task instruction serving as factors. Task instructions were held constant across a block of 72 trials. In each block, each combination of word-identity and side-of-presentation was presented equally often. Procedure. The procedure of Experiment 2 was identical to that of Experiment 1 with the following exceptions: Participants performed 5 blocks each of the Simon and Stroop tasks. All participants began with a block of the Stroop task (identify location) followed by a block of the Simon task (identify word). Task instruction proceeded to alternate between blocks for the remainder of the experiment. Before each block of Simon trials participants were instructed to press the key labeled Left ( z ) with their left index finger if the word read LEFT and to press the key labeled Right ( / ) with their right index finger if the word read RIGHT. Before each block of Stroop trials, participants were instructed to respond with the same Left and Right keys according to which side of the screen the word was presented on. Participants received auditory feedback on their accuracy throughout the experiment, ensuring that they continued to perform the correct task within a block. Results There was a reliable 25.0 ms congruency effect in the Simon task (606.4 ms vs ms, t(37) = 5.98, p <.05) and a reliable 14.5 ms congruency effect in the Stroop task (435.7 ms vs ms, t(37) = 4.07, p <.05). Additionally, although performance was highly accurate in both tasks, there were reliable congruency effects in accuracy as well (Simon: 98.3% vs. 95.6%, t(37) = 3.71, p <.05; Stroop: 99.8% vs. 99.1%, t(37) = 3.68, p <.05) indicating that RT effects are not the result of a speed-accuracy trade off.

15 Stroop vs. Simon 15 The delta plots for the integrated Simon and Stroop effects are shown in Figure 3B. The delta plots certainly differ from those in Experiment 1 in that the Simon effect is larger than the Stroop effect. Nonetheless, the pattern of slopes holds: the slope of the Stroop effect was significantly positive (M =.08, t(37) = 2.81, p <.05) while that of the Simon effect was significantly negative (M =.09, t(37) = 3.09, p <.05). These results confirm that the divergent pattern in slopes reflects processing differences in Stroop and Simon interference rather than procedural elements. Discussion There are two predominant theoretical approaches to interpreting delta plots. We have reviewed the Ridderinkhof and colleagues approach in which the negative slope of the delta plot reflects the deployment of inhibition. According to this approach, the Stroop task is characterized by less inhibition than the Simon task. There is, however, no independent support for such a characterization. A second approach is Kornblum and colleagues dimensional overlap (DO) taxonomy (Kornblum & Lee, 1995; Kornblum, Stevens, Whipple, & Requin, 1999). Accordingly, the critical difference between context tasks is whether the relevant features of the target overlap with the distracting ones, and whether the relevant and distracting features overlap with responses. Factorially combining the ways the relevant features, distracting features, and responses can overlap results in eight distinct categories of context tasks, labeled Type-1 through Type-8 in the DO taxonomy. The main prediction of the theory underlying this taxonomy is that tasks that are of the same type should yield the same delta-plot pattern. This theory is consistent with the different delta plot patterns for typical Stroop and Simon tasks because these tasks are in different categories (Type-8 and Type-3, respectively). The taxonomy, however, appears incompatible with the results of Experiment 2 with the integrated Stroop and Simon task. Both instruction

16 Stroop vs. Simon 16 conditions share exactly the same logical structure and both are members of the Type-8 category: relevant features overlap with distracting ones, and both relevant and distracting features overlap with responses. Hence, both should produce the same mental processing and, consequently, the same delta plot patterns. As shown in Figure 3B, this prediction is not realized. We explore a few alternative mechanisms for explaining the stable difference between Stroop and Simon interference. One possibility is that the differing patterns simply reflect the fact that location and meaning information are processed differently. Accordingly, any task that has location serving as the distracting feature should have a negatively-sloped delta plot while any task that has meaning serving as a distracting feature should have a positively-sloped delta plot. A second possibility comes from the work of Wiegand and Wascher (2005) which implies that the processing of laterality is different than other sources of interference. In the Simon task, the distracting information is the side of presentation, and the mapping from side of presentation to the response is natural and, perhaps, privileged, given that the body has an axis of symmetry dividing left from right. In the Stroop task, in contrast, the distracting information, while automatically and quickly processed, is semantic and does not have the same status. Given the prevailing viewpoints that Simon effects are motoric in nature (e.g., De Jong et al., 1994; Wascher, Schatz, Kuder, & Verleger, 2001; Wiegand & Wascher, 2005) it may be that the side of presentation affects lateralized motor activation more directly than other sources of interference. Wiegand and Wascher (2005) obtained the following result that supports the notion of different processing for laterality. They asked participants to identify the color of a square that was presented either above, below, left, or right of fixation. Participants were instructed to depress a key that was both above and to the left for red boxes and both below and to the right for green boxes. Congruency for above/below targets was defined

17 Stroop vs. Simon 17 analogously to those for left/right targets; for example, a green target above fixation is incongruent. Wiegand and Wascher found a surprising dissociation: the delta plot of targets to the left and right of fixation produced the typical negatively-sloped delta plot, but the targets above and below fixation produced positively-sloped delta plots. Based on this dissociation, they concluded that only left-right lateralized targets produce negatively-sloped delta plots. In Experiment 3 we provide a different test of whether location in general, or laterality in specific, is necessary to produce negatively-sloped delta plots. Experiment 3 Experiment 3 was designed to provide a test of whether laterality has a different basis for interference than spatial location in general. We decided to keep the responses lateralized as in Experiments 1 and 2 and attempted to train a Simon effect for non-lateralized stimuli. In an initial training phase, participants were shown only a blue target either above or below fixation and had to respond with the left hand to the above-fixation targets and with the right hand to the below-fixation ones. In this manner, the locations above and below fixation were associated with the left-hand and right-hand responses, respectively. In the subsequent experimental phase, participants were presented three types of trials: training trials, Simon trials, and mediated Simon trials. Training trials were blue targets presented above and below fixation and were used to refresh the association of these vertical locations to the lateralized responses. On Simon trials, red and green targets were presented to the left and right of fixation with red mapped to the left hand and green mapped to the right hand. The critical trials were the mediated Simon trials: red and green stimuli were presented above and below fixation and participants responded to their color. Stimuli were congruent when the color response matched the associated location response and incongruent otherwise. For instance, red

18 Stroop vs. Simon 18 squares presented above fixation were congruent because the left response indicated red and above-fixation for the training trials. There are two critical questions: first, is there any congruency effect for these mediated Simon trials; and second, if so, is the delta plot slope positive or negative. The lateralization theory predicts that if there is a mediated Simon effect, it should have positive instead of negative slope as the distracting information is not lateralized and cannot directly activate associated motor codes. The location-based theory, in contrast, predicts negative slopes as the distracting information is the (vertical) location of the target. Participants. Twenty-six University of Missouri students participated in Experiment 3 in return for credit toward a course requirement. Stimuli. Stimuli were boxes subtending 2.5 of arc presented 3 above, below, left, or right of a central fixation cross. In training trials, blue stimuli were presented above or below fixation. Design. Experiment 3 was a 3X4 within-subject design with factors of stimulus color (red, green, blue) and stimulus location (up, down, left, right). For two-thirds of the trials in the experimental phase, red and green stimuli were presented equally often in each of the four locations. Those presented to the left and right are termed Simon trials; those presented up and down are termed mediated Simon trials. There were equal numbers of congruent and incongruent Simon and mediated Simon trials. For the remaining third, blue stimuli were presented equally often above or below fixation to reinforce training. Procedure. The procedure of Experiment 3 was similar in many respects to that for the Simon task of Experiment 1. The initial training phase consisted of a single block of 72 trials in which blue boxes were presented above and below fixation with the above location assigned to the left hand ( z key) and the below location assigned to the right hand ( / key). Participants were given feedback and were highly accurate at learning the

19 Stroop vs. Simon 19 mapping. Following training, participants completed six experimental blocks consisting of equal numbers of training, Simon, and mediated Simon trials. Instructions were to simply respond to the location of the target if it was blue, and to the color of the target if it was red (left hand, z key) or green (right hand, / key). Results There was a 15.6 ms congruency effect in the Simon task that failed to reach significance (687.4 ms vs ms, t(25) = 1.33, p =.19). The magnitude of the Simon effect is similar to that found in Experiment 1, however, there is less power to detect an effect in Experiment 3 as there are fewer Simon trials per participant (one-third of experimental trials). There was, however, a large and reliable 58.0 ms congruency effect in the mediated Simon task (669.9 ms vs ms, t(25) = 5.34, p <.05). Additionally, although performance was highly accurate in both tasks, there were reliable congruency effects in accuracy (Simon: 98.4% vs. 95.0%, t(25) = 2.51, p <.05; mediated Simon: 98.7% vs. 91.9%, t(25) = 3.76, p <.05). Delta plots of the Simon effect and mediated Simon effect are shown in Figure 3C. Although there was no reliable Simon effect in mean RT, the slope of the Simon delta plot is significantly negative (M =.11, t(25) = 2.60, p <.05). Alternatively, the slope of the mediated Simon delta plot is significantly positive (M =.11, t(25) = 2.41, p <.05). We note here that the analysis of means misses important phenomena. According to the analysis of means, the mediated Simon effect is much larger than that of the Simon effect. A different interpretation arises from the delta plots. The delta plot slopes are nearly equal. Given the stability of slope as capturing important invariances across experiments, the slope analysis strikes us as more compelling and indicates nearly equivalent magnitudes of effects.

20 Stroop vs. Simon 20 Discussion It is clear from the large mediated Simon effect that the training trials successfully induced an association between vertical stimulus position and the left-right responses. Although the mediated Simon interference is location based, it does not follow the same pattern as Simon interference in fact, the interference is more typical of Stroop interference. This pattern suggests that it is the laterality of distraction in the Simon task that is associated with the negative going delta plot pattern. This result, along with those of Wiegand and Wascher (2005), provide converging evidence for the above conclusion that laterality may be the key functional difference between conventional Simon and Stroop tasks. Experiment 4 The key signature of the Simon task is a negative slope in the delta plot. The Simon task, however, is not the only task that appears to produce a larger context effect for quick responses than for slower ones. Eimer (1999) has shown a seemingly related effect in a priming context. Left or right arrow primes affect the identification of subsequent left-or-right-arrow targets. A congruency effect occurs for fast responses, and the reverse effect occurs for slower ones. A second example comes from Greenwald and colleague s (Greenwald, Abrams, Naccache, & Dehaene, 2003) number priming experiment. In a number priming task participants judge whether a target number is greater than or less than some referent. In a popular version of the task, the targets are the single digits 1,...,4 and 6,...,9 and the referent is 5. Preceding the target is a digit prime which typically results in congruency effects. For instance, the prime 2 speeds the judgment for target 3 and slows that for target 7. Greenwald et al. found that the effect was greatest for the earliest responses and decreased thereafter. At first, it would appear that number primes presented at fixation do not have

21 Stroop vs. Simon 21 lateralized location information as do stimuli in the Simon task. Thus, lacking this laterality, they should produce a positively sloped delta plot. Negative slopes, however, are anticipated by Dehaene et. al. s (Dehaene, Bossini, & Giraux, 1993) theory of number representation. In this theory, numbers are represented in a spatial manner, much like a number line. For single digits, 1 and 9 anchor the left and right sides, respectively; the other digits order accordingly. Hence, the theory predicts that the prime in the number-priming task activates a spatial code much like the side of presentation does in a Simon task. Given this similarity, it is reasonable that the congruency effect is characterized by a negatively-sloped delta plot. In Experiment 4, we assess delta plot slopes for number priming. Experiment 4 Experiment 4 was a number-priming task in which participants classified target digits as less than or greater than 5. Target digits were presented clearly and accuracy was high. Preceding the targets were briefly-presented and subsequently-masked primes. The critical question is how numeric status of the prime (either greater than or less than 5) affected the time to make the numeric-status judgment to the target. The stimulus onset asynchrony (SOA) between prime and target presentation was manipulated in a within-subject manner, similar to Eimer (1999). Participants. Forty-three University of Missouri students participated in Experiment 4 in return for credit toward a course requirement. Design. Experiment 4 was a 3X6X6 within-subject balanced factorial design with SOA (134 ms, 167ms, 267 ms) and prime and target digit serving as factors. The digits 2, 3, 4, 6, 7, and 8 served as both primes and targets. Congruent trials were those in which the prime and target had the same numeric status; incongruent trials were those in which

22 Stroop vs. Simon 22 they differed. Procedure. Each participant performed 5 blocks (108 trials each) of the target-classification task. Each trial began with a blank foreperiod (700 ms), followed by a fixation period (700 ms), a forward mask (67 ms), a prime (50 ms), and a backward mask (67 ms). These masks were character centered over the location of the prime. The short prime duration and masks make the prime difficult though not impossible to see. The backward mask was followed by a variable delay in which the screen was blank. The target was then presented until response. The variable delay was chosen such that resulting SOAs between prime and target was either 134 ms, 167 ms, or 267 ms. To accommodate these particular SOA timings, the CRTs were programmed to refresh with a frequency of 85 hz. Participants classified the targets as less-than or greater-than 5 with the z and / keys, respectively. Results Only trials in which the prime and target were not the same digit were analyzed in order to exclude repetition priming effects. Reaction times were submitted to a two-way repeated measures ANOVA with congruency and SOA as within-subject factors. The analysis revealed a main effect of SOA (F(2,84) = 10.57, p <.05) and an interaction between congruency and SOA (F(2, 84) = 3.49, p <.05). The mean priming effects for the 134, 167, and 267 ms SOA conditions were 11 ms, 4 ms, and -5 ms, respectively. As the delta plot analyses below show, however, the mean effects vastly understate the effect of congruency on target classification. Delta plots of the priming effects for each SOA condition are shown in Figure 4A. From the delta plots it is clear that numeric priming results in negatively sloped delta plots (134 ms SOA: M =.17, t(42) = 4.19, p <.05; 167 ms SOA: M =.14, t(42) = 3.42, p <.05; 267 ms SOA: M =.15, t(42) = 3.42, p <.05). In the figures, the

23 Stroop vs. Simon 23 delta plots appear parallel and this trend is supported by a lack of a main effect of SOA from a one-way repeated measures analysis of the slopes (F(2,84) =.10). The apparent parallel nature of the delta plots indicate that the time course of the congruency effect may depend more critically on the duration between prime onset and the response than the duration between target onset and the response. This finding is in accordance with the results and explanations of Eimer (1999) who showed the importance of SOA in arrow priming. In Figure 4, we have redrawn the delta plots with RT defined as the duration between prime onset and the response. As can be seen, these prime-locked plots tend to fall on top of one another providing graphical evidence that the duration between prime onset and response is more critical than that between target onset and response. Discussion The number-priming delta plots in Figure 4A are unequivocally negatively sloped, much like Simon interference delta plots. The negative slopes are anticipated by and serve as support for the Dehaene et al theory of lateralized spatial representation for digits. General Discussion In this paper, we have advocated a graphical, exploratory method, the delta plot, for examining time courses of context effects. When taken as a whole, the data reveal two stable and robust patterns. In Stroop tasks, congruency effects are minimal for the fastest responses and increase thereafter. In Simon tasks, in contrast, congruency effects are largest for the fastest responses and decreases as RT slows, and, in some cases, even reverse. This later pattern is of great interest because it is in opposition to the nearly ubiquitous pattern that, across a manipulation, the standard deviation of RT increases with mean, and hence, violates the law of Wagenmakers and Brown (2007). We have shown that these two patterns remain even when the tasks are performed across the same

24 Stroop vs. Simon 24 participants (Experiment 1) and with the same stimuli (Experiment 2). The stability of these differing patterns across our experiments as well as others (see Figure 2) imply that the they serve as a core phenomena for theory building. Experiments 3 and 4 help clarify the basis for the two different delta-plot patterns. In Experiment 3, conflict from laterality seems to be different than conflict from other sources. This demonstration is highly concordant with those of Wiegand and Wascher (2005). In Experiment 4, number priming has a time course of congruency that is analogous to Simon tasks and we interpret this finding as concordant with Dehaene et al s theory that numbers have a spatial, lateralized representation (see also Notebaert, Gevers, Verguts, & Fias, 2006). The positively-sloped patterns are broadly consistent with several different simple explanations. One way of understanding the theoretical implications is within a framework of information accumulation. In this framework, information about a decision slowly accrues until criterion (e.g., Audley & Pike, 1965; LaBerge, 1963; Link, 1975; Ratcliff & Smith, 2004; Smith & Vickers, 1988; Reddi & Carpenter, 2003; Usher & McClelland, 2001). There are three different loci of effects in this framework that are concordant with the positive-slope patterns of Figures 2A and 2B: First, information from the distracting dimension may be incorporated into the rates of accumulation (see Figure 5A). Congruent stimuli would, accordingly, have higher rates than incongruent ones. Second, information from the distracting dimension may affect the criterion (Figure 5B). Congruent stimuli may be associated with lower criterion than incongruent ones. Although it may not be immediately obvious, changes in the criterion affects the standard deviation of the RT distribution and is, therefore, associated with a positive delta plot slope. Third, information form the distracting dimensions may be accumulated before the task-relevant dimension (Figure 5C). This explanation is especially appealing for priming-based tasks in which the prime precedes the target (Vorberg, Mattler, Heinecke, Schmidt, & Schwarzbach, 2003). Rouder (1996) showed that if this early

25 Stroop vs. Simon 25 accumulation is modest, then it is equivalent to changing the starting point of accumulation for the task-relevant process. For congruent processes, the starting point is closer to criterion than for incongruent ones and the result is a positively sloped delta plot. Many extant theories of Stroop interference (Cohen, Dunbar, & McClelland, 1990; Lindsay & Jacoby, 1994) are broadly concordant with one of these three loci and are, therefore, concordant with the Stroop-like delta plots. This broad concordance shows that delta plots provide a large-scale view of patterns, but are not suited for fine discriminations between models that make qualitatively similar predictions. The situation is much different for the negatively-sloped delta plots. These plots are fairly constraining in that they cannot be predicted by any of the above simple explanations acting in isolation. Two primary models have emerged. The first is the model of Ridderinkhof (1997) in which a quick, automatic congruency effect is countered by slowly evolving inhibition. In this view, the initial congruency effect for the fastest responses index the automatic effect; the slope of decline thereafter indexes inhibition. Although the model can explain the data patterns for Simon tasks, it does not adequately explain Stroop task patterns. A second explanation is that the Simon pattern indicates quick, automatic motor activation from the distracting information that passively decays in time. Although this explanation is appealing, it does not explain the occasional reversals in delta plots. These reversals can be seen unequivocally in Burle et al (see Figure 2C), and in our Experiments 1 and 4 (Figures 3A and 4). These reversals, which indicate that the distributions for congruent and incongruent stimuli violate stochastic dominance (Speckman, et al., in press), are most concordant with Eimer s model that lateralized motoric responses may be actively inhibited. Although the Ridderinkhof and Eimer models are very similar, the appeal of the Eimer approach is that inhibition is constrained to lateralized motor activity rather than as a general cross-task process. One of the weak points, at present, of the lateralization theory is the tautological

26 Stroop vs. Simon 26 nature of delta plot slope and laterality. The tautology is evident when considering the integrated Stroop Simon task of Experiment 2. Herein, we find positive slopes when the words Left and Right are the distracting information and the participant makes a location judgment. The implication is that these words do not have a lateralized representation because if they had, the slope would have been negative. Hence, slope determines laterality and laterality determines slope. Tautologies of these types, unfortunately, are not uncommon in cognitive psychology (for example, the levels-of-processing theory in memory, Craik and Lockhart, 1972). Given this tautology, we advance the laterality theory in an exploratory and suggestive spirit. This tautology aside, the fact remains that delta plot slopes differ systematically and reasonably across a constellation of tasks and conditions. These differences provide deep challenges for future theory.

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