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Abstract (English):

Short- and long-term memory tasks predict working memory performance, and vice versa.

Neath, Ian. Department of Psychology, Memorial University of Newfoundland, St. John’s, Canada, ineath@mun.ca Saint-Aubin, Jean. École de psychologie, UniversitĂ© de Moncton, Canada Bireta, Tamra J.. Department of Psychology, The College of New Jersey, NJ, US Gabel, Andrew J.. Department of Psychology, Memorial University of Newfoundland, Canada Hudson, Chelsea G.. Department of Psychology, Memorial University of Newfoundland, Canada Surprenant, AimĂ©e M.. Department of Psychology, Memorial University of Newfoundland, Canada

Neath, Ian, Department of Psychology, Memorial University of Newfoundland, St. John’s, Newfoundland and Labrador, Canada, A1B 3X9, ineath@mun.ca

Canadian Journal of Experimental Psychology, Vol 73(2), Jun, 2019. pp. 79-93.

Can J Exp Psychol

US : Educational Publishing Foundation

Canadian Journal of Psychology/Revue canadienne de psychologie

Canada : Canadian Psychological Association Canada : University of Toronto Press

1196-1961 (Print) 1878-7290 (Electronic)

English

memory, Brown– Peterson, working memory, complex span, continual distractor

The Brown–Peterson, operation span, and continual distractor tasks all require people to retain information while performing a distractor task. Scale Independent Memory, Perception, and Learning (SIMPLE), a local relative distinctiveness model, has been fit to aspects of each task and offers the same explanation for

 

 

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each: the distractor task serves to space the items out in time and memory performance depends on the relative distinctiveness of the target item at the time of recall. If this is correct, it follows that performance on all three tasks should correlate, even though the tasks have, at various times, been ascribed to different memory systems, short-term memory, working memory, and long-term memory, respectively. We tested 190 subjects on all three tasks and found that performance on all three tasks is significantly correlated. We then fit the data from each task using SIMPLE. We argue that these results support the relative distinctiveness principle (Surprenant & Neath, 2009). We contrast SIMPLE with other models of the same tasks. (PsycINFO Database Record (c) 2019 APA, all rights reserved)

Les tĂąches de Brown-Peterson, d’empan d’opĂ©ration (OSPAN) et de distraction en continu requiĂšrent toutes que nous retenions des informations en effectuant une tĂąche distractrice. Le modĂšle SIMPLE (mĂ©moire, perception et apprentissage indĂ©pendants de l’échelle), un modĂšle du caractĂšre distinctif relatif local, a Ă©tĂ© adaptĂ© aux aspects de chaque tĂąche et offre la mĂȘme explication pour chacun : la tĂąche distractrice sert Ă  espacer les items dans le temps et le rendement en termes de mĂ©moire varie selon le caractĂšre distinctif relatif de l’item cible au moment du rappel. Si cela est exact, il s’ensuit que le rendement des trois tĂąches corresponde, mĂȘme si les tĂąches ont, Ă  diverses reprises, Ă©tĂ© attribuĂ©es Ă  diffĂ©rents systĂšmes de mĂ©moire, la mĂ©moire Ă  court terme, la mĂ©moire de travail et la mĂ©moire Ă  long terme, respectivement. Nous avons testĂ© 190 sujets par rapport aux trois tĂąches et constatĂ© que le rendement lors des trois tĂąches Ă©tait Ă©troitement liĂ©. Nous avons ensuite adaptĂ© les donnĂ©es issues de chaque tĂąche au moyen du modĂšle SIMPLE. Nous prĂ©tendons que ces rĂ©sultats confirment le principe du caractĂšre distinctif relatif (Surprenant & Neath, 2009). Nous comparons le modĂšle SIMPLE avec d’autres modĂšles pour les mĂȘmes tĂąches. (PsycINFO Database Record (c) 2019 APA, all rights reserved)

Public Significance Statement—Human memory has often been described as consisting of multiple stages such as short-term, working, and long-term memory. We argue that this leads researchers to ignore commonalities among different tasks and focus, instead, on their differences. The current study shows commonalities among three tasks that have been interpreted as tapping different memory systems, thus supporting the idea that general principles of memory can apply in some cases. Ultimately, our data provide a challenge to system theorists to develop a model that offers an in-depth account of a wide range of phenomena. (PsycINFO Database Record (c) 2019 APA, all rights reserved)

Journal Article

*Long Term Memory; *Recall (Learning); *Short Term Memory; *Time Perception; Learning; Memory; Performance; Prediction; Task Complexity

Learning & Memory (2343)

 

 

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Human Male Female

US

Adolescence (13-17 yrs) Adulthood (18 yrs & older) Young Adulthood (18-29 yrs) Thirties (30-39 yrs) Middle Age (40-64 yrs)

Continual Distractor Task Operation Span Task

Sponsor: Natural Sciences and Engineering Research Council of Canada Recipients: Neath, Ian; Saint-Aubin, Jean; Surprenant, Aimée M.

International Conference on Memory, Jul, 2016, Budapest, Hungary

Part of this work was presented at the aforementioned conference.

Empirical Study; Quantitative Study

Electronic

Journal; Peer Reviewed Journal

First Posted: Dec 17, 2018; Accepted: Aug 27, 2018; First Submitted: Jun 20, 2018

20181217

20190523

Canadian Psychological Association. 2018

http://0-dx.doi.org.wizard.umd.umich.edu/10.1037/cep0000157

30556715

cep-73-2-79

2018-64417-001

 

 

Short- and Long-Term Memory Tasks Predict Working Memory Performance, and Vice Versa

By: Ian Neath Department of Psychology, Memorial University of Newfoundland; Jean Saint-Aubin École de psychologie, UniversitĂ© de Moncton Tamra J. Bireta Department of Psychology, The College of New Jersey Andrew J. Gabel Department of Psychology, Memorial University of Newfoundland Chelsea G. Hudson Department of Psychology, Memorial University of Newfoundland AimĂ©e M. Surprenant Department of Psychology, Memorial University of Newfoundland Acknowledgement: This work was supported, in part, by grants from the Natural Sciences and Engineering Research Council of Canada to Ian Neath, Jean Saint-Aubin, and AimĂ©e M. Surprenant. Part of this research formed part of an honours thesis of Chelsea G. Hudson. Part of this work was presented at the sixth International Conference on Memory, Budapest, Hungary, July 2016.

The ancient Greek poet Archilochus wrote that “a fox knows many things, but a hedgehog one important thing,” an idea that has since become closely associated with the philosopher Isaiah Berlin. Greene (2007) applied this idea to the study of memory, noting that at various times memory researchers were more like hedgehogs, in that they sought general principles that applied widely, whereas at others that were more like foxes, in that they examined a myriad of disparate and seemingly unrelated effects. Within the recent past, the foxes have outnumbered the hedgehogs, as indicated by the number of researchers who have argued that general principles of memory do not exist (e.g., Baddeley, 1978; Roediger, 2008; Tulving, 1985), although hedgehogs are not entirely extinct (see, e.g., Surprenant & Neath, 2009). In this article, we examine the extent to which one of the principles proposed by Surprenant and Neath, the relative distinctiveness principle, can explain three different tasks—Brown–Peterson, operation span, and continual distractor—each of which was originally developed to tap a different memory system.

There are a number of reasons why the three tasks might all be fundamentally related (Neath,

Listen American Accent

 

 

VanWormer, Bireta, & Surprenant, 2014). The most obvious, as we describe in more detail later, is that all three tasks alternate a memory storage task and a distracting activity, and therefore performance on each task will depend, at least in part, on how well a person can retain information in the presence of distracting activity. If the tasks are related, then performance on one should correlate with performance on the others. Partial evidence supporting this comes from Unsworth and Spillers (2010b) who found that operation span correlates with performance on a continual distractor task. Although the presence of a correlation is by no means conclusive evidence for relatedness of the tasks, the absence of correlation would have been strong evidence that the two tasks are not related. There is also evidence that an explanation based on relative distinctiveness could account for performance on all three tasks. Unsworth and Engle (2006) have previously suggested that Glenberg’s (1987; Glenberg & Swanson, 1986) temporal distinctiveness theory could account for both continual distractor and operation span data. Similarly, Scale Independent Memory, Perception, and Learning (SIMPLE), a relative local distinctiveness model of memory that is related to temporal distinctiveness theory (see Neath & Brown, 2007), has previously been fit to operation span task data (Neath et al., 2014), as well as some aspects of the Brown– Peterson and continual distractor tasks (Brown, Neath, & Chater, 2007; Neath & Brown, 2006).

However, there are still gaps in the argument that the three tasks are related and the purpose of this article is to fill in two specific gaps. First, we tested 190 subjects on all three tasks and correlated their performance. The prediction is that there should be three significant correlations. Second, we fit SIMPLE (Brown et al., 2007; Neath & Brown, 2006) to these data. Unlike previous fits of SIMPLE to Brown–Peterson data, we treat the three letters that form the consonant trigram as three individual items, just as we treat the words in operation span and continual distractor as separate items. Previous fits of SIMPLE to continual distractor data have focussed on the general pattern of the presence and absence of primacy and recency effects rather than fitting specific data (see Neath & Brown, 2006); here, we fit the observed serial position function. The prediction is that SIMPLE should be able to fit the data from all three tasks. To anticipate, performance on all three tasks correlate, and the data can be adequately fit by SIMPLE. We begin by reviewing each task and then consider theoretical explanations.

Brown–Peterson

The Brown–Peterson task was developed independently at about the same time by two sets of researchers, Brown (1958) and Peterson and Peterson (1959). The purpose was to test how long information would remain in short-term memory (STM) when rehearsal was prevented. Peterson and Peterson presented subjects with a consonant trigram (three consonants presented simultaneously), and then asked the subjects to count backward from a given number for

 

 

anywhere up to 18 s. Following this, the subjects were asked to report the trigram. To be scored as correct, all three letters had to be reported in the original presentation order. The key original finding was that performance decreased as the length of the distractor duration increased and was interpreted as showing rapid forgetting of unrehearsed items in STM (for a review, see Neath & Surprenant, 2003, chapter 3).

Since the initial studies, which were interpreted as showing a process of time-based decay in STM, the focus on Brown–Peterson shifted to examine proactive interference, in which previously experienced items interfere with the ability to remember current information (see Crowder, 1976, for a discussion). Keppel and Underwood (1962) examined performance on a trial-by-trial basis and found equivalent recall of the trigram on the first trial regardless of whether the distractor duration was 3 s or 30 s. However, performance began to diverge such that on subsequent trials, recall was worse in the 30-s condition than in the 3-s condition. This suggestion that proactive interference builds up over trials was confirmed in a variety of different experiments. For example, Loess and Waugh (1967) increased the amount of time that separated each trial in a Brown– Peterson task and found that once this interval was sufficiently large, performance no longer was a function of trial number. Similarly, Wickens (e.g., Wickens, 1970, 1972; Wickens, Born, & Allen, 1963) found that if the type of to-be-remembered item changed, performance improved. They termed the decrease in performance over trials the build-up of proactive interference, and the improved performance with the changed item the release from proactive interference.

Operation Span

Simple span tasks have been in common use since the 1800s, and indeed, the term span was introduced by Jacobs (1887): “It is obvious that there is a limit to the power of reproducing sounds accurately. . . . [T]he highest number correctly reproduced is to be regarded as the limit which we wish to find, and which we term here the span” (p. 76). In such a task, then, the subject is presented with a list of items that are to be immediately repeated in order. It quickly became apparent that memory span varied with the type of material, so as early as 1938, Blankenship noted that span increases as one moves from nonsense syllables to letters to digits to related words (Blankenship, 1938). These tasks became identified with the concept of STM.

In contrast to simple span tasks, complex span tasks were developed following the formulation of Baddeley and Hitch’s (1974) working memory, which differs in important ways from the concept of STM (see Baddeley & Hitch, 1977, for details). Whereas Brown–Peterson was characterised as a test of STM, complex span tasks are characterised as tests of working memory. As Conway et al. (2005) described them, complex span tasks were designed to “require not only information storage

 

 

and rehearsal . . . but also the simultaneous processing of additional information” (p. 771). Operation span, one of a number of complex tasks, was developed by Turner and Engle (1989). There are many variations of this task, and therefore, what follows is a description of just one common version based on Conway and Engle (1996). In this task, the subject reads a mathematical question out loud (e.g., “Is 10 divided by 2 plus 4 equal to 9?”), answers the question, and then sees the first item in the list. The lists randomly vary in length from two to six words, with the math problems alternating with the to-be-remembered items. After all list items have been presented, the subject is asked to recall the words in strict serial order. The measure that is frequently used, OSPAN, is the sum of the list lengths for which all lists that were correctly recalled. That is, if a person recalled four out of six words, those four words are ignored in the OSPAN measure; if a person recalled all three words in a three-item list, then 3 is added to the OSPAN measure. The maximum possible value of OSPAN is 60. This measure is frequently referred to as all-or-nothing scoring, but just as there are variations of the task itself, there are also other scoring methods (for a review, see Conway et al., 2005). One important difference between simple and complex span tasks is that the latter correlate better than the former with higher order cognitive tasks such as reading comprehension, problem solving, and reasoning (see Conway et al., 2005).

Continual Distractor

Although researchers had used a task very much like the continual distractor task earlier (e.g., Murdock, 1965; Silverstein & Glanzer, 1971), the task rose to prominence as a test of the dual- store or modal model account of recency effects. When people recall a long list of items and are then asked to recall the items in any order, they generally recall the last few items first, then recall the first few items, and finally try to recall the midlist items (Spurgeon, Ward, & Matthews, 2014; Tan, Ward, Paulauskaite, & Markou, 2016). This gives rise to both a recency effect, better recall of the last few items, and a primacy effect, better recall of the first few items. The modal model attributed the primacy effect to extra rehearsal that increased the probability of transferring the information from STM to long-term memory. The recency effect, the enhanced recall of the last few list items, was attributed to dumping items from STM. Evidence consistent with this view came from studies such as those of Glanzer and Cunitz (1966). They demonstrated that delaying free recall by adding a distractor task at the end of the list eliminated the recency effect but not the primacy effect. The key feature was using a distractor task that could plausibly prevent rehearsal and therefore also prevent the transfer of information to long-term memory. Thus, continual distractor was seen as test of long-term memory because STM could not play a role: the 30 s of distracting activity was thought sufficient to eliminate the role of STM.

 

 

However, Bjork and Whitten (1974) added the same distractor task after every list item—hence, the term continual distractor—and recency was restored. In the typical continual distractor task, the lists have a dozen or more words, and the distractor activity can last up to 30 s. Presentation of one list of 12 items with 30 s of distracting activity after every item takes over 6 min. Nonetheless, both primacy and recency effects are observed.

Similarities and Differences

As is evident from this brief description, there are many similarities among the three tasks, the most obvious being the requirement to remember something in the face of distraction and that the distractor material differs from the to-be-remembered items such that it minimizes the chance of interference. There are also, however, some notable differences between the three tasks as they are generally used. The number of items that are to-be-remembered varies from one (Brown– Peterson) to a dozen or more (continual distractor), with operation span typically using lists of between two and six items. A second difference is that list length varies in operation span, but remains fixed and therefore predictable in both Brown–Peterson and continual distractor. In Brown–Peterson and continual distractor, the distractor task follows the to-be-remembered item whereas in operation span, the distractor task precedes the to-be-remembered item. Brown– Peterson and operation span use serial recall whereas continual distractor uses free recall. Although there are a number of ways of scoring each task, two tasks are typically scored using all- or-none scoring (Brown–Peterson, operation span) whereas one uses proportion correct at each position (continual distractor).

Theoretical Accounts

There exist a number of models of each individual task. For example, both Laming (1992) and Mewhort, Shabahang, and Franklin (2018) described models of Brown–Peterson. Laming (1992) used an analogy to finding a short segment recorded on video tape. He first assumed that the tape does not degrade and there are no read/write errors; he further assumed all items are stored on the tape. The limit in performance is determined by how long the tape is. Laming proposed a weighting function such that the further back along the tape one has to go to get close to the recorded information, the more likely there will be an error such that the location is missed. Although the actual model is obviously more complex, this basic account reproduces many of the known findings for Brown–Peterson. It is not clear, however, whether the basic explanation would apply to either operation span or continual distractor.

Mewhort et al. (2018) presented a holographic model of Brown–Peterson in which the semantic

 

 

meaning of individual words is represented as a complex series of vectors. The model focuses on accounting for release from proactive interference, when the fourth trial of a Brown–Peterson task changes the category of items. It also accounts for the von Restorff effect, in which a midlist item that comes from a different category than other list items is well recalled. Just like Laming’s (1992) model, this is a foxlike model because it accounts for Brown–Peterson in detail, but the extent to which it could be extended to either operation span or continual distractor it is not clear.

There are fewer models of the continual distractor task. For example, Davelaar, Goshen-Gottstein, Ashkenazi, Haarmann, and Usher (2005) presented a model that retained the distinction between STM and long-term memory. In essence, there is an activation based buffer responsible for short- term storage and a longer-term episodic storage system. This model predicts that recency effects observed in the short term differ from those observed in the long term, and accounts for a number of dissociations between immediate and continual distractor recall. However, this model cannot account for Brown–Peterson due to problems with a decay-based account described previously.

Finally, there are even fewer models of operation span Oberauer, Lewandowsky, Farrell, Jarrold, and Greaves (2012) developed a model that is a variant of the serial-order-in-a-box family and involves a two-layer network that associates items with positions. The model was applied only to fixed list lengths of 5 items, whereas complex span has list lengths that vary, typically between 2 and 6. The model is unlikely to account for continual distractor recall because that involves free recall whereas the focus on the serial-order-in-a-box family of models is serial recall. Due to the complexity of the model, it is not immediately clear whether it could account for Brown–Peterson.

SIMPLE

In contrast to the models described in the previous section, all of which can be described as following in the tradition of the fox, SIMPLE (Brown et al., 2007; Neath & Brown, 2006) follows in the tradition of the hedgehog. It is a relative local distinctiveness model in which items are represented on one or more dimensions in psychological space. In many episodic tasks, the variables are so well controlled that the only systematic variation is time of presentation and therefore the primary dimension is relative time. The zero point is the time when the retrieval attempt of a specific item is made, and the temporal value for a given item is the time since presentation. For example, in a list of four items presented at a rate of one item per second, the first item will have a temporal value of 4 s, the second will have a temporal value of 3 s, and so on at the end of list presentation and prior to any retrieval attempts. Importantly, these values are log transformed. This has the effect of compressing early list items more than later list items (assuming a constant presentation rate) and contributes to the asymmetrical serial position

 

 

function.

SIMPLE is not restricted to using only time as a dimension. Rather, the dimension that is used will be the one (or ones) most useful given the particular task. For example, when identifying tones, the dimension is assumed to be frequency (in Hz); when identifying rods of various lengths, the dimension is assumed to be length (in mm; see Neath, Brown, McCormack, Chater, & Freeman, 2006). It is also possible that people could use a position dimension on serial recall tasks because time and position are frequently confounded (e.g., the items are presented at a constant rate of one per second). For example, Surprenant, Neath, and Brown (2006) found little difference between the temporal and position versions of SIMPLE for regularly spaced items. However, when time and position are not confounded and when the temporal information is predictable, SIMPLE fits the data better when using the temporal dimension but cannot fit the data when using a position dimension (Neath & Brown, 2006).

A fundamental assumption of SIMPLE is another principle: All retrieval is cue driven (Surprenant & Neath, 2009), and the cue used depends on the task. When identifying tones, the cue is the tone itself. For serial recall, the items are assumed to be represented on a temporal dimension, and therefore the cue is the item’s location on the temporal dimension (see Brown et al., 2007; Brown, Chater, & Neath, 2008, for a discussion). In effect, the person is asking, which item occurred here? Although SIMPLE does not provide a specific process, other models do and could, in principle, be incorporated into SIMPLE. For example, OSCAR (Oscillator-based Associative Recall; Brown, Preece, & Hulme, 2000) used oscillator mechanisms, each of which operates on a different frequency. Time can be encoded using these, and “rerunning” the oscillations provides a cue of when something happened. The item most likely to be retrieved as the first item is the one that is most similar (relatively) to the cue (see the modelling section for more details).

Retrieval takes some time; for example, it might take, on average, 1.5 s to retrieve an answer and make a response. This means that the temporal values need to be updated before calculating the probability of retrieving the second item. In this example, each value would be increased by 1.5 s, and then log-transformed again. Ideally, one would know the output order and the time when each item was output, and then would use this information to model the data (see Bireta et al., 2010, for an example). When output time is unknown, plausible assumptions about the mean output time yield reasonable fits (Brown et al., 2007).

The primary difference between serial recall and free recall in SIMPLE is the order in which the items are retrieved and the way in which retrieved items are scored (Brown et al., 2008). For free recall scoring, anytime an item from the list is retrieved, regardless of the position, it is scored as

 

 

correct.

As viewed by SIMPLE, operation span is simply a set of immediate serial recall tests of lists of varying length. Thus, it predicts that when you score operation span as if it were a test of immediate serial recall, you will observe the characteristic serial position function with primacy and recency effects. The model predicts not only the probability of recalling Item 1 in Position 1, but also the probability of errors, that is, recalling Item 1 in other positions. Neath et al. (2014) showed that SIMPLE accurately predicts recall in the operation span task. Similarly, SIMPLE views Brown– Peterson as a list of three items followed by immediate serial recall. When scored this way, the data should show the same general patterns as the three-item lists from operation span (see Quinlan, Neath, & Surprenant, 2015). SIMPLE has been applied to a number of Brown–Peterson results (e.g., Brown et al., 2007; Neath & Brown, 2012), but has not yet been applied when the three letters are considered as individual items in a serial recall task. The continual distractor task is simply a free-recall task in which the items are spaced out along the dimension by the distracting activity. Neath and Brown (2007) have shown how SIMPLE qualitatively accounts for a number of dissociations in the continual distractor task, but did not fit SIMPLE to data.

Experiment

Method Purpose

As noted earlier, there exist no data on whether Brown–Peterson correlates with either operation span or the continual distractor task, and only one study that has examined the correlation between operation span and continual distractor (Unsworth & Spillers, 2010b). An explanation of each task in terms of relative distinctiveness predicts that all three tasks should correlate. One purpose of the experiment, then, was to assess this prediction by examining the full matrix of correlations. A second purpose was to produce data from the same set of subjects for SIMPLE to fit. Two other tasks, Thurstone’s number series and Raven’s progressive matrices, were also included. These were chosen to serve both to break up the memory tasks and also as a manipulation check: Unsworth and Spillers (2010b) included these tasks, which should correlate with each other, and which should also correlate with operation span.

Subjects

One hundred ninety volunteers from the Memorial University of Newfoundland, the College of New Jersey, and the Univeristé de Moncton participated in exchange for either course credit or

 

 

payment. The mean age was 20.35 (SD = 4.48, range = 17–50, Mdn = 19), with one subject not answering that question. One hundred forty-nine identified themselves as female and 41 identified themselves as male. Each subject was tested individually in either one or two sessions, and identified themselves as either native speakers of English or French. Data from an additional 22 subjects were excluded because of failure to complete one or more of the five tasks. The sample size was based on Unsworth and Spillers (2010b).

Materials and procedure

After reading and completing an informed consent form, each subject completed five tasks in the same order: continual distractor, Thurstone number series, operation span, Raven’s progressive matrices, and Brown–Peterson. Students at the UniversitĂ© de Moncton completed French versions of the first, third, and last tasks, which were otherwise equivalent to the English versions.

Continual distractor

This task was based on Watkins, Neath, and Sechler (1989). Twelve-item lists of two-syllable words were presented for 1 s each, with a nominal 12.5 s interval after every item, including the final item. During this distractor interval, three sets of three digits were presented and the subjects considered each set as a number (e.g., “8, 4, 7” as “eight hundred forty-seven”), subtracted 7, and entered the answer on the computer screen. The variability in duration was due to how quickly the subject entered the answer. Each digit lasted 0.5 s, and there was a 2-s pause after every third digit. The digits were presented via headphones. The English words were spoken by the “Tom” voice on MacOS 10.10 and the French words were spoken by the “Thomas” voice. There were 10 trials. The test for the words was written free recall, and the score for the correlational analysis is the proportion of items recalled. Due to a programming error, responses to the distractor task were not recorded accurately, and therefore a measure of performance on this task could not be computed.

Thurstone number series

The items were taken from Form A of Thurstone and Thurstone (1968). A set of seven numbers (e.g., 2, 4, 6, 8, 10, 12, 14) was presented, and the subject was asked to select which of five possible answers (e.g., 12, 14, 16, 18, 20) best completed the series. The possible answers appeared on five buttons on the computer screen, and a response was made by clicking on the desired button. The subjects were given 4.5 min to complete as many items as they could. There are two measures: the number of questions answered (maximum = 36) and the number of

 

 

answers that were correct.

Operation span

The task was based on Conway and Engle (1996; see also Unsworth, Heitz, Schrock, & Engle, 2005) and the English language version was identical to that used by Neath et al. (2014). The French language version substituted French words. Subjects were informed that we were interested in how accurately they could remember the order in which a series of words had been presented whilst solving simple math problems. First, a math question was shown (e.g., “Is [10/2] + 4 = 9?”) and subjects were asked to read it out loud (e.g., “Is 10 divided by two plus four equal to nine?”). They then clicked on a button (yes or no) to answer the question. A word then appeared for 2 s and the subjects were instructed to read the word aloud. Math problems and words alternated until the desired number of words (two, three, four, five, or six) had been presented. Then, response buttons became active and were labelled with the words in alphabetical order. The subjects were asked to indicate the presentation order of the words by clicking on appropriately labelled buttons on the screen using the mouse. There were three practice trials (not scored) with list length of two, and these were followed by 15 scored trials, three lists at each length from two to six. The order of list lengths was randomly determined for each subject. There are three measures. OSPAN is the sum of all correctly recalled stimuli from lists in which all items were correctly placed in order (maximum = 60). The words were also scored according to standard serial recall criteria, for example, if a word were placed in the correct position, it was counted as correct regardless of whether the other items in the list were correct. The third measure was the proportion of math questions answered correctly.

Raven’s standard progressive matrices

The items were taken from Sets C, D, and E of Raven (1956). The “question” was a 3 × 3 matrix with all but the bottom right cell filled with abstract images. The subject was asked to select which of eight images best completed the series. The eight alternatives were displayed on buttons on the computer screen and the subject clicked on the desired button to make a response. The subjects were given 10 min to complete as many items as they could. There are two measures: The number of questions answered (maximum = 36) and the number of answers that were correct.

Brown–Peterson

The task is based on the version of the Brown–Peterson procedure used by Quinlan et al. (2015). On each trial, three consonants were randomly selected and were presented simultaneously for 1

 

 

s. Then, a three-digit number between 200 and 999 (inclusive) was randomly selected to be the start number. The subjects were asked to count backward by threes out loud at a rate of one answer every 1.5 s. The pace was indicated by a circle displayed on the computer screen that alternated colours once every 1.5 s. The duration of the distractor task was either 3, 6, or 12 s. Following the distractor task, the subjects were asked to recall either the consonant trigram or the final number they had said out loud. For both tests, the subject used a mouse to click on appropriately labelled buttons. For letter recall, 21 letters (vowels were excluded) were shown on 21 buttons in alphabetical order. As in the original Peterson and Peterson (1959) study, the consonant trigram was to be recalled exactly (i.e., the first letter reported first, the second letter reported second, and the final letter reported last) by clicking on the appropriately labelled button in the correct order. For indicating the number, 10 digits were shown on 10 buttons in numerical order. Feedback was given after a response for both tasks: For the letter recall, the subject was informed only that the response was correct or not, but for the counting backward task, the correct answer was provided if an incorrect number had been reported. The next trial began when the subject clicked on a button; thus, the experiment was self-paced. There are four measures. Trigram scoring required all three letters to be recalled in the correct order. Serial recall scoring looked at each of the three letters individually: If a letter were placed in the correct position, it was counted as correct regardless of whether the other items were correct. Free recall scoring looked how many of the three letters were recalled, regardless of the position. The fourth measure is accuracy on the distractor task.

Results

We first report the correlational analysis and then report additional analyses for each task.

Correlation Analysis Descriptive information is shown in Table 1. Only one measure, math accuracy on the OSPAN task, had skewness and kurtosis greater than generally accepted levels (Kline, 1998). This was due, in part, to having only 10 of the 190 scores less than 0.85.

 

 

Descriptive Statistics for the Measures Used in the Correlational Analysis

The primary empirical question concerned the prediction of SIMPLE that all three tasks should correlate. Figure 1 shows the scatter plots and Table 2 shows the correlations among the various measures. As can be seen, the three memory tasks all correlated significantly with one another. The correlation between OSPAN and Brown–Peterson (trigram) was r(188) = 0.310, p < .001; the correlation between OSPAN and continual distractor was r(188) = 0.305, p < .001; and the correlation between Brown–Peterson (trigram) and continual distractor was r(188) = 0.235, p < .01. These correlations are comparable to those previously reported in the literature; for example, Unsworth and Spillers (2010b) reported a correlation of r(179) = 0.29 between OSPAN and continual distractor.

 

 

Figure 1. Top row: Scatter plots showing the relation between the three memory tasks when using the traditional scoring for Brown–Peterson and operation span. Bottom row: Scatter plots of the

same tasks but using nontraditional scoring.

Correlations Among the Measures

 

 

Given that we had a measure of reliability for each score, we also computed correlations corrected for attenuation (see Nunnally & Bernstein, 1994). The corrected correlations were 0.420 between OSPAN and Brown–Peterson (trigram), 0.382 for between OSPAN and continual distractor, and 0.273 between Brown–Peterson (trigram) and continual distractor.

Although scoring method did affect the absolute magnitude of the correlation, no correlations among the three main tasks significantly differed as a function of scoring method. For example, the most notable difference was that the correlation between Brown–Peterson and continual distractor which increased from 0.235 for trigram scoring to 0.315 when the Brown–Peterson task was scored as free recall, but this difference was not significant, z = 0.84, p > .40.

For our manipulation check, the number of correct answers on Raven’s and Thurstone were significantly correlated, r(188) = 0.498, p < .001, and both correlated with OSPAN, r(188) = 0.262 and r(188) = 0.335, both ps < 0.001, respectively. This pattern also replicates the results of Unsworth and Spillers (2010b). We now examine performance on each task in more detail.

Operation Span Analysis The mean OSPAN was 32.69 (SD = 11.73, range = 5–60), and accuracy on the math task was 94.90% correct (SD = 0.073, range 0.5–1.0). These values are comparable to previous reports using the computerized version of operation span (e.g., Neath et al., 2014; Unsworth et al., 2005).

Performance was also scored using standard strict serial recall scoring. Figure 2 shows the proportion of times each item was recalled in each position as a function of list length (the data points). For example, with a list length of four, the first item was recalled in the first position 81.4% of the time, in the second position 11.9% of the time, in the third position 6.0% of the time, and in the fourth position 0.7% of the time. These position error gradients are indistinguishable from those seen previously in operation span data (Neath et al., 2014; Unsworth & Engle, 2006) as well as those seen in both short-term (e.g., Healy, 1974) and long-term (e.g., Nairne, 1991) serial recall and reconstruction of order tasks.

 

 

Figure 2. The proportion of times each item was recalled in each position as a function of list length in the operation span task. Closed circles show the data, and the lines show the fit of scale-

invariant memory and perceptual learning (see text for details).

The proportion of words correctly recalled in order at each list length systematically decreased from 0.993 to 0.918, 0.829, 0.680, and 0.579 for list lengths two to six, respectively, F(4, 189) = 272.63, MSE = 0.069, ω = 0.588, p < .001. At the same time, the absolute number of words correctly recalled in order at each list length systematically increased from 1.99, to 2.75, to 3.31, to 3.40, and finally to 3.47 for list lengths two to six, respectively, F(4, 189) = 150.15, MSE = 1.473, ω = 0.311, p < .001. This replicates the results of Beaman (2006), but extends them to operation span data.

Brown–Peterson Analysis The overall accuracy on the math task was 55.46% (SD = 0.213, range = 0–1). This is slightly higher than the accuracy reported by Quinlan et al. (2015). As in that study, two different analyses

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2

 

 

were performed. First, the recall data were scored based on trigram recall: All three letters needed to be correctly recalled in order. As the duration of the distractor task increased, recall decreased. A one-way repeated measures analysis of variance revealed a significant effect of delay, F(2, 378) = 78.896, MSE = 0.030, ω = 0.290, p < 0.001, replicating Quinlan et al. (2015).

Second, the data were scored as if it were a standard serial recall experiment. The proportion of letters correctly recalled in order was analysed with a 3 (Levels of Delay: 3 s, 6 s, 12 s) × 3 (Serial Position) repeated-measures analysis of variances. There was a main effect of delay, F(2, 376) = 103.597, MSE = 0.067, ω = 0.351, p < .001. There was also a main effect of position, F(2, 752) = 25.649, MSE = 0.017, ω = 0.115, p < 0.001. The interaction was not significant, F(4, 752) = 1.206, MSE = 0.014, ω = 0.001, p > .30. This is the same pattern observed by Quinlan et al. (2015).

Figure 3 shows the proportion of times each item was recalled in each position as a function of distractor duration. The top row is the 3-s condition, the middle row is the 6-s condition, and the bottom row is the 12-s condition. As in the data from the operation span task, the position error gradients are indistinguishable from those seen in other paradigms, such as immediate and delayed serial recall and serial reconstruction of order tests (Healy, 1974; Nairne, 1991).

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2

2

2

 

 

Figure 3. The proportion of times each item was recalled in each position as a function of distractor duration in the Brown–Peterson task. The top row is the 3-s condition, the middle row is the 6-s condition, and the bottom row is the 12-s condition. Closed circles show the data, and the lines

show the fit of scale-invariant memory and perceptual learning (see text for details).

Continual Distractor A one-way analysis of variance revealed a significant effect of position, F(11, 2079) = 45.234, MSE = 0.023, ω = 0.189, p < .001. There is no commonly accepted measure that indicates whether primacy and recency effects are present. One way is to compare recall of the first item to later items in the list, and to compare recall of the final item to earlier items in the list (see, e.g., Bireta, Gabel, Lamkin, Neath, & Surprenant, 2018). Tukey’s tests with α = .05 indicated the first item was

2

 

 

recalled significantly more accurately than every other item except for Position 2. They also indicated that the last item was recalled significantly more accurately than the item at Position 11, as well as being more accurately recalled than Items 4–10. There was no difference in the level of recall between the final item and Items 2 and 3.

Unlike the data from the operation span and Brown–Peterson task, the data from the continual distractor task differ from what is usually observed. In typical free-recall tasks with short lists, people tend to recall the lists in order regardless of the free recall instructions; as the list gets longer, people tend to switch to recalling the last few items first (Spurgeon et al., 2014; Tan et al., 2016). This leads to the common finding of more pronounced recency than primacy in immediate free recall of longer lists (Murdock, 1962) as well as with continual distractor lists (Watkins et al., 1989). As can be seen in the right panel of Figure 4, the data show more primacy than recency.

Figure 4. Top row: The continual distractor data when scored using serial recall criteria (left panel), and the mean output position for each of the 12 items (middle panel), and the data (closed circles) when scored using free recall and the fit of scale-invariant memory and perceptual learning (line;

right panel).

Table 3 shows the number of times each word was output first, second, third, and so on. The item most likely to be recalled first was the first word (recalled first 732 times), the item most likely to be recalled second was the second word (544 times), the item most likely to be recalled third was the third word (431 times), and so on. However, the last item was the second most likely to be recalled first (334 times). It is therefore difficult to characterise the output order, but it differs from typical free recall output.

 

 

Number of Times Each Word in the Continual Distractor Task Was Output

The left panel of Figure 4 shows the data scored using strict serial recall scoring: to be counted as correct, the first item had to be written down first, the fourth item had to be written down fourth, and the twelfth item had to be written down twelfth. As can be seen, the first item was recalled first approximately 40% of the time according to this scoring method. Even more surprising, the last item was recalled twelfth almost 5% of the time. The middle panel shows the mean output position of each item. With strict serial recall instructions, you would expect a diagonal line showing mean output position increases with input position. With free recall, you would expect the last few items to be recalled first, then the first few items to be recalled next, and finally the middle items to be recalled last.

Examination of individual data suggest that output variability occurred within a given subject. That is, it was not the case that some subjects were doing serial recall and others were doing free recall; rather, a given subject sometimes initiated recall with the first few items but the same subject sometimes initiated recall with the last few items. We also examined whether subjects’ output order changed as a function of experience. However, the data from Lists 6–10 were indistinguishable from the data from Lists 1–5, with the exception that overall performance was very slightly higher.

Modelling SIMPLE (Brown et al., 2007; Neath & Brown, 2006) is a relative local distinctiveness model in which items are represented on one or more dimensions in psychological space. In many episodic tasks, the variables are so well-controlled that the primary dimension is relative time. The zero point is the time the item the retrieval attempt is made, and the temporal value for a given item is the time since presentation. For example, in a list of four items presented at a rate of one item per

 

 

second, the first item will have a temporal value of 4 s, the second will have a temporal value of 3 s, and so on. These values are log transformed and then the similarity of the log-transformed temporal values is calculated. When the temporal dimension is used, the cue is assumed to be the item’s original time of presentation (see Brown et al., 2007, 2008).

To fit serial recall data, the temporal values are updated for each item to include the effects of output time. For the four-item list, when Item 1 is retrieved, the initial temporal values are 4, 3, 2, and 1. If we assume it takes 1.5 s to select each answer, then when Item 2 is retrieved, the temporal values become 5.5, 4.5, 3.5, and 2.5. These are again updated by 1.5 s when Item 3 is retrieved.

The similarity, ηi,j, between two log-transformed temporal memory representations, Ti and Tj, can be calculated using Equation 1:

The main free parameter in SIMPLE is c. As c increases, a given difference between two values results in a lower similarity value. This implements the idea that higher values of c correspond to less influence of more distant items.

The probability of producing the response associated with item i, Ri, when given the cue for stimulus j, Cj, is given by Equation 2, in which n is the number of items in the set:

 

Operation span

In the operation span task, omissions are not possible, and thus the two equations and one free parameter described so far is everything needed to fit the data. The data were scored using standard serial recall scoring: an item that was placed in the correct position was scored as correct regardless of the other responses on the list. We used the same simulation as described by Neath et al. (2014):

We assumed that the to-be-remembered words were presented with a 5 s stimulus onset asynchrony (SOA), made up of 2 s presentation of the to-be-remembered word followed by 3 s to read and answer the math problem. We further assumed that each item took 1.5 s to recall. These values ignore the

 

 

individual variation that did occur (e.g., some math problems are easier than others), but the values are plausible. Thus, the main temporal dimension at the time that recall of the first item of the 6-item list was attempted had the following values: 27, 22, 17, 12, 7, and 2. When recall of the second item was attempted, these values had become 28.5, 23.5, 18.5, 13.5, 8.5, and 3.5, respectively. (p. 208) With c = 4.15, the model fits the data quite well, as can be seen in Figure 2, where the closed circles are the data and the lines are the output of the model. Each row shows the data and model fit for lists of a particular length, with the top row for list length of two and the bottom row for list length of six. Within a row, each panel shows observed and predicted performance for each item. The first panel shows the proportion of times the first word was recalled in the first position (a correct response), but also the proportion of times the first word was placed in the second position (an error), and so on. The second panel in each row shows the proportion of times the second word was recalled in the first position (an error), the proportion of times the second word was placed in the second position (a correct response), and so on.

SIMPLE is capturing all of the major characteristics of the data, not only the proportion correct but the distribution of errors as well. For list lengths of two through six, respectively, R was 0.999, 0.997, 0.992, 0.961, and 0.890. Note that the value of c was the same for all list lengths; that is, all 90 data points are being accounted for by a single free parameter. The fits are almost identical to those reported by Neath et al. (2014), who reported R for list lengths of two through six of 0.999, 0.997, 0.990, 0.969, and 0.912, respectively. The value of c was also comparable, 4.15 here compared to 4.358 there.

From SIMPLE’s perspective, the math questions serve to spread the list items out in time. Because this time is roughly equivalent for each list, the major determinant of overall performance is the number of items per list. As the length increases, the relative distinctiveness of each item begins to decrease, and therefore the proportion of errors begins to increase.

Brown–Peterson

SIMPLE has previously been fit to a variety of results in the Brown–Peterson paradigm (see Brown et al., 2007). However, these treated each consonant trigram as a single item. For the current fits, we treated each consonant as an individual item. To model the Brown–Peterson task, two additional parameters are needed. In a strict serial reconstruction of order task, such as the one used in the operation span task, the subject is prevented from making omission, repetition, or intrusion errors. In other tasks, such as strict written serial recall or free recall, all of those errors are possible. To reflect this, SIMPLE uses a function which has the effect of increasing recall probabilities that are already high, and decreasing recall probabilities that are already low. This is implemented by Equation 3, in which the probability of output of one of the items on the list, Po, is

2

2

 

 

calculated based on P from Equation 2.

 

The parameter t is the threshold, and varies from 0.0 to 1.0, and the parameter s is the slope of the function. The equation can be thought of as implementing a transformation such that if t = 0.50, and s is very large, all items with p > .5 in Equation 2 will be output, whereas all items with p < .5 will be omitted. As s decreases, this transition from output to omission becomes more gradual. This allows for omissions. One weakness in this account is that SIMPLE is not a process model; rather, it produces a probability matrix, and so repetitions cannot be predicted. SIMPLE can predict intrusions, but to do so, a more complex version of the model is required in which items from prior lists are also represented, but this introduces other complexities; for details, see the appropriate simulations in Brown et al. (2007). For the purpose of this simulation, we avoided these complexities to illustrate the similarities among the three tasks.

One final difficulty in modelling the Brown–Peterson task is that the three letters are traditionally presented simultaneously, as they were in our experiment. We make the assumption that despite the simultaneous presentation, the letters were none the less read sequentially and therefore still differed in terms of time of presentation. We therefore once again represented the items as 3, 2, 1 for the initial temporal values. There were three distractor durations, 3 s, 6 s, and 12 s. To implement this, the initial values were incremented by the distractor duration; for example, a list in the 6-s condition became 9, 8, 7. Each item was again assumed to take 1.5 s to output, as in the operation span simulation. Thus, when the second letter was being retrieved, the values were incremented to 10.5, 9.5, and 8.5.

For modelling purposes, the Brown–Peterson data were scored with serial scoring, just like the operation span data, and the results can be seen in Figure 3, with the closed circles again showing the data. With c = 26.71, s = 3.79, and t = 0.84, the model produced a good fit to the data, R = 0.981. Although there are now three parameters, the same values are used for all three distractor conditions and to fit all 27 data points. The difference in output of the model between the three conditions is entirely due to the change in temporal values depending on whether distractor task lasted 3 s, 6 s, or 12 s.

SIMPLE views the Brown–Peterson task as fundamentally the same as the operation span task, the only difference being that the items are not separated by distractor activity. Performance decreases with increasing distractor duration because the three items are pushed further back

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along the time dimension, making them relatively less distinct. This experiment was not designed to look at how SIMPLE accounts for the build-up of proactive interference; one reason is that on a random half of the trials, the subject was asked to produce the result of the distractor task rather than recall the three letters. However, Brown et al. (2007) include simulations showing how intrusions from prior lists cause the build-up of proactive interference and how separating the lists by longer intervals reduces the amount of interference, as is observed in experiments (Loess & Waugh, 1967) and also how more interference occurs for longer list lengths (Neath & Brown, 2012).

Continual distractor

Previously, SIMPLE has been used to produce qualitative fits of continual distractor data. For example, Neath and Brown (2006) showed how SIMPLE predicts, in general, the dissociation between immediate free recall and continual distractor recall when directed output order changes. With the former, recency is present when subjects are asked to begin recall with the last item first, but recency is absent when subjects are asked to recall the first item first (Dalezman, 1976). With the latter, there are no significant differences as a function of directed output order (Whitten, 1978). To simulate these results, however, we used the same list length and timing in each simulation to highlight that it was simply the relative timing that caused the dissociation within the model. For the current simulation, we are interested in fitting the observed serial position function.

For both the operation span and Brown–Peterson data, the serial recall version of SIMPLE was used because the instructions were to recall the order of the items. We had intended to use the free recall version of SIMPLE to fit the continual distractor data because the instructions were for free recall. However, as discussed previously, the data observed in the continual distractor task differ from the usual pattern in that there is less recency and more primacy, and that the first item, rather than the last item, was more likely to be the first item recalled. Given the difficulty in characterising the output order, it is therefore difficult to identify a version of SIMPLE to apply to the data.

One weakness of SIMPLE’s account, which is shared by other accounts of continual distractor performance, is that it does not predict when a particular output strategy will be used. Rather, it takes a particular output strategy and then produces fits based on that. A second weakness with SIMPLE’s account, as noted earlier, is that it is not a process model. In principle, with a process version of SIMPLE, one could run simulations in which various output orders occurred such that over all the simulations, the mean output positions for each item matched those observed in the data. The test would then be to see if this version produced a reasonable fit to the data. Absent a

 

 

process version, the development of which is beyond the scope of this article, we fit a version that required the fewest assumptions.

Any version of SIMPLE that uses a temporal dimension requires information about output order and the timing of all events. However, the version that uses serial position does not require those assumptions. As noted earlier, Surprenant et al. (2006) found that when the presentation of the items is regularly spaced, there was little difference in the fit of the positional versus the temporal version of the model. The continual distractor task was regularly spaced, in that the task following each item remained the same. Each item was represented by its ordinal position number, which was then log transformed. The rest of the model remained the same as described previously, except free recall rather than serial recall scoring was used. With free recall, anytime the item is produced in response to a cue is counted as correct, regardless of the position. Pi,j in Equation 4 represents the probability of outputting each item, as calculated in Equation 3. The probability of free recalling an item is given by the following (see Lee & Pooley, 2013):

With c = 3.59, s = 4.66, and t = 0.64, the fit accounts for all items except for the last one or two, as can be seen in the rightmost panel of Figure 4. The reason for missing the recency items in particular is that the last item was frequently recalled quite early; the position dimension does not capture this and therefore does not reflect the boost to performance early output provides.

General Discussion

Surprenant and Neath (2009) argued that general principles of memory do exist and do apply widely. One of the principles they identified, the relative distinctiveness principle, states that items will be remembered to the extent that they differ from close neighbors, and has been instantiated within the model SIMPLE. This model follows in the tradition of the hedgehog, proposing a general explanation for a very wide range of phenomena. In particular, because it accounts for performance in the Brown–Peterson, operation span, and continual distractor tasks in the same way, it predicts that performance in each task should correlate with each other. These tasks have variously been ascribed to short-term, working, and long-term memory respectively. Previous work by Unsworth and Spillers (2010b) had found a correlation between operation span and continual distractor, but it was not known if performance on the Brown–Peterson task would also correlate with the other two tasks. The experiment we report confirmed this prediction: Performance on all three tasks correlate, and the correlations remain significant regardless of the particular method of scoring each task.

 

 

We then fit SIMPLE to each task. The fit to operation span and Brown–Peterson included not only the proportion correct but also the error gradients: when an item was not recalled in the correct position, it was most often recalled in an adjacent position. The explanation for both tasks is the same: the distractor task serves to space items out in time, and recall depends on the relative distinctiveness of the item at the time of recall. SIMPLE had some difficulty fitting the continual distractor data because of the atypical output order. The subjects did not follow the typical strategy of recalling the last few items first, and then recalling the first few items second, but instead they tended to initiate recall with the first item, showing something that is a mix of serial recall and free recall output order. SIMPLE uses output order to determine proportion correct, and so it was not clear which version of the model, free or serial recall, to use. We ultimately used position rather than time as the primary underlying dimension because this required fewer assumptions, and obtained a reasonable fit for all but the last one or two items.

There are three points to make about the atypical continual distractor data. First, although we have described our results as “atypical,” it is not entirely clear how typical or atypical they really are. Many experiments that report continual distractor data do not analyse output order. In addition, we know that as list length increases, people generally switch from reporting the first few items first with short lists to reporting the last few items first (Spurgeon et al., 2014; Tan et al., 2016). Rather than being atypical, it may be that our results reflect a later switch in strategies on the part of a large subset of our subjects.

Second, there is the issue of how to treat the correlations involving continual distractor given the atypical output order. We do not think this is a significant issue. Unsworth and Spillers (2010a) had previously shown a correlation between continual distractor and operation span, and our data closely replicate theirs. This replication, then, inspires confidence that the new correlation with Brown–Peterson will similarly be replicable, although of course this is ultimately an empirical question.

Third, there is the issue of how to evaluate the extent to which SIMPLE fits continual distractor data. As noted previously, one common weakness of models of the continual distractor task, including SIMPLE, is that they do not predict output order. Clearly, more theoretical development is required. The work of Ward and colleagues (e.g., Spurgeon et al., 2014; Tan et al., 2016) is providing very useful data in this regard, and the challenge for future models is to incorporate these findings.

Despite the many differences among the tasks, what they have in common is the requirement to remember something in the presence of distracting activity. A further prediction, then, is that

 

 

performance on Brown–Peterson or on continual distractor will predict working memory capacity. We do not, of course, actually recommend using continual distractor rather than OSPAN; one reason is that it takes far longer to collect the data. However, we do think that researchers should keep these results in mind when accounting for working memory capacity. Fundamentally, recall in the continual distractor task has to be from what multiple-systems theorists would term long-term memory, due both to the temporal delay as well as to the large number of items.

In the introduction, we critiqued a number of models primarily on the basis that they were too foxlike: They focused on one particular task and therefore did not make predictions about performance in the other two tasks. In one sense, this criticism is unfair: It could be argued that the only reason that SIMPLE makes these predictions is because it is too hedgehog-like and the ability to make cross-task predictions comes at the expense of making specific, detailed predictions about each task.

Rather than arguing that hedgehog-like models are better than foxlike models—or arguing the reverse—we instead argue that the field as a whole benefits from having both types of models, with each approach having its advantages and disadvantages. In general, foxlike models will have the advantage of depth, in that they are likely to account for more aspects of a specific task, whereas hedgehog-like models will have the advantage of breadth, in that they are likely to account for more different tasks. One notable benefit, in our view, comes from “competition” between the two types of models. As an example of this, consider the following. Davelaar et al. (2005) presented a detailed model of continual distractor performance and noted a number of dissociations between immediate free recall and continual distractor recall that could not be accounted for by single-system models. This fox-like model was, at the time, the most complete account of continual distractor data. This model motivated Neath and Brown (2006) to investigate these dissociations using SIMPLE, and found that SIMPLE could in fact produce these apparent dissociations. In our view, SIMPLE then surpassed the Davelaar et al. model, in that it predicted that serial position functions would be observed in implicit memory, which was recently confirmed (Bireta et al., 2018), and also predicted the multiple demonstrations of serial position functions in semantic memory, many of which have been fit by SIMPLE (e.g., Kelley, Neath, & Surprenant, 2015; Neath, Kelley, & Surprenant, 2016). The challenge now for foxlike models of serial position functions is to address these new findings.

The point we wish to make here is that development of one type of model can spur improvements in the other type of model and this interplay benefits both types of models. Ultimately, a successful model of memory needs to do both: offer an in-depth account of a wide range of phenomena. Until then, which type of model is “better” depends on the specific criteria. Foxlike models are (currently)

 

 

“better” for in-depth accounting of relatively limited scope whereas hedgehog-like models are (currently) “better” for accounting for multiple tasks and paradigms.

Footnotes Web-based implementations of SIMPLE for all three fits, including source code, are available at

https://memory.psych.mun.ca/models/simple/js/correl/.

Because there is only a single parameter, the fit was determined by changing that one parameter.

The fit was obtained using MATLAB’s unconstrained nonlinear minimization function.

Given this statement, the reader may be wondering about the extent to which the positional version of SIMPLE fits the data from operation span and Brown–Peterson. The positional version, also available at https://memory.psych.mun.ca/models/simple/js/correl, produces roughly equivalent fits for operation span, although there are differences especially for middle-length lists. The reason is that operation span uses regularly spaced items where time and position are confounded, just like in continual distractor. The positional version cannot fit the Brown–Peterson data, as there is no mechanism to reflect the different durations of the distractor interval.

The fit was obtained using MATLAB’s unconstrained nonlinear minimization function.

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Submitted: June 20, 2018 Accepted: August 27, 2018

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Source: Canadian Journal of Experimental Psychology. Vol. 73. (2), Jun, 2019 pp. 79-93) Accession Number: 2018-64417-001 Digital Object Identifier: 10.1037/cep0000157

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