Crossmodal temporal discrimination: Assessing the predictions of a general pacemaker counter model

Transcription

1 Journal Perception & Pychophyic 6,?? 68 (?), (7),???-??? Cromodal temporal dicrimination: Aeing the prediction of a general pacemaker counter model ROLF ULRICH and JUDITH NITSCHKE Univerity of Tübingen, Tübingen, Germany and THOMAS RAMMSAYER Univerity of Göttingen, Göttingen, Germany In thi tudy, an extended pacemaker counter model wa applied to cromodal temporal dicrimination. In three experiment, ubject dicriminated between the duration of a contant tandard timulu and a variable comparion timulu. In congruent trial, both timuli were preented in the ame enory modality (i.e., both viual or both auditory), wherea in incongruent trial, each timulu wa preented in a different modality. The model account for the finding that temporal dicrimination depend on the preentation order of the enory modalitie. Neverthele, the model fail to explain why temporal dicrimination wa much better with congruent than with incongruent trial. The dicuion conider poibilitie to accommodate the model to thi and other hortcoming. Thi work wa upported by the Deutche Forchunggemeinchaft (Ul 116/6-3, RA 45/9-3). We thank Suana Ruiz Fernández and Anette Mannhart for their aitance in data collection, and Simon Grondin, Bruno Repp, Bettina Rolke, and an anonymou reviewer for contructive and helpful comment. Correpondence concerning thi article hould be addreed to R. Ulrich, Department of Cognitive and Biological Pychology, Pychological Intitute, Univerity of Tübingen, Friedrichtr. 1, 77 Tübingen, Germany ( ulrich@uni-tuebingen.de). Time i an eential component of our mental life. Hence, it i not urpriing that for many year, philoopher and pychologit have been intrigued by the quetion of how time enter into our experience and thu hape our cognition (Roeckelein, ). For example, the great philoopher Immanuel Kant (1787/1998) argued that pace and time are baic intuition ( a priori Anchauungen ) that tructure our cognition. In addition, he believed that time involve a more ubjective intuition than doe pace (ee Boring, 1957). Thu, among other thing, the tudy of time perception derive from Kant propoal about time. The perception of time alo attracted early pychophyicit (e.g., Mach, 1865; Vierordt, 1868) and ha remained an active field of reearch in pychology up to the preent day (ee Grondin, 1; Meck, 3). More recently, time perception ha become a major object of reearch in the field of the cognitive neurocience (ee Lewi & Miall, 3; Nobre & O Reilly, 4). The quetion of how human perceive time, however, i till a matter of controvery (ee Grondin, 1). Nowaday, variou theorie exit about the mechanim() underlying time perception. Many hare the core aumption of an internal clock baed on neuronal counting (e.g., Allan & Kritofferon, 1974; Creelman, 196; Gibbon, 1991; Grondin, 3; Treiman, Faulkner, Naih, & Brogan, 199). The main feature of uch an internal-clock mechanim are a pacemaker and an accumulator. The pacemaker generate pule, and thee are regitered by the accumulator. The number of pule counted by the accumulator during a certain phyical time interval repreent the perceived duration of thi interval. Thi pacemaker counter model (PCM) ha been uccefully applied to time-related behavior of human (Bendixen, Grimm, & Schröger, 5; Killeen & Taylor, ; Penney, Gibbon, & Meck, ; Rammayer & Ulrich, 1) and animal (Fetterman & Killeen, 1995; Gibbon, 1977). The preent tudy tet new prediction of PCM. More pecifically, we generalized the model uch that it can be applied to a cromodal temporal dicrimination tak. In thi tak, ubject were aked to dicriminate between the duration of a contant tandard and the duration of a variable comparion timulu. The enory modalitie of the tandard and the comparion were either congruent or incongruent. In congruent trial, both the comparion and the tandard timulu were either auditory or viual that i, auditory auditory (a a) or viual viual (v v) wherea in incongruent trial, one timulu wa auditory and the other viual that i, auditory viual (a v) or viual auditory (v a). A hown below, PCM make intriguing prediction for thi tak. Thee prediction were aeed through the reult of three experiment. In Experiment 1 and, the tandard preceded the comparion, wherea in Experiment 3, the comparion preceded the tandard. Copyright 6 Pychonomic Society, Inc. 114

2 CROSSMODAL TIMING 1141 Applying PCM to Cromodal Temporal Dicrimination In thi ection, we extend a general verion of the PCM for temporal dicrimination (Rammayer & Ulrich, 1) to the more complicated ituation in which the tandard timulu and the comparion timulu differ in enory modality. The traditional formulation of PCM (Creelman, 196) aume that the pule rate i identical for both the tandard and comparion interval. Strong evidence exit, however, that the internal clock run at a fater rate when the timulu i auditory than when it i viual (Penney et al., ; Wearden, Edward, Fakhri, & Percival, 1998). Thu, thi traditional formulation of PCM cannot be applied to a bimodal temporal dicrimination tak, in which the tandard and comparion timuli differ in enory modality. To adapt the model to a bimodal ituation, we will aume that the mean interpule time for auditory timuli i horter than the one for viual timuli. On the bai of thi aumption, we will derive the predicted pychometric function of PCM for congruent and incongruent trial, a well a the difference limen (DL) and the contant error (CE) of thi function. Creelman (196) original PCM aume that the pule tream follow a Poion proce. Thi proce implie an exponential interpule ditribution with a modal value of zero; however, thi aumption i generally implauible (ee Rammayer & Ulrich, 1). For example, uch a property i incompatible with the refractory period of neuron, ince ome time need to elape after the production of a pule before the next pule can be generated. Hence, the interpule time could never attain a value of zero. Therefore, Rammayer and Ulrich (1) generalized the aumption of PCM and provided quantitative prediction that do not require pecific ditributional aumption about the interpule time. In order to derive the pychometric function of the generalized PCM, let t and t c be the duration of the tandard interval and the comparion interval, repectively. In any trial, t c may be horter than, longer than, or equal to t. Furthermore, let N(t ) be the number of pule counted during t, and likewie let N(t c ) be the number of pule counted during t c. A in the traditional PCM, ubject are aumed to judge the comparion to be longer than the tandard if N(t c ) N(t ). Therefore, the repone probability of thi judgment C S i computed a Pr{ C S t, t c } Pr{N(t c ) N(t )} Pr{N(t c ) N(t ) } Pr{N(t ) N(t c ) } Pr{D(t, t c ) }. (1) In other word, the repone probability Pr{ C S t, t c } correpond to the probability of the event that the difference D(t, t c ) N(t ) N(t c ) i le than or equal to zero. According to a theorem of renewal theory (ee Rammayer & Ulrich, 1, p. 76), the number of pule N(t) counted during the time interval t i approximately normally ditributed, with mean E[N(t)] t/ and variance Var[N(t)] t / 3. The contant and denote the mean and the tandard deviation of the interpule duration. 1 Note that thi theorem hold for any interpule ditribution, and therefore, no pecific aumption about thi ditribution will be required for deriving prediction from thi model. Predicted Pychometric Function Thi theorem from renewal theory allow the computation of the repone probability Pr{ C S t, t c }, and conequently of the predicted pychometric function. Becaue N(t ) and N(t c ) are (approximately) normally ditributed, the difference D(t, t c ) mut alo be normally ditributed. Specifically, the mean and the variance aociated with thi difference are and E Dt, tc E Nt E Ntc t tc () c Var Dt, t Var Nt Var Nt c c t 3 tc c 3 c. (3) The contant and are the mean and the tandard deviation of the interpule ditribution of the counting proce that prevail during the tandard interval. The correponding mean and tandard deviation of the counting proce during the comparion interval are c and c, repectively. Hence, if the tandard i auditory and the comparion i viual, one would aume c, wherea c hould be aumed if the tandard i viual and the comparion auditory. Since D(t, t c ) i approximately normally ditributed with a mean and variance given by Equation and 3, repectively, Equation 1 extend to E, c Pr" C S", c Dt t t t Var Dt, tc t tc 3 t t tc c 3 c tc t tc c 3 c c 3 c. (4) Note that the ymbol repreent the cumulative ditribution function of a tandard normal ditribution. (It hould be noted, however, that the predicted hape of the pychometric function doe not correpond to the hape of a nor-

3 114 ULRICH, NITSCHKE, AND RAMMSAYER 1. mal ditribution. Thi i becaue the variable t c not only occur in the numerator but alo in the denominator.) The lat expreion can be employed to etablih the pychometric function for the temporal dicrimination tak. Thi i achieved by plotting the repone probability Pr{ C S t, t c } againt the duration t c of the comparion interval. Example of the predicted pychometric function are depicted in Figure 1. Thi example diplay pychometric function for a tandard duration of t 1 mec and for each modality combination of tandard and comparion (a a, v v, a v, and v a). In agreement with previou tudie, a maller mean interpule time for auditory interval than for viual interval i aumed. In addition, we aume a larger tandard deviation for the viual than for the auditory timuli, ince previou reult have indicated a larger pacemaker variability for viual than for auditory interval (ee, e.g., Wearden et al., 1998). Figure 1 reveal everal pecific feature. Firt, a one would expect, repone probability Pr{ C S t, t c } increae monotonically with the duration t c of the comparion. Second, the predicted point of ubjective equality (PSE) of the pychometric function i equal to the tandard duration (1 mec) in congruent but not in incongruent trial. Third, the pychometric function for the congruent auditory condition (a a) i teeper (i.e., ha a maller DL) than the one for the congruent viual condition (v v). Fourth, the magnitude of PSE in incongruent trial depend on whether the comparion i viual or auditory. If it i auditory, the duration of the comparion ha to be horter than that of the viual tandard in order for both interval to be perceived a equally long. If the comparion i viual, however, the duration of the viual comparion ha to be longer than that of the auditory tandard for ubjective equality to be achieved. Both prediction imply reflect the aumption that the internal clock run fater for auditory than for viual ignal. Finally, the preumably mot triking and counterintuitive prediction i that the lope of the pychometric function in v a trial i teeper than in a v trial. In other word, PCM predict a maller DL in the former than in the latter condition. Thi nonobviou order effect on DL i baically due to the longer interpule time for viual than for auditory interval. For example, conider an auditory tandard of 1 mec and aume that one pule i counted, on average, every 5 mec during thi auditory interval. Conequently, pule on average will be counted during the interval. Now conceive a viual comparion with a mean interpule time of 1 mec and aume that an average of 5 pule mut be regitered during the viual interval in order for the comparion to be perceived a longer than the tandard on 75% of all trial. In thi cae, the PSE would correpond to 1 mec, and the DL would reflect the additional duration for generating the five remaining pule that i, DL mec. For the revered timulu order, only 1 pule would be counted on average during the tandard interval. Thu, the PSE would equal mec. Crucially, however, the comparion ha to be further lengthened by DL mec in order to generate 5 more pule, on average, to attain a dicrimination probability of.75, and thi lengthening i le than that required for the comparion in the original order. In ummary, then, the prev a v v Repone Probability Pr { C S } a a a v Duration of Comparion Interval t c (mec) Figure 1. Predicted pychometric function of the pacemaker counter model. Each graph depict the repone probability Pr{ C S t, t c } a a function of the duration t c of the comparion interval. The duration of the tandard, t, i equal to 1 mec. v a, viual tandard with auditory comparion; a a, auditory tandard with auditory comparion; v v, viual tandard with viual comparion; a v, auditory tandard with viual comparion. The mean and the tandard deviation (, ) of the interpule time are ( 1 mec, 4 mec) for auditory interval but ( 13 mec, 1 mec) for viual one.

4 CROSSMODAL TIMING 1143 dicted order effect on DL can alo be attributed to different clock peed for viual and auditory timuli. Predicted DL and CE a Function of Congruency, Modality of the Standard, and Standard Duration In order to enhance the comparion of the predicted with the obtained reult of thi article, it i ueful to derive DL and CE of the generalized PCM. Firt, CE i commonly defined a the difference between the value of t c (.5), which yield Pr{ C S t, t c }.5 (i.e., PSE), and the tandard duration t (i.e., the point of objective equality). The CE can be negative, zero, or poitive. A poitive CE mean that ubject tend to overetimate the duration of the tandard. By contrat, a negative CE indicate an underetimation of the tandard. 3 According to Equation 4, and becaue ().5, the value of t c (.5) mut atify the equation tc(. 5) t. (5) c Solving thi equation for t c (.5) yield the PSE, and inerting the reulting expreion into the definition CE PSE t give c CE t 1. (6) Note that the predicted CE i zero if c, negative if c, and poitive if c. Second, DL i commonly defined a half the interquartile range of the correponding pychometric function that i, tc(. ) tc(. ) DL 75 5, (7) where t c (.5) and t c (.75) are thoe value of t c that yield Pr{ C S t, t c }.5 and Pr{ C S t, t c }.75, repectively. Proceeding from thi definition and from Equation 4, it can be hown that the predicted DL for PCM i a hown in Equation 8 at the bottom of the page, with z The upper panel of Figure provide a numerical illutration of the predicted effect in a bimodal temporal dicrimination tak. Specifically, it how the predicted DL and CE a function of congruency, enory modality of the tandard, and tandard duration t. Firt, a one would expect, DL i larger for the longer tandard. Second, DL i predicted to be omewhat larger for viual than for auditory tandard. Third, DL tend to be lightly maller in congruent than in incongruent trial. Finally, the factor congruency and enory modality are predicted to interact trongly. A wa explained earlier, DL i predicted to be CE (mec) DL (mec) Firt Stimulu - Standard Duration Auditory - 1 mec Viual - 1 mec Auditory - 1, mec Viual - 1, mec Congruent Incongruent Figure. Predicted difference limen (DL, upper panel) and contant error (CE, lower panel) of the PCM a a function of congruency, modality of the tandard, and tandard duration. The legend in the upper panel indicate the modality of the firt timulu and the duration of the tandard; for example, Auditory - 1 mec mean that the firt timulu i auditory and the tandard duration i 1 mec. The mean and the tandard deviation (, ) of the interpule time are ( 1 mec, 4 mec) for auditory interval but ( 13 mec, 1 mec) for viual one. larger in a v than in v a trial and, a one would expect, larger in v v than in a a trial. In addition, the counterintuitive interaction become amplified a tandard duration increae. The lower panel of Figure reveal the predicted CE. In agreement with the previou analyi, and a one would expect, the CE i zero in congruent trial and nonzero in incongruent trial. Specifically, a negative CE i predicted for v a trial and a poitive CE for a v trial. According to PCM, the abolute ize of CE in thee incongruent trial hould increae with tandard duration. We report the reult of three experiment to ae the prediction of PCM for cromodal dicrimination. Specifically, we invetigated whether the pychophyical data reveal a pattern qualitatively imilar to the one in Figure. DL 4 c c c c z z 4 t c / (8)

5 1144 ULRICH, NITSCHKE, AND RAMMSAYER EXPERIMENT 1 Experiment 1 employed a temporal dicrimination tak. On each trial, two ucceive time interval were preented. The firt interval wa the contant tandard, and the econd wa the variable comparion. Subject had to indicate whether the comparion appeared to be horter or longer than the tandard. In congruent trial, the enory modalitie of both the tandard and the comparion were identical (a a or v v), wherea in incongruent trial the modalitie of the timuli differed (a v or v a). The duration of the tandard wa either hort (1 mec) or long (1, mec). When ubject are aked to etimate or compare time interval in the range of econd, ubvocal counting become a very common timing trategy (Grondin, Meilleur-Well, & Lachance, 1999; Poynter, 1989). However, counting ha been hown to be an ineffective trategy for the timing of interval below approximately 1, mec (Grondin et al., 1999). Therefore, in order to avoid explicit counting a an auxiliary timing trategy, the tandard interval for temporal dicrimination of longer interval wa choen not to exceed the critical duration of 1, mec. Method Subject. The ubject were 3 male and 17 female adult volunteer ranging from 19 to 4 year in age (M 5.4, SD 5.). All ubject were undergraduate or graduate tudent at the Univerity of Tübingen and were paid 7.5 for taking part in thi experiment. All had normal hearing and normal or corrected-to-normal viion. They were naive about the purpoe of the experiment. Apparatu and Stimuli. A PC controlled the preentation of the tandard and comparion timuli a well a the recording of the ubject repone. The tandard and comparion timuli were filled auditory or viual interval. The auditory timulu wa a white-noie burt (55.7 db SPL) generated by a SoundBlater-compatible ound card and preented through headphone (Sony MDR-CD 55). The viual timulu wa generated by a green LED diplay (diameter.48º, viewing ditance 6 cm, luminance 48 cd/m ), which wa attached 1 cm above the center of the computer creen. The intenity of the LED wa clearly above threhold, but not dazzling. Procedure. Each ubject wa eated at a table with a keyboard and a computer monitor. A trial tarted with the preentation of a fixation point in the center of the monitor creen. Then, the ubject initiated the trial equence by preing a deignated tart key on the computer keyboard. Thi keypre alo terminated the preentation of the fixation point. After 1, mec, the tandard wa preented. It duration wa either 1 or 1, mec and wa kept contant within a block of trial. The modality of the tandard wa either viual or auditory and varied randomly from trial to trial. Preentation of the variable comparion tarted 1, mec after the offet of the tandard. Again, the comparion wa either a viual or an auditory timulu. The ubject were required to indicate whether the comparion appeared to be horter or longer than the tandard by preing one of two deignated key on the computer keyboard. Thi repone alo reactivated the fixation point. The next trial could be initiated by preing the tart key again. There were eight different type of trial defined by the factorial combination of tandard duration (1 v. 1, mec), enory modality of the tandard (auditory v. viual), and enory modality of the comparion (auditory v. viual). Each trial type wa preented 48 time during a ingle experimental eion of 384 trial. Thi equence of 384 trial wa divided into eight block of 48 trial each. Half of all ubject received at firt four block with the hort tandard and then four block with the long tandard. For the other half of the ubject, thi order wa revered. For each ubject, the order of congruent and incongruent trial wa randomized within a ingle block. There wa a ret period between block, during which performance feedback on the preceding block wa provided on the monitor creen. The ubject initiated the next block when they felt ready to proceed. Before the experiment, the ubject were informed that they would be preented with two ucceive timuli and that the duration of the two timuli would be lightly different. The ubject were told that the enory modality of the two timuli might be identical or different. They were intructed to ignore the variation of enory modality and to focu on timulu duration. Furthermore, the intruction emphaized accuracy, and there wa no requirement to repond quickly. To introduce the tak, the experiment began with the preentation of 3 demontration trial. After thee trial, the ubject were aked whether they undertood the procedure. The purpoe of thee demontration trial wa to familiarize the ubject with the timuli. Then 96 practice trial were adminitered. Thee practice trial conited of a random ample of 48 trial from the 1-mec condition and 48 trial from the 1,-mec condition. The main eion with the 384 experimental trial began after thi training phae. During the main eion, the duration of the comparion interval wa varied according to an adaptive rule (Kaernbach, 1991) to etimate the value t c (.5) and t c (.75) that i, the two comparion interval at which the repone comparion longer wa given with a probability of.5 and.75, repectively. To etimate t c (.5), the duration of the comparion interval wa increaed by mec if the ubject had judged the comparion interval to be horter, and decreaed by mec after a comparion longer judgment. The oppoite tep ize were employed for t c (.75). Thi adaptive procedure wa performed for each of the eight different trial type, reulting in 16 randomly interleaved run. Becaue duration dicrimination i eaier for auditory than for viual interval (ee Goodfellow, 1934; Grondin, 1) and becaue abolute preciion of timing depend on the tandard duration (Rammayer & Grondin, ), the tep ize and were adjuted for each trial type (Table 1). The tarting value of the comparion for the t c (.5) run wa equal to t. Analogouly, the tarting value for the t c (.75) run wa t. A maximum-likelihood procedure wa ued to etimate the difference limen DL and the contant error CE (ee Matte & Ulrich, 1998). Reult and Dicuion Figure 3 depict the average DL and CE a a function of tandard duration, congruency, and enory modality of the firt timulu. It i obviou that the reult reemble the qualitative prediction of PCM. A eparate three-way ANOVA for thee three within-ubject factor wa performed on DL and CE to provide a more explicit aement of the data. Table 1 Step Size and (in Milliecond) to Etimate the Comparion Interval t c (.75) for Each Standard Duration and Each Stimulu Combination Standard (mec) v v a a v a a v , , Note For the t c (.5) run, the value of and above were interchanged.

6 CROSSMODAL TIMING 1145 CE (mec) DL (mec) Firt Stimulu - Standard Duration Auditory - 1 mec Viual - 1 mec Auditory - 1, mec Viual - 1, mec Congruent Incongruent Figure 3. Reult of Experiment 1: Mean difference limen (DL, upper panel) and contant error (CE, lower panel) a a function of congruency, modality of the tandard, and tandard duration. The legend in the upper panel indicate the modality of the firt timulu and the duration of the tandard; for example, Auditory - 1 mec mean that the firt timulu i auditory and the tandard duration i 1 mec. Following the uggetion made by Loftu (), the 95% confidence interval of the mean wa computed from the pooled error term of the repeated meaure ANOVA. The confidence interval aociated with mean DL and mean CE were 13.9 and 4.1 mec, repectively. Difference limen. A one would expect according to Weber law, DL increaed with the duration of the tandard interval [F(1,19) 7., MS e 1,349.3, p.1]. The average DL wa 4 mec for the hort and 18 mec for the long tandard. The enory modality of the firt timulu produced no ignificant main effect and did not interact with tandard duration (F 1). Mean DL wa 65 mec when the tandard wa auditory and 67 mec when it wa viual. Neverthele, the direction and ize of thi difference agree with PCM, which predict only a marginally larger DL for auditory than for viual tandard. The preent reult clearly replicated the common finding that temporal dicrimination i more precie for auditory than for viual timuli (ee Grondin, 1). For the hort tandard, mean DL wa 3 mec on v v trial and 13 mec on a a trial [t(19) 4.61, p.1]. An analogou pattern emerged for the long tandard [13 v. 76 mec; t(19) 4.87, p.1]. Both imple effect were conitent with PCM. Alo in qualitative agreement with PCM, dicrimination performance wa ignificantly better in congruent than in incongruent trial [F(1,19) 1.1, MS e 556.1, p.5]. Mean DL were 6 and 7 mec, repectively. However, thi congruency effect did not vary ignificantly with the duration of the tandard interval [F(1,19).7, MS e 461., p.116]; a ignificant congruency effect wa obtained for both the hort tandard [1 v. 7 mec in the congruent v. incongruent condition; t(19).37, p.8] and the long one [99 v. 117 mec, repectively; t(19).63, p.17]. A predicted by PCM, the congruency effect wa trongly modulated by the enory modality of the tandard timulu, a indicated by the ignificant interaction of congruency and modality [F(1,19).4, MS e 1,619.5, p.1]. A one would expect, performance on temporal dicrimination decreaed when an auditory tandard wa combined with a viual rather than with an auditory comparion. In thi cae, the average DL wa 45 mec for congruent and 86 mec for incongruent trial. In line with PCM, temporal dicrimination actually improved when a viual tandard wa combined with an auditory comparion (DL 58 mec) rather than with a viual one (DL 76 mec). The threefold interaction of all factor revealed that the congruency modality interaction became more pronounced a tandard duration wa increaed [F(1,19) 5.6, MS e 1,9.7, p.9]. For hort interval, DL wa 19 mec when the preentation order wa v a, and it wa 36 mec when thi order wa revered [t(19).78, p.1]. For the long tandard, the correponding figure were 97 and 137 mec, repectively [t(19).4, p.37]. Thi threefold interaction i alo in accord with PCM. Contant error. Unlike the DL, the CE provide information on whether ubject tend to over- or underetimate the duration of the tandard timulu. Except for the main effect of tandard duration [F(1,19) 1.1, MS e 16,468.7, p.314], all factor and their interaction yielded tatitically reliable effect on CE. Senory modality of the tandard produced a ignificant main effect [F(1,19) 11.5, MS e 1,793.7, p.3]: Subject tended to overetimate the duration of auditory tandard in comparion with viual one (CE 5 v. 31 mec, repectively). In other word, and conitent with previou reearch (e.g., Goldtone & Lhamon, 1974; Wearden et al., 1998), ubject judged auditory tandard generally to be longer than viual one. Alo in line with previou reearch (e.g., Goldtone & Goldfarb, 1964; Steven & Greenbaum, 1966), thi modality effect wa more pronounced for long than for hort tandard [F(1,19) 1.5, MS e 8,479.6, p.4]. Furthermore, the main effect of congruency wa ignificant [F(1,19) 6.4, MS e 5,733.7, p.]. CE wa different between congruent and incongruent trial (1 v. 18 mec), and thi congruency effect wa modulated by tandard duration [F(1,19) 13.5, MS e 3,88.6, p.]. Both main effect, however, were baically a conequence of the ig-

7 1146 ULRICH, NITSCHKE, AND RAMMSAYER nificant interaction of tandard modality and congruency [F(1,19) 6.5, MS e 11,666.8, p.19]. Conitent with PCM, CE differed coniderably between the two incongruent condition. Specifically, the average CE wa 6 mec on v v trial and 18 mec on a a trial, wherea it wa 68 mec for v a trial and 3 mec for a v trial. Finally, thi twofold interaction wa modulated by tandard duration [F(1,19) 9.7, MS e 8,393.5, p.6]. At variance with PCM, however, the CE difference between both incongruent condition wa only preent for long, not for hort, tandard. All thing conidered, CE wa mot trongly affected when tandard and comparion differed in modality and when tandard duration wa long. Specifically, ubject tended to underetimate the duration of a viual comparion after an auditory tandard. By contrat, they were inclined to overetimate the duration of an auditory comparion when it followed a viual tandard. Thi reult replicate and extend the finding reported by Goldtone and Goldfarb (1964). Thoe author alo employed congruent and incongruent trial, on which they aked ubject to judge the duration of a variable comparion on a 9-point rating cale. The duration of the tandard wa alway 1, mec, and the comparion varied from 6 to 1,4 mec. A in the preent tudy, mean judged duration wa virtually identical for the two congruent condition but differed coniderably in the incongruent condition, ince auditory timuli were judged a longer in duration than viual one. The preent reult indicate, however, that thi intramodal effect on perceived duration depend on timulu duration (ee Wearden et al., 1998, Experiment 3, for a imilar effect). Summary. The pychophyical data of Experiment 1 agree with the qualitative prediction made by PCM. Mot interetingly, the DL data are conitent with the interaction predicted by PCM. In particular, PCM predicted correctly that dicrimination performance hould be better in v a than in a v trial. Second, the CE data alo tended to be conitent with the prediction of PCM and with previou CE reult on cromodal temporal dicrimination. 4 EXPERIMENT The data of Experiment 1 upport the prediction of PCM and thu validate it aumption. Neverthele, it i poible that the outcome of Experiment 1 could be the ignature of a different account for example, if the tak requirement forced ubject to adopt a pecific trategy. The enory modalitie of both the tandard and the comparion varied randomly from trial to trial, o in each trial there wa uncertainty about the relevant input modality of both the tandard and the comparion. A a reult, ubject might have encountered problem in allocating ufficient attentional reource to the relevant input modality. In order to cope with thi input uncertainty, the ubject might have ignored to ome extent the enory information of the tandard, which occurred before the comparion, but booted the enory information of the comparion. Such a trategy would entail a maller DL with an auditory comparion, becaue it i well documented that the auditory ytem ha better temporal reolution than the viual ytem (Goodfellow, 1934), and temporal dicrimination performance hould then be better for v a than for a v trial. Although PCM alo entail thi order effect, uch an alternative account till need to be ruled out. For thi reaon, Experiment examined the poibility that the previou reult reflect trategic effect due to the input uncertainty mentioned above. In order to avoid uch input uncertainty, all condition were blocked in Experiment. That i, the enory modalitie of both the tandard and the comparion were kept contant acro all trial within a eparate block. In all other repect, thi experiment wa identical to Experiment 1. Method Subject. A freh ample of ubject wa recruited, with 5 male and 15 female adult volunteer ranging in age from 19 to 39 year (M 4.9, SD 5.5). All ubject had normal hearing, normal viion, and were naive about the purpoe of the experiment. Apparatu, Deign, and Stimuli. Thee were identical to thoe in Experiment 1. Procedure. The procedure wa the ame a in Experiment 1, with one modification: The modalitie of the tandard and the comparion were blocked, o each modality combination (a a, v v, a v, and v a) wa adminitered within a ingle block. A in Experiment 1, there were eight block, and the duration of the tandard wa again changed after the firt four block. Block order of all modality combination wa controlled acro ubject according to a balanced Latin quare. Reult and Dicuion Experiment generally replicated the data of Experiment 1, providing further upport for PCM (Figure 4). Thee new reult rule out the poibility that the outcome of Experiment 1 wa due to a trategy aociated with input uncertainty. Difference limen. A before, mean DL wa maller for the hort than for the long tandard duration [16 v. 11 mec; F(1,19) 11.1, MS e,375.8, p.1]. Alo a in Experiment 1, enory modality of the tandard did not produce a ignificant main effect [F(1,19) 1.3, MS e 477.4, p.73] and did not interact with tandard duration [F(1,19) 1.4, MS e 49.1, p.53]. Yet, in line with PCM, DL wa once again omewhat maller when the tandard wa auditory rather than viual (56 v. 6 mec). DL wa alo maller for pure auditory than for pure viual trial [35 v. 63 mec; t(19) 4.69, p.1], and dicrimination performance wa again better in congruent than in incongruent trial [49 v. 68 mec; F(1,19) 36.3, MS e 43.3, p.1]. The long tandard duration even augmented thi congruency effect, a revealed by the ignificant interaction of congruency and tandard duration [F(1,19) 1.1, MS e 446.7, p.1]; the ize of the congruency effect wa 4 mec for the hort tandard, which increaed to 35 mec for the long tandard. Congruency once again interacted with the enory modality of the tandard [F(1,19) 5.4, MS e 961., p.1]. A one would expect, dicrimination performance wa impaired when an auditory tandard wa combined with a viual comparion (DL 78 mec) in-

8 CROSSMODAL TIMING 1147 CE (mec) DL (mec) Firt Stimulu - Standard Duration Auditory - 1 mec Viual - 1 mec Auditory - 1, mec Viual - 1, mec Congruent Incongruent Figure 4. Reult of Experiment : Mean difference limen (DL, upper panel) and contant error (CE, lower panel) a a function of congruency, modality of the tandard, and tandard duration. The 95% confidence interval aociated with mean DL and mean CE were 17.1 and 5.3 mec, repectively. tead of with an auditory one (DL 35 mec) [t(19) 8.65, p.1]. Dicrimination performance appeared to lightly improve, however, when a viual tandard wa paired with an auditory comparion (DL 58 mec) rather than with a viual one (DL 63 mec), but thi difference wa not reliable [t(19).86, p.4]. Finally, the threefold interaction of all factor wa again ignificant, ince the interaction between congruency and modality turned out to be more pronounced for the long than for the hort tandard [F(1,19) 7., MS e 797.6, p.15]. Contant error. The CE reult alo agree well with thoe of Experiment 1, although thi time an ANOVA yielded no reliable reult. There were no ignificant main effect nor ignificant interaction ( p.161), and only the interaction of modality and congruency approached tatitical ignificance [F(1,19) 3.1, MS e 19,455., p.96]. A before, CE wa virtually identical for the two congruent condition but appeared to differ for the two incongruent condition. Summary. The preent reult clearly confirm thoe of Experiment 1. Therefore, the notion that the previou reult were due to input uncertainty, and thu to trategie for coping with thi uncertainty, ha to be rejected. A before, the complete pattern of reult i qualitatively conitent with the prediction of PCM. 5 EXPERIMENT 3 The previou two experiment dicloed a triking order effect in which temporal dicrimination performance wa clearly better on v a than on a v trial. A hown in the introduction, PCM can account for thi order effect. Neverthele, one might be inclined to aume that what matter i merely the order in which the two enory modalitie are proceed. According to thi imple-order account, dicrimination performance hould alway be better on v a than on a v trial. In order to ae thi account, we revered the preentation order of the comparion and the tandard in Experiment 3. PCM make the rather intereting prediction that thi reveral hould alo revere dicrimination performance on v a and a v trial. 6 In contrat, the order account predict that thi change hould not matter, o that the ame effect would be oberved a in the previou two experiment. Figure 5 illutrate the predicted effect of revering the preentation order of the comparion and the tandard. The prediction are baed on model parameter identical to thoe in Figure. A comparion of the figure reveal the following imilaritie and difference: (1) A one would uppoe, dicrimination performance in congruent trial doe not depend on the order of the tandard and comparion. () Mot importantly, dicrimination performance in incongruent trial i predicted to revere, though the average performance in thee trial doe not depend on the preentation order. In other word, performance hould now be better for a v than for v a trial the predicted reveral effect. Note that thi reveral imply reflect the fact that DL i predicted to be maller when the tandard i auditory than when it i viual, becaue of the higher clock peed aociated with auditory than with viual timuli. A wa dicued in our introduction of the PCM, only a mall change of t c i neceary for perceiving a difference between t c and t when the clock peed i relatively high during the proceing of the tandard. (3) The CE pattern i identical in both figure, except that the new pattern i the old pattern turned upide down. All other effect are predicted to be the ame a thoe in the previou two experiment. 7 Method Subject. A freh ample of ubject wa recruited, with 3 male and 17 female adult volunteer ranging in age from 19 to 33 year (M 4.1, SD 4.6). All ubject had normal hearing, normal viion, and were naive about the purpoe of the experiment. Apparatu, Deign, Stimuli, and Procedure. Thee were identical to thoe in Experiment. In contrat to Experiment, however, the comparion timulu now preceded the tandard timulu. Reult and Dicuion Figure 6 depict the reult for mean DL (upper panel) and mean CE (lower panel). A eparate ANOVA with the factor tandard duration, congruency, and modality of the firt timulu wa computed for each dependent meaure.

9 1148 ULRICH, NITSCHKE, AND RAMMSAYER CE (mec) DL (mec) Firt Stimulu - Standard Duration Auditory - 1 mec Viual - 1 mec Auditory - 1, mec Viual - 1, mec Difference limen. The pattern of reult differed from that of the previou two experiment. Specifically, the reult for auditory-firt trial were imilar, wherea thoe for viual-firt trial were different. Mot importantly, temporal dicrimination performance wa now better for a v than for v a trial, confirming the crucial prediction of PCM. In addition, everal other feature of the data agree qualitatively with the reult of the previou experiment. It i quite evident that dicrimination performance wa generally poorer in thi experiment than in Experiment ; the overall mean DL wa 58 mec in the previou experiment but 115 mec in thi one [t(4.6) 5.1, p.1, two-ided t tet with df corrected for unequal variance]. One reaon for the wore overall performance in thi experiment wa that the repone thi time wa delayed with repect to the relevant comparion timulu, unlike in the previou two experiment. (We will return to thi point in the General Dicuion ection.) A in the two previou experiment, DL wa coniderably larger for the long than for the hort tandard [4 v. 191 mec for the hort v. the long tandard; F(1,19) 69., MS e 13,348.5, p.1]. In contrat to the previou reult, temporal enitivity wa higher when the firt timulu wa auditory than when it wa viual [F(1,19) 4.1, MS e 3,99.9, p.1]. Thi difference, however, wa baically a conequence of the revered performance effect oberved with incongruent trial, which reflected an epecially trong deterioration of dicrimination performance in v a trial. In addition, thi effect wa larger for long than for hort interval [F(1,19) 15.1, MS e,53.7, p.1]. Dicrimination performance again wa clearly better in congruent than in incongruent trial [DL 93 v. 138 mec, repectively; F(1,19) 18., MS e 4,618.8, p.1]. Thi effect increaed ubtantially with the duration of the tandard interval [F(1,19) 8.4, MS e 3,556.8, p.9]. Becaue of the revered performance effect in incongruent trial, the interaction of modality with congruency diappeared thi time. In addition, there wa no ignificant interaction of all three factor (F 1). Contant error. The CE reult were analogou to thoe of Experiment 1 and. A one would expect, however, mean of the incongruent condition revealed a pattern oppoite to the one in the preceding CE reult. Although overall mean CE wa cloe to zero, ubject tended to overetimate the comparion when it wa hort, but to Congruent Incongruent Figure 5. Predicted difference limen (DL, upper panel) and contant error (CE, lower panel) of PCM a a function of congruency, modality of the firt timulu (i.e., the comparion in thi cae), and tandard duration. The legend in the upper panel indicate the modality of the firt timulu and the duration of the tandard; for example, Auditory - 1 mec mean that the firt timulu i auditory and the tandard duration i 1 mec. The ame parameter value were ued a in Figure. CE (mec) DL (mec) Firt Stimulu - Standard Duration Auditory - 1 mec Viual - 1 mec Auditory - 1, mec Viual - 1, mec Congruent Incongruent Figure 6. Reult of Experiment 3: Mean difference limen (DL, upper panel) and contant error (CE, lower panel) a a function of congruency, modality of the firt timulu, and tandard duration. The 95% confidence interval aociated with mean DL and mean CE were 31.8 and 6.6 mec, repectively.

10 CROSSMODAL TIMING 1149 underetimate it when it wa long [F(1,19) 9.6, MS e 15,796.3, p.6]. A before, ubject tended to underetimate the duration of a viual firt timulu [F(1,19) 7.9, MS e 7,8.6, p.11], and thi tendency wa again epecially pronounced with the long tandard [F(1,19) 14.1, MS e,66.8, p.1]. Although there wa no main effect of congruency (F 1), the interaction of modality and congruency did reach tatitical ignificance [F(1,19) 7.1, MS e 4,61.1, p.15]; thi interaction effect reflect the fact that CE wa cloe to zero for both congruent condition but wa different from zero, and oppoite in ign, for the two incongruent condition. In contrat to Experiment 1, the interaction of congruency and duration did not reach tatitical ignificance [F(1,19) 1.3, MS e 1,34., p.75], which can be attributed to the predicted performance reveral. In line with the preceding reult, thi interaction wa epecially pronounced for long tandard, a indicated by the threefold interaction of all factor [F(1,19) 8.1, MS e,146.4, p.1]. Summary. In thi experiment, the variable comparion wa preented before the tandard. A implied by PCM, thi experimental change revered dicrimination performance for incongruent trial, and thi clearly refute the idea that the performance difference for incongruent trial reflect a mere order effect in which performance i alway better for v a than for a v trial. The oberved reveral, however, might quite naturally arie from the timing mechanim potulated by PCM, even though thi model property i difficult to grap. 8 It i alo poible that ubject mainly focued on the comparion timulu. A dicued in the introduction to thi experiment, uch a trategy could alo account for the oberved performance reveral. In fact, the overall decreae in temporal dicrimination performance relative to the previou experiment provide ome evidence for the latter notion. GENERAL DISCUSSION Thi tudy aeed whether the generalized pacemaker counter model (Rammayer & Ulrich, 1) provide a reaonable account of the mechanim underlying cromodal duration dicrimination. In all three experiment, ubject were aked to dicriminate between the duration of a contant tandard and a variable comparion. The enory modalitie of the tandard and the comparion were either congruent (a a or v v) or incongruent (a v or v a). In Experiment 1 and, the tandard preceded the comparion, wherea in Experiment 3 the tandard followed the comparion. All four experimental condition were randomized acro trial in Experiment 1. In Experiment and 3, however, each condition wa adminitered in a eparate block of trial. The difference limen DL wa employed to index temporal dicrimination performance, and contant error CE to capture change in perceived duration. Main Finding Thee experiment revealed novel reult and alo confirmed previou finding. Firt, the CE data confirmed the notion that ubject perceive auditory timuli to be longer than viual one of the ame duration (e.g., Goldtone & Goldfarb, 1964; Goldtone & Lhamon, 1974; Wearden et al., 1998). Second, the DL data replicated etablihed finding of time perception that i, that dicrimination performance diminihed a tandard duration increaed and that performance wa wore for viual than for auditory timuli (ee Grondin, 1). Third, dicrimination performance wa definitely better in congruent than in incongruent trial, a reult that i alo in line with thoe of previou tudie (Grondin & Roueau, 1991; Grondin, Ivry, Franz, Perreault, & Metthé, 1996; Klapproth,, 3). Thi congruency effect became more pronounced a tandard duration increaed, and eliminating input uncertainty (Experiment ) did not remove thi effect. Fourth, a trong order effect wa obtained on incongruent trial: That i, in Experiment 1 and, DL wa maller on v a than on a v trial. In Experiment 3, however, thi order effect revered when the comparion preceded the tandard. In other word, dicrimination in the incongruent condition wa alway better with an auditory than with a viual comparion. Finally, revering the preentation order of the tandard and the comparion in Experiment 3 impaired dicrimination performance in general. Pacemaker Counter Model Since the PCM often provide a benchmark in reearch of time perception (ee Grondin, 1), we further elaborated thi model in order to apply it to the cromodal temporal dicrimination tak of thi tudy. Thi elaboration took into account that the rate of pule generation depend on enory modality, becaue previou work ha uggeted a higher pule rate for auditory than for viual timuli (Droit-Volet, 3; Penney et al., ; Wearden et al., 1998). We derived explicit expreion to predict DL and CE from the aumption of thi elaborated model. A other have found many time in the pat (ee, e.g., Wing, ), thi rather imple model capture everal apect of the data. Firt, the model predict a higher temporal dicrimination performance in the congruent condition with auditory than with viual timuli. Second, it tend to produce the correct prediction concerning the CE. Third, and mot urpriing to u, it capture the triking order effect in the incongruent condition, correctly accounting for the finding that performance i better in v a trial than in a v trial if the variable comparion follow the tandard. Fourth, the model correctly predict that thi order effect hould revere when the comparion occur before the tandard (Experiment 3). Fifth, the model can alo account for the finding that ome of the oberved effect become more pronounced a tandard duration increae. For example, according to the model the effect of enory congruency hould increae with tandard duration, and we actually oberved thi pattern, although the oberved congruency effect wa clearly larger than indicated by PCM. Neverthele, thi imple model alo failed to account for ome important apect of the reult. For example, we fitted the model to the data et of each experiment to ee whether it would alo provide a reaonable quantita-

11 115 ULRICH, NITSCHKE, AND RAMMSAYER tive account. Thee fit, however, were le impreive, with root mean quare error (RMSE) ranging from 13 to 35 mec. Apart from problem we experienced in identifying the correct model parameter, it i clear that thi model i an overimplification. For example, when we fitted the model, the pule rate wa not allowed to depend on the tandard duration, a in the work by Rammayer and Ulrich (1), and identical et of parameter were applied to all ubject. We refrained from increaing the model complexity, however, becaue thi would have complicated the fitting procedure even more. Given that the model include relatively few free parameter, it eem poible that future reearch will be able to advance it. Thi quantitative analyi of PCM alo clarified that the current verion of the model cannot account for the rather large effect of enory congruency on temporal dicrimination performance. Thi point wa revealed by computing the predicted congruency effect from the fit of the model. With the hort tandard, the oberved DL wa on average 9.4 mec larger in the incongruent than in the congruent condition. However, PCM predicted an average increae of only.6 mec. Likewie, the average congruency effect wa 41.6 mec with the long tandard, yet the predicted effect wa only.7 mec. Thu, it appear poible that temporal dicrimination on congruent trial could alo benefit from nontemporal enory information (e.g., experienced aroual) within a ingle modality, information that i not captured by the preent verion of PCM. For example, if the experienced level of aroual were the ame in ingle-modality trial, thi would inform the ubject that the tandard and comparion mut be phyically identical in magnitude and extent. However, the incluion of uch additional enory cue would no longer be beneficial when both timuli belonged to different enory modalitie. In agreement with thi propoal, Rammayer and Ulrich (5) found a performance decrement in temporal dicrimination when loudne (i.e., aroual) differed between an auditory tandard and an auditory comparion interval veru when they were equally loud. Although a complete aement of thi propoal i beyond the cope of the preent tudy, future work hould addre in greater detail why dicrimination performance i uually better when both timuli belong to the ame enory modality, and extend PCM accordingly. Finally, there wa another finding that cannot be explained within the preent framework of PCM without invoking further aumption. A mentioned above, average DL wa larger in Experiment 3 than in Experiment 1 and. That i, dicrimination performance wa better when the tandard came before rather than after the variable comparion. Thi outcome, however, can be eaily addreed within the framework of the entrainment model (Large & Jone, 1999). The equence of time interval within a ingle trial in Experiment 1 and formed an iochronou induction equence (Barne & Jone, ) before the comparion wa preented. For example, in the long-tandard condition the temporal equence of a trial wa a follow: 1, mec (warning ignal offet to tandard onet) 1, mec (tandard duration) 1, mec (tandard offet to comparion onet). In other word, the induction equence wa compoed of three 1,-mec interval before the variable comparion wa delivered. Thi induction equence might have entrained an activity, an internal rhythm that facilitated the proceing of the comparion at the end of thi equence (ee Barne & Jone, ; McAuley & Jone, 3). In Experiment 3, however, the induction equence before the comparion wa reduced to only one induction interval, and thu there wa le opportunity to build up uch an entraining activity. Conequently, dicrimination performance in Experiment 3 wa le promoted by thi activity than had been the cae in Experiment 1 and. Thu, another option to advance PCM further would be to link it core aumption to the aumption of the entrainment model. One Timing Mechanim or Several? A fundamental aumption of PCM i that a ingle timing mechanim underlie the perception of time. Thi notion, however, wa already challenged by Hugo Münterberg (1889). He reaoned that the mechanim underlying the perception of hort duration i qualitatively different from the one that underlie the perception of long duration. More pecifically, Münterberg aumed that duration le than one third of a econd can be directly perceived, ince they are primarily proceed by enory mechanim. By contrat, longer duration, he believed, cannot be immediately perceived but need to be recontructed by higher mental procee. Similarly, Michon (1985) argued that temporal proceing of interval longer than approximately half a econd i cognitively mediated, wherea temporal proceing of horter interval i uppoedly of a highly perceptual nature, fat, parallel and not acceible to cognitive control (Michon, 1985, p. 4). Several author have endored thi view of ditinct timing mechanim (e.g., Buonomano & Karmarkar, ; Frankenhaeuer, 1959; Lewi & Miall, 3; Mitrani, Shekerdjiiki, Gourevitch, & Yanev, 1977; Rammayer, 1999; Sturt, 195). 9 Although experimental work pertinent to thi iue i till extremely cant, it ha recently received a freh impetu in the field of timing and time perception (e.g., Michon, 1985; Rammayer, 1999; Rammayer & Lima, 1991; Rammayer & Ulrich, 5) and in the cognitive neurocience (Bendixen et al., 5; Grimm, Widmann, & Schröger, 4; Lewi & Miall, 3). For example, Lewi and Miall recently reviewed neuroimaging data on variou temporal tak. Their review included tudie on timing tak uch a temporal production, tapping, repone ynchronization, velocity dicrimination, and temporal dicrimination. They concluded that an automatic timing ytem i involved in the timing of interval in the range below 1 ec. Thi ytem i aumed to recruit primarily network within premotor and motor brain area and i not amenable to attention. The other hypotheized timing ytem i ubject to cognitive control aociated with activitie in prefrontal and parietal brain region. The reult of the preent experiment, however, do not upport the idea that ditinct timing mechanim operate at hort and long duration. In all three experiment,