How a high working memory capacity can increase proactive interference

Consciousness and Cognition 44 (2016) 130–145

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How a high working memory capacity can increase proactive interference Merle A. Steinwascher ⇑, Thorsten Meiser Department of Psychology, School of Social Sciences, University of Mannheim, Germany

a r t i c l e

i n f o

Article history: Received 3 February 2016 Revised 17 July 2016 Accepted 18 July 2016

Keywords: Proactive interference Working memory capacity Individual differences Generalized linear mixed models Complex span task

a b s t r a c t Previous findings suggested that a high working memory capacity (WMC) is potentially associated with a higher susceptibility to proactive interference (PI) if the latter is measured under high cognitive load. To explain such a finding, we propose to consider susceptibility to PI as a net effect of individual executive processes and the intrinsic potential for PI. With the latter, we refer to the amount of information that is activated at a given time and that has the potential to exert PI subsequently. In two studies deploying generalized linear mixed models, susceptibility to PI was modeled as the decline of performance over trials of a complex span task. The results revealed that a higher WMC was associated with a higher susceptibility to PI. Moreover, the number of stimuli recalled in one trial as a proxy variable for the intrinsic potential for PI negatively affected memory performance in the subsequent trial. Ó 2016 Elsevier Inc. All rights reserved.

1. Introduction Proactive interference (PI) – the detrimental effect of information that was previously learned but has since become irrelevant – has been considered a major cause of forgetting (e.g., Underwood, 1957; Wixted & Rohrer, 1993). One common operationalization of PI is the decline of memory performance over two or more trials of a memory task, where several studies showed that individuals differ systematically in the extent of this decline (e.g., Friedman & Miyake, 2004b; Kane & Engle, 2000; May & Hasher, 1998). Different labels have been used for the respective inter-individually varying variable: resistance to PI (e.g., Friedman & Miyake, 2004b), and proneness or susceptibility to PI (e.g., Kane & Engle, 2000). In addition, these labels have been used with different theoretical connotations. Whereas Friedman and Miyake (2004b) used resistance to PI to denote a cognitive control function, Kane and Engle (2000) used susceptibility to PI more descriptively as a phenomenon the underlying mechanisms of which are yet to be explained. In the following, the term susceptibility to PI is used to draw on the interpretation of Kane and Engle (2000). Individual differences in susceptibility to PI have been ascribed to individual differences in working memory capacity (WMC) in several theoretical frameworks (e.g., Braver, Gray, & Burgess, 2008; Hasher, Lustig, & Zacks, 2008; Kane & Engle, 2000; Lustig, May, & Hasher, 2001; Unsworth & Engle, 2007) sharing the common notion of working memory as ‘‘the ability to keep important information in mind while comprehending, thinking, and doing” (Conway, Jarrold, Kane, Miyake, & Towse, 2008, p. vii). This ability is closely related to cognitive control processes; in fact, in some theoretical accounts of working memory, individual differences in WMC are actually equated with individual differences in cognitive

⇑ Corresponding author at: Department of Psychology, School of Social Sciences, University of Mannheim, Mannheim D-68131, Germany. E-mail address: [email protected] (M.A. Steinwascher). http://dx.doi.org/10.1016/j.concog.2016.07.002 1053-8100/Ó 2016 Elsevier Inc. All rights reserved.

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control – or executive – processes (cf. Kane et al., 2004, p. 190). Thus, when susceptibility to PI is related to WMC, one is usually referring to individual differences in the executive part of working memory. Several previous studies reported a negative relation between indicators of WMC and susceptibility to PI, indicating that an increase in WMC is accompanied by a reduction in susceptibility to PI (e.g., Friedman & Miyake, 2004b; Kane & Engle, 2000; May, Hasher, & Kane, 1999). However, there are also some findings suggesting that in some situations, high WMC individuals are equally or even more susceptible to PI than low WMC individuals (Kaller et al., 2014; Kane & Engle, 2000). Thus, the relation between WMC and susceptibility to PI seems to be more complex than ‘‘the larger WMC, the lower susceptibility to PI”. 1.1. The Relation between susceptibility to PI in working memory and WMC In the present studies, we investigated susceptibility to PI in working memory, where susceptibility to PI is modeled as the decline of working memory performance over a sequence of trials of a complex span task. Complex span tasks are classical indicators of WMC (e.g., Conway et al., 2005; Oberauer, Lewandowsky, Farrell, Jarrold, & Greaves, 2012), in which a storage part (e.g., remembering a sequence of words) alternates with a processing part (e.g., solving arithmetic operations). It has been argued that complex span tasks are a closer approximation to everyday memory requirements than tasks without a processing part (i.e., simple span tasks; Friedman & Miyake, 2004a). Hence, it seems reasonable to model susceptibility to PI using these tasks in order to better approximate susceptibility to PI under everyday memory requirements. Contrary to the majority of studies, we hypothesize that if susceptibility to PI is assessed over a sequence of trials of a complex span task, high WMC individuals are equally or even more susceptible to PI than low WMC individuals. The reason for this deviating expectation are the results from Kane and Engle (2000): In their experiments, participants were screened for their scores in a complex span task, and those scoring in the top quartile (‘‘high-span group”) were compared to those scoring in the bottom quartile (‘‘low-span group”) with respect to their susceptibility to PI. The latter was assessed using three consecutive trials of a simple span task. This PI task was either completed under no or minimal cognitive load (imposed by a simple finger tapping task), or under high cognitive load (imposed by a complex finger tapping task) during encoding, retrieval, or both. The main results revealed that if no or minimal cognitive load was imposed, the high-span group was less susceptible to PI than the low-span group. If a high cognitive load was imposed during encoding, retrieval, or both, the high-span and the low-span group did no longer differ regarding their susceptibility to PI. For predicting the relation between WMC and susceptibility to PI in working memory as assessed by complex span tasks, the results obtained by Kane and Engle (2000) under high cognitive load during encoding are most revealing. This is because in complex span tasks, the presentation of the to-be-remembered stimuli alternates with a processing part, while no additional cognitive load is imposed during recall. Thus, to-be-remembered stimuli have to be encoded and maintained under (conditions of) interference from the processing part, which is most similar to the condition in Kane and Engle (2000) in which a simple span task was completed under high cognitive load during encoding. Thus, the main results from Kane and Engle (2000) suggest that high and low WMC individuals do not differ in their susceptibility to PI if susceptibility to PI is assessed using a sequence of trials of a complex span task. Kane and Engle (2000) proposed the following general account for their results: Under no cognitive load, high-span individuals were able to engage executive processes (controlled attention) to counteract PI, whereas low-span individuals were not. Therefore, increasing cognitive load resulted in an increase of susceptibility to PI in the high-span group, whereas the low-span group, who were not assumed to have been using executive processes to counteract PI anyway, was unaffected. In fact, Kane and Engle (2000) assumed that under high cognitive load, the capability to engage executive processes in counteracting PI was leveled between the low and high-span groups. From our point of view, there are three potential shortcomings of the account of Kane and Engle (2000). First, they assume that low-spans were unable to engage executive processes to counteract PI even under no or low cognitive load. Given that their sample consisted of university students, this seems to be a very strong assumption. The authors themselves qualified this assumption by making recourse to the specificities of their materials. Second, Kane and Engle (2000) assumed that a high cognitive load leveled the low and high-spans’ ability to engage executive processes in counteracting PI. However, it remains unclear why a high cognitive load should specifically affect these executive processes while leaving others unaffected. For example, the high-span group outperformed the low-span group under high load in the first trial, indicating that highspans and low-spans were not equal with regard to their ability to engage executive processes to counteract interference from a concurrent task. Third, the account offered by Kane and Engle (2000) cannot explain the results of their additional analyses: The results reported above were based on proportional PI effects, whereby the number of words in the second (or third, resp.) trial was subtracted from the number of words in the first trial and divided by the number of words in the first trial. If, however, data from the experiments were collapsed and analyses were based on raw recall data instead of proportional PI effects, the high-span group would tend to be more susceptible to PI than the low-span group under high cognitive load. Although this effect was only marginally significant, we attach value to it because it was potentially underestimated: Working memory performance was operationalized by a sequence of consecutive trials of a complex span task, which by now is known to be highly sensitive to the build-up of PI (e.g., Bunting, 2006; May et al., 1999). Thus, individuals scoring high in the complex span task did so at least in part because they were less susceptible to PI than individuals scoring low in the complex span task. Accordingly, there might have been a spurious negative correlation between the indicator of

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WMC and the indicator of susceptibility to PI, which might have prevented finding a stronger positive relation (i.e., stronger susceptibility to PI in high WMC individuals) under high cognitive load. A recent study by Kaller et al. (2014) indicates that the positive relation between WMC and susceptibility to PI reported in Kane and Engle (2000) is not an isolated finding: In their study, patients with schizophrenia were compared to healthy control subjects regarding working memory performance and susceptibility to PI. The results showed that patients with schizophrenia, despite exhibiting a poorer working memory performance, were less susceptible to PI. A further finding of the additional analyses of Kane and Engle (2000) that cannot be explained by their account was that PI was significantly reduced for the low-span group under high cognitive load. Importantly, this finding was not due to a floor effect (Kane & Engle, 2000, p. 351). Given the potential shortcomings of the account of Kane and Engle (2000), we propose a different account that can explain their main findings and the findings of the additional analyses, and that does not require the assumption that low WMC individuals are not able to engage executive processes to counteract PI even under no or low cognitive load. 1.2. The possible role of the intrinsic potential for PI According to our account, low as well as high WMC individuals engage executive processes to counteract PI, with high WMC individuals usually doing so more efficiently than low WMC individuals under low as well as under high cognitive load. Thus, imposing cognitive load will negatively affect the efficiency of executive processes of low as well as of high WMC individuals. Importantly, we assume that (the observed) susceptibility to PI is not only affected by the efficiency of executive processes, but also by a factor that we call the intrinsic potential for PI: By that we mean the number of representations of stimuli that are activated at a given time for a given individual, and that subsequently have the potential to exert PI. The intrinsic potential for PI can be considered a state (in terms of a state-trait distinction) that varies depending on the characteristics of the individual as well as the task: Put simply, an individual who cannot maintain and retrieve a single stimulus in one trial has a minimal potential for PI in the next trial, whereas an individual who maintains and retrieves a large number of stimuli has a high potential for PI in the next trial. As Kaller et al. (2014, p. 486) put it, ‘‘PI can only arise from sufficiently stable representations of information in WM”. Moreover, on average, a trial with only a few to-beremembered stimuli produces a lower intrinsic potential for PI in a subsequent trial than a trial with many to-beremembered stimuli. Naturally, whether the intrinsic potential for PI manifests itself in an observable decline of memory performance (i.e., PI), will also depend on the efficiency of executive processes to counteract it. Among others, Kane and Engle (2000) proposed inhibitory processes, which can be mapped onto the account of Hasher and colleagues (e.g., Hasher et al., 2008). They proposed deletion as an inhibitory mechanism to remove no longer relevant information from working memory. If this process is inefficient, and stimuli from a previous trial are still activated during encoding of the stimuli of a current trial, the respective memory bundle will be cluttered (Hasher et al., 2008, p. 233), and working memory performance declines. Recently, Oberauer et al. (2012) followed up on this idea and proposed and computationally modeled removal as a ‘‘mechanism for clearing working memory of no-longer-relevant contents” (p. 781). The efficiency of this mechanism, which is modeled to gradually remove no longer relevant information, varies among individuals. Although it has thus far only been modeled as a within-trial process (e.g., to remove information from the no longer relevant processing part within a trial), it is a helpful notion of how inhibitory processes can operate to counteract PI. Thus, a higher potential for PI makes higher demands on the efficiency of inhibitory processes (removal/deletion) to counteract it. Accordingly, the observed susceptibility to PI is assumed to be a net effect of the intrinsic potential for PI and the efficiency of inhibitory processes to counteract it. If cognitive load is absent or low in a given trial (e.g., in a simple span task), low and high WMC individuals can be expected to maintain and recall a comparable number of stimuli, so on average, their intrinsic potential for PI will be comparable in the next trial. The reason is that under no interference from a concurrent task, routines like rehearsal are likely to be engaged, which are only sensitive to a small degree to individual differences in executive processes (cf. Engle, Tuholski, Laughlin, & Conway, 1999). With an equal intrinsic potential for PI of low and high WMC individuals, but more efficient inhibitory processes of high WMC individuals, the latter can be expected to be less susceptible to PI under no or low cognitive load. This is in line with the results of Kane and Engle (2000) showing that under no or low cognitive load, the low and the high-span group did not differ in performance in the first trial, and the high-span group was less susceptible to PI than the low-span group. If cognitive load is high in a given trial, as is presumable the case in a trial of a complex span task, individual differences in WMC can be expected to take effect, so compared to a trial with no cognitive load, memory performance of low WMC individuals will be reduced to a greater extent than memory performance of high WMC individuals. This is consistent with the results of Kane and Engle (2000). Accordingly, the intrinsic potential for PI in the next trial is, on average, higher for high WMC individuals than for low WMC individuals. Thus, within a given timespan, high WMC individuals will need more efficient inhibitory processes to reduce their intrinsic potential for PI to a level comparable to that of low WMC individuals. If they succeed in doing so, high WMC individuals are expected to be equally or less susceptible to PI than low WMC individuals. If they do not succeed, for example, because cognitive load is also high in the subsequent trial, high WMC individuals are expected to exhibit a higher level of susceptibility to PI than low WMC individuals. For high WMC individuals, performance in the first trial can be expected to be comparable under low and high cognitive load, as was found in Kane and Engle (2000). Thus, the intrinsic potential for PI for the second trial is comparable under low

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and high load. However, if cognitive load is high in the second trial as well, the efficiency of inhibitory processes is reduced, and high WMC individuals are expected to be more susceptible to PI under low than under high load. Conversely, low WMC individuals can be expected to show a greater reduction in performance in the first trial under high load, so the intrinsic potential for PI is lower under high than under low cognitive load. Accordingly, if the reduction of the intrinsic potential for PI under high load outweighs the reduction of the efficiency of inhibitory processes under high load, low WMC individuals can be expected to be less susceptible to PI under high load than under low load. 1.3. The present studies In the present studies, we investigated the relation between WMC and susceptibility to PI in working memory with susceptibility to PI being measured over a sequence of trials of a complex span task. As described above, Kane and Engle (2000) found no relation between susceptibility to PI and working memory under high cognitive load when analyses were based on proportional PI effects. Based on the raw recall data, they found a tendency for a positive relation. As outlined above, a stronger positive relation could have remained concealed due to the fact that the indicator of WMC probably also captured variance determined by individual differences in susceptibility to PI. Accordingly, the first goal of Study 1 was to test the hypothesis that the correlation between the indicators of WMC and susceptibility to PI is positive, if this potentially spurious correlation is minimized, and susceptibility to PI is measured using a complex span task which is comparable to measuring susceptibility to PI under high cognitive load. That is, high WMC individuals are expected to be more susceptible to PI than low WMC individuals. The second goal of Study 1 was to examine our assumptions regarding the effect of the intrinsic potential for PI on working memory performance more directly. We approximated the intrinsic potential for PI with the number of stimuli recalled in one trial, and used this variable to predict the probability of correctly recalling a stimulus in the subsequent trial. We expected the respective effect to be negative; that is, with an increasing number of stimuli recalled in one trial, the probability of correctly recalling a stimulus in the next trial should decrease. In Study 2, the findings of Study 1 were to be replicated and generalized to a different type of complex span task. The second goal of Study 2 was to test the assumption that individual differences in executive processes play a role for susceptibility to PI even under high cognitive load. This assumption clearly differs from the account of Kane and Engle (2000), who assumed that high cognitive load equalizes the efficiency of executive processes in low and high WMC individuals. Finally, the third goal of Study 2 was to test the hypothesis that if the intrinsic potential is experimentally reduced, susceptibility to PI should decrease as well. 2. Study 1 In Study 1, participants completed a series of trials of a reading span task. In each trial, participants judged a sequence of statements as either correct or incorrect while attempting to maintain a sequence of letters for later serial recall (cf. Lewandowsky, Oberauer, Yang, & Ecker, 2010). Susceptibility to PI was operationalized as the decline of memory performance over the trials of the reading span task. By applying generalized linear mixed models (GLMM), it was possible to model the decline of memory performance over trials as a random slope, that is, as a random effect varying over individuals. Moreover, WMC was operationalized as the random intercept, reflecting individual differences in working memory performance in the first trial. Choosing working memory performance in the first trial of the complex span task as an indicator of WMC should minimize the influence of PI on this indicator. Thus, we also minimized the potential for a spurious correlation that possibly prevented Kane and Engle (2000) from finding a significant positive relation between WMC and susceptibility to PI. Under these conditions – high cognitive load imposed by using a complex span task and little amount of variance in the WMC indicator determined by individual differences in susceptibility to PI – we expected the following: High WMC individuals (as indicated by a positive value in the random intercept) should show an above-average decline over trials (as indicated by a negative value in the random slope). That is, we expected high WMC individuals to be more susceptible to PI than low WMC individuals reflected by a negative correlation between the random slope and the random intercept. Moreover, we have proposed that the intrinsic potential for PI plays an important role for understanding the relation between individual differences in susceptibility to PI and WMC. As a proxy variable for the intrinsic potential for PI in a given trial, the number of stimuli recalled in the previous trial was used. According to our assumptions, we expected the respective effect to be negative: That is, a higher intrinsic potential for PI (i.e., more items retrieved in the previous trial) should be associated with a lower probability of recalling a stimulus in the subsequent trial. 2.1. Method 2.1.1. Participants 225 young adults were recruited from the University of Mannheim and local vocational schools. Mean age was 22.3 years and 65.3% were female. Participants received either course credit or monetary compensation.

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2.1.2. Materials and design Each participant completed 15 trials of a reading span task with letters as to-be-remembered stimuli.1 One trial comprised four to eight sentences to be verified and a respective number of letters to be remembered. Three trials were presented for each set size. For this purpose, 112 sentences from the reading span task included in the working memory test battery for MATLAB (Lewandowsky et al., 2010) were translated into German. Half of the sentences were correct statements, the remaining were incorrect ones. The letters were consonants excluding Q and Y. Ninety (45 correct and 45 incorrect) sentences were randomly assigned to the 15 experimental trials, 12 sentences were assigned to three practice trials of size three, four, and five, respectively, and ten sentences were used to determine the individual presentation time (see below). Equivalently, letters were randomly assigned to experimental and practice trials. Each letter occurred between four and six times over the sequence of trials. The composition of each trial remained constant for all participants. Three blocks of trials were constructed; each block comprised one trial of each set size. Trial assignment to blocks was fixed; however, the order in which the trials were presented within a block was randomized for each participant. 2.1.3. Procedure Completion of the reading span task was computer-based. Each trial started with a one-second fixation phase, followed by the first statement to be judged as either correct (e.g., ‘‘A week has seven days”) or incorrect (e.g., ‘‘Cotton is fragile”). Participants were instructed to respond as quickly and as accurately as possible by pressing either ‘‘s” for a correct or ‘‘l” for an incorrect statement. Presentation time was individually adapted (see below). As soon as a response was given, or when presentation time elapsed, a letter to be remembered was shown for one second. Afterwards, the next statement was to be judged and so on. An input window indicated the end of a trial and the letters had to be entered in the correct order with the possibility of entering a blank if one did not remember a letter for a specific position. There were no breaks during the 15 trials. Individual presentation times for the sentences were determined as follows: In a first practice session, participants assessed 15 sentences as correct or incorrect, without remembering letters. The first five sentences were developed by the authors in addition to the 112 sentences mentioned above. The mean individual reaction time was calculated for the last ten sentences and 2.5 times the individual standard deviation was added to it. This value was used as maximum individual presentation time for each sentence in the trials of the reading span task (procedure taken from Unsworth, Heitz, Schrock, & Engle, 2005). 2.1.4. Data analysis Data were analyzed by applying generalized linear mixed models (GLMM; e.g., De Boeck & Wilson, 2004) with crossed random effects for persons and stimuli (e.g., Baayen, Davidson, & Bates, 2008). In these models, the probability pps was modeled for person p to recall a specific stimulus s on the correct position within a given trial. Accordingly, there were 90 unique observations per person. In the first model (Model 1), pps was predicted by a random intercept for persons, b0p, a random intercept for stimuli, b0s, and a linear trend variable reflecting the trial’s position (trialpos; ranging from 0 to 14) with an effect b1p that was allowed to vary over persons (i.e., a random slope). pps and the predictors were linked by the logistic function, so that pps = exp(b1ptrialpos + b0p + b0s)/(1 + exp(b1ptrialpos + b0p + b0s)). The random effect b1p can be rewritten as b1p = c10 + u1p, where c10 is the mean (or fixed) effect of trialpos over persons. The mean probability of recalling a letter in its correct position was assumed to decrease over trials, reflecting PI. Thus, c10 was expected to be negative. u1p is the individual deviation from the mean effect and was interpreted as the individual’s susceptibility to PI in working memory. Thus, individuals with a negative value in u1p were more susceptible to PI than the average, whereas individuals with a positive value in u1p were less susceptible to PI than the average. The variance of u1p is denoted as r2u1p . Due to the coding of trialpos, the random intercept for persons, b0p, reflects performance in the first trial of the complex span task. It can be rewritten as b0p = c00 + u0p, where c00 reflects the mean performance in the first trial, and u0p is the person’s deviation from it. u0p with variance r2u0p was used as an indicator of WMC on which the influence of PI was minimized. According to our hypothesis, high WMC individuals were expected to be more susceptible to PI than low WMC individuals. Within the GLMM, this is reflected by a negative correlation between the random person intercept and the random slope of trialpos. This correlation is denoted ru01 . The random intercept for stimuli, b0s, reflects the effect of a specific letter within a specific trial on recall probability that is not explained by the predictor trialpos. Note that because the compilation of each trial was fixed for all persons, the random intercept for stimuli reflects the effect of the characteristics of the letter (e.g., frequency), the effect of the position of the letter, and the set size. A second model (Model 2) was estimated in which the number of stimuli recalled in the previous trial (nprev) was added as a proxy variable for the intrinsic potential for PI. For this person-by-stimulus variable, a fixed effect b2 = c20 was estimated, which was expected to be negative. Thus, the more stimuli are recalled in one trial (indicating a higher intrinsic potential for PI), the lower the probability of correctly recalling a stimulus in the subsequent trial. 1

The reading span task was part of a larger study of individual differences measures.

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Table 1 Descriptive statistics of Study 1: Mean number of words recalled at the correct position per trial. Standard errors in parentheses. Trial Trial Trial Trial Trial Trial Trial Trial Trial Trial Trial Trial Trial Trial Trial

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

3.86 3.71 3.80 3.82 3.68 3.79 3.81 3.70 3.90 3.68 3.78 3.84 3.59 3.80 3.57

(0.12) (0.12) (0.12) (0.12) (0.11) (0.11) (0.12) (0.12) (0.11) (0.12) (0.12) (0.12) (0.12) (0.13) (0.12)

All analysis were conducted in R (R Core Team, 2015) with the glmer function of the R package lme4 (Bates, Maechler, Bolker, & Walker, 2014). 2.2. Results The mean number of words recalled at the correct position as well as standard errors per trial are displayed in Table 1. The estimates of the generalized linear mixed models are provided in Table 2. An alpha level of 0.05 was used for all statistical tests. The results of Model 1 indicated that, on average, the probability of recalling a stimulus decreased significantly over trials (c10 =
0.030, z =
2.163, p = 0.031), indicating PI. The correlation between the random effect of the trial’s position and the random intercept was negative, ru01 =
0.62. Thus, individuals with a higher working memory performance in the first trial exhibited a more pronounced decline in working memory performance over trials compared to individuals with lower initial working memory performance. Fig. 1 displays the mean recall probabilities as predicted by Model 1 as well as the empirical mean recall probabilities as a function of the trial’s position for each quartile of the random intercept distribution. As can be seen, the negative correlation did not result from a floor effect, that is, a large concentration of the data near very low recall probabilities that cannot decline further. In order to evaluate the significance of the correlation between the random slope and the random intercept, a conditional likelihood ratio test was conducted comparing Model 1 with a more restrictive model in which the correlation was fixed to zero, ru01 = 0. The respective conditional likelihood ratio test was significant, v2(1) = 53.469, p < 0.001, indicating a significantly better fit for the less restrictive Model 1. Thus, we may conclude that the correlation was substantial. The results of Model 2 revealed that recall probability decreased significantly with an increasing number of stimuli recalled in the previous trial as the indicator of the intrinsic potential for PI (c20 =
0.069, z =
5.559, p < 0.001). Adding this variable resulted in a no-longer significant mean effect of trialpos (c10 =
0.015, z =
1.047, p = 0.295). Finally, the correlation

Table 2 Parameter estimates of Model 1 and Model 2 in Study 1.

Fixed effects

c00 (intercept) c10 (trialpos) c20 (nprev) Variances of random effects r2u0p (person intercept)

r2u0s (stimulus intercept) r2u1p (trialpos)

Model 1

Model 2

Coefficient (s.e.) 0.99 (0.21)*
0.03 (0.01)* –

Coefficient (s.e.) 1.13 (0.22)*
0.02 (0.01)
0.07 (0.01)*

1.83

2.06

2.53

2.53

0.01

0.01


0.62


0.61

Correlation of random effects

ru01

Note. trialpos = linear trend indicating the position of a trial, nprev = number of letters recalled in the previous trial, s.e. = standard error. * p < 0.05.

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1.0

1.0

0.8

0.8

Empirical mean recall probability

Predicted mean recall probability

136

0.6

0.4

Fourth quartile Third quartile Second quartile First quartile

0.2

0.6

0.4

Fourth quartile Third quartile Second quartile First quartile

0.2

0.0

0.0 0

2

4

6

8

Trial position

10

12

14

0

2

4

6

8

10

12

14

Trial position

Fig. 1. Predicted (left panel) and empirical (right panel) mean recall probabilities as a function of the trial’s position for each quartile of the random intercept distribution.

between the random effect of the trial’s position and the random intercept was ru01 =
0.61. To make sure that the effect of nprev was still substantial when the set size of the previous trial was controlled for, another model was estimated in which this variable (denoted sprev) was added. The results revealed that the effect of nprev was still significant (c20 =
0.057, z =
4.507, p < 0.001), as was the effect of sprev (c30 =
0.043, z =
3.992, p < 0.001). 2.3. Discussion The first goal of Study 1 was to test the hypothesis that high WMC individuals are more susceptible to PI than low WMC individuals if susceptibility to PI is measured using a complex span task. The results supported our hypothesis: Within the GLMM, the correlation between the random intercept and the random slope was negative, indicating that individuals with a higher initial working memory performance exhibited a steeper decline of working memory performance over trials compared to individuals with a lower initial working memory performance. Note that individual differences in susceptibility to PI may still have contributed to performance in the first trial since participants completed three practice trials before the first test trial. If this were the case, the reported correlation between the random intercept and the random slope would be positively biased. Differently stated, the reported correlation would underestimate the correlation between an indicator of WMC unaffected by PI and susceptibility to PI. However, we expect the influence of PI on the first test trial to be small: First, practice trials were clearly labeled as such, and second, participants received additional instructions between the last practice trial and the first test trial. Both can be expected to increase discriminability between trials, which in turn should reduce PI.2 The finding that high WMC individuals can be more susceptible to PI is quite a new finding that cannot be easily explained by current accounts linking susceptibility to PI and WMC. They can, however, be explained if one assumes that the intrinsic potential for PI plays a role. Precisely this role of the intrinsic potential for PI was also tested in Study 1. Specifically, the results supported our hypothesis that the number of stimuli recalled in one trial – our proxy variable for the intrinsic potential for PI – has a negative effect on working memory performance in the subsequent trial. Thus, the more stimuli are maintained and recalled in one trial, the lower the probability to recall a stimulus in the subsequent trial. Note that we could not test the direct effect of the intrinsic potential for PI on susceptibility to PI as reflected by the decline over trials. In a multilevel context, our indicator of the intrinsic potential for PI is on a lower level than our indicator for susceptibility to PI, and it is not possible to estimate a direct effect of a lower-level-variable on a higher-level-variable. However, the finding that adding the indicator of the intrinsic potential for PI resulted in a no-longer significant effect of the

2 Participants received practice trials of size three, four, and five in ascending order. Thus, modeling the decline of memory performance over these three trials and the first test trial to estimate PI in the first test trial would confound set size and trial position. Instead, we estimated the change in performance from the last practice trial (trial = 0) to the first test trial (trial = 1) by applying a GLMM of the form pps = exp(b1ptrial + b0p + b0s)/(1 + exp(b1ptrial + b0p + b0s)). This model was applied to a subsample of those participants whose first test trial was of size five (n = 31), thereby holding set size constant. The results indicated that on average, there was no significant PI over these two trials (c10 = 1.996, z = 1.178, p = 0.239).

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indicator of susceptibility to PI suggests that both share common variance in explaining changes of working memory performance across trials. One could, however, object that the findings regarding the relation between WMC and susceptibility to PI are a result of regression to the mean. We therefore re-estimated Model 1, but this time, trialpos was centered (thus ranging from
7 to 7) so that the intercept reflected working memory performance in the 7th (middle) trial. The rationale is that the impact of regression to the mean should become smaller in later trials, so the correlation between the random intercept that reflects performance in the 7th trial and the random slope should likewise be less affected by regression to the mean. Accordingly, the correlation just mentioned can be considered a more conservative estimate of the relation between WMC and susceptibility to PI in working memory. In the respective model, the correlation was
0.21 which was still significant (the likelihood ratio test comparing the full model with a more restrictive model in which the correlation was fixed to zero was v2(1) = 4.993, p = 0.025). Note, however, that in case of centering trialpos, the intercept also reflects individual differences in susceptibility to PI, which might lead to an estimate of the correlation between the random intercept and the random slope that is positively biased. We will revisit the issue of regression to the mean in Study 2. 3. Study 2 In Study 2, we pursued three goals: First, we were interested in replicating the findings of Study 1 as well as generalizing them to another type of complex span task with different types of to-be-remembered stimuli. Whereas in Study 1 a reading span task with letters as stimuli was used, an operation span task with words as stimuli was used in Study 2. In one condition of Study 2, participants completed the operation span task without any additional instructions (in contrast to the other condition, see below), so this condition was suitable to replicate the findings of Study 1. The second goal in Study 2 was to test the assumption that individual differences in the efficiency of executive (or more specifically, inhibitory) processes play a role for susceptibility to PI even under high cognitive load. By contrast, Kane and Engle (2000) assumed that high cognitive load equalizes the efficiency of executive processes of low and high WMC individuals, meaning that they did not expect any effect of individual differences in executive processes on susceptibility to PI under high cognitive load. In order to directly test the effect of inhibitory processes on susceptibility to PI under high load as imposed by a complex span task, performance in an antisaccade task was used to predict individual differences in the decline of performance over trials (i.e., susceptibility to PI). The antisaccade task was chosen because it is a relatively wellestablished indicator of individual inhibitory (sub-)processes (Friedman & Miyake, 2004b; Kane, Bleckley, Conway, & Engle, 2001; Miyake et al., 2000). Predicting susceptibility to PI by performance in the antisaccade task also allowed to test the possibility that the negative correlation between the random intercept and the random slope was a mere methodological artefact in the sense of regression to the mean: If this was the case, individual differences in the decline should not be predictable by a substantial variable. The third goal of Study 2 was to test the hypothesis that if the intrinsic potential for PI is experimentally reduced, susceptibility to PI should be reduced as a consequence. To test this hypothesis, participants in the second condition in Study 2 were informed in advance that there would be a final recognition test on the words to be remembered in the operation span task (in the following, this condition is labeled informed condition, whereas the condition in which participants were not informed about the final recognition test is labeled not informed condition). We expected participants in the informed condition to put more effort into encoding and maintaining words for long-term retention for the final recognition test, which should occur at the expense of the number of words recalled within a given trial. The rationale was that given limited cognitive resources, if more resources are spent for encoding and maintaining a given word in a given trial for the final test, then less resources are left for later words in that trial. Thus, announcing a final test was expected to reduce the intrinsic potential for PI, which in turn should reduce susceptibility to PI. A reduction of the intrinsic potential for PI implies that performance in the first trial should be reduced in the informed condition compared to the not informed condition. Moreover, since we expected that participants in the informed condition put more effort into encoding and maintaining words for long-term retention, they should outperform participants in the not informed condition in the final recognition test. Both assumptions were tested as a manipulation check. 3.1. Method 3.1.1. Participants 121 participants were recruited from the University of Mannheim. Mean age was 23.1 years, with one participant not having indicated his or her age. Thereof, 71.9% were female. Participants received either course credit or monetary compensation for participation. Data for the antisaccade task was not available for three participants due to software malfunctioning. 3.1.2. Materials Participants completed ten trials of an operation span task, a recognition task, and an antisaccade task. 3.1.2.1. Operation span task. Each trial of the operation span task consisted of six arithmetic operations to be verified and six words to be remembered. 80 unique operations were created analogously to Bunting (2006): They were all of the form

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(5 ⁄ 10)
9 = 41, where the first term in brackets could either be a multiplication or a division of two integers ranging from one to ten. Then, in half of the trials, a number between one and nine was added to the first term; in the other half, a respective number was subtracted. The operations were constructed in a way that the result always was a non-negative integer. Moreover, one half of the operations were correct, whereas the other half were incorrect. Incorrect operations were obtained by adding ‘‘2” to the correct result. 60 operations were randomly assigned to the ten experimental trials, six operations were assigned to a practice trial, and 14 operations were used to determine the individual presentation time per operation within the trials of the operation span task. 72 words were sampled from six semantic categories (animal, clothes, fruit, instruments, professions, vehicles), twelve from each category. Words were selected according to highest typicality (Schröder, Gemballa, Ruppin, & Wartenburger, 2012), with the following exceptions: A word was not selected if it consisted of more than three syllables or ten phonemes, or if it comprised already selected words (e.g., if ‘‘strawberry” was already selected, ‘‘raspberry” or ‘‘blackberry” were excluded). From these twelve words per category, ten words were randomly assigned to the experimental trials of the operation span task, whereas the remaining two words were considered for potential use in the recognition task (see below). In addition, six unrelated words were used in the practice trial. The order of operations used to determine the individual presentation time was constant for all participants, as was the composition of the practice trial. Each experimental trial comprised one word from each semantic category, where assignment of words and operations to trials was random for each participant. 3.1.2.2. Recognition task. For the recognition task, the second and the fifth words within each trial were collected for each participant to be used as ‘‘old” probes. Moreover, ten of the twelve words (see above) sampled from the same six semantic categories used in the operation span task were randomly chosen to be used as ‘‘new” probes, as well as ten words from unrelated semantic categories. The 40 words of the recognition task were presented in a randomized order for each participant. 3.1.2.3. Antisaccade task. The antisaccade task was constructed according to the antisaccade practice and experimental block described in Kane et al. (2001): Each trial of this task started with a fixation signal that remained on screen for a variable amount of time (200–2200 in steps of 400 ms). 50 ms after the fixation signal disappeared, a ‘‘=” appeared to the left or right of the fixation, unpredictable for the participant. The ‘‘=” appeared two times for 100 ms, separated by a 50 ms blank screen, giving the impression of briefly flashing on and off. This flashing signal is assumed to be a strong attractor of attention (Kane et al., 2001). 50 ms after the flashing signal disappeared, the letter B, P, or R was presented for 100 ms on the opposite side of the screen. The participant’s task was to detect which letter was presented, and to enter the respective letter on the keyboard. Thus, in order to detect the letter, participants had to resist looking at the attention-attracting flashing signal and look to the opposite side of the screen. The letter was backward-masked by an H for 50 ms, then by a questions mark ‘‘?” that remained on screen until a response was given. Participants completed 90 trials of the antisaccade task: 18 practice trials and 72 experimental trials. Based on the latter, the proportion of correct responses (i.e., the proportion of correctly identified letters) was determined for each participant as an indicator of the efficiency of executive processes. 3.1.3. Design There were two between-participants conditions. In the first condition, participants were informed about the recognition task after the operation span task, whereas participants in the second condition were not informed. Specifically, just before the first experimental trial of the operation span task started, participants in the informed condition were informed that some of the words that would be presented in the course of the operation span task would again be tested in a later recognition test. After the first five experimental trials of the operation span task, participants in the informed condition were reminded of the subsequent recognition test during a 20 s break. Participants in the not informed condition were not informed about the later recognition test; during the 20 s break after the first five experimental trials, they were told that the next trial would start automatically after a short pause. 3.1.4. Procedure Completion of all tasks was computer based. Each trial of the operation span task started with a two second fixation, followed by the first arithmetic operation to be judged as either correct or incorrect. Participants were instructed to respond as quickly and as accurately as possible by pressing either ‘‘l” for a correct or ‘‘s” for an incorrect operation. Presentation time was individually adapted (see below). As soon as a response was given or when presentation time elapsed, a word to be remembered was shown for one second. Afterwards, the next operation was to be judged and so on. An input window indicated the end of a trial and words had to be entered in the same order as they had been presented. Participants were instructed to guess if they did not remember a word in a specific position (cf. Lewandowsky et al., 2010). Individual presentation times were determined based on 14 practice operations that were to be judged as correct or incorrect at the beginning of the experiment. Mean reaction time was calculated and 2.5 times the individual standard deviation was added to the value. This was used as maximum individual presentation time for each operation in the trials of the operation span task (procedure taken from Unsworth et al., 2005). After the last trial of the operation span task, participants

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in both conditions were given instructions for and completed the recognition task.3 After the recognition task, participants received instructions for and completed the antisaccade task. 3.1.5. Data analysis As in Study 1, generalized linear mixed models (GLMM) were estimated, this time, however, within a multiple group framework. Thus, the parameters of the GLMM – the fixed as well as the random effects – were allowed to vary across the two experimental conditions. Within the models, the probability ppsc was modeled for person p to recall a specific stimulus s on the correct position within a given trial in condition c. In the following, c = 1 refers to the informed condition in which participants were informed in advance about the final recognition test, whereas c = 2 refers to the not informed condition in which participants were not informed about the final recognition test. The first model (Model 1) included a condition-specific random intercept for persons, b0pc, and a linear trend variable reflecting the trial’s position (trialpos) with a condition-specific effect b1pc that was allowed to vary over persons. Trialpos was coded from 0 to 4 because the break after the fifth trial potentially elicited release of PI. Thus, a discontinuous course over the ten trials was expected, making a coding of 0 to 9 inappropriate. To make sure that the effect of trialpos did not change over the two blocks, the predictor block (coded with
0.5 and 0.5) with effect b2c = c20c as well as the interaction between trialpos and block with effect b3c = c30c were included. It was expected that c10c, that is, the average effect of trialpos indicating PI, as well as the correlation between the random intercept and the random slope, ru01c , would be negative in the not informed condition, thus replicating the findings of Study 1. Moreover, announcing a final test was expected to reduce the intrinsic potential for PI, and, as a consequence, susceptibility to PI. Thus, the condition-specific fixed intercept reflecting the average performance in the first trial, c00c, as well as the average effect of trialpos, c10c, were expected to be smaller in magnitude in the informed compared to the not informed condition. In Model 2, the number of stimuli recalled in the previous trial (nprev) was added as a proxy variable for the intrinsic potential for PI. The respective fixed effect, b4c = c40c, was expected to be negative in both conditions. Moreover, adding nprev to the model should result in a significant reduction of the effect of trialpos, as was suggested by the results of Study 1. Finally, in Model 3, performance in the antisaccade task (antisacc) was added as a predictor for the random intercept b0pc and the random slope b1pc. Thus, b0pc = c00c + c01cantisacc + u0pc, and b1pc = c10c + c11cantisacc + u1pc, respectively. c01c was expected to be positive in both condition, reflecting the well-established relation between WMC and performance in the antisaccade task (e.g., Kane et al., 2001). c11c was also expected to be positive. Thus, other things being equal, participants with more efficient inhibitory processes as indicated by a higher performance in the antisaccade task were expected to reveal a less pronounced decline over trials than participants with a lower performance in the antisaccade task. All GLMM-analyses were conducted with Mplus Version 7.31 (Muthén & Muthén, 1998–2012). 3.2. Results The following results of estimating the GLMM are based on data from 118 participants because three participants, for whom data for the antisaccade task were missing, were excluded for better comparability over models. Including them in Model 1 and Model 2 did not change the results substantially. Condition-specific means and standard errors based on the 118 participants are displayed in Table 3. The results of estimating the GLMM are displayed in Tables 4–6, for Model 1, Model 2, and Model 3, respectively. The results of Model 1 revealed that neither block nor the interaction between block and trialpos had a significant effect in either condition (all zs < 1.164).4 As expected, the mean decline over trials indicating PI was significant in both conditions, c101 =
0.034, z =
8.158, p < 0.001, and c102 =
0.076, z =
22.273, p < 0.001, respectively. These two parameters differed significantly between conditions, as indicated by a Wald test of parameter constraints, v2(1) = 59.826, p < 0.001. Thus, PI was more pronounced in the not informed than in the informed condition. However, contrary to the prediction, the average performance in the first trial in the informed condition, c001 = 0.128, z = 1.341, p = 0.180, and in the not informed condition, c002 = 0.142, z = 1.098, p = 0.272, did not differ significantly, as indicated by a Wald test of parameter constraints, v2(1) = 0.008, p = 0.930.5

3 Besides indicating whether a probe word was old or new by clicking on a certain button, participants were also instructed to indicate whether they ‘‘remembered” or ‘‘knew” an old word by clicking on a respective button. This was done for exploratory reasons, but this distinction is of no theoretical interest for the present hypotheses. Thus, results are not reported. 4 Additionally, a contrast analysis on the number of words recalled on the correct position was conducted to investigate release from PI. To test release from PI regardless of condition (i.e., the main effect), mean performance in the fifth trial was weighted with
0.5, mean performance in the sixth trial was weighted with 0.5, and mean performance in all other trials was weighted with 0. To test whether release from PI differed between the informed and the not informed condition (i.e., the interaction), mean performance in the fifth trial in the informed condition and mean performance in the sixth trial in the not informed condition was weighted with 1, mean performance in the sixth trial in the informed condition and mean performance in the fifth trial in the not informed condition was weighted with
1, and mean performance in all other conditions was weighted with 0. The results revealed that performance increased significantly from the fifth to the sixth trial (t = 2.685, p < 0.01), indicating release from PI. This effect was not significantly qualified by condition (t = 1.691, p = 0.094). 5 No significant differences in the first trial, but more pronounced PI in the not informed than in the informed condition might suggest that participants in the informed condition actually recalled more words in the complex span task altogether compared to participants in the not informed condition. To test this, an independent-samples t-test on the overall number of words correctly recalled in the complex span task was conducted. The result indicated that overall recall performance did not differ significantly between conditions (t(116) = 0.298, p = 0.766).

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Table 3 Descriptive statistics of Study 2: Mean number of words recalled at the correct position per trial. Standard errors in parentheses.

Trial Trial Trial Trial Trial Trial Trial Trial Trial Trial

1 2 3 4 5 6 7 8 9 10

Informed condition (n = 59)

Not informed condition (n = 59)

2.88 2.88 2.61 2.73 2.71 2.88 2.68 2.85 2.61 2.76

3.02 2.78 2.15 2.49 2.41 3.15 2.68 2.61 2.90 2.81

(0.23) (0.20) (0.22) (0.22) (0.23) (0.22) (0.23) (0.21) (0.22) (0.22)

(0.22) (0.24) (0.22) (0.21) (0.24) (0.24) (0.23) (0.23) (0.25) (0.24)

Table 4 Parameter estimates of Model 1 in Study 2. Condition

Fixed effects c00 (intercept) c10 (trialpos) c20 (block) c30 (block ⁄ trialpos)

Informed

Not informed

Coefficient (s.e.) 0.13 (0.10)
0.03 (0.00)*
0.03 (0.18) 0.01 (0.07)

Coefficient (s.e.) 0.14 (0.13)
0.08 (0.00)* 0.04 (0.15) 0.09 (0.07)

0.46 (0.15)*

1.29 (0.39)*

*

0.03 (0.00)*

Variances of random effects

r2u0p (person intercept) r2u1p (trialpos)

0.01 (0.00)

Covariance of random effects

r2u01


0.10 (0.02)*

0.00 (0.01)

Note. trialpos = linear trend indicating the position of a trial within a block, s.e. = standard error. * p < 0.05.

Table 5 Parameter estimates of Model 2 in Study 2. Condition Informed

Not informed

Fixed effects c00 (intercept) c10 (trialpos) c20 (block) c30 (block ⁄ trialpos) c40 (nprev)

Coefficient (s.e.) 0.09 (0.11)
0.01 (0.00)*
0.03 (0.19) 0.01 (0.07)
0.04 (0.03)

Coefficient (s.e.) 0.02 (0.15)
0.03 (0.00)* 0.03 (0.17) 0.10 (0.08)
0.09 (0.03)*

Variances of random effects r2u0p (person intercept)

0.48 (0.17)*

1.49 (0.42)*

*

0.04 (0.00)*

r

2 u1p

(trialpos)

0.01 (0.00)

Covariance of random effects

r2u01

0.01 (0.01)


0.09 (0.03)*

Note. trialpos = linear trend indicating the position of a trial within a block, nprev = number of stimuli recalled in the previous trial, s.e. = standard error. * p < 0.05.

Moreover, the results of Model 1 showed that in the not informed condition, the covariance between the random intercept and the random slope was significantly negative, r2u012 =
0.095, z =
3.882, p < 0.001, thus replicating the findings of

Study 1. Conversely, in the informed condition, the respective covariance was not significant, r2u011 = 0.003, z = 0.401, p = 0.689.6 Finally, a noteworthy finding was that the variance of the random intercept was reduced in the informed as 6 Mplus does not provide standardized estimates for multilevel models. To obtain the condition-specific correlation between the random slope and the random intercept, the estimated covariance was divided by the square root of the estimated variance of the random slope times the square root of the estimated variance of the random intercept. This resulted in ru011 = 0.067 and ru012 =
0.471, respectively.

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Table 6 Parameter estimates of Model 3 in Study 2. Condition Informed

Not informed

Fixed effects c00 (intercept) c10 (trialpos) c20 (block) c30 (block ⁄ trialpos) c40 (nprev) c01 (antisacc on inter) c11 (antisacc on slope)

Coefficient (s.e.) 0.09 (0.11)
0.01 (0.00)*
0.03 (0.19) 0.01 (0.07)
0.04 (0.03) 1.17 (0.55)*
0.01 (0.03)

Coefficient (s.e.) 0.02 (0.14)
0.03 (0.00)* 0.04 (0.17) 0.10 (0.08)
0.09 (0.03)* 2.46 (0.78)* 0.08 (0.02)*

Variances of random effects r2u0p (person intercept)

0.45 (0.16)*

1.31 (0.35)*

r

0.01 (0.00)*

0.04 (0.00)*

0.01 (0.01)


0.10 (0.03)*

2 u1p

(trialpos)

Covariance of random effects

r2u01

Note. trialpos = linear trend indicating the position of a trial within a block, nprev = number of stimuli recalled in the previous trial, antisacc on inter = effect of performance in the antisaccade task on the random intercept, antisacc on slope = effect of performance in the antisaccade task on the random slope, s.e. = standard error. * p < 0.05.

compared to the not informed condition. Fig. 2 displays the mean recall probabilities as predicted by Model 1 (left column) as well as the empirical mean recall probabilities (right column) as a function of the trial’s position for each quartile of the random intercept distributions in the not informed (upper row) as well as in the informed condition (bottom row). The results of Model 2 revealed that, in line with the hypothesis, the number of stimuli recalled in the previous trial had a significantly negative effect in the not informed condition, c402 =
0.093, z =
3.282, p = 0.001. However, the respective effect was not significant in the informed condition, c401 =
0.037, z =
1.392, p = 0.164. Adding nprev as a predictor reduced the mean effect of trialpos, c10, in both conditions. To test whether this reduction was significant, two models were estimated in which c101 and c102, respectively, were fixed to their value in Model 1. Comparing these models to Model 2 with a conditional likelihood ratio test revealed that the reduction of the trialpos effect in the informed condition was marginally significant, v2(1) = 3.722, p = 0.054, whereas it was significant in the not informed condition, v2(1) = 9.091, p = 0.003. As expected, the results of Model 3 revealed that the effect of antisacc on the random intercept was significant in the informed condition, c011 = 1.166, z = 2.112, p = 0.035, as well as in the not informed condition, c012 = 2.463, z = 3.169, p = 0.002. By contrast, the effect of antisacc on the random slope was only significant in the not informed condition, c112 = 0.083, z = 3.882, p < 0.001, whereas it was not significant in the informed condition, c111 =
0.011, z =
0.427, p = 0.669. Finally, as a manipulation check, we tested the hypothesis that participants in the informed condition outperform participants in the not informed condition in the final recognition test. To this end, A0 as a nonparametric measure of sensitivity was calculated (cf. Stanislaw & Todorov, 1999). Since the prediction was directional, the respective t-test was one-tailed7. As intended by the manipulation, participants in the informed condition exhibited a higher sensitivity to discriminate old from new probes (MA0 = 0.879; SE = 0.060) than participants in the not informed condition (MA0 = 0.852; SE = 0.089), t(118) = 1.968, p = 0.026 (one-tailed). 3.3. Discussion The first goal of Study 2 was to replicate the findings of Study 1 and generalize them to a different type of complex span task with different types of to-be-remembered stimuli. The results of Study 1 could be replicated under comparable conditions, that is, if participants were not informed about a final recognition test: First, susceptibility to PI in working memory and WMC were positively related, indicating that high WMC individuals are more susceptible to PI than low WMC individuals if susceptibility to PI is modeled over a sequence of trials of a complex span task (i.e., under high cognitive load).8 Second, the more words were recalled in one trial, the lower was the probability of recalling a word in the subsequent trial, reflecting the negative effect of the intrinsic potential for PI on working memory performance. Finally, adding the indicator

8 As in Study 1, we investigated the potential influence of the practice trial on performance in the first test trial. Again, the practice trial was clearly labeled as such, and participants received some more instructions between the practice and the first test trial. We investigated the condition-specific change in performance from the practice trial (coded as 0) to the first test trial (coded as 1) by applying a GLMM of the form pps = exp(b1ptrial + b0p)/(1 + exp(b1ptrial + b0p)) in each condition. The results revealed that on average, there was no significant PI neither in the informed condition (c10 =
0.138, z =
0.603, p = 0.547) nor in the not informed condition (c10 =
0.065, z =
0.426, p = 0.670).

Not informed condition 1.0 Fourth quartile Third quartile Second quartile First quartile

0.8 0.6 0.4 0.2 0.0 0

1

2

3

4

Empirical mean recall probability

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Predicted mean recall probability

142

Not informed condition 1.0 Fourth quartile Third quartile Second quartile First quartile

0.8 0.6 0.4 0.2 0.0 0

1

Informed condition 1.0 Fourth quartile Third quartile Second quartile First quartile

0.8 0.6 0.4 0.2 0.0 0

1

2

Trial position

2

3

4

Trial position

3

4

Empirical mean recall probability

Predicted mean recall probability

Trial position

Informed condition 1.0 Fourth quartile Third quartile Second quartile First quartile

0.8 0.6 0.4 0.2 0.0 0

1

2

3

4

Trial position

Fig. 2. Predicted (left column) and empirical (right column) mean recall probabilities for each quartile of the random intercept distribution for the not informed (upper row) and the informed condition (bottom row).

of the intrinsic potential for PI to the model resulted in a significant reduction of PI, implying that the intrinsic potential for PI explains some of the variance in susceptibility to PI. The second goal of Study 2 was to test the hypothesis that differed from what Kane and Engle (2000) assumed, namely that individual differences in the efficiency of inhibitory processes affect susceptibility to PI even under high cognitive load. The results supported this prediction if participants were not informed about a final recognition test: In this case, inhibitory processes as indicated by performance in the antisaccade task had a positive effect on susceptibility to PI. Note that this does not contradict the finding that high WMC individuals were more susceptible to PI in the not informed condition. Rather, it implies that other things being equal, individuals with more efficient inhibitory processes are less susceptible to PI than individuals with less efficient inhibitory processes. This finding also supports our conclusion from Study 1 that the negative correlation between the random intercept and the random slope is not a mere methodological artifact due to regression to the mean. Finally, the third goal of Study 2 was to test the hypothesis that if the intrinsic potential for PI is experimentally reduced, susceptibility to PI is reduced as well. The intended manipulation implied that the average performance in the first trial should have been lower in the informed than in the not informed condition. However, this was not the case. Therefore, although PI was less pronounced in the informed than in the not informed condition as predicted, it has to be concluded that the manipulation did not work as intended. Since participants in the informed condition nevertheless outperformed participants in the not informed condition in the final recognition test, they must have used different strategies to maintain stimuli over the long term. One possibility is that some participants tried to maintain stimuli from previous trials during later trials. Such a strategy can be expected to interfere with encoding and maintaining stimuli from the current trial, thereby contributing to a reduction of working memory performance over trials. Thus, in the informed condition, the decline of memory performance over trials might not only reflect individual differences in susceptibility to PI, but also individual differences in strategies in response to the announcement of a final test. Such an interpretation is also supported by further findings in the informed condition: First, the individual decline over trials was neither correlated with the indicator of WMC (working memory performance in the first trial) nor with the indicator of the efficiency of inhibitory processes (performance in the antisaccade task). Second, the number of stimuli recalled in the previous trial did not have an effect on the probability to recalling a stimulus from the current trial. Interpreting these correlational patterns as part of a nomological network, one can speculate that announcing a final test might have induced cognitive processes that ultimately led to a change of the fundamental meaning of the variable thought to reflect susceptibility to PI (i.e., the decline over trials).

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If this assumption turns out to be tenable, it could have implications for research on PI in the context of testing: Some authors (e.g., Szpunar, McDermott, & Roediger, 2008) suggested that testing in terms of an immediate recall after each trial of a memory task insulates against PI. However, one seemingly subsidiary feature of their design is that a final test is announced in all experimental conditions to ensure the continued processing of the stimuli over trials. The results of the present study therefore gives rise to the question of whether the conclusions based on such a design – namely, that an immediate recall prevents PI – are still valid if participants do not expect a final test. However, more research is needed to better understand the implications of announcing a final test on the level of induced cognitive processes. 4. General discussion In the present paper, we investigated the relation between susceptibility to PI in working memory and WMC. Based on results of Kane and Engle (2000), we hypothesized that if susceptibility to PI is modeled over a sequence of trials of a complex span task, one has to expect that high WMC individuals are more susceptible to PI than low WMC individuals, at least if the indicator of WMC does not capture individual differences in susceptibility to PI. Since a higher susceptibility to PI of high WMC individuals could not be explained by the account of Kane and Engle (2000), we proposed that susceptibility to PI does not only reflect individual differences in the efficiency of inhibitory processes, but also the individual intrinsic potential for PI. The results of the two studies were in line with our main assumptions: First, susceptibility to PI and WMC were positively related, indicating that high WMC individuals were more susceptible to PI than low WMC individuals if susceptibility to PI is modeled over a sequence of trials of a complex span task. Second, the intrinsic potential for PI negatively affected susceptibility to PI. This was reflected by the finding that the number of stimuli recalled in one trial as a proxy variable for the intrinsic potential for PI had a negative effect on the probability of recalling a stimulus in the next trial. Third, individual differences in inhibitory processes substantially influenced susceptibility to PI under high cognitive load, a finding that contradicts Kane and Engle (2000) assumption that high cognitive load levels executive processes to counteract PI between low and high WMC individuals. Note that this assumption was necessary in the account of Kane and Engle (2000) to explain the finding of their main analyses that the low and the high-span group were equally susceptible to PI under high cognitive load. Based on previous research as well as on our own results, we propose an account of the relation between WMC and susceptibility to PI that is depicted in Fig. 3. In the following, we will discuss this account in some more detail, integrate our results, and critically discuss them. 4.1. The direct effect of WMC on susceptibility to PI First, we assume that WMC directly affects susceptibility to PI in a negative manner, implying that other things being equal, individuals with more efficient executive processes are less susceptible to PI. This has been suggested by several other authors before, with different accounts of the exact mechanisms subsumed under WMC and assumed to counteract PI. According to the account of Hasher and colleagues (e.g., Hasher et al., 2008), individual differences in WMC reflect individual differences in inhibitory processes, where deletion is probably the most relevant in counteracting PI. Kane and Engle (2000), among other things, discussed a non-inhibitory process in which low and high WMC individuals differ and that possibly contributes to individual differences in susceptibility to PI: High WMC individuals might have generated more efficient retrieval cues (‘‘time tags”) during encoding that helped to discriminate successive trials from one another at recall. More recently, Unsworth and Engle (2007) also proposed a non-inhibitory process in which low and high WMC individuals differ, namely, controlled search: High WMC individuals are assumed to use more efficient retrieval cues at recall. As a consequence, their set of potential recall candidates – called search set – is more focused to the relevant stimuli than that of low WMC individuals, resulting in a higher recall performance of high than of low WMC individuals. Given that PI has been considered as a consequence of lack of discriminability by several authors (Bäuml & Kliegl, 2013; Crowder, 1976; Wixted & Rohrer, 1993), one can derive the expectation from the account of Unsworth and Engle (2007) that individual differences in controlled search is another (non-inhibitory) process that directly affects individual differences in susceptibility to PI. In the present paper, we have focused on inhibitory processes that have a direct effect on susceptibility to PI. The reason is that regarding the few studies that directly related individual differences in susceptibility to PI to WMC, there seems to be more direct evidence for a role of inhibitory than non-inhibitory processes (e.g., Friedman & Miyake, 2004b; May et al., 1999). However, we do not claim that individual differences in non-inhibitory processes do not have a direct effect on

Cognitive load WMC

+/0

Intrinsic potential for PI

-

+

Susceptibility to PI

Fig. 3. Proposed model underlying the relation between WMC and susceptibility to PI.

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susceptibility to PI. Rather, based on the finding of Oberauer et al. (2012) that individual differences in an inhibitory process – removal – and individual differences in a non-inhibitory factor – discriminability – together account for individual differences in (within-trial) performance in complex span tasks, we speculate that both inhibitory and non-inhibitory processes contribute to individual differences in susceptibility to PI. Finally, we assume that the efficiency of executive processes can be reduced by cognitive load. However, different from Kane and Engle (2000), we assume a constant effect for different levels of WMC. Conversely, Kane and Engle’s (2000) assumption that cognitive load equalizes the efficiency of executive processes (to counteract PI) would be tantamount to assuming a moderating effect of cognitive load on the effect of WMC on susceptibility to PI. 4.2. The indirect effect of WMC on susceptibility to PI via the intrinsic potential for PI The new contribution of our account is the indirect effect of WMC on susceptibility to PI that is mediated by the intrinsic potential for PI. Importantly, the indirect effect of WMC on susceptibility to PI is of opposite sign than the direct effect, so the observed relation between WMC and susceptibility to PI will depend on the relative strength of the indirect and direct effect. The strength of the effect of WMC on the intrinsic potential for PI (and, as a result, the strength of the indirect effect) is assumed to depend on the amount of cognitive load during a task. Thus, the effect of WMC on the intrinsic potential for PI is assumed to be moderated by the amount of cognitive load: Under no or low cognitive load, the intrinsic potential for PI does not depend on individual differences in WMC to a large extent because routines like rehearsal can be engaged to maintain stimuli, and these routines are little indicative of differences in WMC (e.g., Engle et al., 1999; Oberauer et al., 2012). The results of Kane and Engle (2000) were in line with this assumption, showing that the low and the high-span group did not differ in performance in the first trial under no cognitive load. With increasing cognitive load, individual difference in executive processes should increasingly take effect, so high WMC individuals will maintain and recall more stimuli than low WMC individuals, implying a higher intrinsic potential for PI of high than of low WMC individuals. Thus, with increasing cognitive load, the strength of the effect of WMC on the intrinsic potential for PI increases. This is in line with the finding of Kane and Engle (2000) that under high cognitive load, the low and the high-span group differed in performance in the first trial, whereas they did not under low cognitive load. Finally, the intrinsic potential for PI is assumed to have a positive effect on susceptibility to PI, implying that other things being equal, a higher intrinsic potential for PI results in a more pronounced susceptibility to PI. Note that the general idea that the number of interfering stimuli from a previous trial reduces performance in a subsequent trial is not new, but is an inherent feature of accounts ascribing PI to failures of trial discrimination (e.g., Crowder, 1976; Wixted & Rohrer, 1993). Specifically, these accounts assume that if a previous trial cannot be discriminated from a subsequent one, the stimuli from the previous trial intrude into the search set when trying to recall the stimuli from the current trial. Consequently, the search set is enlarged and the probability of correctly recalling a stimulus from the current trial decreases. The potential contribution of our account is to consider the number of potentially interfering stimuli as an individually varying variable that depends on WMC, where the strength of this dependency is moderated by the amount of cognitive load. In the present studies, we have of course only made a first step in contributing evidence for our account. The results regarding the negative effect of the number of stimuli recalled in one trial on the probability of correctly recalling a stimuli in the next trial can be considered as a first hint at the role of the intrinsic potential for PI for susceptibility to PI. However, as already mentioned in the Discussion of Study 1, we could not test the respective direct effect with the current operationalizations of susceptibility to PI and the intrinsic potential for PI. For future research, it therefore seems desirable to choose different operationalizations. Specifically, if the intrinsic potential for PI changes from trial to trial, it seems natural to model susceptibility to PI more dynamically as well, for example, as the decline of performance between two successive trials, or by using response latencies in each trial (cf. Wixted & Rohrer, 1993). 5. Conclusion In the present studies, we investigated the relation between susceptibility to PI in working memory and WMC, revealing that high WMC individuals were more susceptible to PI than low WMC individuals if susceptibility to PI is modeled over a sequence of trials of a complex span task. This finding cannot be explained by any current account. However, they can be explained if one assumes that the intrinsic potential for PI plays a role, where the intrinsic potential for PI denotes the amount of information that is activated at a given time and that has the potential to exert PI subsequently. In two studies, we found initial evidence for the assumptions, indicating that the intrinsic potential for PI and its interplay with executive processes to counteract PI can potentially contribute to a better understanding of the complex relation between susceptibility to PI and WMC. References Baayen, R. H., Davidson, D. J., & Bates, D. M. (2008). Mixed-effects modeling with crossed random effects for subjects and items. Journal of Memory and Language, 59(4), 390–412. http://dx.doi.org/10.1016/j.jml.2007.12.005. Bates, D., Maechler, M., Bolker, B., & Walker, S. (2014). lme4: Linear mixed-effects models using Eigen and S4. R package version 1.1-7 .

M.A. Steinwascher, T. Meiser / Consciousness and Cognition 44 (2016) 130–145

145

Bäuml, K. H. T., & Kliegl, O. (2013). The critical role of retrieval processes in release from proactive interference. Journal of Memory and Language, 68(1), 39–53. http://dx.doi.org/10.1016/j.jml.2012.07.006. Braver, T. S., Gray, J. R., & Burgess, G. C. (2008). Explaining the many varieties of working memory variation: Dual mechanisms of cognitive control. In A. R. A. Conway, C. Jarrold, M. J. Kane, A. Miyake, & J. N. Towse (Eds.), Variation in working memory. Oxford: University Press. Bunting, M. (2006). Proactive interference and item similarity in working memory. Journal of Experimental Psychology: Learning, Memory, and Cognition, 32 (2), 183–196. http://dx.doi.org/10.1037/0278-7393.32.2.183. Conway, A. R. A., Jarrold, C., Kane, M. J., Miyake, A., & Towse, J. N. (Eds.). (2008). Variation in working memory. Oxford: University Press. Conway, A. R. A., Kane, M. J., Bunting, M. F., Hambrick, D. Z., Wilhelm, O., & Engle, R. W. (2005). Working memory span tasks: A methodological review and user’s guide. Psychonomic Bulletin & Review, 12(5), 769–786. http://dx.doi.org/10.3758/BF03196772. Crowder, R. G. (1976). Principles of learning and memory. Hillsdale, N.J.: Erlbaum. De Boeck, P., & Wilson, M. (Eds.). (2004). Explanatory item response models. A generalized linear and nonlinear approach. New York: Springer. Engle, R. W., Tuholski, S. W., Laughlin, J. E., & Conway, A. R. A. (1999). Working memory, short-term memory, and general fluid intelligence: A latent-variable approach. Journal of Experimental Psychology: General, 128(3), 309–331. Friedman, N. P., & Miyake, A. (2004a). The reading span test and its predictive power for reading comprehension ability. Journal of Memory and Language, 51 (1), 136–158. http://dx.doi.org/10.1016/j.jml.2004.03.008. Friedman, N. P., & Miyake, A. (2004b). The relations among inhibition and interference control functions: A latent-variable analysis. Journal of Experimental Psychology: General, 133(1), 101–135. http://dx.doi.org/10.1037/0096-3445.133.1.101. Hasher, L., Lustig, C., & Zacks, R. (2008). Inhibitory mechanisms and the control of attention. In A. R. A. Conway, C. Jarrold, M. J. Kane, A. Miyake, & J. N. Towse (Eds.), Variation in working memory. Oxford: University Press. Kaller, C. P., Loosli, S. V., Rahm, B., Gossel, A., Schieting, S., Hornig, T., & Katzev, M. (2014). Working memory in schizophrenia: Behavioral and neural evidence for reduced susceptibility to item-specific proactive interference. Biological Psychiatry, 76(6), 486–494. http://dx.doi.org/10.1016/j. biopsych.2014.03.012. Kane, M. J., Bleckley, M. K., Conway, A. R. A., & Engle, R. W. (2001). A controlled-attention view of working-memory capacity. Journal of Experimental Psychology: General, 130(2), 169–183. http://dx.doi.org/10.1037/0096-3445.130.2.169. Kane, M. J., & Engle, R. W. (2000). Working-memory capacity, proactive interference, and divided attention: Limits on long-term memory retrieval. Journal of Experimental Psychology: Learning, Memory, and Cognition, 26(2), 336–358. http://dx.doi.org/10.1037//0278-7393.26.2.336. Kane, M. J., Hambrick, D. Z., Tuholski, S. W., Wilhelm, O., Payne, T. W., & Engle, R. W. (2004). The generality of working memory capacity: A latent-variable approach to verbal and visuospatial memory span and reasoning. Journal of Experimental Psychology: General, 133(2), 189–217. Lewandowsky, S., Oberauer, K., Yang, L. X., & Ecker, U. K. H. (2010). A working memory test battery for MATLAB. Behavior Research Methods, 42(2), 571–585. http://dx.doi.org/10.3758/Brm.42.2.571. Lustig, C., May, C. P., & Hasher, L. (2001). Working memory span and the role of proactive interference. Journal of Experimental Psychology: General, 130(2), 199–207. http://dx.doi.org/10.1037//0096-3445.130.2.199. May, C. P., & Hasher, L. (1998). Synchrony effects in inhibitory control over thought and action. Journal of Experimental Psychology: Human Perception and Performance, 24(2), 363–379. http://dx.doi.org/10.1037/0096-1523.24.2.363. May, C. P., Hasher, L., & Kane, M. J. (1999). The role of interference in memory span. Memory & Cognition, 27(5), 759–767. http://dx.doi.org/10.3758/ BF03198529. Miyake, A., Friedman, N. P., Emerson, M. J., Witzki, A. H., Howerter, A., & Wager, T. D. (2000). The unity and diversity of executive functions and their contributions to complex ‘‘frontal lobe” tasks: A latent variable analysis. Cognitive Psychology, 41(1), 49–100. http://dx.doi.org/10.1006/cogp.1999.0734. Muthén, L. K., & Muthén, B. O. (1998-2012). Mplus user’s guide (7th ed.). Los Angeles, CA: Muthén & Muthén. Oberauer, K., Lewandowsky, S., Farrell, S., Jarrold, C., & Greaves, M. (2012). Modeling working memory: An interference model of complex span. Psychonomic Bulletin & Review, 19(5), 779–819. http://dx.doi.org/10.3758/s13423-012-0272-4. R Core Team (2015). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. . Schröder, A., Gemballa, T., Ruppin, S., & Wartenburger, I. (2012). German norms for semantic typicality, age of acquisition, and concept familiarity. Behavior Research Methods, 44, 380–394. http://dx.doi.org/10.3758/s13428-011-0164-y. Stanislaw, H., & Todorov, N. (1999). Calculation of signal detection theory measures. Behavior Research Methods, Instruments, & Computers, 31(1), 137–149. http://dx.doi.org/10.3758/Bf03207704. Szpunar, K. K., McDermott, K. B., & Roediger, H. L. (2008). Testing during study insulates against the buildup of proactive interference. Journal of Experimental Psychology: Learning, Memory, and Cognition, 34(6), 1392–1399. http://dx.doi.org/10.1037/a0013082. Underwood, B. J. (1957). Interference and forgetting. Psychological Review, 64(1), 49–60. http://dx.doi.org/10.1037/H0044616. Unsworth, N., & Engle, R. W. (2007). The nature of individual differences in working memory capacity: Active maintenance in primary memory and controlled search from secondary memory. Psychological Review, 114(1), 104–132. http://dx.doi.org/10.1037/0033-295x.114.1.104. Unsworth, N., Heitz, R. P., Schrock, J. C., & Engle, R. W. (2005). An automated version of the operation span task. Behavior Research Methods, 37(3), 498–505. http://dx.doi.org/10.3758/Bf03192720. Wixted, J. T., & Rohrer, D. (1993). Proactive interference and the dynamics of free recall. Journal of Experimental Psychology: Learning, Memory, and Cognition, 19(5), 1024–1039. http://dx.doi.org/10.1037//0278-7393.19.5.1024.