Carving Executive Control At Its Joints: Working Memory Capacity Predicts Stimulus-Stimulus, But Not Stimulus-Response, Conflict

Matt E Meier; Michael J Kane

doi:10.1037/xlm0000147

. Author manuscript; available in PMC: 2016 Nov 1.

Published in final edited form as: J Exp Psychol Learn Mem Cogn. 2015 Jun 29;41(6):1849–1872. doi: 10.1037/xlm0000147

Carving Executive Control At Its Joints: Working Memory Capacity Predicts Stimulus-Stimulus, But Not Stimulus-Response, Conflict

Matt E Meier ¹, Michael J Kane ¹

PMCID: PMC4630123 NIHMSID: NIHMS701952 PMID: 26120774

Abstract

Three experiments examined the relation between working memory capacity (WMC) and two different forms of cognitive conflict: stimulus-stimulus (S-S) and stimulus-response (SR) interference. Our goal was to test whether WMC’s relation to conflict-task performance is mediated by stimulus-identification processes (captured by S-S conflict), response-selection processes (captured by S-R conflict), or both. In Experiment 1, subjects completed a single task presenting both S-S and S-R conflict trials, plus trials that combined the two conflict types. We limited ostensible goal-maintenance contributions to performance by requiring the same goal for all trial types and by presenting frequent conflict trials that reinforced the goal. WMC predicted resolution of S-S conflict as expected: Higher-WMC subjects showed reduced response time interference. Although WMC also predicted S-R interference, here, higher-WMC subjects showed increased error interference. Experiment 2A replicated these results in a version of the conflict task without combined S-S/S-R trials. Experiment 2B increased the proportion of congruent (non-conflict) trials to promote reliance on goal-maintenance processes. Here, higher-WMC subjects resolved both S-S and S-R conflict more successfully than did lower-WMC subjects. The results were consistent with Kane and Engle’s (2003) two-factor theory of cognitive control, according to which WMC predicts executive-task performance through goal-maintenance and conflict-resolution processes. However, the present results add specificity to the account by suggesting that higher-WMC subjects better resolve cognitive conflict because they more efficiently select relevant stimulus features against irrelevant, distracting ones.

Keywords: working memory capacity, executive control, cognitive control, interference, individual differences

…our initial specification of the central executive was so vague as to serve as little more than a ragbag into which could be stuffed all the complex strategy selection, planning, and retrieval checking that clearly goes on when subjects perform even the apparently simple digit span task. This still seems a sensible way of starting to explore working memory, as it accepts the complexities and the ultimate need to explain them, while concentrating on analysing the simpler and presumably more tractable slave systems. (Baddeley, 1996, p. 6)

Working memory’s “executive” processes are typically characterized as general-purpose mechanisms that control and coordinate the activities of subordinate brain networks in the service of complex, goal-directed behavior (e.g., Baddeley, 1986; Norman & Shallice, 1986). As Baddeley (1996) recognized, however, such broad characterizations may offer little more than an ill-specified homunculus that masks the extent of our ignorance about the self-regulation of cognition and behavior (see also Burgess, 1997; Towse & Houston-Price, 2001). The present work takes a combined psychometric-experimental approach toward incrementally specifying the nature of executive control and its contribution to working memory capacity (WMC). Our logic follows Cronbach (1957) and Underwood (1975) in suggesting that psychological theories can be developed and tested by considering individual differences in the constructs of interest, especially in the ways that they interact with experimental treatments and elicit patterns of convergent and discriminant validity in their selective associations with other constructs (Campbell & Fiske, 1959; Cronbach & Meehl, 1955; Kosslyn et al., 2002; Vogel & Awh, 2008). In order to specify the central executive’s nomological network, then, we will seek its correlational boundary conditions. That is, we will explore whether individual differences in WMC are differentially associated with the control processes elicited by distinct forms of cognitive conflict.

Fractionating the Central Executive

Our approach has some parallels to the fruitful research program initiated by Miyake et al. (2000) into the “unity and diversity” of executive functions thought to be linked to the brain’s frontal lobes (for a review, see Miyake & Friedman, 2012). Their correlational studies have used latent-variable, factor-analytic techniques to indicate the individual-differences variance that is shared versus not shared among theoretically derived cognitive and neuropsychological tasks (i.e., to demonstrate both convergent and discriminant validity). Three broad domains, or factors, of executive functions have thus been identified: inhibiting, switching, and memory updating. These factors are partially dissociable in their correlations with one another and in their differential predictions of cognitive and behavioral outcomes (e.g., Friedman et al., 2006; 2007), indicating that the executive control construct is not monolithic. At the same time, all three factors also share considerable common variance, and this common executive factor is highly heritable and strongly predicts intelligence and externalizing behavior problems, indicating some domain general mechanisms of cognitive control (Friedman et al., 2008; Miyake & Friedman, 2012; Young et al., 2009). Of most importance here, this line of “unity and diversity” work began from relatively informal, descriptive conceptions of executive functions and, through individual-differences findings alone, has progressed to facilitate the preliminary development of formal theoretical models to instantiate different control processes (e.g. Chatham et al., 2011).

While similarly relying on individual-differences analyses, the present study more narrowly examines how normal variation in WMC, as assessed by complex memory span tasks, responds to different experimental manipulations of conflict within a single response-time (RT) task. Complex span tasks require subjects to immediately recall short lists of items that are interleaved with an unrelated processing task. These tasks are of theoretical interest because their performance predicts a variety of important cognitive capabilities, such as reading comprehension (e.g., Daneman & Carpenter, 1980; McVay & Kane, 2012a), learning (Kyllonen & Stephens, 1990; Shute, 1991), multitasking (e.g., Bühner, König, Pick, & Krumm, 2006; Hambrick, Oswald, Darowski, Rench, & Brou, 2010), and reasoning through novel intellectual problems (e.g., Kane, Hambrick, & Conway, 2005; Oberauer, Schulze, Wilhelm, & Süß, 2005). As well, normal variation in WMC predicts how well people perform seemingly simple attention-control tasks, such as dichotic listening and antisaccade (e.g., Colflesh & Conway, 2007; Conway, Cowan, & Bunting, 2001; Kane, Bleckley, Conway, & Engle, 2001; Unsworth, Schrock, & Engle, 2004). The apparent generality of WMC’s predictive power, and its association with lower-level attention capabilities, has led some theorists to propose that a small number of domain-free attention or executive functions largely drive WMC variation and its covariation with other abilities (e.g., Barrouillet & Camos, 2012; Engle & Kane, 2004; Hasher, Lustig, & Zacks, 2007).

Consistent with the Miyake-Friedman “unity and diversity” findings described above (e.g. Miyake et al., 2000; Miyake & Friedman, 2012), however, recent individual-differences research indicates that WMC variation and covariation may fundamentally reflect a number of core abilities beyond attention control (e.g., Shipstead, Lindsay, Marshall, & Engle, 2014; Unsworth & Engle, 2007a, 2007b; Unsworth & Spillers, 2010), and also that WMC correlates selectively with only some attentional-control processes and not others. Many studies have yielded associations between WMC measures and attention tasks that elicit some form of conflict between target versus distractor stimuli, or between habitual versus required responses (e.g., Ahmed & de Fockert, 2012; Bleckely, Durso, Crutchfield, Engle, & Khanna, 2003; Colzato, Spapé, Pannebakker, & Hommel, 2007; Conway et al., 2001; Heitz & Engle, 2007; Hutchinson, 2011; Kane & Engle, 2003; Long & Prat, 2002; McVay & Kane, 2009, 2012b; Meier & Kane, 2013; Morey et al., 2012; Redick & Engle, 2006; Unsworth et al., 2004; but see Keye, Wilhelm, Oberauer, & van Ravenzwaaij, 2009; Redick, Calvo, Gay, & Engle, 2011). In sharp contrast, WMC does not appear to correlate with performance of prototypical visual search tasks – even those thought to involve top-down influences (Kane, Poole, Tuholski, & Engle, 2006; Poole & Kane, 2009; Sobel, Gerrie, Poole, & Kane, 2007; but see Anderson, Vogel, & Awh, 2013) – unless those tasks require constraining search to only particular locations or subtle stimulus dimensions (Poole & Kane, 2009; Sobel et al., 2007). Similarly, in the auditory domain, a meta-analysis conducted by Sorqvist et al. (2013) suggests a dissociation between WMC variation and two types of auditory distraction. WMC appears to be uniquely related to oddball auditory distractions (with higher-WMC subjects showing less of a cost to the oddball distraction), but it does not correlate with susceptibility to more continuous forms of auditory distraction.

So, WMC does not predict performance in all varieties of attention-control tasks. We view findings like these, which point to the discriminant validity of WMC, as being especially important for specifying the executive-control construct. Through an inductive process of identifying boundary conditions to the association between WMC and attention control, we may eventually reverse-engineer the central executive (at least in part) to gain traction regarding the specific control processes it encompasses and how these processes relate to broader cognitive abilities.

Specifying the Executive Attention Account of WMC

In addition to the attentional control tasks mentioned above that are sensitive to WMC variation (i.e., dichotic listening, antisaccade, constrained search, and auditory distraction), research into the executive attention account of WMC has focused on the relation between WMC measures and executive-control tasks that elicit cognitive conflict, such as Stroop (1935) and flanker (Eriksen & Eriksen, 1974) tasks. These tasks demand control, in part, by requiring the flexible regulation of behavior in the pursuit of endogenous goals (Egner, 2008), typically by presenting subjects with multiple sources of information, some task-relevant and some irrelevant. When relevant and irrelevant task information elicit competing responses, cognitive conflict is generated. The general pattern of results from investigations of the relation between WMC and cognitive control is that the higher the subject’s WMC, the better he or she performs on cognitive control measures. According to the executive attention account (Engle & Kane, 2004; Kane & Engle, 2003; Kane et al., 2007; Unsworth, Spillers, Brewer, & McMillan, 2011), WMC counters interference in two ways: proactively keeping task goals accessible (i.e., resisting lapses of attention) and reactively resolving cognitive conflict (i.e., resolve interference online). Here, we are primarily focused on the latter factor of in-the-moment conflict resolution.

Executive control (or “cognitive control”) is a broad, arguably ambiguous construct (Braver, Gray, & Burgess, 2007; Funes, Lupianez, & Humphrey, 2010a) that refers to mental processes ostensibly operating from perception to action. Therefore, linking WMC to cognitive control allows WMC many possible entry points into information processing. To move WMC theory forward, we must further specify how WMC works to resolve cognitive conflict. To understand how WMC impacts performance (and to better understand cognitive control, itself), it should be helpful to decompose cognitive-control tasks into subcomponents that more clearly map onto aspects (or stages) of information processing, analogous to Baddeley’s (1996) call and effort to “fractionate” the central executive component of the working memory system.

The Dimensional Overlap Taxonomy

Kornblum’s dimensional overlap taxonomy (Kornblum, 1992; Kornblum, Hasbroucq, & Osman, 1992) provides a potential blueprint for decomposing cognitive-control tasks into separable processing elements. Tasks that provide conflicting information about which stimulus is the target or which response is to be made on a given trial are often called cognitive-control tasks because control is presumably needed to counter the interference elicited by the conflicting information. According to Kornblum, the strength of the conflict experienced by a subject is the result of the degree to which opposing task dimensions overlap. Here, overlap refers to how perceptually, conceptually, or structurally similar the sets (i.e., the entire stimulus and response sets) and the elements (i.e., individual items within the stimulus and response sets) are to one another (Kornblum & Lee, 1995). That is, the more overlap there is among conflicting task sets and elements, the more the irrelevant task element (i.e., the feature that provides information that will lead to an incorrect response) will disrupt performance.

Kornblum’s dimensional overlap taxonomy distinguishes choice-RT tasks based not on conflict strength, but rather on the task dimensions that provide the conflicting information. Conflict may arise between relevant and irrelevant stimulus dimensions (stimulus-stimulus, or S-S conflict), between irrelevant stimulus dimensions and relevant response dimensions (stimulus-response, or S-R conflict), or between irrelevant stimulus dimensions and both relevant stimulus and response dimensions (S-S plus S-R conflict). Information processing is often characterized by at least three broad (and further decomposable) stages: stimulus identification, response selection, and motor execution (e.g., Proctor & Vu, 2003). Accordingly, different types and combinations of dimensional overlap create different processing problems: S-S conflict impedes stimulus selection and/or identification, whereas S-R conflict interferes with response selection and/or motor execution.

To test whether S-S and S-R conflicts are independent of each other, Kornblum (1994) had subjects respond to stimuli that varied on relevant stimulus, irrelevant stimulus, and response dimensions. Color words or neutral words appeared in the center of a rectangle, which was divided into colored (red or green) and dark halves. The color of the rectangle was the relevant stimulus dimension, the words were irrelevant stimulus dimensions and the side of rectangle that was colored (left, right, top, and bottom) was also an irrelevant stimulus dimension. Subjects responded to color by pressing left or right keys (e.g., left key for a red patch), and completed four conflict-type blocks: pure S-S (color word was congruent or incongruent with the color patch; the color patch was presented on the top or bottom of the rectangle, making these neutral trials on the S-R dimension), pure S-R (color patch location was congruent or incongruent with the left-right response; the words were color-neutral), mixed S-S and S-R (presenting both S-S-only and S-R-only trials), and a combined-type S-S/S-R block where the irrelevant stimulus dimension overlapped with both the relevant stimulus dimension and the response (e.g., trials presenting a red color patch on right side of the rectangle [when a left response is called for] and the word GREEN in the rectangle’s center). Kornblum found that S-S and S-R effects were additive on trials that contained both and interpreted this as support for independence of S-S and S-R conflict (but see Hommel, 1997).

Additional behavioral evidence for the utility of the dimensional overlap taxonomy comes from investigations of congruency-sequence effects, in which the prior trial’s congruency modifies the magnitude of the present trial’s congruency effect (Funes, Lupianez, & Humphrey, 2010a, 2010b). Subjects performed series of mixed S-S and S-R trials (mixed with congruent trials presenting no conflict). Carry-over effects of control were conflict-specific: S-S interference was reduced after incongruent S-S trials but not after incongruent S-R trials (and vice versa), suggesting that the control processes initiated by the preceding incongruent trial were specialized for responding to that particular type of conflict (see also Verbruggen, Liefooghe, Notebaert, & Vandierendonck, 2005, Experiment 2). Time-course data also suggest distinct origins for S-S and S-R conflict, as S-R interference tends to decrease as RTs get longer, whereas S-S interference tends to increase with increasing RTs (Pratte, Rouder, Morey, & Feng, 2010). Finally, neuroimaging data further suggest S-S versus S-R dissociations, with hemodynamic responses in parietal cortex areas particularly associated with S-S conflict, and activity in the motor cortex more strongly associated with S-R conflict (Egner, Delano, & Hirsch, 2007; Liston, Matalon, Hare, Davidson, & Casey, 2006; Liu, Banich, Jacobsen, & Tanabe, 2004). Here, then, we propose that the dimensional overlap taxonomy may help specify the executive-control processes that are related to WMC.

Dimensional Overlap and WMC

Higher-WMC subjects resolve interference from Stroop color-words a bit more quickly than do lower-WMC subjects in tasks that present a high proportion of incongruent trials (Kane & Engle, 2003; Long & Prat, 2002; Meier & Kane, 2013). These findings suggest that WMC affects performance, in part, through conflict-resolution processes (the accuracy advantage that higher-WMC subjects in low-incongruency Stroop tasks is argued to reflect, in part, goal-maintenance abilities; e.g., Hutchison, 2011; Kane & Engle, 2003). According to the Dimensional Overlap taxonomy, the color-word Stroop task presents both S-S and S-R conflict: The irrelevant stimulus dimension (word identity) overlaps with both the relevant stimulus dimension (word color; S-S conflict) and the response dimension (naming the color aloud; S-R conflict). Given the Stroop task’s complex structure involving both S-S and S-R conflict, prior WMC-related findings have an ambiguous locus. That is, it is unclear if stimulus-selection and identification processes, or response-selection processes, or both, enable higher-WMC subjects to achieve superior performance to lower-WMC subjects.

Some light may be shed on the contributions of stimulus selection by examining WMC correlations with purer S-S interference tasks. In fact, higher-WMC subjects exhibit less interference from conflicting task elements in an Eriksen-type flanker task than do lower-WMC subjects (Heitz & Engle, 2007; Redick & Engle, 2006; but see Keye, Wilhelm, Oberauer, & van Ravenzwaaij, 2009). In the Kornblum taxonomy, the typical flanker task is an S-S conflict task, because conflict is generated when response-irrelevant stimulus information (i.e., flankers) provides information opposed to the information carried by the target representation. Here, it is argued that the conflict is generated by the overlap and conflicting nature of relevant and irrelevant stimulus features. The data thus suggest that higher-WMC subjects achieve better cognitive control, in part, because they are better able to resolve conflict between stimulus dimensions than are lower-WMC subjects. In this scenario higher-WMC subjects could either be inhibiting the irrelevant stimulus dimensions (Hasher et al., 2007) or amplifying the relevant stimulus dimensions early on in the information processing sequence (Egner & Hirsch, 2005).

However, we cannot yet be sure that higher-WMC subjects’ superior flanker performance is the result of better S-S interference resolution. It remains possible that, at stimulus identification and selection, both lower and higher-WMC subjects allow the same information (both task relevant and conflicting) into the processing stream, but then higher-WMC subjects are better able to resolve the conflict at the subsequent response-selection stage (perhaps by better suppressing conflict stimulus information through inhibition at a later processing stage; Ridderinkhof, van den Wildenberg, Wijnen, & Burle, 2004). Stated differently, although conflict originates in an S-S task from the overlapping stimulus dimensions between targets and distractors, performance differences can be achieved by either blocking this conflicting information from further processing (i.e., “early,” at stimulus identification and selection) or by more efficiently resolving the resulting conflict from the distractor information after it has entered the system (i.e., “late,” at response selection). This ambiguity is the product of the information-processing sequence where stimulus-identification processes must happen before response-selection processes. Therefore, by exclusively examining individual differences in a traditional flanker task, we still cannot determine what higher-WMC subjects do to achieve their superior performance. It should also be noted that recent work by Keye and colleagues (Keye et al., 2009) has reported null relations between WMC and interference in flanker tasks, and so earlier work on WMC-flanker task performance may have overestimated their association.

In order to most effectively discriminate between the contributions of stimulus-identification and response-selection processes to the associations between WMC and conflict tasks, we should compare conflict performance on S-S-type trials to performance on trials that only present S-R interference. Then, via subtractive logic (Donders, 1869), we may judge how WMC impacts performance. More precisely, if WMC-related differences were found in an S-S conflict task, but not in a task that presents interference only at the response selection phase (S-R task), it would suggest that WMC affects performance prior to the response-selection — most likely during the stimulus identification or selection processes.

According to the Kornblum taxonomy, one way to assess S-R conflict is via the Simon effect (Simon & Small, 1969), which reflects the overlap between the irrelevant stimulus dimension and the response. The Simon effect is typically demonstrated in tasks where subjects push a right- or left-positioned key depending on the identity of the stimulus (e.g., circle or square), and the stimulus is either presented on the left or right side of the screen. S-R conflict is produced because the stimulus location is coded as left or right and so is the response: If the stimulus is on left side of the screen, the “left” response is primed, which causes interference when the relevant dimension of the stimulus actually indicates a right response. The irrelevant stimulus location and the relevant stimulus dimension (usually the shape or color of a single object) do not overlap, so there is no opportunity for conflict between these stimulus elements (i.e., there is no S-S interference). Considerable behavioral evidence indicates that that the Simon effect involves response selection and not stimulus identification (Acosta & Simon, 1976; Mewaldt, Connelly, & Simon, 1980; Simon, 1982; Simon, Acosta, Mewalt, & Speidel, 1976; Van der Molen & Keuss, 1981). For example, degrading the quality of visual stimuli, which should affect stimulus identification, does not affect the magnitude of the Simon effect (Acosta & Simon, 1976), but the size of the to-be-executed response set executed does (Mewalt, Connelly, & Simon, 1980). Therefore, the Simon task seems to provide a relatively pure window into the response-selection stage of information processing.

The evidence for WMC predicting performance in Simon tasks is mixed and limited (and seemingly more limited than that described above connecting WMC to tasks involving S-S conflict). WMC is uncorrelated with Simon effects in RTs when trials are 50% congruent (Keye, Wilhelm, Oberauer, & van Ravenzwaaij, 2009; Weldon, Mushlin, Kim, & Sohn, 2013) and 75% congruent (Miller, Watson, & Strayer, 2012, who also found no WMC effect on Simon-task errors). In an 80% congruent task, however, Weldon et al. observed a modest correlation between WMC and the Simon RT effects (r = −.22). It is notable that Weldon et al. only observed a significant WMC association in a Simon task with a high proportion of congruent trials. Optimal performance on incongruent trials in high proportion-congruency conditions puts a premium on the ability to maintain the goal of the task because on the frequent congruent trials, correct responding can be achieved by either attending to the goal-mandated target or irrelevant information (Kane & Engle, 2003). In this context, the goal is infrequently reinforced by incongruent trials, which results in slowed or erroneous responding by subjects who have not adequately maintained the task goal. WMC effects in high-congruency contexts may therefore have little to do with in-the-moment conflict resolution.; WMC effects in high-congruency contexts may therefore have little to do with in-the-moment conflict resolution. In any case, the lack of a relation between WMC and Simon effects under normal task conditions suggests that WMC is not (or is only weakly) related to performance in tasks that provide only response-related conflict.

Experiment 1 tested whether WMC helps resolve S-S interference, S-R interference, or both, within a single task to avoid the ambiguities that arise when making across-task comparisons (e.g., differences in stimuli or task approach between Flanker and Simon tasks). We limited the influence of goal-maintenance abilities and task switching by using a task that, first, had the same goal for S-S and S-R conflict trials and, second, presented enough conflict trials (i.e., 50%) to reinforce task goals and minimize goal neglect. Subjects responded to upward or downward facing arrows by pressing left- or right-positioned keys. All that distinguished S-S from S-R trials was the location of the arrows on-screen. Therefore, any relations between WMC and conflict type should reflect differences in conflict-resolution processes.

Experiment 1

Method

Here, and in the Results section that follows, we report how we determined our sample size, all data exclusions, all manipulations, and all measures in the study (Simmons, Nelson, & Simonsohn, 2012).

Subjects

Two hundred and thirty six undergraduates (aged 18–30 years) from the University of North Carolina at Greensboro (UNCG) participated and received partial credit for a psychology course requirement. The goal was to test at least 200 subjects in the course of a single semester, and our stopping rule for data collection was the end of the semester.

General Procedure

Subjects volunteered to complete three testing sessions in groups of 1 – 4, with an experimenter present throughout each session to read instructions aloud and monitor subjects’ progress through the tasks. Only the relevant tasks from the first two sessions are described and analyzed here; the other tasks were all completed after the present ones, and were designed for other studies by different sets of authors (reflecting a mix of attention and long-term memory tasks, one of which included thought probes to assess mind-wandering). On average, these two sessions (for subjects who completed both) were completed 13 days apart (SD = 12). In the first session, we administered only the Operation Span task (OSPAN), the S-S/S-R task, and then the Reading Span task (RSPAN). In the second session, the Symmetry Span task (SSPAN) was administered as the first task, followed by the tasks for other studies. Each session was scheduled for 1.5 hr. Subjects were allowed to leave when everyone in their session finished the final task (for all sessions, no task was begun until all subjects in the session had completed the preceding task). Experimenters read on-screen instructions for each task aloud while subjects read along silently. Dell desktop computers, with 17 in cathode ray tube (CRT) monitors (85 MHz refresh rate) and running E-Prime (1.2) software, presented all task stimuli and recorded all responses.

WMC Tasks

We assessed WMC with three automated “complex span” tasks (OSPAN, SSPAN, and RSPAN; Redick et al. 2012; Unsworth, Heitz, Schrock, & Engle, 2005; Unsworth, Redick, Heitz, Broadway, & Engle, 2009). In these tasks, subjects attempt to maintain or recover mental access to memory items while intermittently completing an unrelated processing task. To prevent trading off between the processing and memorial portions of the task, an individualized response deadline (M + 2.5 SDs) was used for the processing portion, calculated during 15 processing-task-only items. For the processing portion of OSPAN, subjects verified (via mouse-clicking a “yes” or “no” onscreen) solutions to compound arithmetic equations (e.g., (3 * 2) − 1 = 4). In RSPAN, subjects judged (via “yes”/“no” mouse-click) whether or not sentences made sense (e.g., "I like to run in the sky."). In SSPAN, subjects assessed (via “yes”/“no” mouse-click) whether or not 8 × 8 black-and-white matrix patterns were vertically symmetrical.

The memory items in OSPAN and RSPAN were capital letters (randomly selected without replacement on each trial from these twelve: F, H, J, K, L, N, P, Q, R, S, T, Y). A letter followed 200 ms after the response to each processing item in the task and appeared for 250 ms. After 3–7 processing-letter pairs, all 12 letters appeared onscreen in a grid formation next to a check box. Subjects identified the letters presented in serial order, via mouse click in the check box. When a subject selected a letter, it appeared on the bottom of the screen in the order it was selected (arranged left to right). Subjects were instructed to click on a “blank” button on the screen for forgotten letters, to preserve item order. Pressing the blank button placed a dash in the array of letters on the bottom of the screen. OSPAN and RSPAN presented each set length (3–7) three times in random order.

In SSPAN, 200 ms after the symmetry judgment was made, one square of a 4 × 4 grid was shaded red for 650 ms. After 2–5 symmetry judgment-grid pairs, subjects recalled the locations of the shaded squares in serial order by mouse-clicking on the squares within an empty grid. When a square was clicked, it turned red with a number inside it to indicate its serial order. As with the OSPAN and RSPAN, there was an option to click on a “blank” button. The SSPAN presented each set length (2–5) three times in random order.

In all of the complex span tasks, subjects first completed four practice trials of just the recall portion (set sizes 2 and 3), then 15 processing-portion-only practice trials, and then three combined practice trials (set size 2) of both processing and recall. Task instructions warned subjects that they must achieve 85% accuracy on the processing portion for their data to be used in the study. Between sets, the programs provided subjects with accuracy feedback for the processing and memory portions of the task for the last set and also their cumulative accuracy for processing across all preceding sets.

S-S/S-R Task

Stimuli and trial types

We modeled the S-S/S-R task after Liu et al. (2004; see also Verbruggen et al., 2005). The stimuli were black arrows on a grey background. At a viewing distance of 60 cm, the arrows each occupied approximately 2° × 2° degrees of visual angle (although we did not physically restrict viewing distance, we placed tape on the floor, 60 cm from the screen on each side of each subject’s chair, and instructed them that the chair and their eyes should stay at this distance from the screen throughout the task). The target arrows pointed either upward or downward. We instructed subjects to press one key for an up arrow and another key for a down arrow, using the Q and P keys on a QWERTY keyboard, which were approximately 15.5 cm apart. We counterbalanced the mapping of arrows to keys between subjects (i.e., for some subjects, upward-pointing arrows required a left-handed response [Q key] and downward-pointing arrows required a right-handed response [P key], and for other subjects upward-pointing arrows required a right-handed response [P] and downward arrows required left-handed response [Q]).

S-R trials were located on the horizontal axis with congruency manipulated by changing the location of the up-down arrow stimulus with regard to the response to be made. For example, for a congruent S-R trial, the stimulus that called for a left-handed response was displayed to the left of the screen’s center; for an incongruent S-R trial a stimulus that called for a left-handed response was displayed to the right of the screen’s center. S-S trials were located on the vertical axis, with congruency manipulated between the stimulus’ location on the screen (i.e., up vs. down location) and the identity of the arrow (i.e., up arrow vs. down arrow).

Response-Mapping practice trials presented arrows at the center of the CRT screen. For S-S/S-R task trials, the arrows appeared in eight different locations around the center of the screen. The arrows appeared approximately 2° (at a 60 cm viewing distance) from the center of the screen in one of eight locations: left, right, above, below, left-and-below, left-and-above, right-and-below, or right-and-above (see Figure 1). We randomized trial order in every block for every subject. Stimuli were congruent half of the time at each stimulus location (e.g., an upward-pointing arrow presented above the center of the screen; an arrow requiring a right-key response presented on the right side of the screen). When stimuli were presented in the corner positions (e.g. left-and-above, right-and-below), S-S and S-R conflict were factorially crossed.

Depiction of some conflict trial types in Experiment 1for subjects who received the instructions to press the Q key (located on left of QWERTY keyboard) for up arrows and the P key (located on right of QWERTY keyboard) for down arrows. Combination trials in which one conflict type was incongruent and the other congruent are not pictured here (e.g., S-S congruent/S-R incongruent).

Procedure

Each S-S/S-R task trial presented subjects with one arrow pointing upward or downward in one of the eight locations, and the experimenter (and onscreen instructions) asked subjects to quickly and accurately press a key to indicate whether each arrow pointed upward or downward. Subjects first completed 10 trials of mapping practice with immediate feedback, by responding to arrows presented in the center of the screen. Following incorrect responses, the screen flashed red for 100 ms. Next, subjects completed 100 mapping-practice trials (again, with centered arrows) with accuracy and RT feedback provided only at the end of the block.

Following response-mapping practice, subjects completed 24 practice trials in which the arrows could appear in any of the eight positions around the center of the screen; subjects received trial-level error feedback (screen flashing red after errors). Next, for the actual task, subjects completed four blocks of 120 trials, with short breaks (< 30 seconds) permitted between blocks. The target arrow appeared directly above, below, to the left, or to the right of fixation on 80 trials per block (20 in each of those locations). On half of these trials the arrow direction was congruent with the arrow location. On the other 40 trials per block, the arrows appeared diagonally oriented to fixation (e.g., right-and-above; left-and-below) with left, right, up, and down locations being factorially crossed. That is, in a single block subjects were presented with 20 incongruent S-S trials, 20 congruent S-S trials, 20 incongruent S-R trials, 20 incongruent S-R trials. These trials were neutral in regard to the other dimension. In addition to these 80 trials, subjects also completed 10 mixed trials (appearing in the diagonal locations) that were congruent on both S-S and S-R dimensions, 10 that were incongruent on S-S and S-R dimensions, 10 that were congruent on S-S and incongruent S-R dimensions, and 10 that were incongruent on S-S and congruent on S-R dimensions. In Experiment 1, we distinguish “pure” trials that provided congruent or incongruent information on one conflict type (while being neutral in terms of the other conflict type) from “mixed” trials that present this information (i.e., congruent or incongruent) on both conflict types.

Every trial began with a central, black fixation cross, in 90 point bold Courier New font, for 500 ms, which remained on-screen during the 100 ms arrow presentation. After the target arrow, subjects saw a blank screen for 1250 ms. We recorded responses during the first 1150 ms of this screen. After each of the four blocks, subjects received RT and error feedback for that block. Finally, subjects completed another 100 trials of mapping (identical to the 100 mapping trials completed before the S-S/S-R task trials).

Inferential Analyses

We used the lme4 package (Bates, Maechler, & Bolker, 2013) in the R system for statistical computing (R Development Core Team, 2013) to compute inferential statistics. For RTs (from accurate trials only), we used linear mixed models (LMM). We interpreted parameters — determined by restricted maximum likelihood estimation — with t-values greater than 2 as significant; with a large number of observations the t-distribution becomes indistinguishable from the standard normal distribution, where absolute values over 2 reflect an alpha < .05. We used generalized linear mixed models (GLMM) for accuracy analyses, in order to account for the binomial distribution of trial-level accuracy (Dixon, 2008). In the raw data, correct trials were scored a 0 and incorrect trials were a 1. The betas for the GLMMS are log odds ratios with higher log odds ratios indicating that an error is more likely to be committed. In all models, we entered subjects as random effects (random intercept only) to account for the non-independence of the data, and WMC (centered on the grand mean of this experiment) was treated as a continuous variable.

Results

We dropped all data from fifteen subjects, eight who did not achieve 85% accuracy on the processing portion of at least two complex span tasks (e.g., Conway et al., 2005; Redick et al., 2012; two of these subjects never returned for the second session), and seven subjects — identified using box plots — who were further than three times the interquartile range from the mean accuracy for either the response-mapping or the congruent trials in the S-S/S-R task. Data remained from 221 subjects.

WMC Screening Results

The sum of items correctly recalled in serial position was the score for each complex span task (Conway et al., 2005); the theoretical maximum score was 75 for OSPAN and RSPAN and 42 for SSPAN. If a subject did not achieve 85% accuracy on the processing portion of a span task, the score from that task was not used in analyses (all data from subjects with fewer than two valid span scores were dropped from analyses). We converted span task scores (these raw Ms and SDs are reported with the correlations below) to Z scores (using the Ms and SDs from our laboratory database of more than 3000 UNCG students; for norms generated from this sample, see Redick et al., 2012) and averaged them into a WMC composite. Using a composite WMC measure is consistent with the evidence and theoretical perspective that WMC-related differences in cognitive performance are driven largely by domain-general processes (Kane et al., 2004). Moreover, it is preferable to draw conclusions at the level of hypothetical constructs rather than at the level of individual complex span tasks, each of which reflects not only WMC but also task-specific sources of measurement error. The raw span scores correlated with rs of .68 (RSPAN [M = 50, SD = 15] × OSPAN [M = 53, SD = 14]; N = 199), .51 (OSPAN × SSPAN [M = 26, SD = 7]; N = 178), and .43 (SSPAN × RSPAN; N = 184). Ns varied due to individually dropped tasks. The WMC composite was unimodal and symmetrically distributed (M = 0.08; SD = 0.81; skew = −0.72; kurtosis = 0.01).

Response-Mapping Trials

Response Times

On the pre-task mapping trials (M = 448 ms, SE = 4 ms), higher-WMC subjects responded faster than did lower-WMC subjects (b = −10 ms, SE = 5 ms, t = −2.2). We further divided the pre-task mapping trials to examine WMC’s relation to RTs for the first versus second half of mapping. Higher-WMC subjects responded significantly faster than did lower-WMC subjects on the first 50 mapping trials (b = −9 ms, SE = 5 ms, t = −2.0) and the second 50 mapping trials (b = −11 ms, SE = 5 ms, t = −2.3). When we examined only the last 25 trials of mapping, higher-WMC subjects were no longer significantly faster than lower-WMC subjects (b = −9 ms, SE = 5 ms, t = −1.8), but the modest WMC effect on RTs was of similar magnitude no matter how we analyzed it. In the post-task mapping trials (M = 464 ms, SE = 4 ms), WMC did not predict RTs (b = −5 ms, SE = 5 ms, t = −1.0).

Errors

We entered subjects as a random effect and WMC as fixed effect in a GLMM predicting errors. Higher-WMC subjects were less likely to commit errors than were lower-WMC subjects, overall (b = −0.26, SE = 0.06, Z = −4.2), on the first 50 trials (b = −0.31, SE = 0.07, Z = −4.2), and over the last 50 trials (b = −0.26, SE = 0.06, Z = −4.2). As in mapping RTs, when we examined only the last 25 trials, we did not find significant WMC-related differences (b = −0.09, SE = 0.08, Z = −1.2).

Although WMC-related differences in mapping RTs and errors seemed to be resolving over the last 25 trials of practice, one might be concerned that overall differences in responding to arrow stimuli without conflict might affect any WMC-related differences in conflict resolution with these stimuli. Previous work has suggested that WMC is related to the ability to form stimulus-response mappings (Wilhelm & Oberauer, 2006), and so we wanted to examine WMC-related differences in conflict resolution while limiting the potential confound of WMC-related abilities to map stimuli with responses. We thus adopted a conservative strategy that used subjects’ centered mean RTs or error rates from the last 25 trials of pre-task mapping as a covariate in all of the following analyses (we also report all theoretically important effects that changed without the covariate, to eliminate concerns about researcher degrees of freedom; Simmons, Nelson, & Simonsohn, 2011). No interaction terms with this covariate were included our models. Unless otherwise noted, we entered subjects as a random effect and WMC and trial congruency as fixed effects. We coded trial congruency as a −.5/+.5 contrast, so this parameter represents the experimental effect.

S-S Trials

Response Times

Table 1 presents descriptive statistics for Experiment 1. We found significant S-S interference, such that responses to incongruent trials (e.g., downward pointing arrows presented above central fixation) were slower than responses to congruent trials (e.g., downward pointing arrows presented below fixation; b = 38 ms, SE = 1 ms, t = 32.8). WMC did not predict RTs, overall (b = −3 ms, SE = 4 ms, t = −0.7). However, higher-WMC subjects experienced less S-S interference than did lower-WMC subjects (b = −7 ms, SE = 1 ms, t = −5.1); that is, higher-WMC subjects showed a smaller RT difference between incongruent and congruent trials. To decompose this interaction between WMC and trial type, we analyzed congruent and incongruent trials separately: Higher-WMC subjects did not significantly differ from lower-WMC subjects on congruent-trial RTs (b = 1 ms, SE = 4 ms, t = 0.3) or on incongruent-trial RTs (b = −6 ms, SE = 4 ms, t = −1.7), but it appears that the significant reduction in S-S interference for higher-WMC subjects was due primarily to better performance on incongruent trials. (Parallel analyses without the mapping-RT covariate similarly indicated significant S-S interference [b = 38 ms, SE = 1 ms, t = 32.8] and a significant WMC × trial-type interaction [b = −7 ms, SE = 1 ms, t = −5.1], but additionally showed a main effect of WMC on RTs [b = −11 ms, SE = 5 ms, t = −2.2].)

Table 1.

Experiment 1 Descriptive Statistics


Trial Category/DV	Trial Type	M	Std Err	Min	Max	Skew	Kurtosis
Pure/RT	S-R congruent	457	4	310	629	0.48	−0.16
	S-R incongruent	502	4	351	708	0.46	−0.16
	S-S congruent	471	4	322	633	0.41	−0.32
	S-S incongruent	509	4	376	742	0.63	0.24
Pure/ER	S-R congruent	0.04	0.00	0.00	0.16	1.64	3.59
	S-R incongruent	0.13	0.01	0.00	0.48	1.16	1.94
	S-S congruent	0.04	0.00	0.00	0.20	1.50	2.60
	S-S incongruent	0.10	0.00	0.00	0.49	1.53	4.68
Combination/RT	S-R con/ S-S con	453	4	283	646	0.36	−0.26
	S-R incon/S-S con	480	4	342	666	0.58	0.08
	S-R con/S-S incon	490	5	324	749	0.66	0.51
	S-R incon/S-S incon	516	4	373	791	0.68	0.75
Combination/ER	S-R con/S-S con	0.03	0.00	0.00	0.20	1.78	3.56
	S-R incon /S-S con	0.06	0.00	0.00	0.25	1.31	1.41
	S-R con/S-S incon	0.09	0.00	0.00	0.38	1.31	2.04
	S-R incon/S-S incon	0.14	0.01	0.00	0.50	0.96	1.40

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Note: M = mean of subject means. ER = error rate. RT = response time. Std Err = standard error. S-S = stimulus-stimulus. S-R = stimulus-response. Con = congruent. Incon = incongruent.

Errors

Error rates also demonstrated significant S-S interference, with subjects making more errors on incongruent than on congruent trials (b = 0.87, SE = 0.05, Z = 19.2). WMC did not predict errors overall (b = 0.06, SE = 0.06, Z = 1.1), nor did it interact with trial congruency (b = −0.08, SE = 0.06, Z = −1.4). (Without the mapping-accuracy covariate, the only parameter to change was for the WMC main effect, which remained non-significant [b = 0.00, SE = 0.07, Z = 0.3].)

S-R Trials

Response Times

Subjects exhibited significant S-R interference, such that responses to incongruent stimuli (e.g., an arrow requiring a right-key response presented to the left of fixation) were slower than to congruent stimuli (e.g., an arrow requiring a right-key response presented to the right of fixation; b = 45 ms, SE = 1 ms, t = 39.8). WMC did not predict overall RT (b = −3 ms, SE = 3 ms, t = −0.9), nor did WMC interact with S-R interference (b = −1 ms, SE = 1 ms, t = −0.9); in contrast to S-S interference, then, S-R interference was insensitive to variation in WMC. (Analyses without the mapping-RT covariate showed no change to the parameters representing S-R interference [b = 45 ms, SE = 1 ms, t = 39.8] or the WMC × trial-type interaction [b = −1 ms, SE = 1 ms, t = −0.9], but the main effect of WMC on RTs was significant [b = −12 ms, SE = 5 ms, t = −2.3].)

Errors

Subjects made more errors on incongruent trials then on congruent trials, indicating significant S-R interference (b = 1.39, SE = 0.05, Z = 29.6). Overall, WMC did not predict errors (b = −.04, SE = 0.05, Z = −0.8), but WMC did interact with S-R congruency (b = 0.13, SE = 0.06, Z = 2.3). Here, higher-WMC subjects were non-significantly more likely to commit an error on incongruent trials than were lower-WMC subjects (b = 0.02, SE = 0.05, Z = 0.4), and non-significantly less likely to commit an error on congruent trials (b = −0.11, SE = 0.07, Z = −1.6), but the WMC effect seemed to reflect primarily greater facilitation on congruent trials for higher WMC subjects. (Without the mapping covariate, the only parameter that changed was for the main effect of WMC, which remained non-significant [b = −0.10, SE = 0.06, Z = −1.7].)

Comparison of S-S and S-R trials

For these analyses, conflict type was dummy-coded. S-R trials (arrows presented directly to the right or left of fixation) were set as the reference level and S-S trials (arrows presented directly above or below fixation) were the comparison level.

Response Times

S-S trials yielded slower responses than did S-R trials (b = 11 ms, SE = 1 ms, t = 13.1) and subjects exhibited less S-S than S-R interference when contrasting incongruent to congruent trials (b = −7 ms, SE = 2 ms, t = −4.2). As evident in the significant interaction depicted in Figure 2a, WMC influenced the S-S interference difference score more than the S-R difference score (WMC × S-S × S-R interaction, b = −6 ms, SE = 2 ms, t = −3.0).¹ That is, consistent with results reported above, higher-WMC showed a greater advantage over lower-WMC subjects in resolving S-S interference than in S-R interference. (None of these parameters changed in analyses without the mapping-RT covariate.)

Errors

Error rates were statistically equivalent across S-S and S-R trials (b = −0.04, SE = 0.03, Z = −1.4), but subjects again showed less S-S than S-R interference when contrasting congruent to incongruent trials (b = −0.53, SE = 0.07, Z = −8.1). As depicted in Figure 2b, WMC negatively predicted interference in S-S trials and positively predicted interference in S-R trials, yielding a significant interaction among WMC, S-S, and S-R conflict types (b = −0.21, SE = 0.08, Z = −2.6). (None of these parameters changed in analyses without the mapping covariate.)

S-S/S-R Combination Trials

To analyze the trials that were composed of a factorial combination of congruency and S-S and S-R conflict types, we entered S-S and S-R conflict separately as fixed effects (entered as −.5/+.5 contrasts). Data from only the combination trials were included in these analyses.

Response Times

Subjects showed significant S-S interference (b = 27 ms, SE = 1 ms, t = 23.1) and S-R interference (b = 36 ms, SE = 1 ms, t = 31.6) and, consistent with prior research (e.g., Kornblum, 1994), these effects did not interact on trials that contained both conflict types (b = −1 ms, SE = 2 ms, t = −0.3). There was no main effect of WMC on RT, overall (b = −2 ms, SE = 4 ms, t = −0.6). Consistent with results from the pure trials analyzed above and, as shown in Figure 3a, higher-WMC subjects experienced less S-S interference than did lower-WMC subjects (b = −4 ms, SE = 1 ms, t = −2.7), but this pattern did not hold for S-R interference (b = −2 ms, SE = 1 ms, t = −1.1). However, the three-way interaction among WMC, S-S conflict, and S-R conflict was not significant (b = −3 ms, SE = 3 ms, t = −1.0). (In an analysis without the mapping-RT covariate, the only parameter that changed was the overall main effect of WMC on RT, which was now significant [b = −11 ms, SE = 5 ms, t = −2.1].)

Experiment 1 (E1) model parameters of stimulus-response (S-R) and stimulus-stimulus (S-S) interference from combination S-S/S-R trials as a function of composite working memory capacity Z-score (WMCz) in response times (RTs; panel A) and errors (panel B). The dotted lines represent the standard error of the estimate.

Errors

Subjects’ error rates showed both significant S-S (b = 0.67, SE = 0.5, Z = 13.5), and S-R interference (b = 1.14, SE = 0.05, Z = 23.0) but here, in contrast to the RT analyses, trials that presented both S-S and S-R conflict yielded an under-additive interaction approaching our significance criterion (b = −0.18, SE = 0.10, Z = −1.8). Again, there was no main effect of WMC on errors in these combination trials (b = 0.02, SE = 0.06, Z = 0.4). As in the pure conflict trials, WMC did not predict S-S interference (b = 0.07, SE = 0.6, Z = 1.2), but, as depicted in Figure 3b, higher-WMC subjects exhibited more S-R interference than lower-WMC subjects (b = 0.19, SE = 0.6, Z = 3.1). The three-way interaction among WMC, S-S conflict, and S-R conflict was not significant, however (b = −0.17, SE = 0.13, Z = −1.3). (Without the mapping-errors covariate in the analyses, only the main effect of WMC changed, becoming non-significantly negative [b = −0.03, SE = 0.06, Z = −0.5].)

Delta Plots

Next, we examined whether WMC-related differences in resolving interference were more pronounced in particular parts of the RT distribution. That is, we tested whether higher-WMC subjects showed an advantage over lower-WMC subjects because they experienced less interference on the fastest trials, on the slowest trials, or across the whole RT distribution. Previous work has suggested that different patterns of interference across the RT distribution reflect different conflict-resolution mechanisms. A pattern of decreasing interference with increasing RTs has been interpreted as reflecting a suppression mechanism with a fast automatic congruency effect being countered by a slow-to-arise inhibition (Ridderinkhof et al., 2004). In contrast, a pattern of increasing interference with increasing RTs may reflect selective attention processes, with irrelevant stimulus dimensions either affecting the rate of information accumulation or changing decision criteria on trials where attention is not focused on relevant stimulus dimensions from the trial onset (Pratte, Rouder, Morey, Feng, 2010).

Here, then, we tested whether WMC would differentially predict either pattern and thus provide evidence for the mechanism(s) through which WMC affects performance. We binned all subjects’ correct-trial RTs (from pure trials only), separately for congruent and incongruent trials, into five bins each. The bins were ordered so that each subject’s fastest 20% of trials represented the first bin, second fastest 20% of trials the second bin, etc., until we had five bins of approximately equal size for each subject for both conflict types for congruent and incongruent trials. We then subtracted each congruent-trial bin from its corresponding incongruent-trial bin, which left with five difference scores per subject for each conflict type.

S-S Trials

For illustrative purposes, we plot these bins collapsed across the highest and lowest third of WMC scores. As shown in Figure 4, the differences between higher and lower-WMC subjects were not localized to any specific portions of the RT distribution. This observation was confirmed by a LMM with subjects as a random effect and WMC (as a continuous variable) and bin (1–5) as fixed effects. Only bin (b = −2 ms, SE = 1 ms, t = −2.8) was a significant predictor of the S-S conflict difference score, with interference decreasing across bins. Typically, in tasks that present only S-S conflict in isolation, more interference is observed on the slowest trials (Pratte et al., 2010). However, when in tasks presenting both S-S and S-R conflict trials mixed within blocks, we know less about the expected delta-plot pattern. Here, we did not observe the main effect of WMC, possibly because of reduced power attending the loss of information in analyses of aggregated data (here, aggregating into 5 RT bins per participant going from 360 data points per participant to five). In any case, of most importance here is the null interaction between WMC and bin (b = −1 ms, SE = 1 ms, t = −1.6), suggesting that the significant effect of WMC we observed in our initial non-aggregated analysis above was relatively constant throughout the RT distribution.

Delta plots of stimulus-stimulus (S-S) interference as a function of upper (high) and lower (low) tercile of composite working memory capacity Z-score (WMC) in Experiment 1.

S-R Trials

Although our prior analyses showed that WMC did not predict resolution of S-R interference in RTs, for completeness we examined their delta plots, as well. On blocked S-R trials, where the irrelevant stimulus feature is stimulus location and the stimuli are presented horizontally, interference effects typically decrease with RTs (Pratte et al., 2010; Proctor, Miles, & Baroni, 2011). But again, we know less about what to expect when S-S and S-R trials are mixed. Figure 5 shows a good deal of overlap between the distributions, as well as some separation among WMC scores at the slowest RTs. The only statistically significant predictor in the LMM, however, was bin (b = 2 ms, SE = 1 ms, t = 2.9), with the difference scores increasing with RTs. As in the S-S trial analyses above (and consistent with the null WMC effect in S-R interference), WMC did not interact with bin (b = −1 ms, SE = 1 ms, t = −1.5).

Delta plots of stimulus-response (S-R) interference as a function of upper (high) and lower (low) tercile of composite working memory capacity Z-score (WMC) Experiment 1.

Discussion

Here, in a task that presented 50% conflict trials as a means to control for WMC-related differences in goal maintenance (e.g., Kane & Engle, 2003), higher-WMC subjects showed less S-S interference in RTs than did lower-WMC subjects, but they showed equivalent S-R interference in RTs. Indeed, not only did higher-WMC subjects not experience less S-R RT interference than did lower-WMC subjects, they actually experienced greater S-R interference in errors than did lower-WMC subjects. This pattern of results was evident in both pure and combination trials. Clearly, Experiment 1 yielded a dissociation in the relation of WMC variation to performance on trials that present conflict between stimulus elements and trials that present conflict between stimulus and response elements.

Delta plots did not reveal any localized WMC-related differences in the experience of either S-S or S-R interference across the RT distribution. Differential slowing in the tail end of the RT distribution, with lower-WMC subjects experiencing greater slowing, has previously been interpreted as evidence for WMC-related differences in (lapses of) goal maintenance (Unsworth, Redick, Spillers, & Brewer, 2011). Because we saw no such localized differences here, we interpreted the dissociation of WMC with S-S versus S-R interference as consistent with the notion that higher WMC facilitates resolving conflict between relevant and irrelevant stimulus features, but is less effective (or even detrimental, with respect to errors) in resolving conflict between irrelevant stimulus dimensions and response dimensions. This dissociation indicates a conflict-specific WMC-related individual difference in identifying or selecting among competing visual stimuli.

We note, however, that our delta-plot findings, with a task that presented both S-S and S-R conflict, were inconsistent with many others from the literature with tasks presenting only S-S or S-R conflict. These discrepancies call into the question the generalizability of the effects and the processes implicated in single-conflict and dual-conflict contexts. If the characteristic delta plot pattern of ascending interference with S-S conflict and descending interference with S-R conflict only occur within single-conflict tasks, task approach at a global level may play an instrumental role. That is, the conflict types do not change between single and dual-conflict tasks, but the way the task is approached by the subject does. Therefore, S-S conflict, by itself, may not produce an ascending pattern of interference, but S-S conflict in a task that only presents S-S conflict may produce the ascending pattern because the single-task context encourages the subject to use a certain strategic approach. Task approach plus conflict type may produce the distinctive ascending and descending patterns previously seen.

We sought to replicate our novel WMC-related finding in Experiment 2A, which eliminated arrows in the diagonal positions so that we could determine whether the WMC-conflict dissociation would be found when arrows could appear only in four locations (e.g. above, below, left, and right). That is, we simplified the task environment as a way to rule out that WMC was somehow related only to performance on S-S trials because of the sheer number of stimulus-response pairings in the original version (16 stimulus-response pairs in Experiment 1 versus 8 stimulus-response pairs in Experiments 2A and 2B). In Experiment 2B, we additionally increased the proportion of congruent trials from 50% to 80% for both S-S and S-R trials, to bring goal maintenance processes into play; here we tested whether WMC would thus moderate performance across both conflict types. In a goal-supportive context (like that in Experiment 1 and Experiment 2A) where the task goal is reinforced by frequently occurring incongruent trials (forcing subjects to try to attend only to the relevant stimulus feature), WMC-related differences in goal maintenance are minimized. However, in a context where a majority of the trials are congruent, allowing subjects to respond correctly by either attending to the relevant or irrelevant stimulus features, lower-WMC subjects seem to lose access to the task goal periodically. They therefore show greater interference than do higher-WMC subjects when they encounter the infrequent incongruent trials (Kane & Engle, 2003). In addition, previous work using the Experiment 1 task has shown that increasing the proportion of congruent trials affects performance across conflict types (Funes et al., 2010a). In Experiment 2B, we tested whether WMC interacts with this generalized (i.e., not conflict-type specific) control.

In Experiments 2A and 2B, in addition to testing whether WMC was differently related to S-S and S-R conflict resolution, we examined a potential mediator of this differential relation: the effect of prior trial congruency on the performance of the current trial. Congruency sequence effects are often used as markers of in-the-moment cognitive control (Botvinick et al., 2001; for a review, see Egner, 2007). Using the same task as the present one, Funes et al. (2010a, 2010b) found a large reduction in interference following an incongruent trial only when the previous trial type was the same as the current trial type. For example, interference decreased for incongruent S-S trials that followed incongruent S-S trials and on incongruent S-R trials that followed incongruent S-R trials, but not on incongruent S-S trials following incongruent S-R trials (and vice versa). Prior findings indicate that WMC is unrelated to congruency sequence effects in Stroop (Meier & Kane, 2013; Unsworth et al., 2011) and flanker tasks (Keye et al., 2009; Unsworth et al., 2011), but lower-WMC subjects may show larger congruency sequence effects than do higher-WMC subjects in Simon tasks that present only S-R conflict (Keye et al., 2009; Weldon et al., 2013). Our aims for congruency-sequence analyses in Experiments 2A and 2B were to place our findings in the context of the prior work examining WMC and to test whether congruency sequence effects were responsible (at least in part) for any WMC-related differences in the resolution of S-S and S-R conflict.