Spatial effects on temporal categorisation

Perception, 2009, volume 38, pages 748 ^ 762 doi:10.1068/p6165 Spatial effects on temporal categorisation Marie-Eéve Roussel, Simon Grondinô Eècole de Psychologie, Universiteă Laval, Queăbec, QC G1K 7P4, Canada; e-mail: simon.grondin@psy.ulaval.ca Peter Killeen Arizona State University, Tempe, AZ 85287, USA Received 20 November 2007; in revised form 25 September 2008 Abstract We examined the influence of spatial factors in temporal processing Participants categorised as short or long empty intervals marked by two brief flashes delivered from locations differing in height and depth (experiment 1), or from two of three locations on a vertical plane (experiment 2) The perceived duration of intervals, as determined by the point of subjective equality, was affected by the height and depth of the signals (experiment 1) Experiment showed that the point of fixation plays a critical role in perceived duration The duration of an interval located in the upper visual field is perceived as longer when participants fixate the higher visual source and shorter when the fixation point is set in the middle; this latter result also generally applies when the fixation point is in the lower source Finally, for the sensitivity level, there was a significant segment (upper versus lower)6direction (descending versus ascending) interaction in experiment 1; a similar interaction effect varied according to the fixation point in experiment In experiment 2, the Weber fractions were around 0.22 Most results can be explained in terms of the need to shift attention from one visual sourceöfor marking time intervalsö to another Introduction The relationship between time and space has intrigued experimental psychologists interested in perceptual processes (eg Cohen et al 1954, 1955; Collyer 1977; Miyatani 1984 ^ 1985; Suto 1952, 1955; Yoblick and Salvendy 1970) almost as much as it has physicists interested in general relativity (Yourgrau 2005) The visual-perception literature is replete with space ^ time investigations, embodied in various more contemporary issues, including time-to-arrival or time-to-collision (see for instance Bootsma and Oudejans 1993) The literature on auditory perception has also shown the importance that spatial intervals between sound sources play in the temporal organisation of auditory sequences (Grondin and Plourde 2007; Lakatos 1993; ten Hoopen 1995) Classical examples of the mutual influence between space and time are the complementary kappa and tau effects (Jones and Huang 1982) The kappa effect refers to the subjective dilation of time when its interval is marked by more spatially distant events (Cohen et al 1953; Newman and Lee 1972; Price-Williams 1954) The tau effect refers to the subjective dilation of space when its extent is marked by more temporally distant events (Helson 1930; Helson and King 1931) These Greek effects are not always found The kappa effect typically occurs when three brief successive signalsö1, 2, and 3öare presented, marking intervals usually shorter than s If intervals ^ and ^ are equal in time, the ^ duration is perceived as longer if the spatial distance between and is greater than the one between and Here, a response relative to the length of a single temporal interval is made after each presentation of a sequence of only two visual signals, a constellation of spatial conditions of the type that often does not reveal kappa effects With such a single-stimulus method (eg Morgan et al 2000), it has been shown that more spatial distance between the locations of sources of the signal marking time does not ô Author to whom all correspondence should be addressed Space and time categorisation 749 necessarily result in longer perceived duration Indeed, some studies have shown that more distance resulted in shorter perceived duration, both for visual signals (Guay and Grondin 2001) and auditory signals (Roy and Grondin 2005) The purpose of the present study was to further test the effect of visual signals at different locations in space on the perceived duration of temporal intervals in conditions that might carry the single stimulus paradigm a step closer to the type that generate a kappa effect In the first experiment, the distance between the LEDs takes several values and the segments between two flashes are located at different combinations of depth and height (see figure 1) In the second experiment, the spatial distance between signals is kept constant, there is no manipulation of depth, and the segments have one of two heights; however, there is a control on the fixation point A A M M B B Experiment Experiment Figure Schematic of experiments and The experiments also provide an opportunity to estimate the sensitivity for discriminating intervals in different visuospatial conditions, which includes an investigation conducted with two base durations, in experiment 2, in order to examine the change of the variability over time Experiment Given the kappa effect, more space between visual signals should result in longer perceived duration Therefore, any condition providing an impression that there is more distance, or more space, between signals, might result in longer perceived duration In the present experiment, visual signals are delivered from several locations varying in depth and in height in the visual field The stimuli consist of a high distant LED (A, for above, or away); a low, close LED (B, for below); an LED placed between A and B (M, for middle or matrix) In all experimental sessions, the interval in a given trial is marked by either A and M, or by M and B The M stimulus is set at one of 25 locations (one location per session, 25 sessions) made of the combinations of locations in depth, and in height Within each session, the participant is presented with one of four intervals marked by the following combinations of LEDs: B ^ M, M ^ A, M ^ B, and A ^ M Therefore, there are two intervals located in the upper visual field (M ^ A and A ^ M) and two in the lower visual field (B ^ M and M ^ B) Two of four signal sequences go in an ascending and receding direction (B ^ M and M ^ A), and two in a descending and approaching direction (A ^ M and M ^ B) 2.1 Method 2.1.1 Participants Ten Laval University students, aged 19 to 34 years (M ˆ 24 years) took part in the experiment They received Can $100 for their participation 2.1.2 Apparatus and stimuli The intervals to be discriminated were marked by 20 ms visual signals (markers) produced by two of three circular, red-light-emitting diodes (LEDs: Radio-Shack #276-088) During the entire experiment, the A and B LEDs remained at the same places: A was 400 cm away from participants and 210 cm above the floor, and B was 150 cm away and 10 cm above the floor The M LED took one of 25 locations (one per session), selected from depth (Md1 , Md2 , Md3 , Md4 , and Md5 ) 750 M-E Roussel, S Grondin, P Killeen Table Location of below (B), middle (M), and above (A) LED on height and depth plane Height=cm Depth=cm 210 160 133.6 110 86.4 60 10 Location of M in depth 150 212.5 245.5 275 304.5 337.5 400 M5 M4 M3 M2 M1 M10 M9 M8 M7 M6 M15 M14 M13 M12 M11 M20 M19 M18 M17 M16 M25 M24 M23 M22 M21 Md1 Md2 Md3 Md4 Md5 Location of M in height A Mh5 Mh4 Mh3 Mh2 Mh1 B by height (Mh1 , Mh2 , Mh3 , Mh4 , and Mh5 ) possibilities (see figure and table 1) The locations divided the distance in depth, or the distance in height, according to the following proportions: 0:25 À 0:75; 0:62 À 0:38; 0:5 À 0:5; 0:38 À 0:62; and 0:75 À 0:25 All aspects of the experiment were controlled by a Zenith microcomputer 2.1.3 Procedure Each trial consisted of the presentation of a single interval (the singlestimulus methodöMorgan et al 2000) There were 25 sessions, one for each of the 25 M locations One session began with presentations of the standard interval, 335 ms, followed by five blocks of 96 experimental trials Within each block, there were 24 presentations, in a random order, of each of four marker conditions, B ^ M, M ^ B, A ^ M, or M ^ A For each of these four conditions, there were repetitions, in a random order, of each of the eight intervals The intervals lasted for 160, 210, 260, and 310 ms (short), and 360, 410, 460, and 510 ms (long), with arithmetic mean 335 ms Each observer was seated in a chair, in a dimly lit corridor, and asked to indicate whether the interval presented belonged to the short or to the long category by pressing the left or the right button, respectively The response box was on a table in front of the participant One participant was assigned to each of the five following session orders (see table for description of these conditions): conditions to 25; conditions to 25 followed by to 5; conditions 11 to 25 followed by to 10; conditions 16 to 25 followed by to 15; and conditions 21 to 25 followed by to 20 One participant was assigned to each of the five reversed session orders: conditions 25 to 1, etc 2.1.4 Data analysis For each participant and for each of the 100 conditions (2626565), 8-point psychometric functions were constructed, with the eight intervals on the x-axis and the probability of responding ``long'' on the y-axis Each point on the psychometric function was based on 15 presentations A pseudo-logistic function rule (Killeen et al 1997) was fit to the functions The pseudo-discrimination function is a psychometric function constructed on the assumption that Weber's law holds: that is, that the uncertainty associated with both training and test stimuli is proportional to their magnitude It is called `pseudo' because it is not a true distribution function as it asymptotes below 1.0 In the case of the logistic function, the corresponding pseudo ^ logistic function is À1 pt ˆ f1 ‡ exp‰À…t À m†=wtŠg , where m is the mean, or point of subjective equality (PSE) and w is the Weber fraction (WF) Two indices of performance were estimated from each psychometric function: one reflecting the mean perceived duration and the other the sensitivity The key dependent variable was the PSE, the t value corresponding to the 0.50 probability of a long response Space and time categorisation 751 The shift of the PSE observed for different conditions can be interpreted as an indication of differences in the perceived duration of the stimuli A shift of the PSE to the left indicates that the stimuli are more often reported to be long The standard deviation (SD ˆ wm) of the psychometric functions around the PSE provided an index of sensitivity (Grondin 2001a, 2005; Grondin et al 2005; Killeen and Weiss 1987) 2.2 Results For the 1000 psychometric functions (100 functions for each of the participants), the mean goodness-of-fit (R ) is 0.94; with the exclusion of a few outliers (like one R value at 0.09), it increases to 0.98 Out of 1000 scores, there were 12 outlier values for the PSE, and 52 for the sensitivity (SD) An outlier for one given participant is a value that is more than two SDs for the distribution of scores for this person The replacing score is the mean of two scores based on two linear regression analyses, one for valid scores of all other participants, and one for valid score of a specific participant 2.2.1 Perceived duration The mean results for perceived duration in each condition are reported in table Overall, the PSEs are larger than 335 ms, the base duration This indicates that participants tend to respond ``short'' more often than ``long'' Table Mean point of subjective equality (PSE, in ms) as a function of the height and depth of the signals Height=cm Depth=cm 62.5 95.5 Depth=cm 125 154.5 187.5 62.5 95.5 125 154.5 187.5 60 86.4 110 133.6 160 Ascending seriesÐinferior segment 351 377 391 360 369 362 369 366 362 355 363 381 347 355 344 362 374 342 353 332 351 369 339 355 341 Ascending seriesÐsuperior segment 333 365 364 345 331 328 352 350 327 351 338 396 361 355 365 358 368 366 364 355 374 349 358 362 363 60 86.4 110 133.6 160 Descending seriesÐinferior segment 345 408 381 343 354 356 353 357 323 354 342 373 333 333 334 327 369 331 333 330 340 344 306 347 319 Descending seriesÐsuperior segment 365 392 369 356 362 365 382 365 359 366 365 402 355 359 366 370 384 349 369 363 357 382 341 364 352 A repeated-measures ANOVA, according to a segments (upper/lower)62 series (ascending/descending)65 depth65 height design, was conducted on the PSEs The Greenhouse ^ Geisser correction was applied to degrees of freedom when required Only one main effect, depth, is significant (F4, 36 ˆ 2:65, p 0:05, Z ˆ 0:23) The PSE is farther to the rightöindicating that durations are perceived as shorter öwhen the M LED is located at 245.5 cm from the participant (ie 86.4 cm beyond Bötable 2) The series6height interaction was significant (F4, 36 ˆ 5:00, p 0:01, Z ˆ 0:36ö see figure 2) Five t tests for paired samples, with a level at 0.05/5 according to Bonferroni correction, were used to compare the ascending versus descending conditions for each of the height conditions, but no difference was significant In addition, two repeatedmeasures ANOVAs were conducted for each series for comparing the different height conditions The analyses revealed no significant difference in the ascending series, but for the descending series, the effect was significant (F4, 396 ˆ 4:78, p 0:01, Z ˆ 0:05) with a significant linear trend (F1, 99 ˆ 8:39, p 0:01, Z ˆ 0:08); higher signals resulted in lower PSE 752 M-E Roussel, S Grondin, P Killeen 370 Ascending series Descending series 365 PSE=ms 360 355 350 345 Figure Mean point of subjective equality (Ỉ SE) for each series as a function of the location of the middle (M) LED in experiment Dots indicate base duration 340 335 330 60 86.4 110 133.6 Height of M=cm 160 The segment6height interaction was also significant (F4, 36 ˆ 4:35, p 0:01, Z ˆ 0:33ösee figure 3) Five t tests for paired samples were used to compare the upper versus lower conditions for each of the height conditions Significant differences were observed at the two highest locations of M (Mh4 , t9 ˆ 3:80, p 0:01; and Mh5 , t9 ˆ 3:60, p 0:01) In both cases, the PSE is smaller when the interval is presented in the lower portion In addition, two repeated-measures ANOVAs were conducted for each segment for comparing the different height conditions The analyses revealed no significant difference in the upper segment condition, but for the lower segment there were significant differences, but the series of t tests (with adjusted a) revealed no significant difference No other interactions were significant 370 Lower segment Upper segment 365 PSE=ms 360 355 350 345 Figure Mean point of subjective equality (Ỉ SE) for each segment as a function of the location of the middle (M) LED in experiment Dots indicate base duration 340 335 330 60 86.4 110 133.6 Height of M=cm 160 2.2.2 Sensitivity The mean results for sensitivity in each condition are reported in table Overall, the SDs vary between 60 and 108 ms A repeated-measures ANOVA, according to a 2626565 design, was conducted on the SD Once again, the Greenhouse ^ Geisser correction was applied to degrees of freedom when required No main effect was significant, and only two interaction effects were significant One is the series6segment interaction (F1, ˆ 6:09, p 0:05, Z ˆ 0:41) In the ascending condition, the SD in the upper segment condition is larger than the SD in the lower segment condition (t24 ˆ 2:99, p 0:05); and, on contrary, for the descending condition, the SD in the lower segment condition is larger than the SD in the upper segment condition (t24 ˆ 4:77, p 0:05) The other significant effect is the series6height interaction (F4, 36 ˆ 3:98, p 0:01, Z2 ˆ 0:31) A comparison of the descending and ascending series for each height Space and time categorisation 753 Table Mean standard deviation (SD, in ms) as a function of the height and depth of the signals Height=cm Depth=cm 62.5 95.5 Depth=cm 125 154.5 187.5 62.5 95.5 125 154.5 187.5 60 86.4 110 133.6 160 Ascending seriesÐinferior segment 72.1 86.4 65.9 68.9 101.6 66.5 68.5 85.7 80.9 85.1 79.2 86.3 73.5 101.3 75.9 74.6 71.5 66.6 91.4 77.7 60.4 98.2 92.1 95.5 71.7 Ascending seriesÐsuperior segment 104.1 99.0 89.0 83.0 102.3 77.4 79.2 93.0 70.9 103.4 72.9 107.6 80.9 92.2 106.9 80.2 70.4 103.9 83.4 90.9 82.7 98.8 91.6 75.1 73.2 60 86.4 110 133.6 160 Descending seriesÐinferior segment 79.6 92.3 82.8 83.2 96.5 88.2 79.7 80.3 94.9 85.9 80.8 86.3 69.5 95.0 73.2 87.5 81.9 85.3 95.2 103.2 95.8 120.0 83.2 87.7 93.2 Descending seriesÐsuperior segment 73.3 79.5 96.7 79.9 87.8 81.6 86.9 92.4 78.4 90.1 76.6 86.9 75.7 65.1 77.3 84.3 63.9 75.8 89.0 67.5 64.7 92.4 63.4 75.8 74.8 condition revealed no significant difference (once the Bonferroni correction is applied, 0.05/5), but note that the SD was much smaller in the descending than in the ascending condition at mid-height (110 cm; Mh3 : t9 ˆ 2:79, p ˆ 0:021) Experiment In experiment 1, the height of the M signal exerted an effect on perceived duration, but this effect interacted with the fact that the intervals were presented in the upper or lower part of the visual field (VF), and with the fact that the sequence of signals was ascending (and going farther away) or descending (and getting closer to the participant) For the intervals delivered in the lower part of the VF, the higher the M signal was, the longer was the perceived duration In other words, more space resulted in longer duration; however, this effect was restricted to the lower part of the VF In the upper part of the VF, a higher M signal meant a smaller distance between M and A, but this didn't lead to systematic effect on perceived duration Indeed, the impression that objects higher in the VF are located farther away applies to objects located below the fixation point on the horizon In other words, different results obtained for the lower versus upper parts of the VF might depend on the fixation point The main purpose of experiment is to provide a direct test of the influence on perceived duration exerted by the height in the VF of signals delimiting a temporal interval As indicated earlier, the height of objects in the VF contributes to the perception of distance, but this contribution might well depend on the point of fixation in the horizon In this experiment, there is a series of comparisons of the effect on perceived duration of the interval location The distance between the signals marking the upper or lower intervals is kept constant (M remains equidistant between A and B) More specifically, the upper segment condition is either A ^ M or M ^ A, and the lower one is either M ^ B or B ^ M, and M has only one location (instead of 25ö565öas in experiment 1) Staring at the A, M, or B point is probably a critical factor, not only because of the consequence on the interpretation of distance, but also because a visual target is often detected more correctly and more rapidly when presented in the upper VF (Previc and Naegele 2001) and because the fixation point determines the distance between where attention is located and where it should be located (arrival point of the first marker) Finally, because there were fewer location points tested in the present experiment, the present investigation was extended to an additional range of duration 754 M-E Roussel, S Grondin, P Killeen 3.1 Method 3.1.1 Participants Thirteen Laval University students, nine females and four males, aged 21 to 30 years (M ˆ 25 years) took part in the experiment They received Can $60 for their participation 3.1.2 Apparatus and stimuli The material was the same as in experiment 1, but the experiment was conducted in another room, also dimly lit The intervals were marked by two of three LEDs located m in front of the participant on a vertical plane The LEDs were placed 50 cm apart, the middle (M) one being approximately at the height of the participants' eyes (at 110 cm above the ground) Each LED subtended a visual angle of about 0.29 deg, with the visual angles between the middle LED and the one above (A) and the one below (B) both being 148 3.1.3 Procedure As in experiment 1, the single-stimulus method was used There were two base durations: 200 and 335 ms For the 200 ms base duration, intervals lasted 95, 125, 155, and 185 ms (short category), and 215, 245, 275, and 305 ms (long category), with arithmetic mean 200 ms In the 335 ms base duration condition, the intervals lasted 160 to 510 ms (same as in experiment 1) The interval was presented either in the lower part (B ^ M or M ^ B sequences) of the VF, or in the higher part (M ^ A or A ^ M sequences) The direction of the sequence was referred to as a descending (A ^ M or M ^ B) or an ascending (B ^ M or M ^ A) series The three fixation points were the A, M, or B LED The experiment lasted for twelve experimental sessions, six for each of two base durations At each base duration there were three pairs of two consecutive sessions, each pair featuring a single fixation point condition, A, M, or B There were three orders of assignment to the fixation conditions: A ^ M ^ B, B ^ A ^ M, and M ^ B ^ A In one of the two consecutive sessions, the series were ascending, in the other descending Overall, there were twelve session orders, based on the combination of 200 and 335 ms first or second, ascending and descending first or second, and three fixation point orders One participant was assigned to eleven of them, and two participants to one of them Each session began with six presentations of the base duration, following which there were four blocks of 60 trials, with a 15 s pause between the blocks There was no feedback Within each session, there was only one fixation point, one base duration and one ascending or descending condition; but two height conditions 3.1.4 Data analysis For each participant and for each of the 24 conditions (2 base durations62 segmentsöupper versus lower62 seriesöascending versus descending 63 fixation pointsöA, M, or B), 8-point psychometric functions were constructed Each point on the psychometric function was based on 15 presentations The same model as in experiment was used to fit the resulting curves Because there are two base durations in the present experiment, the PSE was transformed into constant error (CE), ie the difference between the PSE and the base duration (200 or 335 ms); the more negative the CE, the longer the stimuli are judged to be As well, the SD of the psychometric functions served to calculate the Weber fraction: WF ˆ SD/base duration 3.2 Results and discussion The pseudologistic functions generally described the data very well Out of the 24 experimental conditions, the lowest mean r value for the thirteen participants was 0.954, observed with a 200 ms base duration for the higher portion in the ascending direction when the fixation point was B The highest mean r value, 0.985, was obtained in the same combination of conditions, but with a 335 ms base duration Space and time categorisation 755 Constant error=ms 45 40 35 30 25 20 15 10 À5 À10 À15 À20 Constant error=ms 3.2.1 Perceived duration The mean results in each condition for perceived duration are reported in figure An ANOVA on CE based on a 2626263 design with repeated measures on all factors (with Greenhouse ^ Geisser corrections when necessary) revealed no significant main effects However, the following interactions were significant: the segment6fixation point interaction (F2, 24 ˆ 16:88, p 0:01, Z ˆ 0:58); segment6base duration interaction (F1, 12 ˆ 12:80, p 0:01, Z ˆ 0:52); the series 6base duration interaction (F1, 12 ˆ 5:95, p 0:05, Z ˆ 0:33); and the segment6 series6fixation point interaction (F2, 24 ˆ 11:37, p 0:01, Z ˆ 0:49) As illustrated in figure 5, the direction of the segment and series effects varied with the fixation points 20 15 10 À5 À10 À15 À20 À25 À30 À35 Lower segment Upper segment 40 30 20 10 À10 À20 below middle Fixation point above À30 below middle above Fixation point Figure Mean constant error (Ỉ SE) for each experimental condition in experiment 2: (left) ascending; (right) descending; (top) 200 ms; (below) 335 ms Because of series of significant interaction effects, three additional 26262 ANOVAs, one for each fixation point, were conducted For the fixation point set on B, there were two significant main effects: segment (F1, 12 ˆ 12:91, p 0:01, Z ˆ 0:52) and series (F1, 12 ˆ 8:96, p 0:05, Z ˆ 0:43) The three double interactions were also significant: segment6series (F1, 12 ˆ 5:95, p 0:05, Z ˆ 0:33); segment6base duration (F1, 12 ˆ 12:60, p 0:01, Z ˆ 0:51); and series6base duration (F1, 12 ˆ 6:48, p 0:05, Z ˆ 0:35) Two additional (series)62 (segments) ANOVAs, one for each base duration, were conducted At 200 ms, the analysis revealed no effect of series, but the effect of segment (F1, 12 ˆ 6:50, p 0:05, Z ˆ 0:35) and the series6segments interaction (F1, 12 ˆ 11:31, p 0:01, Z ˆ 0:49) were significant In the ascending series, the CE for the upper segment was 8.28 ms, and 5.12 ms for the lower segment; in the descending series, the CE for the upper segment was 29.30 ms, and À9:56 ms for the lower segment At 335 ms, there was a significant segment effect (F1, 12 ˆ 20:75, p 0:01, Z ˆ 0:63) and a significant series effect (F1, 12 ˆ 14:49, p 0:01, Z ˆ 0:55) The interaction effect was not significant The CE value was smaller with the lower than with the upper segment, and lower in the ascending series than in the descending series 756 M-E Roussel, S Grondin, P Killeen Lower segment Upper segment 20 Constant error=ms 15 10 À5 À10 Constant error=ms À15 11 10 À1 À2 À3 Ascending series Descending series Figure Constant error (Ỉ SE) as a function of the fixation point for the lower versus upper segment conditions (upper panel) and for the ascending versus descending series (lower panel) below middle Fixation point above For the middle point of fixation, the only significant effect observed was on the segment variable (F1, 12 ˆ 5:34, p 0:05, Z ˆ 0:31) The CE was lower (longer perceived duration) with intervals presented in the lower portion of the visual field than in presentations in the upper portion With the fixation point set on A, the ANOVA revealed significant segment effect (F1, 12 ˆ 26:96, p 0:01, Z ˆ 0:69) The CE was larger (shorter perceived duration) with intervals presented in the lower portion of the VF than in presentations in the upper portion No other effects were significant with either the M or A fixation point 3.2.2 Sensitivity The mean sensitivity results in each condition, expressed with the WF, are reported in figure An ANOVA according to a 2626263 design, with repeated measures on all factors, revealed that there was a significant base duration effect (M ˆ 0:243 and 0.207 at 200 and 335 ms, respectivelyöF1, 12 ˆ 13:90, p 0:01, Z ˆ 0:54) However, this effect interacted with the series effect (F1, 12 ˆ 9:06, p 0:05, Z ˆ 0:43) The series6fixation point interaction was also significant (F2, 24 ˆ 11:46, p 0:01, Z ˆ 0:49), as was the segment6series (F2, 24 ˆ 4:83, p 0:05, Z ˆ 0:29) and the segment6fixation point (F2, 24 ˆ 14:74, p 0:01, Z ˆ 0:55) Three additional 26262 ANOVAs, one for each fixation point, were conducted For the fixation point set on B, there was no significant effect, but note p ˆ 0:071, Z ˆ 0:25, for the base duration effect, the WF being larger at 200 than at 335 ms For the M fixation point, besides the based duration effect ( p ˆ 0:055), there is only a segment6series significant effect (F1, 12 ˆ 13:71, p 0:01, Z ˆ 0:53) While for the lower segment the WF was 0.25 in the ascending series and 0.19 in the descending series, the WF was reversed for the upper segment, and 0.20 and 0.23 in the ascending Space and time categorisation 757 0.35 Lower segment Weber fraction 0.30 Upper segment 0.25 0.20 0.15 0.10 0.05 0.00 0.35 Weber fraction 0.30 0.25 0.20 0.15 0.10 0.05 0.00 below middle Fixation point above below middle Fixation point above Figure Mean Weber fraction (Ỉ SE) for each experimental condition in experiment 2; (left) ascending; (right) descending; (top) 200 ms; (below) 335 ms and descending series, respectively For the fixation point set on A, there was only a segment6base duration significant effect (F1, 12 ˆ 8:84, p 0:05, Z ˆ 0:42) For the lower segment, the WF was nearly the same at 200 (0.228) and 335 (0.237) ms, but differed in the upper segment (0.249 and 0.196, respectively) General discussion There were two dependent variables of interest in the present study, one related to perceived duration and the other to the sensitivity for discriminating intervals The main theoretical questions addressed were related to the influence of visuospatial factors on perceived duration 4.1 Perceived duration The general purpose of the study was to investigate the extent to which the perceived duration of single intervals marked by brief visual signals is linked to the spatial distance between signals Previous empirical investigations led to the conclusion that more space between signals results in longer perceived duration, which is referred to as the kappa effect The present work contributes to show that the influence of space on time perception is not that simple: more space between signals marking time does not necessarily lead to longer perceived duration In experiment 1, the location of the signals (upper versus lower segments) in the visual field, and their direction (ascending versus descending), were randomised within blocks of trials Both location and direction exerted a significant effect on perceived duration, but the effect interacted with the height of the M signals In the case of direction, while the PSE remained relatively constant for the different height conditions in the ascending condition, the lower the M signals in the descending series were, the shorter was perceived duration However, lower M signals also means closer to 758 M-E Roussel, S Grondin, P Killeen participants Therefore, when one or two events marking intervals are low and close to participant, and seems to come in the direction of the participant, duration is perceived as shorter Maybe more important is the interaction observed in experiment involving height and location For the two highest locations of M, the duration is perceived as shorter for the upper than for the lower segment Indeed, on average, the highest M signals are also closer to the A signal than to the B signal Consequently, the spatial distance between A and M is on average shorter than the spatial distance between M and B In other words, shorter perceived duration in these cases might have been caused by shorter spatial distance, a result consistent with the kappa effect While spatial distance seemed to influence perceived duration in experiment 1, another critical factor affecting the estimating of temporal intervals was revealed in experiment Figure helps summarising the findings regarding perceived duration in experiment In this figure, the various experimental conditions are ordered from left to right as a function of the CE average over observers and base duration, from the lowest to the highest, ie from the intervals perceived as longer to intervals perceived as shorter It is important to remind that in this experiment, only upper versus lower segments were randomised within blocks of trials; the fixation point and direction (ascending or descending) were kept constant within a session In this experiment, the longest and second shortest perceived intervals were issued from the same blocks of trials (ascending and fixation on A), as were the shortest and second longest (descending and fixation on Bösee figure 7) When the fixation point is B, if the interval is marked by a A ^ M descending sequence, ie if marker is very far from the fixation point and marker is also different from the fixation point, the interval is perceived as short (the shortest perceived interval); as well, if the fixation point is A, the B ^ M ascending sequence is perceived as short (second shortest) In the latter case (fixation point set at A), the M ^ A ascending sequence was perceived as the longest one When the fixation point was set on B, the M ^ B descending sequence was the second longest In other words, when the fixation point is B, the lower segment is perceived more frequently as long and the upper segment as short, and when the fixation point is A, it is the upper segment that is perceived more frequently as long and the lower as short Figure The constant error (CE) averaged over subjects and base durations, and presented in order of magnitude The squares correspond to the fixation points and the arrows the trajectory of the stimuli The more negative the CE, the more likely a stimulus was to be judged long À20 À10 CE=ms 10 20 One potential explanation for these differences in perceived duration in experiment might not be related to the integration of space per se into the temporal representation of a time interval, but to the consequence on attentional mechanisms of the distance between the signals marking time Temporal judgments are often argued to be based on the output of an internal clock described as a pacemaker-counter device (Killeen and Weiss 1987; see Grondin 2001b for a review), the accumulation in the counter of the pulses emitted by the pacemaker determining the experience of time (when more pulses are accumulated, duration is perceived as longer) It is also recognised that this accumulation is under the control of attention Reducing attention in time Space and time categorisation 759 reduces the accumulation of pulses, which results in shorter perceived duration (Brown 2008; Grondin and Macar 1992; Macar et al 1994) Brown noted that such interference with timing by competing tasks was ``the most well-replicated finding in all the time perception literature'' (page 119) The shortest perceived durations in experiment would result from the disturbance of attention caused by the shifting from a fixation point to distanced signals marking time Indeed, to some extent, the effects of attentional demands found in the present study could be seen as another instance of the well-documented phenomenon of inattentional blindness (eg Shahab Ghorashi et al 2007), but here the blindness is due to the task-relevant processing of information from an internal, not external, source In the present study, configurations of stimuli requiring the greatest movement of attentionötherefore generating the longest periods of inattentional blindnessöresulted in the shortest perceived durations; they were the farthest to the right in figure (1) This need to move attention is quite a powerful factor In an experiment with a set of LEDs on a vertical plane like the one used in experiment 2, but with less distance separating the source of the signals and with intervals marked by all combinations of A, M, and B lights (and subjects always fixated on the centre stimulus), Guay and Grondin (2001) reported that duration is perceived as much shorter as the distance between LEDs is increased For instance, an interval marked by an A ^ B sequence is perceived as shorter than intervals marked by an A ^ M or M ^ B sequence even if there is twice as much spatial distance between A and B In other words, the potential integration of space in temporal judgments reported in experiment seems to be less powerful than the need to displace attention between sensory sources marking time, as experiment indicates Experiment also revealed a significant depth effect When the M signals are located 245.5 cm from the participant in depth, the intervals are judged as short more often than when located at any of the four other depth conditions Interestingly, the depth condition is not the farthest or the closest to participants (see table 1); for instance, it is not because this distance is the closest that the intervals are judged as short more often Indeed, it is the second shortest distance to participants The cause of this main effect of depth remains an open question; all we can say here is that the location of the M signals where the effect occurred corresponds to a separation of A and B signals according to the golden ratio.(2) 4.2 Sensitivity Although secondary, the present experiment is also an occasion to assess the capacity to categorise brief time intervals in different spatial marking contexts In general, there was no systematic (main) effect of the height or depth of signals on sensitivity in experiment However, there was a significant series (ascending versus descending)6height interaction mainly caused by the fact that, when the M signal is located at 110 cm (ie mid-point in height between A and B), participants make less discrimination errors (higher sensitivity) in the descending than in the ascending series Experiment also revealed a significant series6segment (upper versus lower) interaction Sensitivity is higher for upper than for lower segments in the descending condition, and the opposite results are obtained for the ascending condition Interestingly, with the (1) The effect described here goes in an opposite direction to an effect in the visual mode described recently by Yarrow et al (2001) and referred to as chronostasis (Hodinott-Hill et al 2002, found a similar effect in the auditory mode), where the second hand takes longer to move to its next position when someone makes voluntary saccadic eye movements to a silently ticking clock (2) Take a segment, AC: l l l A B C There is only one location of B where (AB)=(BC) ˆ (BC)=(AC) This famous proportion is called the golden ratio, ie approximately 0.618 760 M-E Roussel, S Grondin, P Killeen fixation point set at M in experiment 2, the opposite pattern of results was obtained Indeed, the series6segment interaction effect of experiment is closer to what is observed in experiment when the fixation point is set on A Therefore, when no specific instructions are given to participants regarding the fixation point as is the case in experiment 1, participants might tend to look higher in the visual field than mid-point Returning to the preceding paragraph, M at 100 cm is located at mid-point between A and B, a condition comparable to that of experiment If participants were looking higher in the visual field in this condition, this would permit to reduce the need to shift attention in the descending series If less attentional shifts result in less variability, this would explain why sensitivity was higher in the descending than in the ascending series The magnitude of the shift appears actually to be critical for analysing sensitivity data of experiment For instance, the highest WF with a B fixation point was obtained with the upper segment-descending series, but with an A fixation point, it is actually with this same condition that the WF was the lowest As well, with the M fixation point, the best performances (lower WF) were obtained with the first signal delivered at M (lower-descending or upper-ascending) In brief, when the initial stimulus is not at the fixation point, a substantial amount of variance is added to the judgments As interpreted for the perceived duration results, not fixating the initial source of stimulation requires the allocation of more attentional resources for a nontemporal aspect of the task, leaving less for processing of time (Macar et al 1994) Experiment also offers the possibility to address a fundamental issue in the study of time perception, the constancy of WF over time (Killeen and Weiss 1987) According to the classic Weber's law, the average error of estimates should be proportional to time, which entails that the standard deviation to time ratio, ie the Weber fraction (WF), should be constant In experiment 2, the mean overall WFs were 24% and 21%, in the 200 and 335 ms conditions, respectively Note, however, that for the lower segment, when the fixation point was set at A, there was no difference between the WF at 200 and 335 ms The slightly higher WF in the 200 ms than in the 335 ms condition observed in most cases is consistent with the generalised form of Weber's law It is recognised in psychophysics that WF tends to increase at very low magnitudes of a sensory continuum (Grondin 1993; Killeen and Weiss 1987) These WF values remain larger than those reported in the literature for visual temporal discrimination For standard duration equal to 300 ms, Grondin (2001a) found WFs that were 10% ^ 15% Although this difference between experiments might depend on methodological differences, it could also be due to the variance added to time processing caused by the need to shift attention between spatially disparate signals (see also Grondin 1998) It could also be due to the fact that, within a given block of trials, there were more than one interval type that could be presented, which causes uncertainty Any uncertainty involving an interval presentation seems to result in more variance in the discrimination process Grondin and Rammsayer (2003) showed that randomising the foreperiod, ie the length of the period preceding an interval to be discriminated generates more discrimination errors In the present study, the uncertainty is not temporal but spatial: the participant does not know where the signal will be delivered, and this hinders the full allocation of attention to time What is more, in experiment 2, there were two possible intervals within blocks of trials: upper versus lower In experiment 1, there were four (2 segments62 series) An overall comparison of the performance levels of experiment and of the 335 ms portion of experiment revealed that performance is better in experiment 2, ie when there is less spatial uncertainty Space and time categorisation 761 Conclusion The present study clarifies some issues regarding the temporal processing of intervals marked by visual signals at different spatial locations Clearly, perceived duration is influenced by the location of signals Experiment showed that for the lower VF, more distance between signals resulted in longer perceived duration, but there was no such effect in the upper visual field This different effect with the lower and upper segments indicated that the height of the gaze might be an important source of influence on perceived duration Experiment confirmed that the fixation point affects the relative perceived duration of the upper and lower VF segments, and led to an attentional interpretation of the results The close connection between time and space emerging from the so-called and well-recognised kappa effect where more space between signals marking time results in longer perceived duration cannot be generalised It is possible that the kappa effect is restricted to conditions where at least three signalsötwo intervalsöare presented successively In other words, the kappa effect would be a genuine perceptual effect, and a task like ours would appear to involve a cognitive componentöthe retention of previous intervalsöthat is very sensitive to slight attentional effects Indeed, in some conditions, the greater the attentional load caused by the need to shift attention from one visual source to another, the shorter the judgments of the time intervals The need to move attention from one point to another adds delays and significant variance to temporal judgments, and the magnitude of this variance depends on the combination of the height of the signals in the visual field (upper or lower segments), on the direction of a sequence (ascending versus descending) and on where an observer is looking Acknowledgments This research was made possible by scholarship awarded to MER by the Natural Sciences and Engineering Council of Canada, by a research grant awarded to SG by NSERC and NSF IBN 0236821 to PRK We would like to thank two anonymous reviewers for their comments on a previous version of this article References Bootsma R J, Oudejans R R D, 1993 ``Visual information about time-to-collision between two objects'' Journal of Experimental Psychology: Human Perception and Performance 19 1041 ^ 1052 Brown S W, 2008 ``Time and attention: Review of the literature'', in Psychology of Time Ed S Grondin (Bingley, UK: Emerald Publishing Group) pp 112 ^ 138 Cohen J, Hansel C E M, Sylvester J D, 1953 ``A new phenomenon in time judgment'' Nature 172 901 Cohen J, Hansel C E M, Sylvester J D, 1954 ``Interdependence of temporal and auditory judgments'' Nature 174 642 ^ 644 Cohen J, Hansel C E M, Sylvester J D, 1955 ``Interdependence in judgments of space, time and movement'' Acta Psychologica 11 360 ^ 372 Collyer C E, 1977 ``Discrimination of spatial and temporal intervals defined by three light flashes: Effects of spacing on temporal judgments and of timing on spatial judgments'' Perception & Psychophysics 21 357 ^ 364 Grondin S, 1993 ``Duration discrimination of empty and filled intervals marked by auditory and visual signals'' Perception & Psychophysics 54 383 ^ 394 Grondin S, 1998 ``Judgments of the duration of visually marked empty intervals: Linking perceived duration and sensitivity'' Perception & Psychophysics 60 319 ^ 330 Grondin S, 2001a ``Discriminating time intervals presented in sequences marked by visual signal'' Perception & Psychophysics 63 1214 ^ 1228 Grondin S, 2001b ``From physical time to the first and second moments of psychological time'' Psychological Bulletin 127 22 ^ 44 Grondin S, 2005 ``Overloading temporal memory'' Journal of Experimental Psychology: Human Perception and Performance 31 869 ^ 879 Grondin S, Macar F, 1992 ``Dividing attention between temporal and nontemporal tasks: A performance operating characteristic öPOCöanalysis'', in Time, Action, Cognition: Towards Bridging the Gap Eds F Macar, V Pouthas, W Friedman (Dordrecht: Kluwer) pp 119 ^ 128 Grondin S, Plourde M, 2007 ``Discrimination of time intervals presented in sequences: Spatial effects with multiple auditory sources'' Human Movement Science 26 702 ^ 716 762 M-E Roussel, S Grondin, P Killeen Grondin S, Rammsayer T, 2003 ``Variable foreperiods and duration discrimination'' Quarterly Journal of Experimental Psychology A 56 731 ^ 765 Grondin S, Roussel M E, Gamache P L, Roy M, Ouellet B, 2005 ``The structure of sensory events and the accuracy of judgments about time'' Perception 34 45 ^ 58 Guay I, Grondin S, 2001 ``Influence on time interval categorization of distance between markers located on a vertical plane'', in Proceedings of the 17th Annual Meeting of the International Society for Psychophysics Eds E Sommerfeld, R Kompass, T Lachman (Berlin: Pabst Science Publishers) pp 391 ^ 396 Helson H, 1930 ``The tau effect: An example of psychological relativity'' Science 71 536 ^ 537 Helson H, King S M, 1931 ``The tau effect: An example of psychological relativity'' Journal of Experimental Psychology 14 202 ^ 217 Hodinott-Hill I, Thilo K V, Cowey A, Walsh V, 2002 ``Auditory chronostasis: Hanging on the telephone'' Current Biology 12 1779 ^ 1781 Jones B, Huang Y L, 1982 ``Space ^ time dependencies in psychophysical judgment of extent and duration: Algebraic models of the tau and kappa effect'' Psychological Bulletin 91 128 ^ 142 Killeen P R, Fetterman J G, Bizo L A, 1997 ``Time's cause'', in Time and Behavior: Psychological and Neurobehavioral Analyses Eds C M Bradshaw, E Szabadi (Amsterdam: North-Holland/Elsevier Science) pp 79 ^ 131 Killeen P R, Weiss N A, 1987 ``Optimal timing and the Weber function'' Psychological Review 94 455 ^ 468 Lakatos S, 1993 ``Temporal constraints on apparent motion in auditory space'' Perception & Psychophysics 54 139 ^ 144 Macar F, Grondin S, Casini L, 1994 ``Controlled attention sharing influences time estimation'' Memory & Cognition 22 673 ^ 686 Miyatani M, 1984 ^ 1985 ``The time and distance judgments at different levels of discriminability of temporal and spatial information'' Hiroshima Forum for Psychology 10 45 ^ 55 Morgan M J, Watamaniuk S N J, McKee S P, 2000 ``The use of an implicit standard for measuring discrimination thresholds'' Vision Research 40 2341 ^ 2349 Newman C V, Lee S G, 1972 ``The effect of real and imputed distance on judgments of time: Some experiments on the kappa phenomenon'' Psychonomic Science 29 409 ^ 411 Previc F H, Naegele P D, 2001 ``Target-tilt and vertical asymmetries in free-scan search for 3-D targets'' Perception & Psychophysics 63 445 ^ 457 Price-Williams D R, 1954 ``The kappa effect'' Nature 173 363 ^ 364 Remington R, Johnston J, Yantis S, 1992 ``Involuntary attentional capture by abrupt onsets'' Perception & Psychophysics 51 279 ^ 290 Roy M, Grondin S, 2005 ``Effect of space on auditory temporal processing with a single-stimulus method'', in Fechner Day 2005: Proceedings of the 21st Annual Meeting of the International Society for Psychophysics Eds J S Monahan, S M Sheffert, J T Townsend (Mt Pleasant, MI: The International Society for Psychophysics) pp 297 ^ 302 Shahab Ghorashi S M, Smilek D, Di Lollo V, 2007 ``Visual search is postponed during the attentional blink until the system is suitably reconfigured'' Journal of Experimental Psychology: Human Perception and Performance 33(1) 124 ^ 136 Suto Y, 1952 ``The effect of space on time estimation (S-effect) in tactual space I'' Japanese Journal of Psychology 22 45 ^ 57 Suto Y, 1955 ``The effect of space on time estimation (S-effect) in tactual space II: The role of vision in the S-effect upon skin'' Japanese Journal of Psychology 26 94 ^ 99 ten Hoopen G, 1995 ``Auditory spatial alternation transforms auditory time (again): Comments on Lakatos (1993) [Temporal constraints on apparent motion in auditory space]'' Perception & Psychophysics 57 569 ^ 572 Yarrow K, Haggard P, Heal R, Brown P, Rothwell J C, 2001 ``Illusory perception of space and time preserve cross-saccadic perceptual continuity'' Nature 414 302 ^ 305 Yoblick D A, Salvendy G, 1970 ``Influence of frequency on the estimation of time for auditory, visual, and tactile modalities: The kappa effect'' Journal of Experimental Psychology 86 157 ^ 164 Yourgrau P, 2005 A World Without Time: The Forgotten Legacy of Go«del and Einstein (New York: Basic Books) ß 2009 a Pion publication ISSN 0301-0066 (print) ISSN 1468-4233 (electronic) www.perceptionweb.com Conditions of use This article may be downloaded from the Perception website for personal research by members of subscribing organisations Authors are entitled to distribute their own article (in printed form or by e-mail) to up to 50 people This PDF may not be placed on any website (or other online distribution system) without permission of the publisher  ... conditions): conditions to 25; conditions to 25 followed by to 5; conditions 11 to 25 followed by to 10; conditions 16 to 25 followed by to 15; and conditions 21 to 25 followed by to 20 One participant... There was no feedback Within each session, there was only one fixation point, one base duration and one ascending or descending condition; but two height conditions 3.1.4 Data analysis For each participant... the ascending condition, the SD in the upper segment condition is larger than the SD in the lower segment condition (t24 ˆ 2:99, p 0:05); and, on contrary, for the descending condition, the SD in