Some memories are odder than others: Judgments of episodic oddity violate known decision rules

Journal of Memory and Language 64 (2011) 299–315

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Journal of Memory and Language

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Some memories are odder than others: Judgments of episodic oddityviolate known decision rules

Akira R. O’Connor a,⇑, Emily N. Guhl b, Justin C. Cox c, Ian G. Dobbins c

a University of St. Andrews, United Kingdomb University of Chicago, United Statesc Washington University in St. Louis, United States

a r t i c l e i n f o a b s t r a c t

Article history:Received 16 November 2010revision received 20 January 2011Available online 2 March 2011

Keywords:Episodic memoryRecognitionCognitive models

0749-596X/$ - see front matter � 2011 Elsevier Incdoi:10.1016/j.jml.2011.02.001

⇑ Corresponding author. Address: School of PsycSt. Andrews, St. Mary’s College, South Street, St. AnScotland, United Kingdom. Fax: +44 (0) 1334 46 30

E-mail address: [email protected] (A.R

Current decision models of recognition memory are based almost entirely on one para-digm, single item old/new judgments accompanied by confidence ratings. This task resultsin receiver operating characteristics (ROCs) that are well fit by both signal-detection anddual-process models. Here we examine an entirely new recognition task, the judgmentof episodic oddity, whereby participants select the mnemonically odd members of triplets(e.g., a new item hidden among two studied items). Using the only two known signal-detection rules of oddity judgment derived from the sensory perception literature, theunequal variance signal-detection model predicted that an old item among two new itemswould be easier to discover than a new item among two old items. In contrast, four sepa-rate empirical studies demonstrated the reverse pattern: triplets with two old items werethe easiest to resolve. This finding was anticipated by the dual-process approach as thepresence of two old items affords the greatest opportunity for recollection. Furthermore,a bootstrap-fed Monte Carlo procedure using two independent datasets demonstrated thatthe dual-process parameters typically observed during single item recognition correctlypredict the current oddity findings, whereas unequal variance signal-detection parametersdo not. Episodic oddity judgments represent a case where dual- and single-process predic-tions qualitatively diverge and the findings demonstrate that novelty is ‘‘odder’’ thanfamiliarity.

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Introduction

The number and nature of processes contributing toepisodic recognition memory and confidence remainsheavily debated in both behavioral and neuroscience liter-atures (e.g., Diana, Reder, Arndt, & Park, 2006; Donaldson,1996; Dunn, 2004; Vilberg & Rugg, 2008; Wais, 2008; Wix-ted & Stretch, 2004). Given this, it is somewhat surprisingthat for the most part, research has focused on a singletask, namely, the judgment of items presented in isolation

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hology, University ofdrews, Fife KY16 9JP,42.. O’Connor).

as either studied or novel, usually supplemented with rat-ings of confidence (e.g., Bayley, Wixted, Hopkins, & Squire,2008; Jang, Wixted, & Huber, 2009; Khoe, Kroll, Yonelinas,Dobbins, & Knight, 2000). As an illustration of this heavytask reliance, we conducted an informal search of priorwork published in the Journal of Memory and Languageusing the key word ‘‘recognition memory’’. The search re-turned 109 articles, 66 of which were actually focused onepisodic recognition. Of these, 58 (88%) employed the sin-gle item old/new paradigm. As we argue below, this heavyreliance on this one task has potential drawbacks. Beforedoing so however, we first briefly describe the two domi-nant decision models of recognition memory.

One of the most successful decision models of singleitem recognition is the unequal variance signal-detection

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300 A.R. O’Connor et al. / Journal of Memory and Language 64 (2011) 299–315

model – a unidimensional model which provides astraightforward decision rule (see Fig. 1 panel a. for agraphical representation of the unequal variance model).During single item recognition, observers are assumed toevaluate a continuous strength of evidence (or ‘familiarity’)variable evoked by each item relative to an internal old-new criterion: if signal strength exceeds the old/new crite-rion, the item is judged old; if it falls below the criterion,the item is judged new. The distribution of evidence valuesacross the test is characterized by two normal distribu-tions, one for old items and one for new items, separatedby a distance, d0, that corresponds to the observer’s sensi-tivity to the category distinction. Considerable research

Fig. 1. (Panel a) The unidimensional signal-detection model with old item distrfavor of an item being old increases the further an item is positioned to the rightoddity trials. The triangular rule is the optimal signal-detection decision ruleobservation decision rule applied to old and new item isolate trials. The indepenoddity task when no rove is in place.

examining the cumulative relationship between the confi-dence and accuracy of reports (viz., the receiver operatingcharacteristic, ROC) indicates that in order for the normaldistribution model to hold, the variance of old item evi-dence must be assumed greater than that of the new itemevidence (Egan, 1975; Heathcote, 2003; Ratcliff, Sheu, &Gronlund, 1992).

In contrast to the unidimensional signal-detection ap-proach to recognition judgments, dual-process models as-sume that studied materials are capable of evoking botha relatively continuous sense of prior occurrence (i.e. famil-iarity) and recollections of specific contextual details asso-ciated with the prior encounter of the memory probe (i.e.

ibution variance greater than new item distribution variance. Evidence in. (Panel b) The triangular decision rule applied to old and new item isolatefor the oddity task when a rove is in place. (Panel c) The independent-dent-observation rule is the optimal signal-detection decision rule for the

Fig. 3. Simulated proportion of responses correct using the independent-observation decision rule. In all simulations, d0 and criterion location(represented on x-axis as deviation from lopt calculated using Eq. (4)) arevaried but old item distribution variance is kept constant at 1.25 (newitem distribution variance is 1). As the criterion shifts from lopt, overallperformance declines.

A.R. O’Connor et al. / Journal of Memory and Language 64 (2011) 299–315 301

episodic recollection). The specifics of the models vary, butall assume that it is inappropriate to characterize recogni-tion evidence as solely unidimensional (e.g., Atkinson &Juola, 1973; Hintzman & Curran, 1994; Jacoby, 1991; Man-dler, 1980; Yonelinas, 1994). Furthermore, most dual-pro-cess models assume that in comparison to familiarity,recollection affords greater behavioral control, leads tomore confident endorsement, and requires deliberate re-trieval attempt (Atkinson & Juola, 1973; Jacoby, 1991;Mandler, 1980).

Compared to the dual-process model, the unequal vari-ance signal-detection model appears to have a slight butreliable advantage in fitting confidence-based ROCs duringsingle item recognition (Heathcote, 2003; Jang et al., 2009;Smith & Duncan, 2004; Yonelinas, Dobbins, Szymanski,Dhaliwal, & King, 1996). However, the small magnitudeof this advantage is arguably underappreciated. For exam-ple, Fig. 2 shows the aggregate ROC from 26 participants ina single item recognition task fit by both the dual-processmodel of Yonelinas (1994) and the unequal variance sig-nal-detection model (see General Discussion for details ofthe procedure). The ROC is formed by taking the most con-fident ‘‘old’’ response proportions to old and new items asthe initial point on the function. By convention the y-axisspecifies the response rates to old items and the x-axis tonew items. Following this, the next most confident ‘‘old’’response rates are added to the initial response rates,forming the second point on the ROC. This cumulative pro-cess is repeated until the data are exhausted and results ina function linking cumulative accuracy to confidence (Mac-millan & Creelman, 2005).

For the aggregate ROC in Fig. 2, both models fit the dataextremely well, accounting for more than 99% of the vari-ance. When applied to individuals, there is a slight advan-tage for the unequal variance signal-detection model(99.90% versus 99.86% variance accounted for) although

Fig. 2. Aggregate ROC fits from 26 participants in a single item recogni-tion task.

it is not reliable in this data set (15 of 26 subjects;Z = .59, p > .55, sign test). The recognition confidence ROCis typically convex and asymmetrical about the negativediagonal. As noted above, the unequal variance model ac-counts for this asymmetry by assuming that the old itemevidence is more variable than the new (Fig. 1 panel a).In contrast, the dual-process model assumes that the mostconfident hit rates reflect a mix of recollection and famil-iarity, with all other responses reflecting the contributionof an equal variance signal-detection familiarity process.Critically, because the single item recognition ROC has aform that is often easily accommodated by both modelsit is important to look for other tasks in which the twomodels may make more divergent predictions. Further-more, examining other decision tasks may help elucidatewhich model more naturally generalizes across tasks andprovides a more general understanding of how observersactually decide about their own recognition evidence invarious situations. The task we consider here is one thatis historically used in perception research, often in caseswhere the basis of the perceptual distinction subjects areasked to make would be difficult to verbalize, rendering asingle item procedure less than ideal (e.g., Brandt & Arnold,1977; Helm & Trolle, 1946). Indeed, the ease with whichsubjects appear to be able grasp this task’s requirementsis perhaps best illustrated by its frequent use on children’seducational programs such as Sesame Street, where amus-ingly it even has its own song: ‘‘One of these things is notlike the others.’’

Judgments of oddity

The oddity task requires that the observer identify the‘odd-man-out’ of a triplet. As noted above, this is ajudgment task that is often understandable even when


the exact basis for discrimination is quite difficult to artic-ulate (Amerine, Pangbourn, & Roessler, 1965; Frijters,Kooistra, & Vereijken, 1980; Macmillan & Creelman,2005; Peryam, 1958; Versfeld, Dai, & Green, 1996), Asan example, Macmillan and Creelman (2005) discuss thequestion of whether novices are able to discriminate be-tween Burgundy and Claret. For novices, one assumes thatthe verbal descriptions of the bouquets would not be par-ticularly helpful since they do not presumably have an ex-plicit characterization of ‘‘Burgundyness’’. However, theyare capable of attempting to judge which of three glassesof wine tastes different from the others and may be suc-cessful even if they cannot articulate the basis of the dif-ference they are using for the discrimination. Similarly,one could question whether observes can discriminate or-ganic from traditionally grown fruit, 80% dark chocolatefrom 85% dark chocolate, etcetera. Here we consider therelative oddness of recognition memories. Namely, weconsider how subjects identify either experienced noveltyor experienced familiarity as contextually odd. Interest-ingly, one of the most oft cited anecdotes in support ofdual-process models is linked to the detection of a mne-monically odd item. Specifically, Mandler (1980) describesa seemingly ubiquitous experience that suggests the po-tential need for dual retrieval processes. During the anec-dote an observer notices a face on a bus that strikes himas surprisingly familiar but is initially unable to specifi-cally note why the face seems so familiar. This is followedby a period of deliberate memory search wherein he orshe tries to resolve this ambiguous sense of familiarity,in this example, ultimately retrieving the appropriate con-textual detail indicating that the individual is in fact thebutcher from the supermarket. Critically, it is the familiar-ity of the passenger that is ‘‘odd’’ in the context of theother unfamiliar passengers, and it is the use of recollec-tion that successfully resolves the rapidly perceived famil-iarity oddness.

Returning to the use of the oddity task, within the con-text of basic recognition memory its use is straightforward.Subjects are presented with triplets in which the odd itemis either studied or new to the experiment. Critically, be-cause the query ‘‘Which is odd?’’ does not indicate whetherthe isolate is old or new, the observer cannot reduce thetask to a maximum or minimum evidence selection rule;sometimes the odd item will be studied whereas othertimes it will be novel.

Under the signal-detection model, there are currentlyonly two possible decision rules assumed for oddity: thetriangular rule (Ennis, Mullen, & Frijters, 1988; Frijters,1979; Peryam, 1958); and the independent-observationrule (Macmillan & Creelman, 2005; Versfeld et al., 1996).Which rule observers should select depends upon howthe triplets are constructed and whether observers aresensitive to the locations of the putative underlying evi-dence distributions. The triangular rule is simplest, and ismost appropriate for designs that use a ‘roving’ standard.During roving designs there are no stationary evidencedistributions across the trials. For example, an auditoryfrequency discrimination oddity task may use triplets frommany different portions of the frequency continuum,although on any given trial those items would have the

same hypothetical relative distance between the isolateand non-isolates. As noted by Versfeld et al. (1996), underthese conditions the triangular rule is statistically optimal.During this rule, the observer simply compares the relativeevidence distances among the members of the triplet (seeFig. 1 panel b). The two items closest on the evidencedimension are assumed similar and the remaining itemis classified as odd. The triangular rule is optimal whenthere is a large rove as there is no other basis of informa-tion upon which to make the judgment. Because the itemscan come from any portion of the evidence axis, the abso-lute location on this axis of any particular item is whollyuninformative, and only the relative distances among theitems matters. The algebraic equation describing the trian-gular rule is:

Zi ¼j xi � �x j ð1Þ

where Zi is the absolute value of the differencebetween each member of the triplet and the mean ofthe triplet, �x. The member with the largest Z value is theitem selected as odd. This is equivalent to thepsychological characterization of the rule above, namely,that observers find the two most similar items (in termsof evidence values) and then select the remaining item asthe isolate.

The triangular rule is not statistically optimal if thestimuli are drawn from two constant locations (with addednoise) on the evidence axis. Under these conditions, if theobserver also explicitly knows the locations of the twoevidence distributions, he or she can use this additionalinformation to help solve the oddity problem by using arule termed ‘‘independent-observation’’ (Macmillan & Cre-elman, 2005; Versfeld et al., 1996). This rule can bethought of as an augmentation of the triangular rule wherethe observer uses both relative evidence among the items,and the position of the evidence along the evidence axis torender a judgment. Using this rule, the observer examinesthe evidence for all items (x1, x2, x3) and the selects theitem with the greatest absolute distance (Z) from the meanevidence of the current triplet (�x), adjusted by a constant,namely the central tendency of the two evidence distribu-tions (l).

Zi ¼ xi �3x� l

2

��: ð2Þ

The link between the independent-observation rule andthe mental operations of the observer is not particularlytransparent from the form of Eq. (2). However, the rule re-duces to the following steps. First the observer orders thestimuli along the evidence axis. Second, he or she classifiesthe center item along this axis using a standard single itemrecognition judgment and the criterion location l in Eq.(2), which corresponds to the optimal criterion midwaybetween the old and new evidence distributions for sucha judgment. If the item falls above this criterion then theminimum of the triplet is designated odd, if the intermedi-ate item falls below this location then the maximum of thetriplet is designated as odd (see Fig. 1 panel c). The

1 This equation provides the optimal criterion placement on the x-axis atwhich old and new item distributions intersect, above which returnedevidence is more indicative of an old item than a new item, and belowwhich returned evidence is more indicative of a new item than an old item.For formal derivation see the appendix of Stretch and Wixted (1998). Wehave not ascertained that this solution is analytically optimal for oddityjudgments by maximum likelihood estimation, but we assume that this isthe case since it would be optimal under single item recognition (see Fig. 3).It should also be noted that there is an additional intersection (lalt) of oldand new item distributions at the lower end of the new item distributionlocated at:

lalt ¼�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffid0

2r2 þ 2r4 lnðrÞ � 2r2 lnðrÞ

q� d0

r2 � 1: ð3Þ

Below this intersection, driven by its greater variance, the probabilitydensity function for the old item distribution once again exceeds theprobability density function for the new item distribution. Whilst a com-prehensively optimal decision rule would incorporate this lower criterion,the proportions of old and new item evidence distributions falling belowthis intersection are extremely small (4.02 � 10�10 and 3.21 � 10�10

respectively for a d0 of 1.5 and a variance ratio of .80). Thus consistentwith prior approaches we disregard this second location and the rulewe present reflects the maximal performance achievable if the observerapplies a single evidence criterion at the upper intersection in order toparse the old/new continuum.


‘‘independent’’ nomenclature refers to the fact that the cri-terion, l, is independent of the relative distances betweenthe items.

If the two classes of items under discrimination are cho-sen from stationary distributions, then the independent-observation rule is superior to the triangular rule becausethe criterion, l, is optimal for classifying any given itemas old or new (Versfeld et al., 1996). In the case of typicalrecognition memory experiments, the independent-obser-vation rule would appear to be superior because the evi-dence distributions are assumed to be stationary.However, the ability of observers to use such a rule de-pends critically upon their awareness of the locations ofthe distributions and their appreciation of the superiorityof this more complex rule. Since there is considerabledoubt about the ability of observers to directly appreciateor deduce the positions and shapes of hypothetical evi-dence distributions during recognition (e.g., Benjamin &Bawa, 2004; Criss, 2009; Healy & Jones, 1975) we examineboth rules here.

The importance of the unequal variance assumption

Although it is not widely appreciated, the unequal var-iance assumption of the standard signal-detection ap-proach to recognition bears critically on judgments ofmnemonic oddity. This is because the model is a statementregarding the perceived similarity of old and new itemmemoranda during recognition. Put simply, the model as-sumes that the evidence values for new items are moresimilar to one another than the evidence values for olditems (Fig. 1 panel a). Because successful judgments ofoddity are heavily dependent on the similarity of thenon-odd items, the model predicts an asymmetry in per-formance depending upon whether the odd item is old ornew. Looking at Fig. 1 panel a. it is intuitively clear that un-der the situation in which the new item is odd (new itemisolate trial) performance is more likely to be disruptedby the high variability of old items than under a situationin which the old item is odd. In this latter case, the lowervariability of new item evidence is less likely to obscurethe oddness of the single old item of a triplet. This intuitiveprediction is verified below in the simulation section,which demonstrates that for the range of d0 and old itemvariance values typically assumed in the literature, itshould be quite robust. The mechanics of the decision rulesare almost wholly unaffected by the unequal varianceassumption. In the case of the triangular rule, Eq. (1) holdsunaltered; the observers again find the two most similaritems and then select the remaining item as odd. In thecase of the independent-observation rule, l in the equationmust be replaced with a criterion on the evidence axis thatis optimal for a single item recognition judgment. Thus tobring the rule into line with the unequal variance signal-detection approach typically used in the literature (e.g.,Glanzer, Hilford, & Maloney, 2009; Ratcliff et al., 1992;Squire, Wixted, & Clark, 2007; Stretch & Wixted, 1998),the l term in Eq. (1) is replaced by an optimal single crite-rion (lopt) for the specific unequal variance model beingsimulated using the following equation (with d0 and r2

representing the mean and variance of the old item distri-

bution with the new item distribution mean and varianceset at 0 and 1 respectively)1:

lopt ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffid02r2 þ 2r4 lnðrÞ � 2r2 lnðrÞ

q� d0

r2 � 1: ð4Þ

Fig. 3 shows that this approach indeed appears to yieldthe maximum proportion of overall correct respondingduring the independent-observation rule when variancesare unequal. The figure illustrates the proportion of overallcorrect responding, estimated through Monte Carlo simu-lation, for observers with an old item standard deviationof 1.25 and various criterion positions relative to lopt ofEq. (4). As the criterion shifts from this position, overallperformance declines.

In summary, the literature contrasting the unequal var-iance signal-detection and dual-process models has reliedalmost entirely on a single recognition paradigm, namelysingle item old/new recognition judgment accompaniedby confidence reports. Although the fits of the models sys-tematically favor the unequal variance signal-detectionmodel, both signal-detection and dual-process models typ-ically account for the vast majority of data and make qual-itatively similar predictions. However, when the only twodecision rules known for oddity judgments are consideredin light of the unequal variance assumption, an arguablysurprising prediction is made; as long as optimal decisionrules from the sensory-perceptual domain hold withinthe memory domain, it should be more difficult to detectan odd new item than an odd old item. As we discuss morefully later, this is not a natural prediction for dual-processmodel approaches because they assume that individualshave more information at hand for old items (familiarityand recollection) versus new items (familiarity informa-tion only). Given this, there is more information to workwith given a triplet with one new item and two old items(new item isolate trial) compared to a triplet with only oneold item and two new items (old item isolate trial). If, asasserted by the Mandler (1980) anecdote, recollection is


useful for disambiguating the familiarity of items then it isreasonable to assume that subjects will perform better forresolving triplets with two versus one old item present.This prediction is opposite that of the unequal variance sig-nal-detection model and is explored more formally in theGeneral Discussion.

While the decision modeling considerations above sug-gest that the oddity task may inform the single- versusdual-process memory debate, it is also important toemphasize that this research question bears critically uponthe comparability of decision models for recognition mem-ory and perception judgments. The original application ofthe theory of signal-detection to recognition memoryhinged on the assumption that recognition memory, likeperceptual discrimination, could be treated as a unidimen-sional statistical decision problem (e.g., Banks, 1970; Parks,1966) and the oddity task provides us with another oppor-tunity to critically re-evaluate this assumed comparabilityoutside of single item judgments. Additionally, unlike sin-gle item recognition testing, recognition judgment outsidethe laboratory is often conducted against a background ofsimultaneous novelty or familiarity. For example, search-ing for a new acquaintance in the midst of an unfamiliarcrowd is arguably a mnemonic oddity task. Similarly,although great pains are taken to warn eyewitnesses thatperpetrators may be absent from lineups, it is nonethelessthe case that the observers may treat these tasks as ones ofrelative mnemonic oddity judgment (for discussion seeWells et al., 1998). That is, they may assume that the arrayhas an old item isolate (the perpetrator) present and searchfor the member whose familiarity isolates him or her mostfrom the other members of the array. Thus understandingwhether observers find new or old item isolates easier toresolve and evaluating which if any current decision mod-els anticipate these observed differences (and generalizesamong tasks), has importance outside of the single- versusdual-process model debate.

Before turning to simulations to solidify the predictionsof the single- and dual-process theories outlined above, wefirst summarize the findings of four separate experimentscontrasting the accuracy of oddity judgments for new ver-sus old item isolate triplets. To preview the data, underoddity participants reliably find it easier to detect a newitem hidden among two old items compared to the reverse.Basic Monte Carlo simulations then show this finding to beat odds with the predictions of the unequal variance sig-nal-detection model using known optimal decision rules.To address this, in the General Discussion we develop en-tirely new decision rules to verify that the dual-processmodel anticipates the data and to attempt to salvage theunequal variance signal-detection model.

Empirical findings

General methods

OverviewWe conducted four computer-presented experiments

focusing on oddity recognition judgments. In all experi-ments, a three-alternative forced-choice (3-AFC) control

task was also administered. In the 3-AFC task, participantswere cued to identify the old item or the new item accord-ing to triplet construction (e.g., ‘‘Which is old?’’ or ‘‘Whichis new?’’ as opposed to ‘‘Which is odd?’’ under oddity). The3-AFC task provides a useful point of comparison due tothe identical triplet construction and analogous require-ment of participants to identify one item that satisfiesthe criteria indicated in the cue.

Before describing the procedures for each experimentwe briefly describe the rationale for the conditions thatwere considered across the experiments. Experiment 1contrasted forced-choice recognition and oddity recogni-tion judgments for identically constructed triplets. As dem-onstrated below, only oddity judgment was sensitive to theconstruction of the triplets, demonstrating an advantagefor new item isolate trials versus old item isolate trials. Be-cause performance was fairly low during the oddity judg-ments of Experiment 1, Experiment 2 incorporated alevels of processing (LOP) manipulation in order to im-prove general performance on the task and to determinewhether the new item isolate advantage remained at high-er levels of performance (Craik & Lockhart, 1972). Theexperiment again demonstrated that triplet constructiondid not affect forced-choice decisions but did influenceoddity judgments, with the new item isolate advantagepresent at fairly high levels of performance. Althoughforced-choice remained insensitive to the construction ofthe triplets, we wondered if this factor would affect out-comes if observers were instead asked to rate each mem-ber of a triplet independently for simple item recognition(without confidence). Thus Experiment 3 introduced thisindependent classification task using the triplets, whileagain examining forced-choice and oddity in order to rep-licate the prior findings. Neither the independent classifi-cation task nor the forced-choice task was sensitive totriplet construction, but again, the oddity judgment was,confirming that the effect seems fairly specific to this task.Finally, because all three experiments intermixed trials ofdifferent types, Experiment 4 re-examined forced-choiceand oddity, but in a blocked fashion, in order to confirmthat the new item isolate advantage during oddity wasnot somehow an artifact of trial mixing.

StimuliFor each participant, a different set of words was ran-

domly sampled from source lists comprising 1607 com-mon nouns in Experiment 1 and 1216 common nouns inExperiments 2–4. Randomization ensured the linguisticcharacteristics were matched across new and old item iso-late oddity tasks.

Participants

Twenty-two (18 women), 31 (20 women), 16 (10 wo-men) and 26 (18 women) participants were tested. Datafrom an additional three participants in Experiment 4 werediscarded due to overall performance being at chance. Par-ticipants in Experiments 1, 2 and 4 were compensated withcourse credit and participants in Experiment 3 receivedpayment. Informed consent was obtained in accordancewith the Institutional Review Board of Washington Univer-


sity. The behavioral data in Experiment 3 were collectedduring a functional magnetic resonance imaging studywith participants situated in a scanner: the imaging dataare not presented here.

Procedure: Experiment 1After the presentation of on-screen instructions and a

practice phase in which participants were familiarizedwith all the judgments to be made, there were four self-paced study-test cycles, each consisting of 120 words atstudy and 80 triplets at test. During encoding participantscounted the number of syllables in each serially presenteditem. In each self-paced encoding trial, single words werepresented above the cue ‘‘Syllables? 1/2/3/4 or more’’ andparticipants responded by pressing the appropriate keyon the keyboard numberpad (1 through 4). Immediatelyfollowing each study list, a test comprising randomlymixed trials was administered. The recognition trials were20 oddity trials and 20 3-AFC trials (each with 10 new itemisolate trials and 10 old item isolate trials). In all self-pacedtest trials, triplets were presented below a cue and werecomposed of either two old words (previously studied)and one new word (not previously studied), or two newwords and one old word. Words were presented in a singlecolumn in three rows numbered 1 through 3; the isolatewas equally likely to occupy each of the positions. Partici-pants responded by pressing the number on the keyboardnumberpad corresponding to the item they believed satis-fied the criteria indicated by the cue. Oddity trials werecued by the prompt ‘‘old/new: ODD?’’ indicating the par-ticipant should select the item whose recognition statuswas odd. 3-AFC trials were cued by the prompt ‘‘old/new:NEW?’’ or ‘‘old/new: OLD?’’ indicating that participantsshould select either the new item or the old item. Acrossthe entire experiment, there were a total of 40 trials ofeach type (oddity new item isolate, oddity old item isolate,3-AFC new item isolate, 3-AFC old item isolate). Equivalentoddity and 3-AFC judgments were made using semanticcriteria (living/non-living judgments) in other intermixedtrials, but these do not bear centrally on the currenthypotheses about episodic memory and are not discussed.


practice phase in which participants were familiarizedwith all the judgments to be made, there were four self-paced study-test cycles, each consisting of 96 words atstudy and 64 triplets at test. In each study phase half thestudy items were encoded using a shallow LOP syllablecounting task cued by the prompt ‘‘Syllables? 1/2/3/4 ormore’’ and the remainder were encoded using a deep LOPpleasantness rating task cued by the prompt ‘‘Pleasant-ness? 1/2/3/4’’ (it was explained to participants in theinstructions that a rating of 1 corresponded to the leastpleasant rating and a rating of 4 corresponded to the mostpleasant rating). Deep and shallow LOP encoding taskswere randomly intermixed within the same study phase.All other aspects of the study procedure were identical tothose of Experiment 1. In each test run, there were 16 odd-ity judgments for triplets using shallowly encoded materi-als, 16 oddity judgments for triplets using deeply encoded

materials, 16 forced 3-AFC trials for triplets using shal-lowly encoded materials and 16 3-AFC trials for tripletsusing deeply encoded materials (each with 8 new item iso-late trials and 8 old item isolate trials). Encoding typeswere never mixed within a single triplet. Across the entireexperiment this yielded a total of 32 triplets for each of thefour recognition conditions under both oddity and 3-AFC(deeply encoded old items [new and old item isolate trip-lets]; shallowly encoded old items [new and old item iso-late triplets]). Trials were cued by the same prompts asin Experiment 1. For oddity trials, following the indicationof which member of the triplet they believed to be odd,participants also justified their selection by indicatingwhether they believed the selected item was old or new.These justifications are not presented or discussed here.


practice phase in which participants were familiarizedwith all the judgments to be made, there were twostudy-test cycles, each consisting of 72 words at studyand 48 triplets at test. During self-paced, unscannedencoding trials, participants made pleasantness ratingscued by the prompt ‘‘Is Pleasant?’’, responding with MRI-safe button-box button-presses corresponding to either‘‘yes’’ or ‘‘no’’. Immediately following each study list, ascanned test comprising randomly mixed trials wasadministered. In each test run, there were 16 oddity trials,16 3-AFC trials and 16 independent classification trials(each with 8 new item isolate trials and 8 old item isolatetrials). Oddity and 3-AFC trials were presented in the samemanner as previous experiments and participants re-sponded with button-presses corresponding to the num-bered item they believed satisfied the criteria indicatedin the cue. Oddity trials were cued by the prompt ‘‘Whichis Different?’’ and 3-AFC trials were cued by the prompt‘‘Which is New?’’ or ‘‘Which is Old?’’ Independent classifi-cation trials were presented and responded to in a differentmanner. In each triplet, the three item numbers were re-placed by an arrow that moved progressively down the listof three items indicating to which item participants wererequired to make ‘‘Old/New?’’-cued responses. Responseswere made using button-presses corresponding to either‘‘new’’ or ‘‘old’’. In each trial, participants had 7 s to rendera response (or all three responses in the independent clas-sification condition). If responses were not rendered com-pletely by the end of the response period, the responsewas coded as incorrect and the next trial was initiated.Across the entire experiment, this procedure yielded a totalof 16 trials of each isolate type (new and old item isolatetriplets) for oddity, 3-AFC and independent classification.Passive fixation trials, in which participants were in-structed to ‘‘relax’’, were intermixed throughout the recog-nition judgments.


practice phase in which participants were familiarizedwith all the judgments to be made, there were fourstudy-test cycles, each consisting of 72 words at studyand 48 triplets at test. There were two cycles of intermixed


test trials and two cycles of blocked test trials. Duringintermixed cycles, as in the previous experiments, partici-pants made oddity judgments intermixed amongst 3-AFCjudgments in a randomized order within the same cycle.During blocked cycles, participants made only oddity judg-ments (one cycle) or 3-AFC judgments (one cycle). The or-der of the cycles was counterbalanced among participants.For all cycles, during encoding participants made self-paced pleasantness ratings in a procedure identical toExperiments 1 and 2. Immediately following each studylist, a self-paced test was administered. In intermixed cy-cles, test runs comprised 24 oddity trials and 24 3-AFC tri-als (each with 12 new item isolate trials and 12 old itemisolate trials). Across the entire experiment this yielded atotal of 24 trials of each isolate type (new and old item iso-late triplets) for oddity and 3-AFC during intermixed cy-cles. In one blocked cycle the test comprised 48 odditytrials and in the other the test comprised 48 3-AFC trials,again yielding 24 trials of each isolate type for both oddityand 3-AFC. In all cycles, oddity trials were cued by theprompt ‘‘which is ODD?’’ and 3-AFC trials were cued bythe prompt ‘‘which is NEW?’’ or ‘‘which is OLD?’’ Partici-pants made responses using the keyboard numberpad ina manner identical to Experiments 1 and 2.

Results

Mean (and standard deviation) isolate identificationaccuracies for oddity, 3-AFC and independent classificationtasks are shown in Table 1.

OddityFig. 4 shows six separate comparisons of new item iso-

late and old item isolate oddity performance across allexperiments. In Experiment 1, t(21) = 4.02, p < .001, d =.852, and Experiment 3, t(15) = 3.157, p = .006, d = .753,performance was significantly better for new item isolatesthan old item isolates. Results from Experiment 2 were en-tered into a 2 � 2 (LOP � isolate type) repeated measuresANOVA revealing a main effect of LOP, F(1, 30) = 63.06,p < .001, g2 = .678, indicative of an overall accuracy advan-tage for triplets containing deeply processed items. Therewas no main effect of isolate type across LOPs,F(1, 30) = 1.87, p = .182, g2 = .059, but crucially there wasa significant interaction, F(1, 30) = 23.31, p < .001, g2 =

Table 1New and old item isolate identification accuracy.

Isolate Oddity 3-

New Old N

Experiment 1 .46 (.16) .33 (.15) .6Experiment 2: Shallow .54 (.15) .58 (.18) .7Experiment 2: Deep .78 (.18) .66 (.19) .8Experiment 3 .70 (.20) .53 (.25) .8Experiment 4: Blocked .69 (.23) .57 (.27) .8Experiment 4: Intermixed .66 (.22) .55 (.25) .7

Note. Mean isolate identification accuracy for new and old item isolate tripletsindependent classification. Standard deviations are shown in parentheses. Undparticipants selected the isolate as the odd item (oddity) or the new or old item (of trials in which all items were classified correctly.

.437. Post hoc pair-wise contrasts demonstrated perfor-mance that was significantly better for new item isolatesthan old item isolates for triplets containing deeply en-coded items, t(30) = 3.89, p < .001, d = .666, but not for trip-lets containing shallowly encoded items, t(30) = �1.17,p = .249, d = �.254. Results from Experiment 4 were en-tered into a 2 � 2 (presentation condition [blocked orintermixed] � isolate type) repeated measures ANOVArevealing no main effect of presentation condition,F(1, 25) = 1.07, p = .310, g2 = .041, suggesting that accuracywas similar for oddity regardless of whether these judg-ments were in isolation (blocked) or mixed amongst 3-AFC judgments (intermixed). There was a main effect ofisolate type, F(1, 25) = 23.80, p < .001, g2 = .488, with per-formance better for new item isolate identification thanold item isolate identification collapsed across blockedand intermixed trials, and there was no significant interac-tion, F < 1. Planned contrasts confirmed the new item iso-late identification advantage in both blocked, t(25) = 3.55,p = .002, d = .492 and intermixed cycles, t(25) = 3.83,p < .001, d = .478.

3-AFC and independent classificationUnder 3-AFC, in all experiments there were no signifi-

cant differences in performance across new and old itemisolate identification trials: Experiment 1, t(21) = 1.39,p = .178, d = �.255; Experiment 2 shallow encoding,t(30) = �1.29, p = .206, d = �.163 and deep encoding,t(30) = �1.01, p = .322, d = �.125; Experiment 3, t(15) =0.85, p = .410, d = .101; and Experiment 4 blocked cycles,t(25) = �0.72, p = .480, d = �.109 and intermixed cycles,t(25) = �0.97, p = .340, d = �.088.

The only task not considered above was the indepen-dent classification task in Experiment 3. As with theforced-choice comparisons, the construction of the tripletsdid not significantly affect accuracy on the task, which wasscored as the proportion of trials in which all three sepa-rate judgments were correct, t(15) = 1.87, p = .080, d = .274.

Results summaryThe only recognition judgment that was reliably af-

fected by the construction of the triplets was the judgmentof mnemonic oddity. In five of the six comparisons therewas a significant advantage for the new item isolate trip-lets over the old item isolate triplets. Thus the effect is

AFC Independent classification

ew Old New Old

2 (.17) .58 (.15) – –1 (.16) .74 (.13) – –8 (.11) .89 (.10) – –5 (.16) .83 (.20) .66 (.20) .60 (.24)0 (.28) .83 (.17) – –7 (.26) .79 (.23) – –

under conditions of oddity, three-alternative forced-choice (3-AFC) ander oddity and 3-AFC, accuracy reflects the proportion of trials in which3-AFC). Under independent classification, accuracy reflects the proportion

Fig. 4. Mean proportion of responses correct in Experiments 1–4 for the oddity task. Error bars represent standard errors of the means.


quite reliable. In contrast, forced-choice judgments wereinsensitive to this stimulus difference in all six cases, andthe independent classification task of Experiment 3 wasalso not sensitive to the construction of the triplets. Thusthere is an empirical regularity in recognition data demon-strating that observers find it easier to identify a new itemhidden among two old items compared to an old item hid-den among two new items. Analogously, one could charac-terize this pattern as demonstrating that pairs of old itemsare more easily perceived as mnemonically similar to oneanother than pairs of new items. Below we formally simu-late the dual-process and unequal variance models dis-cussed in the introduction and demonstrate that thedual-process account more easily anticipates this findingbased on the parameters that one typically observes duringstandard single item recognition procedures.

Before turning to the simulation results we comment onthe one oddity comparison that failed to demonstrate anew isolate advantage, namely, the triplets constructedwith shallowly encoded old items in Experiment 2. As isclear from Experiment 1, the effect does occur when suchtriplets are judged in isolation, thus it appears that the trialmixing of these types of triplets, with triplets whose olditems have been encoded deeply, is what results in theelimination of the effect. Here we can only speculate onwhy this occurs, but it presumably reflects the fact thatthe retrieval of deep or vivid encoding information some-how serves to overshadow episodic information poten-tially available for the shallow triplets. We suspect thiseffect is linked to phenomena noted in the reality monitor-ing literature of Johnson, Raye, Foley, and Foley (1981), of-ten referred to as the ‘‘it-had-to-be-you’’ effect. During thetask, observers attempt to discriminate whether testprobes were previously self-generated or instead providedby an external agent. Critically, the test also contains newitems. The general finding is that when observers incor-rectly endorse new items as coming from the study epi-sode, they also tend to ascribe them to the externalsource. This pattern is thought to reflect that fact thatobservers are monitoring their memories in search of evi-dence particularly diagnostic of prior self generation (e.g.,

evidence of cognitive operations). While some portion ofnew materials may seem spuriously familiar, they willgenerally lack this type of information, leading observersto conclude they originated from the external source.

In the current Experiment 2, we suspect that observersare similarly looking for vivid evidence indicative of havingperformed the deep processing task on the items (did I ratethis for pleasantness?) Such a retrieval orientation argu-ably renders it less likely that they will recover or con-sciously apprehend the episodic information linked to theshallowly encoded materials. Since, as we more fully detailbelow, the dual-process model assumes the new item iso-late advantage is a recollective retrieval phenomenon, thisdeep retrieval orientation would necessarily reduce thephenomenon for study materials whose prior processingpoorly matches the sought after episodic content (for sim-ilar ideas see Jacoby, Shimizu, Daniels, & Rhodes, 2005).Although consistent with prior frameworks, this accountclearly should be replicated in the context of oddity judg-ment, where support for it would strengthen the assump-tion that the effect is heavily linked to recollection.Nonetheless, it is important to note that the null effectfor the shallowly processed materials in Experiment 2 doesnot weaken the general finding that the new item isolateadvantage was found in four experiments and five separatecontrasts, and thus is a robust phenomenon.

Turning to the simulation results, predictions of theoddity decision rules were generated by simple Monte Car-lo procedures in which random samples of triplets(500,000) were drawn from old and new item distributionsto generate old or new item isolate triplets (e.g., two drawsfrom the old item distribution and one from the new itemdistribution for new item isolate triplets). For each simula-tion, the odd item was selected according to the relevantdecision rule and the proportion of correct selections re-corded. Oddity results from Experiments 1–4 are shownalongside simulation results for the unequal variancesignal-detection model across a range of selected keyparameter values in Fig. 5. In the empirical data, the resultsare clear. Participants find the detection of new isolateseasier than the detection of old isolates. That is, their

Fig. 5. Simulated old and new item isolate oddity task accuracies for thetriangular (panel a) and independent-observation (panel b) decision rules.The dashed line represents the line along which new and old item isolateaccuracies are equal. Simulations with varying d0s (from 0.5 to 2.0 in stepsof 0.5, represented by points shaded from white to black) and old itemdistribution variances (from 1.0 to 3.0 in steps of 0.4, represented bypoints with an increasing area; the new item distribution variance is fixedat 1.0) are shown.


performance is superior for the condition with two olditems and a new item, compared to the condition withone old item and two new items. In contrast, the shadedsymbols of the figure demonstrate the expectation of theonly two known signal-detection rules assumed for oddityjudgments. For both the simple triangular rule, in whichthe evidence values are directly compared, and the morecomplex independent classification rule with an optimalcriterion, all data points lie clearly below the diagonal indi-cating that the model generally predicts that performanceon the old item isolate trials is expected to be higher thanthat on the new item isolate trials. Thus the empirical dataare categorically at odds with the only two decision rules

known for oddity judgment under signal-detection theory;rules which are assumed valid in the domain of sensoryperception (Frijters, 1979; though see also O’Mahoney,1995).

As Fig. 5 demonstrates, the misprediction of the signal-detection rules spans the range of d0 values and old to newitem variance differences that one would typically expectduring single item recognition paradigms if the unequalvariance signal-detection model were correct. Again, thisis noteworthy because these are the only known signal-detection rules for such judgments and typically assumedcorrect for perceptual judgments. Furthermore, the inde-pendent-observation rule is in fact the optimal rule for rec-ognition memory given the assumption of stationaryevidence distributions (although it is unclear how observ-ers would determine this). Nonetheless, both rules cate-gorically fail in the way expected given simple visualconsideration of the unequal variance model in Fig. 1. Thuseven without consideration of the dual-process predictionsformalized below, the data clearly show that the optimaldecision rule for oddity, based on a likelihood ratio crite-rion, fails to predict the current empirical findings. Giventhat several current approaches assume that observersuse an optimal likelihood criterion during recognition(e.g., Glanzer et al., 2009) this finding is newsworthy.

In the General Discussion we consider ways in whichthe independent-observation signal-detection decisionrules might be brought more in line with the data. We thenpropose a second viable decision rule that is consistentwith dual-process models and move onto suggest waysin which the two competing decision rules might be fur-ther tested.

General discussion

With respect to the unequal variance signal-detectionmodel, the current data present two possibilities. First,the only two known decision rules for oddity may be incor-rect for episodic recognition judgments, indicating thatrules that work for perceptual judgments do not transferto recognition memory. Second, the unequal variance sig-nal-detection model itself may be fundamentally flawed.If the first possibility is true then a viable signal-detectionrule can be found. If the second possibility is true, then thesignal-detection model should be abandoned. Of course, achallenge to the signal-detection approach would benefitby demonstrating a plausible decision rule derived froman alternate model. Below we present a new decision ruleappropriate to each of the circumstances outlined above:first, an alternative signal-detection-based rule; and sec-ond, a dual-process-based rule. Finally, we evaluate thetwo new rules using empirical data from single item recog-nition via a bootstrap-fed Monte Carlo simulation methodto see which model actually generalizes from independentsingle item recognition data to the current oddity findings.

Before contrasting the novel signal-detection and dual-process rules presented below, it is important to note thatthey both share a commonality. Both rules start from thepremise that observers pay unique attention to theintermediate item of the triplet. In the case of the original


independent-observation rule this was already clear giventhe single item classification of the intermediate item viaan optimal criterion. As we detail below, the dual-processrule also assumes that the intermediate item receives addi-tional processing. In this case however, it is assumed thatobservers attempt to recollect context for this item. Impor-tantly, the reason that both models assume additional pro-cessing for the intermediate item of the triplet is because itis this item that is decidedly ambiguous under oddityinstructions. Under oddity instructions, observers explic-itly know that every triplet contains at least one old itemand one new item. Given this, the maximum and minimumitems, with respect to the single evidence dimension undersignal-detection or the familiarity process under dual-pro-cess, are most likely to have arisen from the old and newevidence distributions regardless of model. In short, onthe vast majority of trials, the identities of these two itemsare not ambiguous, however, this ease of attribution doesnot hold for the intermediate evidence item whose likelyorigin is unclear. In the original triangular and indepen-dent-observation rules the inherent ambiguity of the inter-mediate item is resolved either one of two ways; by eitherdetermining whether it is most similar to the maximum orminimum (triangular rule), or by evaluating it with respectto an optimal absolute criterion (lopt; independent-obser-vation rule). Given the categorical failure of these tworules, we examine two different ways to further processthe intermediate item that might yield the correct patternof performance for new and old item isolate triplets.

Alternative viable decision rules

Flexible criterion independent-observation ruleThe standard independent-observation rule uses an

optimal criterion (lopt) to facilitate performance and im-prove upon the triangular rule. This fixed, optimal criterion

Fig. 6. Simulated old and new item isolate oddity task accuracies for the in(rectangles and crosses) criterion placements. Simulations with varying d0s (froblack) and old item distribution variances (from 1.0 to 3.0 in steps of 0.4, represeis fixed at 1.0) are shown. The dashed line represents the line along which neplacement was 0.5 above optimal and the liberal criterion placement was 0.5 b

placement maximizes accuracy for stationary distributions(Fig. 3) but one can instead ask, what would happen if sub-jects systematically chose a non-optimal location for thecriterion position. That is, what if all subjects tended tobe liberal or conservative in the criterion that is appliedto the intermediate item during the independent-observa-tion rule. Unlike the two parameter model previously dis-cussed, this flexible criterion model uses three keyparameters: the distance between old and new distribu-tions (d0); the variance of the old item distribution (r2);and crucially, a non-optimal criterion chosen for the classi-fication of the intermediate item (c). As shown in Fig. 6,assuming a generally liberal criterion (rectangles), as op-posed to conservative criterion (crosses), aligns the deci-sion rule with the experimental findings in that it nowpredicts a new item isolate advantage. Thus, if one takesthe independent-observation rule, adds an unequal vari-ance assumption, and then assumes that observers interro-gate the intermediate using an old/new discriminationwith a generally liberal criterion, then the signal-detectionmodel is able to accommodate the current data. However,this approach faces at least two criticisms. First, the modelis clearly ad hoc. As emphasized above, under signal-detec-tion this is not the optimal approach to the task and theneed to assume a generally liberal criterion directly contra-dicts with the assumption that in general observers use anoptimal likelihood ratio criterion for single item recogni-tion judgment (e.g., Hirshman, 1995; Shepard, 1967). In-deed, in the empirical data illustrated in Fig. 2 and usedfor the first bootstrap Monte Carlo simulation, the 26 par-ticipants’ mean criterion estimates did not differ from themean optimal criterion (Ms = 0.916 versus 0.999; optimalcriterion determined using Eq. (4)), t(25) = �1.327,p = .196, d = �.219. Thus not only would the current partic-ipants need to use a liberal criterion that reduces overalloddity performance (Fig. 3), but this criterion deviates

dependent-observation decision rule with optimal (circles) and flexiblem 0.5 to 2.0 in steps of 0.5, represented by points shaded from white tonted by points with an increasing area; the new item distribution variancew and old item isolate accuracies are equal. The conservative criterion

elow optimal.

Fig. 7. Simulated old and new item isolate oddity task accuracies for thedual-process decision rule. The dashed line represents the line alongwhich new and old item isolate accuracies are equal. Simulations withvarying d0s (from 0.5 to 2.0 in steps of 0.5, represented by circles shadedfrom white to black) and recollection thresholds (R; from .3 to .7 in stepsof 0.2, represented by circles with an increasing radius; the new andfamiliarity item distribution variances are fixed at 1.0) are shown.

2 The triangular rule utilizes the distances from the maximum andminimum familiarity items to the intermediate item. It can lead to errorseven when the ordering of items is correct (a new item presents with thelowest familiarity and an old item presents with the highest familiarity) ifthe two like items are further apart than the odd and intermediate items.The additional context recovered when using the dual-process rule cansometimes overcome these distance-related errors, but only for new itemisolate trials (where the intermediate item affords the potential for contextrecovery). For example, consider a potential recollection rate of 30% with amoderate d0 of 1.5. Under these conditions, approximately 8% of trials thatwould have been incorrect using the triangular rule alone are saved bysuccessful recollection with the intermediate item using the dual-processrule. It should also be noted that the dual-process rule can very rarely leadto errors in new item isolate trials that would not result from using thetriangular rule alone. In just under 1% of trials, the new item isolate willspuriously present with maximum familiarity (displacing both of the olditems), and recollection will succeed for the intermediate (old) item,leading to the incorrect conclusion that the minimum item is odd.However, because of therelative infrequency of recollection induced lossescompared to gains (an 8% gain vs. a 1% loss), use of the dual-process ruleresults in increased accuracy overall for new item isolatetrials compared towhen only the triangular rule is used (58% correct vs. 51% correct).


from the neutral criterion observed under the signal-detec-tion model for single item recognition. Second, this versionof the independent-observation model is arguably over-parameterized in that it can accommodate every possiblenew and old item isolate performance relationship duringthe oddity task. That is, as Fig. 6 shows, it is quite capableof producing an old item isolate advantage even thoughone never actually occurs in the data. Far from represent-ing admirable characteristic, such flexibility is the hall-mark of an unfalsifiable model. If there were a modelthat, with an equal or lesser number of parameters, couldnot produce data in the lower half of Fig. 6, it would bepreferable on these grounds alone. As we show below,the dual-process model makes this more restricted andhence riskier prediction.

Dual-process ruleBefore outlining a viable dual-process decision rule, it is

important to clarify the assumed nature of ‘recollection’ inorder to establish how it might contribute to successfuldecision-making during the oddity task. Within dual-pro-cess theories, there are several postulated characteristicsthat distinguish recollection from familiarity. Here we fo-cus on the assumption that compared with familiarity, rec-ollection is a deliberate retrieval process that is resourceintensive and is therefore employed in a strategic fashion(as opposed to relatively automatic employment of famil-iarity; e.g., Dehn & Engelkamp, 1997; Gruppuso, Lindsay,& Kelley, 1997; Jacoby, 1991; Yonelinas & Jacoby, 1996).This assumption is key to Mandler’s (1980) ‘butcher onthe bus’ anecdote and was also formalized in Atkinson &Juola’s (1973) dual-process model, in which recollectionsearch is initiated only if the initial rapid interrogation offamiliarity returns an inconclusive outcome.

In the proposed dual-process decision rule for oddity,we draw on this assumption that recollection is resourceintensive and therefore strategically employed when itcan decisively resolve a clear ambiguity in familiarity. Asnoted above, during oddity there is only one item whosefamiliarity is routinely ambiguous, namely, the item ofthe three with the intermediate familiarity value on theevidence dimension (Fig. 1 panel c). Whereas the indepen-dent-observation signal-detection decision rule attemptsto resolve the ambiguity of this item by applying an old/new unequal variance judgment, the dual-process decisionrule instead attempts to resolve the ambiguity of this inter-mediate item through a recollection attempt. If this at-tempt is successful, then the observer can conclude thatthe intermediate and maximum item are in fact old andhence will select the minimum item as odd. However, ifrecollection fails, then the item indicated by the triangularrule is selected. Thus the dual-process decision rule is asfollows: participants order the stimuli along the equal var-iance signal-detection familiarity axis and evaluate themedian item for recollection; if recollection succeeds thenthe minimum item is taken as odd; in the absence of recol-lection for the intermediate item, the triangular method isapplied to the unidimensional familiarity values. In short,the dual-process rule is a simple extension of the triangu-lar rule, in which the intermediate item is evaluated forrecollection. If successful then the outcome of this retrieval

attempt dictates the odd item. If it fails, then subjects fallback on the item that appears odd based on the triangularrule. Dual-process decision rule simulation outcomes areshown in Fig. 7 for several values of recollection andfamiliarity.

The dual-process rule is able to accommodate the ob-served oddity findings: it predicts a prominent new itemisolate advantage. This occurs because participants canpotentially recover recollective context for the intermedi-ate familiarity items-an important source of additional evi-dence that can override the triangular rule on trials inwhich its use alone would otherwise lead to an error.2 Itis important to note that these predictions are not strictlydependent upon recollection search being applied only to


the intermediate strength item. We have assumed this forsimplicity and because it is consistent with the idea ofobservers limiting recollection attempts to materialswhose familiarity content is ambiguous and hence con-serving resources. Nonetheless, the predictions hold evenif observers interrogate both the intermediate and themaximum familiarity items. This is because, in all possibleoutcomes, the recollection status of the most familiar itemis incidental to the rendered judgment. For example, if theintermediate item evokes recollection, but the maximumitem does not, this would still lead to the classification ofthe minimum item as the odd item: failures of recollectionare not diagnostic of novelty and the maximum item hasalready returned high levels of familiarity. Conversely, ifthe observer recovers recollection for the maximum famil-iarity item but not for the intermediate item, the observeridentifies the maximum as old via recollection-this wouldalready have been assumed as it had returned the maxi-mum familiarity. Thus the observer would still have to re-sort to the triangular rule in order to determine the statusof the intermediate item. If recollection occurred for bothitems, the observer again gains no benefit from this out-come on the maximum familiarity item because he orshe would have classified the minimum as odd based so-lely on the successful recollection for the intermediateitem. Thus in general, the decision rule we present here,in which only the ambiguous intermediate item is interro-gated for recollection, is optimal in terms of effort ex-pended but identical patterns of behavior would also beobtained from a more comprehensive recollection searchin which both the intermediate and most familiar itemsof the triplet were interrogated for recollection. Finally,we do not assume recollection is attempted for the mini-mum familiarity valued item because it conceptuallymakes little sense for observers to interrogate itemsperceived as novel for recollection of the study context.Critically, not only does the dual-process model correctlypredict the new item isolate advantage using the typicalparameters shown in Fig. 7, it is notable for what it doesnot or cannot predict. Unlike the flexible criterion indepen-dent-observation rule, the dual-process model cannotproduce an old item isolate advantage. If recollection com-pletely fails (i.e., R = 0) then the model predicts that newand old item isolate performance is equivalent. Otherwise,as recollection increases, a new item isolate advantage iscorrectly predicted. Thus the model cannot produce pat-terns that do not seem to occur in actual empirical data.

Which approach is superior?The two newly derived rules accommodate the clear

new item isolate advantage in the empirical data via twofundamentally different mechanisms. In the case of the sig-nal-detection approach, the asymmetry arises strictly be-cause observers are systematically liberal in their old/new classifications of the intermediate item. Thus the ef-fect is not a retrieval phenomenon but a systematic deci-sion bias that just happens to favor the new item isolatetriplets. In contrast, the dual-process approach assumesthat observers attempt to retrieve additional recollectiveinformation for the intermediate item in order to resolveits ambiguous familiarity. Thus the explanation is one of

retrieval not decision bias. Below we discuss both ap-proaches before presenting two bootstrap Monte Carlosimulations that address the question ‘‘which of the twoapproaches is most likely to generalize to the currentempirical data given the parameters actually observed instandard single item recognition?’’

The newly derived signal-detection rule for odditydeveloped above may strike some as a suitable alternativegiven the errant predictions of the traditional triangularand independent-observation rules. For example, the factthat the intermediate item is evaluated with a single itemrecognition judgment process means a similar recognitionprocess is applied during the task as would be applied dur-ing a test of single item recognition (albeit one that is aug-mented by an ordering process, an inferential selectionrule, and a liberal criterion placement). However, the re-vised decision rule is potentially open to criticism on anumber of fronts.

The first criticism is that summaries of the prior litera-ture do not suggest that observers are systematically liber-al during standard single item recognition paradigms. Wedemonstrate this empirically below, however the aggre-gate data of the prior literature also suggests that observ-ers, if anything, are typically somewhat conservative withrespect to recognition judgments across a broad range ofconditions. For example, Ratcliff, McKoon and Tindall’s(1994) participants demonstrated conservative criteriafor strongly encoded recognition items and also weakly en-coded items during standard recognition procedures. Sim-ilarly, Snodgrass and Corwin (1988) demonstrated thatelderly control participants typically held conservative cri-teria with only neurologically impaired participants some-times demonstrating liberal criteria.

The second criticism, as noted earlier, is that the modelis overly flexible and in fact capable of producing an olditem isolate advantage that does not occur in the empiricalfindings. The third criticism focuses on the number ofparameters that are necessary in order to simulate theempirical effect. Whereas the viable signal-detection mod-el utilizes three key parameters (d0, r2, and c), the dual-process decision rule utilizes only two (d0 and R). Onceagain, this affords the signal-detection rule flexibility notafforded to the dual-process rule, which neverthelessmakes the correct prediction despite the smaller numberof parameters.

Because arguments of parsimony and excessive flexibil-ity can be subjective, we statistically evaluate which modelmore naturally predicts the current data given what is al-ready known about single item recognition performance.More specifically, we take the parameters obtained fromfitting two sets of independent single item recognition dataand use these parameters to generate a distribution of ex-pected oddity outcomes using the bootstrap principle incombination with Monte Carlo simulation. We then evalu-ate whether the current findings are statistically unlikelygiven these outcome distributions. The use of independentdatasets to obtain typical parameters from the models isnecessitated by the fact that single item recognition datawith confidence judgments were not collected in the cur-rent study, and so fits of ROCs cannot be estimated forthese particular participants. Nonetheless, it is important


to note that in terms of testing model generalizability, theuse of independent data is in fact preferable because thestarting parameters obtained from such data cannot inany way be contaminated by the specific procedures usedin the current multi-item experiments. Despite this com-plete independence, a truly generalizable model shouldnonetheless be able to easily generate the correctpredictions.

Bootstrap Monte Carlo A: As noted in the Introduction,Fig. 2 shows an aggregate ROC from a standard single itemrecognition test with 26 participants. These data arewholly independent of Experiments 1–4 and were usedto generate the parameters for Bootstrap Monte Carlo A.Following a syllable counting task performed on 180 items,each participant immediately performed old/new recogni-tion classifications followed by a three point confidencerating (3 = high, 2 = medium, 1 = low) for 120 test items(60 old, 60 new). We fit the ROCs of each individual usingthe dual-process model of Yonelinas (1994) and the un-equal variance signal-detection model, using nonlinearregression, a least squares criterion, and the Solver add-in in Microsoft Excel (for a detailed explanation see Harris,1998). Table 2 shows the mean parameter estimates ob-tained for each model and the average quality of fit. Criti-cally, for each model this provides a set of parameterssampled from a theoretical population of parameters that,for single item recognition, are ideal. We then appliedthese parameters to the current decision rules using abootstrap principle. That is, a random sample of 20 param-eter fits (with replacement) was repeatedly drawn fromeach full set of fitted parameters. This is referred to as aparametric bootstrap and the purpose of the procedure isto introduce variability across the sampled sets of param-eters (in this case samples of 20) that should closelyapproximate how one might expect the parameters to varyif we had conducted a large number of identical experi-ments using 20 participants, repeatedly drawing from thestudent population (Efron & Tibshirani, 1993). Followingeach re-sampling, the mean old and new item isolate per-formance estimates for the sample were then generatedusing the Monte Carlo simulation applied to each casewithin the sample. Forty trials of each isolate type weredrawn for each simulated participant. For example, if Sub-ject #1 had a d0 of 1.25, an old item standard deviation of1.25, and a criterion location of .50, then these three valueswould be used in the Monte Carlo simulation to generatethe percentages for the new item and old item isolate trialsusing the independent-observation signal-detection rule

Table 2Single item recognition parameter estimates.

Bootstrap Model d0 c

A Signal-detection 1.77 (0.81) 0.92 (0.40)Dual-process 1.11 (0.58) 0.88 (0.37)

B Signal-detection 2.35 (1.00) 1.15 (0.41)Dual-process 1.50 (0.57) 1.13 (0.40)

Note. Mean parameter estimates and% variance explained under signal-detectiondeviations are shown in parentheses. d0 (old item distribution mean) and c (criterprocess oddity decision rule. r2 (old item distribution variance) is fixed at 1 undedual-process model.

applied to the 80 draws. This procedure is repeated forall 20 re-sampled subjects’ parameter sets and then themean new and old isolate performance across the 20 casesis plotted for this particular bootstrap resample. Followingthis, the next bootstrap resample is drawn and the processrepeated again to generate the next pair of mean percent-ages for the old versus new item isolate tasks. This was re-peated for 1000 experiment resamples.

Bootstrap Monte Carlo B: The same bootstrap procedurewas carried out on a second independent dataset with 40participants to generate Bootstrap Monte Carlo B. To gen-erate this independent dataset, participants performed asyllable counting task on 60 items, and then immediatelyperformed old/new recognition classifications followedby a three point confidence rating (3 = high, 2 = medium,1 = low) for each of 120 test items (60 old, 60 new). Table2 shows the mean parameter estimates and quality of fitfor each model.

This bootstrap-fed Monte Carlo process yields an ex-pected distribution of experiment outcomes (1000 experi-ments each with 20 participants) under each model. If theempirical oddity findings are considerably more unlikelyunder one rule than the other, then the former is rejectedin favor of the latter, which by simulation demonstratesgreater generalization across single item recognition andthe current oddity recognition paradigm. This approach fa-vors the model that is capable of generating accurate pre-dictions of the current empirical data pattern based solelyon the bootstrapped population of parameters typicallyobserved during single item recognition performance. Thusthe analysis is a formal test of model generalizability. Crit-ically, the predictions are not in any way statisticallydependent upon the empirical findings in the currentexperiments because the parameters are obtained throughthe fitting of independent data gathered during single itemrecognition.

As shown in Fig. 8, the bootstrap-fed Monte Carlo sim-ulations from both sets of parameters favor the dual-pro-cess model. In 98.8% (Bootstrap Monte Carlo A) and 100%(Bootstrap Monte Carlo B) of the bootstrapped samples,the dual-process model yielded a new item isolate advan-tage consistent with the pattern in the empirical data. Thismeans that the parameters that are typically encounteredwhen fitting standard recognition data following syllableencoding, lead directly to the prediction of a new-isolateitem advantage in the current oddity task. In contrast,the unequal variance signal-detection model yielded thisoutcome in only 18.4% (Bootstrap Monte Carlo A) and

r2 R % Variance explained

2.30 (1.80) – 99.90 (0.15)1 (–) .29 (.20) 99.86 (0.17)

2.29 (1.62) – 99.95 (0.05)1 (–) .35 (.22) 99.92 (0.10)

and dual-process models for datasets used in Bootstraps A and B. Standardion) are estimated for both models though c is not utilized within the dual-r the dual-process model and R (recollection rate) is estimated only for the

Fig. 8. Bootstrap simulation outcomes for Bootstrap Monte Carlo A (panela) and Bootstrap Monte Carlo B (panel b) for dual-process and indepen-dent-observation (with flexible criterion) decision rules. 1000 experi-ments each with 20 participants were simulated using parametersestimated from single item recognition data. Each point represents themean outcome from one simulated experiment.


6.2% (Bootstrap Monte Carlo B) of the bootstrapped sam-ples-predictions that are markedly different to that of thedual-process model, and far less consistent with the overallpattern of results observed in Experiments 1–4. Put simply,the current empirical outcomes, in which four separateexperiments demonstrated a new item isolate advantage,are anticipated well by the recollection (R) and familiarity(d0) parameters one typically obtains in fits of the dual-pro-cess model to single item recognition data. The same can-not be said for the unequal variance model and its

parameters (d0, r2, and c), which in turn means that it re-quires parameters of a direction and magnitude that wouldbe unusual in order to capture the current phenomenon.Thus the simulations favor the interpretation of the currentnew item isolate advantage in terms of episodic retrieval,not an unusually liberal response bias.

Although the data and simulations favor the dual-pro-cess model and decision rule further testing is warrantedgiven this new and interesting task. Given that recollectionis often argued to decline more rapidly than familiaritywith aging (e.g., Grady & Craik, 2000; Jacoby, 1999; Jen-nings & Jacoby, 1997; Titov & Knight, 1997) the model alsopredicts that the new item isolate advantage should conse-quently decline with age. Additionally, because recollectionis effortful and presumably mediated by resource-limitedprefrontal cortex mechanisms (e.g., Dobbins, Foley, Schact-er, & Wagner, 2002; Henson, Shallice, & Dolan, 1999; Rugg,Fletcher, Chua, & Dolan, 1999; Simons, Owen, Fletcher, &Burgess, 2005), one might also predict that the new itemisolate advantage may be disrupted by the addition of ademanding secondary task during oddity judgment or thespeeding of oddity decisions (e.g., Yonelinas & Jacoby,1996). These testable hypotheses follow directly from therationale on which the decision rule is founded–a failureto support them would therefore pose problems to thedual-process decision rule we have proposed to explainthe oddity findings.

Conclusion

The current data demonstrate a novel, robust, andimportant empirical phenomenon; a decided accuracyadvantage for new versus old item isolates in judgmentsof mnemonic oddity. This effect is not predicted or accom-modated by existing oddity task decision rules and repre-sents the only case that we are aware of in whichdecision rules with support in the perception literature,are nonetheless demonstrably invalid in the case of recog-nition memory judgment. To address this, we developedtwo novel decision rules capable of accommodating thenew item isolate advantage in oddity. Although these com-peting decision rules both required additional processingof the intermediate familiarity item of each triplet, theydiffered in their theoretical foundations (signal-detectionversus dual-process) and how they addressed the inherentambiguity of the intermediate strength item of the triplets.The flexible criterion independent-observation rule as-sumes the phenomenon reflects a systematic decision biason the part of observers, whilst the dual-process rule as-sumes the effect results from context recollection. Givenits consistency with findings supporting the use of recol-lection to disambiguate trace strength when classifyingmemory probes (Hintzman, 1988; Huppert & Piercy,1978; Mandler, 1980), we favor the retrieval-driven dual-process decision approach. Additionally, the bootstrap-fed Monte Carlo simulations demonstrated that the ob-served empirical findings are entirely consistent with thegenerated predictions of the dual-process model basedon the fitting of simple, single item recognition data. Thusthe model clearly generalizes across two fairly differentrecognition tasks. In contrast, the simulation establishes


that endorsement of the unequal variance signal-detectionmodel would require one to assume that oddity judgmentsrepresent a special case of recognition task, whereby forentirely unknown reasons, observers deviate systemati-cally from how they typically place the old/new criterionduring standard single item recognition and do so in adecidedly non-optimal manner. It would also require oneto favor the model that is arguably over-parameterizedas it is also capable of accommodating findings that donot actually occur in the empirical data (viz., an old itemisolate advantage).

Returning to the actual empirical finding, it is perhapsimportant to note the uniqueness of the current effect.Traditional dissociations in recognition memory researchoften revolve around manipulations of the featural prop-erties of the test stimuli (e.g., the word frequency effect),the processes engaged at encoding (e.g., levels of process-ing manipulations), or tasks engaged during recognition(e.g., item versus associative recognition). In contrast,the current finding illustrates a robust difference thatarises solely from the memorial context. That is, the onlything separating new and old item isolate triplets duringoddity judgments is the background of memory evidenceagainst which the isolate occurs. Critically however, allfour experiments demonstrated that triplet constructionhad absolutely no effect on forced-choice recognition per-formance. Thus, overall, the empirical findings suggestthat there is something very special about the way deci-sion processes interact with triplet construction duringoddity judgments.

Acknowledgment

This work was supported by National Institutes ofHealth Grant MH073982.

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Some memories are odder than others: Judgments of episodic oddity violate known decision rules

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