A Diffusion Model Account of Masked Versus Unmasked Priming: Are They Qualitatively Different?

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1 Journal of Experimental Psyhology: Human Pereption and Performane 2013, Vol. 39, o. 6, merian Psyhologial ssoiation /13/$12.00 DO: /a Diffusion Model ount of Masked Versus Unmasked Priming: re They Qualitatively Different? Pablo Gomez DePaul University Manuel Perea Universitat de Valènia Roger Ratliff The Ohio State University This doument is opyrighted by the merian Psyhologial ssoiation or one of its allied publishers. This artile is intended solely for the personal use of the individual user and is not to be disseminated broadly. n the past deades, hundreds of artiles have explored the mehanisms underlying priming. Most researhers assume that masked and unmasked priming are qualitatively different. For masked priming, the effets are often assumed to reflet savings in the enoding of the target stimulus, whereas for unmasked priming, it has been suggested that the effets reflet the familiarity of the prime target ompound ue. n ontrast, other researhers have laimed that masked and unmasked priming reflet essentially the same ore proesses. n this artile, we use the diffusion model (R. Ratliff, 1978, theory of memory retrieval, Psyhologial Review, Vol. 85, pp ) to aount for the effets of masked and unmasked priming for identity and assoiatively related primes. The fits of the model led us to the following onlusion: Masked related primes give a head start to the proessing of the target ompared with unrelated primes, whereas unmasked priming affets primarily the quality of the lexial information. Keywords: priming, lexial deision, RT, diffusion model n visual-word reognition laboratory tasks (e.g., lexial deision, naming), the response to a target stimulus an be influened by the previous presentation of a related item the so-alled prime (e.g., the response to the string DOCTOR is faster or more aurate when following a related prime suh as nurse than when following an unrelated prime suh as horse). Priming effets an our in the absene of expliit instrution to use the prime s information when responding to the target. Early researh in visual-word reognition foused on visible, unmasked primes, and the potential role of partiipants strategies under these irumstanes led a number of researhers to manipulate the stimulus onset asynhrony (SO) between prime and target (e.g., eely, 1977) to explore issues around automati versus ontrolled proesses (Posner & Snyder, 1975). long these lines, the introdution of masked priming (Forster & Davis, 1984) was an important development; the assumption behind masked priming was that the results would reflet early automati proesses. n this study, we used an expliit modeling method (Ratliff s, 1978, diffusion model) to examine This artile was published Online First May 6, Pablo Gomez, Department of Psyhology, DePaul University; Manuel Perea, Departamento de Metodologia, Universitat de Valènia, Valenia, Spain; Roger Ratliff, Department of Psyhology, The Ohio State University. This researh was funded by Grant PS from the Spain Ministry of Siene to Manuel Perea and by Grant R01-G17083 from the ational nstitute on ging and Grant F from the ir Fore Offie of Sientifi Researh to Roger Ratliff. Correspondene onerning this artile should be addressed to Pablo Gomez, Department of Psyhology, DePaul University, Chiago, L pgomez1@depaul.edu 1731 the differenes among masked versus unmasked priming in the most popular laboratory word identifiation task: lexial deision (e.g., see Dufau et al., 2011). The masked priming paradigm has been used to examine the initial stages of visual-word reognition (Forster & Davis, 1984; see also Forster, Mohan, & Hetor, 2003; Grainger, 2008; Kinoshita & Lupker, 2003, for reent reviews). The typial trial in a masked priming experiment onsists of a mask (e.g., #####) that is presented for 500 ms, whih is followed by a briefly presented lowerase prime (for around ms) and is subsequently replaed by an upperase target (e.g., the target word TRL may be preeded by the identity prime trial or by an unrelated prime suh as oean). Under these onditions, partiipants are not only not aware of the prime s identity, but are often also unaware of its existene. One basi tenet in masked priming studies is that the obtained priming effets are qualitatively different from priming effets in standard (unmasked) priming paradigms (Forster et al., 2003; Grainger, 2008). ndeed, funtional MR evidene has revealed that masked primes produe some ativation in the so-alled visual word form area, and ativation is negligible in frontal and parietal areas; in ontrast, unmasked primes produe a muh larger ativity at parietal, prefrontal, and ingulate areas (see Dehaene et al., 2001). Unlike unmasked priming, whih an be mediated by an episodi memory trae of the prime, masked priming effets are supposed to reflet a transitory hange in the aessibility of lexial/semanti information. However, work by Bodner and Masson (2003; see also Bodner & Masson, 2001) has alled into question the alleged qualitative differene between masked and unmasked priming. Bodner and Masson (2001) suggested that, for both masked and unmasked priming, a prime event reates a memory resoure that an be reruited during target presentation to

2 1732 GOMEZ, PERE, D RTCLFF This doument is opyrighted by the merian Psyhologial ssoiation or one of its allied publishers. This artile is intended solely for the personal use of the individual user and is not to be disseminated broadly. aid in the enoding of the target (p. 646). Bodner and Masson s (2001) aount is supported by a key finding: The size of the masked identity priming effet in lexial deision is greater when the proportion of identity trials in the stimulus list is high (0.80) rather than low (0.20; Bodner & Masson, 2001; see also Bodner & Masson, 2003, for a parallel effet with assoiative/semanti primes; f. Perea & Rosa, 2002). This finding mathes the usual result from the standard long-term priming with visible stimuli. Bodner and Masson (2001) argue that this is so beause the masked prime establishes an episodi reord, just like the unmasked prime (i.e., onsious awareness would not be a prerequisite for establishing an episodi reord). The dissoiation of different proessing mehanisms in behavioral experiments is often ontentious, espeially when the mean lateny is the sole dependent variable. n this study, we ontrasted two views of masked/unmasked priming using Ratliff s diffusion model (Ratliff, 1978, 1981, 1985, 1988; Ratliff, Van Zandt, & MKoon, 1999) in an experiment that ompared masked versus unmasked priming. Ratliff s diffusion model has been suessfully applied to lexial deision data (Ratliff, Gomez, & MKoon, 2004; see also Gomez, Ratliff, & Perea, 2007; Ratliff, Perea, Colangelo, & Buhanan, 2004; Ratliff, Thapar, Gomez, & MKoon, 2004; Wagenmakers, Ratliff, Gomez, & MKoon, 2008; see orris, 2009, for a omplete model of lexial aess that shares assumptions with the diffusion model). mportantly, the model allows ognitive proessing to be divided into several omponents: the rate of evidene aumulation (whih reflets the goodness of math between the test string and lexial memory), the deision riteria (i.e., how muh information must be aumulated before a deision an be made), the nondeision omponents of proessing (both enoding and response exeution), and variabilities in the various omponents. n the following paragraphs, we first desribe the diffusion model, and then we indiate what omponents ould be affeted in masked versus unmasked priming depending on whether or not the priming effets originate from the same soures. n partiular, we examine two of the most studied types of relationships between primes as targets: identity priming and assoiative/semanti priming. The Diffusion Model and the Lexial Deision The diffusion model was developed to aount for those deisions that involve a two-alternative hoie and take less than a few seonds (Ratliff, 1978; Ratliff & Rouder, 1998). n the model, the deision-relevant information is aumulated over time in a noisy manner (see Figure 1). response is initiated when the noisy aumulation of evidene reahes one of the two deision boundaries. The loation of the deision boundaries is related to the amount of evidene needed to make a response. The two parameters of the model that desribe the boundary positions are z, the loation of the starting point, 1 and a, the distane between the deision boundaries (with the loation of the negative boundary assumed to be set at zero). The values of a and z reflet speed auray trade-offs and response biases. 2 n the present study, two aspets of the diffusion model are of partiular interest beause they most likely apture the observed priming effets: the enoding of the pereptual information and the quality of suh information. Figure 1. Representation of the diffusion model. () Sequene of events in a trial of a lexial-deision task (x enoding; y evidene aumulation; z motor response). (B) ondeisional omponents of the reation time (RT), whih have a mean expressed by the T_{er} parameter and a range expressed by the s_t parameter. (C) Diffusion model. The parameters represented in Panel C are a boundary separation (z starting point; s_z variability in starting point aross trials; v drift rate; h(greek letter eta) variability in the drift rate aross trials; and s variability in drift rate within a trial). Enoding and Response Exeution Time The diffusion model assumes that the reation time (RT) for a given trial is a sum of three omponents: (1) the enoding time, (2) the time taken by the aumulation of evidene proess, and (3) the time taken by the response exeution stage. The sum of Components 1 and 3 is represented by the nondeision parameter T er. ote that enoding and response exeution annot be separated in the model. This nondeision time is assumed to be uniformly distributed with range s t. Of partiular interest here is the possible ontribution of the masked and unmasked primes to the enoding proess. Some verbally formulated explanations of priming posit that the presentation of a related prime provides a head start in the proessing of the target (see Forster, 1998), whih an be implemented in a diffusion model framework as affeting the enoding time (T er parameter). We must note here that the term enoding has a speifi interpretation in the diffusion model. t represents proesses that terminate before the beginning of the aumulation of evidene in the deision proess (i.e., the deision proess itself, represented by the jagged lines in Panel C of Figure 1). This might not be the same as other proesses that are also termed enoding proesses in other models and theories. Drift Rate The average rate of aumulation of evidene is termed drift rate. t an be thought of as a quality of the extration of evidene. 1 The model assumes variability in the z parameter, whih is uniformly distributed with range s z. 2 For a omprehensive exploration of the behavior of these parameters in the lexial-deision task, see Wagenmakers et al. (2008).

3 MODELG MSKED D UMSKED PRMG 1733 This doument is opyrighted by the merian Psyhologial ssoiation or one of its allied publishers. This artile is intended solely for the personal use of the individual user and is not to be disseminated broadly. Easy stimuli, suh as high-frequeny words in a lexial-deision task, are assoiated with large positive drift rates (Ratliff, Gomez, & MKoon, 2004). Similarly, non word-like nonwords are assoiated with large but negative drift rates. Within a trial, the aumulation of evidene has variability that is refleted in the jagged line in Figure 1. n addition to the within-trial variability, there is normally distributed variability in the drift rate from trial to trial (parameter ). This is so beause all trials that nominally are in the same ategory (e.g., high-frequeny words) annot be expeted to have exatly the same disriminability. On the Qualitative Differenes Between Masked Versus Unmasked Priming n Forster s view, masked priming would reflet a savings effet, in whih some of the proessing arried out on the prime is transferred to the word target (see Forster, 2009; Forster et al., 2003). Speifially, Forster (1999) indiated that the magnitude of masked identity priming ought to be equal to the duration of the prime (assuming that the target appears immediately after the prime) (p. 10), and he provided data supporting this view. f this interpretation is orret, masked identity priming should be revealed as a shift in the entire RT distribution, without any hange in spread. Thus, if we implement Forster s verbal explanation within a diffusion model framework, the effet of the masked identity prime would be refleted as a hange in the nondeision omponent (T er ), whereas the rate of aumulation of information would be the same aross onditions. With respet to masked assoiative/semanti priming, Forster (2009) indiated that the semanti evaluation of the target is ompleted more rapidly beause the relevant semanti information retrieved by the prime is still stored in the semanti buffer (p. 46). We believe that this latter verbal desription does not have a lear translation into the diffusion model parameters. One ould imagine that this buffer provides a head start (i.e., a hange in T er ), but it ould also asade into the evidene being aumulated in the diffusion proess (i.e., a hange in drift rate). Similar views of masked priming are used in the spatial oding model (Davis, 2010) and in the letters in time and retinotopi spae (LTRS) model (delman, 2011). n the spatial oding model, the mehanism at play during masked priming is that the letter units are reset with the presentation of a new stimulus (e.g., when the prime is removed to give plae to the target). When this happens, if there is lexial ativation already in ourse, this ativation is not reset and produes the advantage of the identity ondition over the unrelated ondition. Similarly, in the LTRS model, priming is onsidered as a savings effet or a head start that takes plae during the time in whih the target is a andidate for lexial identifiation of the prime (delman, 2011). To explain unmasked priming effets, one influential view is that when the prime is visible, prime and target are merged in short-term memory to form a ompound ue (see Ratliff & MKoon, 1988, for further details). 3 More speifially, Ratliff and MKoon (1988) indiated that the familiarity value given by the omputation of the strength of the ompound ue is used as the drift rate in a diffusion (random walk) deision proess (p. 388; i.e., rate of aumulation of information). This implies that the RT distribution in the related ondition would be less skewed than in the unrelated ondition. We should stress that this mehanism would apply similarly to assoiative priming and identity priming, with the (obvious) differene that the familiarity of the ompound ue of two idential words would be stronger than that of two semantially related words (i.e., identity priming implies not only semanti overlap but also form/phonologial overlap). Therefore, both unmasked identity and unmasked assoiative priming would reflet hanges in drift rate aross onditions in a diffusion model. lternatively, in Bodner and Masson s (2001, 2003) view (see also Plaut & Booth, 2000), both masked and unmasked primes would form an episodi trae independent of the visibility and the awareness of the prime. The explanation proposed by Bodner and Masson (2001, 2003) is similar to that of Ratliff and MKoon (1988) for unmasked priming. The only differene is that, unlike Ratliff and MKoon, the ompound ue would be reated regardless of the partiipant s awareness of the prime. Therefore, the predition is lear: The ompound ue of the event would determine drift rate (i.e., rate of aumulation of information). n a diffusion model, this would imply that priming effets would be refleted in terms of drift rate for both unmasked and masked primes. Previous researh omparing masked versus unmasked priming from an expliit model perspetive is very sare. n a reent study, Balota, Yap, Cortese, and Watson (2008) ompared the RT distributions of semanti priming effets with masked versus unmasked primes using the estimates from the ex-gaussian distribution rather than fits from the diffusion model. Using a masked priming paradigm at a 42-ms SO, Balota et al. (Experiment 7) found a nonsignifiant 13-ms effet of semanti priming; note that the size of this effet is in line with previous masked semanti priming experiments (e.g., Perea & Lupker, 2003). n addition, using visible primes at a 200-ms SO, Balota et al. (Experiments 2 and 3) found that the semanti priming effet was larger at the higher quantiles; unexpetedly, this pattern was not refleted in ex-gaussian fits in whih only the and parameters were affeted by priming, but not the parameter (whih has been traditionally related to hanges in spread). The presene of an inreasing assoiative/semanti priming effet at the higher quantiles is onsistent with a ompound-ue model (see above), whereas the apparent mismath with the fits might be due to misspeifiation of the ex-gaussian parameters. With respet to unmasked identity priming, previous appliations of the diffusion model to the lexial-deision task suggest that it might affet drift rates (and onsequently the spread of the RT distribution). n a long-term (unmasked) identity priming experiment in whih items were presented more than one in the experiment, Ratliff, Gomez, and MKoon (2004) found that the item identity yielded hanges in the drift rate. To our knowledge, very few published studies have analyzed the differenes between masked and unmasked priming from a modeling perspetive; nonetheless, we would like to note that Pollatsek, Perea, and Carreiras (2005) reported that form-related priming produed a shift in the RT distribution relative to an unrelated priming on- 3 lthough we aknowledge that there are other potential explanations of unmasked priming, the ompound ue model has three advantages: (1) t provides a unified aount of identity and assoiative priming, (2) it makes straightforward preditions in terms of the diffusion model, and (3) the idea of a ompound ue has also been adopted (with some hanges) in the ompeting view of Bodner and Masson.

4 1734 GOMEZ, PERE, D RTCLFF This doument is opyrighted by the merian Psyhologial ssoiation or one of its allied publishers. This artile is intended solely for the personal use of the individual user and is not to be disseminated broadly. dition. Similarly, Kinoshita, Mozer, and Forster (2011) examined the prime proportion effets on masked and unmasked priming and showed that visible primes (but not masked primes) showed adaptation to the prime target ontingeny. Taken together, these data suggest that the mehanism underlying masked and unmasked priming might be different. n addition, previous researh has tried to aount for priming from a modeling perspetive. otably, Jaobs and Grainger (1992) were the first to simulate the masked (form) priming task with a quantitative model of visual-word reognition the interativeativation model (see also Perea & Rosa, 2000, for simulations of masked identity priming with this model). n these simulations, the prime is presented for a short number of proessing yles and then it is replaed by the target (see also Davis, 2010, for a similar logi for the simulations with the spatial oding model). That is, masked priming simulations with the interative ativation model and the spatial oding model assume that the prime offers a head start similar to Forster s predition (e.g., Forster, 1999; Forster et al., 2003). t is important to note, however, that the spatial oding model also employs Rumelhart and Siple s (1974) upperase font. This implies that the prime and the target in the simulations would be exatly the same. s Jaobs and Grainger indiated, a useful extension of the [interative-ativation] model would inlude a set of lowerase letters, thus allowing a more preise simulation of priming studies involving a hange in ase (p. 1179). Finally, it may be worth notiing that this approah of modeling priming effets in an interative-ativation model annot tell masked from unmasked priming effets. Overview of the Experiment n the present experiment, we used the diffusion model to test Forster s (e.g., Forster, 1999; Forster et al., 2003) versus Bodner and Masson s (2001, 2003) aount of the differenes between masked and unmasked priming. We foused on identity and assoiative/semanti priming beause these are the two most studied phenomena in previous priming experiments. To best ompare the effets of the fators of interest in lexial-deision performane, we performed all manipulations within subjets. n our experiment, we manipulated the relationship between the prime and the target through identity priming (prime: house; target: HOUSE) and assoiative priming (prime: dotor; target: URSE). n addition, these targets ould be preeded by a masked prime or by an unmasked visible prime. Method Partiipants Twenty DePaul University students partiipated for redit in an introdution to psyhology lass. Materials For the assoiative priming and the identity priming experiments, we seleted 160 words for eah type of stimulus. They were mathed in word frequeny: M 129 per million (Kuera & Franis, 1967) and other relevant variables (see the Tables 1 and 2). For the assoiative priming onditions, the items were obtained from the University of South Florida free assoiation norms (elson, MEvoy, & Shreiber, 2004). The mean assoiation for the assoiative priming pairs was Proedure Partiipants were tested in groups of one to three. PCompatible omputers ontrolled presentation of the stimuli and reording of RTs. Stimuli were presented on a 15-in. omputer monitor in 24-point BrHand font (similar to nonproportional Courier fonts). For the masked bloks, on eah trial, a forward mask onsisting of a row of hash marks (#s) of equal length to the stimulus (i.e., four, five, or six haraters long) was presented for 500 ms in the enter of the sreen. ext, the prime was presented in lowerase letters and stayed on the omputer sreen for 56 ms. The prime was then followed by the presentation of the target stimulus in upperase letters. Both prime and target were presented in the same sreen loation as the forward mask. The target stimulus remained on the sreen until the partiipant s response. For the unmasked bloks, there was a fixation area that mathed the size of the stimulus in terms of number of letters (e.g., ) for 200 ms; the prime was presented in lowerase letters for 200 ms, and then the target in upperase letters was kept on the sreen until a response was made. Partiipants were told that words and nonwords would be displayed on the monitor in front of them, and that they should press the? key to indiate whether the upperase item was an English word and a different key (Z) to indiate whether the stimulus was not a word. They were instruted to respond as quikly as possible while trying not to make errors. Eah partiipant reeived a different random order of stimuli, and half of the partiipants performed the masked priming trials first, followed by the unmasked priming trial. Eah partiipant reeived a total of 20 pratie trials prior to the experimental phase. Partiipants were presented with 40 items per ondition (40 words preeded by an identity prime, 40 words preeded by a identity ontrol prime, 40 words preeded by an assoiative prime, 40 words preeded by an assoiative ontrol prime, 40 nonwords preeded by an identity prime, and 40 nonwords preeded by a ontrol prime). There were 160 filler nonwords with word primes and 80 filler words with unrelated nonword primes; this way, the primes were not preditive of the lexial status of the target. The experimental session lasted approximately 45 min. Results Empirial Findings Responses shorter than 250 ms or longer than 1,800 ms were removed from the analyses (less than 3% of the data); in addition, one subjet was removed beause s/he pressed the word button more than 90% of the trials regardless of ondition. The results are straightforward (see Table 3 for a summary of the empirial results), and beause our goal was not to establish the existene of either identity or assoiative priming (whih are very well established), but instead to provide a diffusion model aount 4 The materials are available online at WPL/Online_ppendies_files/materials.txt

5 MODELG MSKED D UMSKED PRMG 1735 Table 1 Parameters of Materials for the Word tems Obtained With -wath (Davis, 2005) Priming target CELEX KF-FR BC-FR EST-FR FM LE-L O O2 MG MG2 dentity Mean SD ssoiative Mean SD This doument is opyrighted by the merian Psyhologial ssoiation or one of its allied publishers. This artile is intended solely for the personal use of the individual user and is not to be disseminated broadly. ote. See Davis (2005) for a full disussion of these statistis. CELEX, KR-FR, and BC-FR word frequeny ounts aording to the Celex (Baayen, Piepenbrok, & van Rijn, 1995), Kuera and Franis (1967), and British ational Corpus (Leeh, Rayson, & Wilson, 2001), respetively; EST-FR estimated word frequeny (Balota et al., 2001); FM familiarity in a (1 to 7 sale); LE-L number of letters; Coltheart s neighborhood size; O and O2 age of aquisition based on Gilhooly and Logie (1980) and Bird, Franklin, and Howard (2001), respetively, MG and MG2 imaginability from MRC Psyholinguisti Database (Coltheart, 1981) and Bird et al., respetively. of these phenomena, the results are disussed only briefly. s expeted, for both masked and unmasked modalities, the word targets were responded to faster when preeded by an identity prime than when preeded by an unrelated prime: masked, priming effet 60 ms, t(18) 4.55, p.001; unmasked, priming effet 105 ms, t(18) 9.98, p.001. Similarly, for the assoiative pairs, target words (in both the masked and unmasked onditions) were responded to faster when preeded by an assoiatively related prime than when preeded by an unrelated prime, although only for the unmasked ondition was the priming effet signifiant: masked, priming effet 12 ms, t(18) 1.08, p.29; unmasked, priming effet 44 ms, t(18) 4.75, p.001. (ote that, despite being nonsignifiant, the size of the masked assoiatively priming effet is similar to that in previous experiments in the literature; e.g., Perea & Lupker, 2003.) The priming effets for the nonword targets (i.e., identity masked priming and identity unmasked priming) did not produe any signifiant effets (ts 1), and in fat there were very small inhibitory trends. n terms of the auray data, performane for all word onditions were at a near-eiling performane (all auraies were at or above 95%), and none of the t tests showed signifiant effets. The analysis of the nonword targets, on the other hand, showed a lower auray for the nonwords when preeded by an identity prime than when preeded by an unrelated prime in the masked ondition: auray for primed versus auray for ontrol 0.944, t(18) 2.19, p.04, as well as the unmasked ondition, auray for primed.910 versus auray for ontrol 0.936, Table 2 Parameters of Materials for the onword tems Obtained With -wath (Davis, 2005) t(18) 2.77, p.01. This effet is disussed with the fits of the model to nonword data. Modeling We use the diffusion model to test Forster s (Forster, 1999; Forster et al., 2003) versus Bodner and Masson s (2001, 2003) aount of the differenes between masked and unmasked priming. We fitted the data from the masked and the unmasked trials separately. We performed the fits of the model in two ways: First, for display in the figures and tables, we present the fits to the grouped data that we obtained using the fitting routines desribed by Ratliff and Tuerlinkx (2002). We alulated the auray and lateny (i.e., the RTs at the 0.1, 0.3, 0.6, 0.7, and 0.9 quantiles) for word and nonword responses for all onditions and for all subjets, and we obtained the group-level performane by averaging aross subjets (i.e., vinentizing; Ratliff, 1979; Vinent, 1912). Seond, for the analyses of the effets of priming on the parameters of the model, we fitted the model to eah subjet s data and then examined the differene in the T er and drift rate parameters using standard inferential statistis tehniques. Fitting averaged data is an appropriate proedure for fitting the diffusion model. n previous researh (Ratliff, Thapar, et al., 2004; Ratliff, Thapar, & MKoon, 2001), fits to averaged data provided similar parameter values to parameter values obtained by averaging aross fits to individual subjets. The quantile RTs were fed into the diffusion model. Table 3 Summary of Results Condition Related Control RT t(18) p onword item BTK BTY TTK TTY HFMX FM Mean SD ote. See Davis (2005) for a full disussion of these statistis. BTK and BTY bigram token and type frequenies obtained from the COBULD/ CELEX (Baayen et al., 1995) orpus; TTK and TTY trigram token and type frequenies obtained from the COBULD/CELEX orpus; Coltheart s neighborhood size; HFMX highest frequeny of a neighbor; HFM mean frequeny of neighbors. Masked assoiative words 634 (0.04) 646 (0.04) Masked identity words 604 (0.04) 665 (0.05) Masked nonwords 750 (0.08) 743 (0.06) Unmasked assoiative words 654 (0.04) 698 (0.03) Unmasked identity words 599 (0.04) 704 (0.05) Unmasked nonwords 763 (0.09) 761 (0.06) ote. Error rates appear within parentheses. RT reation time.

6 1736 GOMEZ, PERE, D RTCLFF Masked Unmasked This doument is opyrighted by the merian Psyhologial ssoiation or one of its allied publishers. This artile is intended solely for the personal use of the individual user and is not to be disseminated broadly. ms For the two modeling methods (i.e., grouped data and subjetby-subjet), the model generated for eah response the predited umulative probability within the timeframes bounded by the five quantiles. Subtrating the umulative probabilities for eah suessive quantile from the next higher quantile yields the proportion of responses between eah quantile, whih are the expeted values for the hi-square omputation. The observed values are the empirial proportions of responses that fall within a bin bounded by the 0.0, 0.1, 0.3, 0.5, 0.7, 0.9, and 1.0 quantiles, multiplied by the proportion of responses for that hoie (e.g., if there is a response proportion for the word alternative, the proportions would be , , , , , and ). Masked priming. There are two features of the masked priming data that needed to be aounted for (see Figure 2): (1) There was a shift in the RT distributions as a funtion of both identity and assoiative priming; and (2) there was a null effet of priming in the mean RT for nonwords; however, there was an effet of the RT distributions: n lower quantiles, the RTs were shorter for the related ondition than for the unrelated ondition and, at the same time, this pattern reversed in the higher quantiles. Grouped data. Our model omparison strategy for the grouped data was to begin with the simplest implementation of the model (with the fewest number of free parameters) and then to add free parameters until the gain in the quality of fits was negligible. 5 n other words, we p(orret) ms p(orret) Figure 2. Lateny probability funtion for unmasked and masked priming onditions for the grouped data. The points represent (from bottom to top) the 0.1, 0.3, 0.5, 0.7, and 0.9 quantiles. Within eah panel, from left to right, the olumns of quantile reation times (RTs) represent the responses to assoiative/semanti primes () and their ontrols (), identity primes () and their ontrols (), and nonwords () and their ontrols (). The light irles show the model s fits. looked to jointly maximize desriptive auray (goodness of fit) and parsimony (small number of free parameters). Pure distributional shifts (hanges in the loation of the distributions) are naturally aounted for by allowing the T er parameter to vary from the unrelated primes to the related primes. model with a single T er for all onditions yielded 2 362, and allowing T er to vary yielded , whih is 77% smaller (see Ratliff & Smith, 2010, p. 90, Table 1, for a similar result). model with only T er free to vary as a funtion of priming, however, ould not aount for the pattern of results for nonwords. Hene, we needed to allow the drift rate for the primed nonwords to be different from the drift rate for their ontrols, with less negative drift rate for the primed nonwords than for their ontrols. 6 ndividual subjet data. nother way to analyze the effet of manipulations on the parameters of the model is by fitting a model with free parameters to data for eah subjet, and then to arry out standard inferential statistis on the model s parameters. To this end, we onduted subjet-by-subjet fits and we obtained the drift rates and T er parameters for eah of the onditions. Planned t tests 5 The hi-square values in Table 4 are based on group data, so they annot properly be used as absolute measures of fit. 6 For the T er -only model, , and for the T er drift nonword model, ; hene Ter Ter drift 6.75, or an 8% improvement in the quality of the fit.

7 MODELG MSKED D UMSKED PRMG 1737 Table 4 Parameters of the Diffusion Model Masked priming a z s z Drift T er s t p 0 2 This doument is opyrighted by the merian Psyhologial ssoiation or one of its allied publishers. This artile is intended solely for the personal use of the individual user and is not to be disseminated broadly Words: W asso: W id: W id: W ntrl: W ntrl: W id: W ntrl: Unmasked priming W asso: W id: W id: W trl & asso: W trl: W id: W id: W trl: W trl: ote. W asso word targets with assoiative primes; W id word targets with identity primes; W rtl word targets with unrelated primes; W id nonword targets with identity primes; W rtl word targets with unrelated primes. were performed to ompare the parameter values for the primed onditions against the parameter values for their ontrols. For T er, all effets of priming were signifiant: for assoiative priming, t(18) 2.154, p.045; for identity priming, t(18) 9.749, p.01; and for nonwords, t(18) 2.158, p.045. For the drifts, neither word identity priming nor assoiative priming yielded signifiant differenes, t(18) 1; however, for nonwords, there was a signifiant differene in drift rate between related and ontrol items, t(18) 2.411, p.027. The two fitting methods provide onverging evidene: ording to the diffusion model-based aount, the lous of the masked priming effets for words is the enoding proess (with larger effets in the T er parameter for identity priming than for assoiative priming, as an be seen in Table 4). n ontrast, for nonwords, identity priming seems to failitate the enoding proess (reduing the T er value) while inreasing the word likeness of the stimuli (making the drift rate value less negative). Unmasked priming. Compared with masked priming, unmasked priming produed numerially larger effets in the mean RT as a funtion of priming. For the nonwords, although there was no signifiant differene in the mean RT between the related targets and their ontrols, the RTs for the 0.1 and 0.3 quantiles were shorter for the related ondition than for the unrelated ondition. However, for the 0.7 and 0.9 quantiles, the diretion of the effet reversed. Grouped data. For unmasked priming, the first model we fit to the data was the one we used for the masked priming ondition (with T er allowed to vary as a funtion of priming). This model missed some important features of the data quite badly ( ). Bear in mind that hanges in the T er parameter produe shifts in the RT distributions; however, in unmasked priming for word targets, the effets go beyond a shift in the distribution and inlude a larger spread in the higher quantiles for the unrelated onditions relative to the related onditions. n addition, for nonword targets, there was a nonmonotoni effet of priming as a funtion of quantiles. dding a free drift rate parameter for primed nonwords improved the quality of the fits for nonwords but still misses the qualitative features of the word data ( for the T er drift primed.nonwords model). ugmenting the model by allowing not only the T er parameter but also the drift rates to vary as a funtion of primes for both word and nonwords trials improved the quality of the fits, , whih is smaller by 110 from the T er -only model. We prefer this augmented model beause, with two extra parameters the gain in goodness of fit is quite large. ote that for the assoiative unmasked priming ondition, the T er parameter has the same value as the unrelated ontrol ondition, and there is no loss in the goodness of fit if the T er parameter is kept the same for the unrelated ondition and for the assoiative priming ondition. This finding reveals that although unmasked assoiative priming inreases the word likeness of the target item, it does not ontribute to the enoding of the target string. t is worth mentioning that although the fous of this researh was not the effets of priming on nonwords, there is a robust debate on this issue. Our analysis suggests that the failitatory effets on T er and the inhibitory effets on drift rate anel eah other out, so future researh might need to inlude a neutral ondition to fully explore this issue. n any ase, Kinoshita and orris (2010) have shown robust masked priming effets for nonwords in a same different task, whih suggests a prelexial status of the failitatory effet. ndividual data. The subjet-by-subjet fits were arried out the same way as for the masked priming data. The effets of priming on the drift rates were signifiant for assoiative priming of words, t(18) 2.509, p.022; for identity priming of words, t(18) 2.134, p.046; and also for nonwords, t(18) 2.911, p.009. The effets of unmasked priming on T er were signifiant for all priming onditions; for word identity priming, t(18) 7.808, p.01; for nonword identity priming, t(18) 3.030, p.01. Somewhat surprisingly, we also found an effet on T er for assoiative priming, t(18) 2.150, p.045, although the effet was numerially very small. Disussion The empirial results of the present experiment are lear: Masked identity priming effets were approximately the same at eah quantile in the RT distributions (i.e., they involved a shift in the entire distribution); in ontrast, unmasked priming effets (both identity priming and assoiative priming) involved a hange in the spread of the RT distributions. More important, these findings an

8 1738 GOMEZ, PERE, D RTCLFF This doument is opyrighted by the merian Psyhologial ssoiation or one of its allied publishers. This artile is intended solely for the personal use of the individual user and is not to be disseminated broadly. be aounted for by the diffusion model in a straightforward manner: On the one hand, masked identity priming affets the parameter orresponding to enoding proesses (T er ), but not the parameter orresponding to the quality of information (drift rates). On the other hand, unmasked priming affets both parameters: the quality of information (drift rates) in both assoiative and identity priming, and also the enoding proess (partiularly for identity priming; note that in the subjet-by-subjet fits, there was a fairly small but signifiant effet in the differene in T er between the related and unrelated primes for assoiative unmasked priming). Therefore, masked priming is qualitatively different from unmasked priming. To our knowledge, this is the first dissoiation between these two parameters in the model in the lexial-deision task. The diffusion model is a model of the deisional proess in the lexial-deision task and is void of a lexion or expliit word reognition proesses. However, we an use the parameter behavior in the present work to deepen our understanding of the priming proesses by interpreting existing models through the lens of the diffusion model. To this end, theories that have been verbally stated of even omputationally implemented an be mapped into diffusion model parameters. f we interpret the diffusion model fits in light of other theories, we find that our aount of masked identity priming is ompatible with a savings aount, in whih priming ours mainly beause of hanges in enoding time (e.g., note that the value of T er is lose to that of the prime duration; see Forster, 1999), whereas unmasked priming is onsistent with a ompound-ue aount in whih prime target relatedness inreases the quality of the lexial information that drives the deision proess. To our knowledge, this is the first dissoiation between drift rate and T er in the model within the lexial-deision task. The effet on T er has several impliations for theories of priming and for general theories of pereptual deision making. The assumption behind this parameter is nontrivial: There is a stage in the proessing of pereptual information in whih the inoming evidene is not used toward the aumulation of evidene driving the deision proess (e.g., the word vs. nonword deision in the lexial-deision task). Hene, to make a deision about a string of letters, partiipants must first enode it, and only after that proess is over, an they math the obtained pereptual representation against their lexial knowledge. 7 Within the ontext of evidene aumulation models as applied to lexial proesses, two questions arise: (1) How is it that the system ends the aumulation-free enoding stage and begins the aumulation proess (the diffusion per se)? (2) What exatly do we mean by enoding in the domain of masked priming? Regarding the first question, Ratliff and Smith (2010) offered two possible explanations in the ontext of a letter disrimination task; aording to the first one, it is not until the stimulus is enoded in visual short-term memory that the aumulation of evidene begins; aording to the seond one, there is large inhibition of the aumulation of evidene proess until the quality of the stimulus representation reahes a threshold. n their researh, Ratliff and Smith found that the effets in the first quantiles of the RT distributions happened only when a more abstrat representation was needed to perform the task (i.e., there was an effet for letter disrimination but not for luminosity disrimination). rguably, the lexial-deision task requires an even more oneptual representation than their letter disrimination task. This leads us to the seond issue: What is the nature of the enoding proess in masked priming? dentity priming amounts to a head start relative to an unrelated prime, and identity priming does not seem to affet the quality of the lexial information in the deision; however, it does not seem to affet the quality of the lexial information. number of models are ompatible with this view, most notably, those that assume that there is some form of reset or self-inhibition mehanism (see Grainger & Jaobs, 1999) in whih a mismath between inoming sensory information (e.g., a prime and a target) triggers an inhibitory reset. Jaobs and Grainger (1992) had a similar intuition when they suggested that in an interative-ativation model-based aount, identity priming amounts to having a head start of a few yles of proessing (see also delman, 2011, and Davis, 2010, for reent modeling efforts along the same lines). ote, however, that the mapping from an interative-ativation model into a stohasti aumulation of evidene framework (e.g., the diffusion model) is not trivial. This is beause ativation of nodes in the interative ativation arhiteture is deterministi, and errors our beause of stohasti hoie only at the very end of proessing. The diffusion model represents noise in the deision proess (within-trial noise) and noise in the stimulus/lexial representation driving the deision proess as aross-trials variability in drift rate. The distintion between the enoding proess and the evidene aumulation proess is partiularly lear in the ase of identity priming for nonwords. Related nonwords (ompared with their ontrols) are less aurate, have shorter RTs at 0.1 and 0.3 quantiles, but have longer RTs at 0.7 and 0.9 quantiles. 8 dentity priming seems to provide time savings relative to the unrelated ontrols, and it makes it more diffiult to orretly identify the string as a nonword. Modeling unmasked priming with drift-only and T er -only models does not allow us to apture a pattern like this. The interplay of these two parameters yields inonsistent effets of priming on nonword targets (see Perea, Gomez, & Fraga, 2010, and Whitney, Bertrand, & Grainger, 2011, for disussion). Different studies might have eliited different proportions of failitatory and inhibitory trials, and future researh should try to dissoiate the fators that may ontribute to the enoding benefits from the fators that may inhibit the identifiation of a nonword target. t is important to note that our findings are onsistent with the semanti priming experiments onduted by Balota et al. (2008). With unmasked primes, they found an inreasing semanti priming effet at the higher quantiles (see Figures 7 and 8 of Balota et al.); note, however, that they failed to find a hange in the parameter of the ex-gaussian distribution. 9 With masked primes, Balota et al. 7 t is important to note that during this stage, noise (without the signal from the stimulus) is most likely not aumulated either, as that would reate a large proportion of fast errors. 8 We explored whether this pattern of results might have been produed by a ombination of a few items produing failitation and other items produing inhibition; to this end, we performed a multiple regression using all the orthographi variables as regressors and the priming effet as the dependent variable, but none of the effets were signifiant. We also wondered whether this pattern was produed by just a handful of subjets, but 15 of the 19 partiipants showed it. 9 n Experiments 2 and 3 of Balota et al. (2008), the effet of semanti priming was assumed to be due to hanges in the and omponents of the ex-gaussian distribution and not in the omponent, whih is usually the responsible for the tail of the RT distribution.

9 MODELG MSKED D UMSKED PRMG 1739 This doument is opyrighted by the merian Psyhologial ssoiation or one of its allied publishers. This artile is intended solely for the personal use of the individual user and is not to be disseminated broadly. found a small, nonsignifiant masked semanti priming effet, as also ourred in the present experiment. Clearly, the small magnitude of masked semanti priming does not allow to make strong inferenes on the preise nature of the underlying effets; note that previous experiments with masked assoiative/semanti priming have usually employed a large sample size to obtain a signifiant effet (e.g., see Perea & Lupker, 2003). n summary, by using expliit modeling methods (i.e., fits from the diffusion model), the present lexial-deision experiment has revealed that masked and unmasked priming involve different ognitive proesses: Related primes give a head start to the proessing of the target ompared with unrelated primes, whereas unmasked priming involves hanges in the deision proesses. This provides support for the use of the masked priming tehnique to examine the enoding mehanisms during the early stages of visual-word reognition. Referenes delman, J. (2011). Letters in time and retinotopi spae. Psyhologial Review, 118, doi: /a Baayen, R. H., Piepenbrok, R., & van Rijn, H. (1995). 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