The left visual field attentional advantage: No evidence of different speeds of processing across visual hemifields

Consciousness and Cognition 37 (2015) 16–26

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Consciousness and Cognition journal homepage: www.elsevier.com/locate/concog

The left visual field attentional advantage: No evidence of different speeds of processing across visual hemifields Miguel A. García-Pérez ⇑, Rocío Alcalá-Quintana Departamento de Metodología, Facultad de Psicología, Universidad Complutense, Campus de Somosaguas, 28223 Madrid, Spain

a r t i c l e

i n f o

Article history: Received 26 May 2015 Revised 20 July 2015 Accepted 5 August 2015

Keywords: Simultaneity Temporal order Timing processes Decisional processes

a b s t r a c t Temporal-order judgment (TOJ) and simultaneity judgment (SJ) tasks are used to study differences in speed of processing across sensory modalities, stimulus types, or experimental conditions. Matthews and Welch (2015) reported that observed performance in SJ and TOJ tasks is superior when visual stimuli are presented in the left visual field (LVF) compared to the right visual field (RVF), revealing an LVF advantage presumably reflecting attentional influences. Because observed performance reflects the interplay of perceptual and decisional processes involved in carrying out the tasks, analyses that separate out these influences are needed to determine the origin of the LVF advantage. We re-analyzed the data of Matthews and Welch (2015) using a model of performance in SJ and TOJ tasks that separates out these influences. Parameter estimates capturing the operation of perceptual processes did not differ between hemifields by these analyses, whereas parameter estimates capturing the operation of decisional processes differed. In line with other evidence, perceptual processing also did not differ between SJ and TOJ tasks. Thus, the LVF advantage occurs with identical speeds of processing in both visual hemifields. If attention is responsible for the LVF advantage, it does not exert its influence via prior entry. Ó 2015 Elsevier Inc. All rights reserved.

1. Introduction In studies on time perception, ‘‘time stimuli” (temporal durations or temporal events) are delivered via stimuli of some sensory modality (visual, auditory, tactile, etc.). In studies involving stimuli of different modalities (e.g., auditory and visual), conditions are created such that the different propagation speeds of each signal in the environment do not introduce unwanted delays in the time at which each signal reaches its target sense organ, unlike what happens in a fireworks show where light and sound are simultaneously produced when a shell explodes up in the air but their signals reach an observer on the ground at different times. When stimuli of different modalities reach their target sense organs, peripheral processing and neural transmission up the applicable sensory pathways incur delays that eventually provide the information needed to infer relative timing, given that we do not have a sense organ for time. But, in any given sensory modality, neural processing and transmission also incur different delays for different types of stimuli: In vision, low-spatial-frequency stimuli processed via the magnocellular pathway are transmitted faster than high-spatial-frequency stimuli processed via the parvocellular pathway (Mihaylova, Stomonyakov, & Vassilev, 1999); in audition, the cochlear place-frequency map delays the processing of low-frequency tones relative to high-frequency tones (Robles & Ruggero, 2001). Time perception involves low-level mechanisms related to this peripheral processing and transmission (which allow inferring temporal events from the perceived ⇑ Corresponding author. E-mail address: [email protected] (M.A. García-Pérez). http://dx.doi.org/10.1016/j.concog.2015.08.004 1053-8100/Ó 2015 Elsevier Inc. All rights reserved.

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onset or offset of stimuli) and high-level mechanisms that subsequently use perceived onsets and offsets to infer temporal durations. The processes of time perception are generally referred to as ‘‘timing processes” to differentiate them from the sensory processes responsible for perceiving physical features of the stimuli used to deliver the ‘‘time stimulus” (e.g., their brightness, color, pitch, etc.). Identifying the temporal order of presentation of two stimuli (whichever they are) requires a comparison of the perceived onset of each stimulus and a judgment as to which one was first, with subjective simultaneity arising when the evidence is insufficient to identify temporal order. Perceived onset times, the crucial pieces of evidence for these judgments, are delayed with respect to actual onset times by peripheral processing and neural transmission onto a central decision mechanism. The decision made there may simply be based on the arrival time of each signal, but it may also favor one of the stimuli by a natural bias on the part of the observer or as a result of experimental manipulations. Because only low-level timing processes are involved in these cases, judgments of temporal order or simultaneity are informative of the speed of neural processing and they are used to study, among other issues, differences in processing speed across sensory modalities (e.g., auditory vs. visual), across stimulus characteristics (e.g., low-frequency vs. high-frequency tones), across groups of observers given some pair of stimuli (e.g., video game players vs. non-players), across experimental conditions involving different types of cues (e.g., prior-entry studies), or across conditions eliciting temporal recalibration processes. For reviews, see Spence and Parise (2010) or Keetels and Vroomen (2012). Data collected in these studies reflect observers’ performance in simultaneity judgment (SJ) or temporal-order judgment (TOJ) tasks. Each trial in these tasks presents two stimuli, one of which is designated as the reference whereas the other is the test. The onset of the test stimulus relative to the onset of the reference is manipulated across trials, rendering a stimulus onset asynchrony (SOA) defined as positive (negative) when the test stimulus lags (leads) the reference stimulus. In SJ tasks, observers report whether or not presentation of the stimuli was subjectively simultaneous; in TOJ tasks, observers must report which stimulus was subjectively presented first, with no option to report subjective simultaneity. Performance measures such as the point of subjective simultaneity (PSS) or the just noticeable difference (JND) have consistently been reported to differ across SJ and TOJ tasks, but recent analyses have shown that this is not a sign of different timing processes involved in each task but, rather, the result of task-dependent decisional and response processes whose influence can be separated from that of the timing processes of interest (García-Pérez & Alcalá-Quintana, 2012a, 2015; see also Matsuzaki et al., 2014; Regener, Love, Petrini, & Pollick, 2014). In other words, the multiple determinants of performance in SJ and TOJ tasks preclude an unequivocal interpretation of observed outcomes in terms of timing processes. Analyses capable of separating out the distinct contributions of timing, decisional, and response processes are needed to provide a fitting account of observed performance and an accurate portrait of timing processes. Matthews and Welch (2015) reported the results of a study aimed at assessing differences in performance on SJ and TOJ tasks between the left visual field (LVF) and the right visual field (RVF). Observers carried out SJ and TOJ tasks on pairs of visual stimuli (randomly-oriented, achromatic Gabor patches) presented on the LVF or on the RVF. The stimulus feature whose onset was manipulated was a 90-deg change in the orientation of each Gabor patch. On each trial, observers fixated on the center of the monitor (where a concurrent identification task was performed) and Gabor patches thus appeared peripherally in the LVF or in the RVF, one in the top part of the display and the other in the bottom part. Trials for SJ or TOJ tasks in the LVF or in the RVF were administered in several randomly-ordered repeat blocks and observers knew in advance which task and visual field was involved in each block. The main outcome measures were proportion correct (for TOJ data) and d0 (for SJ data), as a function of SOA in each visual field. Both turned out to be higher in the LVF, which led Matthews and Welch to claim an attentional advantage in the LVF. This advantage was observed with stationary Gabor patches (in their main experiment) and with patches flickering in counterphase at 30 Hz (in their luminance transient control experiment). Because of the multiple determinants discussed above, we looked at the results reported by Matthews and Welch (2015) from an explicit model that separates out the timing, decisional, and response components that determine observed performance in SJ and TOJ tasks. The model allows for an explicit test of the hypothesis that low-level timing processes (i.e., speed of neural processing) differ between hemifields, which is accomplished by fitting the data on the assumption that they do not differ between hemifields. If this assumption were incorrect, the model would not fit the data. We found instead that the model fits the data remarkably well under this assumption, which implies that the performance differences across visual hemifields reported by Matthews and Welch do not rule out identical timing processes in both hemifields. This was also corroborated in alternative analyses that removed the constraint: When timing parameters were estimated separately for each hemifield, the estimates did not differ significantly. The next two sections describe the model and our testing approach. Subsequent sections present the results of our analyses and discuss the implications. 2. Model of timing judgments The independent-channels (IC) model used in our analyses has been presented in full detail elsewhere (García-Pérez & Alcalá-Quintana, 2012a) but a brief description is given here tailored to the experimental conditions of Matthews and Welch (2015). Specifically, we will assume that perceived onsets have identical characteristics for the two stimuli presented in each trial, as they were identical Gabor patches (except for their random orientation) presented at the top or at the bottom of the same visual hemifield. Yet, perceived onsets might have different characteristics in each hemifield. The IC model

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captures in quantitative terms the ideas embodied in the model sketched by Matthews and Welch in their Fig. 1: Each of the two stimuli presented in a trial is subject to processing delays before its signal reaches a central mechanism that applies a different decision rule to judge simultaneity (in SJ tasks) or temporal order (in TOJ tasks). The IC model also assumes that timing processes are invariant across SJ and TOJ tasks whereas decisional and response processes vary across tasks. For empirical evidence supporting these assumptions, see García-Pérez and Alcalá-Quintana (2012a, 2015). In the model, the perceived onsets Tt and Tb of stimuli presented at the top or at the bottom in a given hemifield are random variables with densities gt and gb given by the shifted exponential distributions

g i ðtÞ ¼ ki exp½ki ðt  ðDti þ si ÞÞ;

t  Dt i þ s i ;

i 2 ft; bg;

ð1Þ

where Dti is the actual onset of stimulus i and ki and si are parameters describing the distribution of peripheral processing and transmission times. Exponential distributions are used because of causality (i.e., the perceived onset of a stimulus cannot precede its physical onset) and also because they are a common choice for describing the distribution of arrival latencies or peripheral processing and transmission times (e.g., Colonius & Diederich, 2011; Diederich & Colonius, 2015; Heath, 1984; Ulrich, 1987). Other causal distributions could be used that would produce analogous outcomes (see García-Pérez & Alcalá-Quintana, 2012a). If the bottom stimulus is the reference, Dtb = 0 by convention and Dt  Dtt is the asynchrony with which the pair is presented, where Dt < 0 (Dt > 0) reflects that the onset (i.e., the time at which the change in orientation occurs) of the top stimulus precedes (lags) the onset of the bottom stimulus. Under the assumption that perceived onsets have identical characteristics for stimuli presented in the same hemifield, kt = kb = k and st = sb = s so that

g b ðtÞ ¼ k exp½kðt  sÞ;

t P s;

g t ðtÞ ¼ k exp½kðt  ðDt þ sÞÞ;

ð2Þ t P Dt þ s:

ð3Þ

The top panel in Fig. 1a and b shows two sample distributions when Dt = 50 ms (i.e., the change in orientation occurs 50 ms later for the stimulus at the top), reflecting the variability with which top and bottom onsets are perceived across trials with this Dt, with the same distribution except for the shift caused by Dt. On a trial, perceived onsets come from these distributions and judgments arise from a decision rule applied to the perceived-onset difference D = Tt  Tb, which has the Laplace distribution

f ðd; DtÞ ¼

k exp½kjd  Dtj: 2

ð4Þ

Across trials with the same Dt, perceived-onset differences thus vary from large and negative to large and positive and their mean occurs at D = Dt. The left panels in the bottom parts of Fig. 1a and b show the distribution of D for the gi’s shown at the top, where Dt = 50 ms. Whether the trial is from an SJ or a TOJ task, observers make a judgment based on the sample value of D in the current trial. This implies a decision rule that partitions the continuum of D into three regions, as illustrated by the vertical lines (decision boundaries at d1 and d2) in the left panels in the bottom parts of Fig. 1a and b. Then, ‘‘top-first” (or ‘‘downward”; D) judgments arise when D is large and negative (D < d1), ‘‘bottom-first” (or ‘‘upward”; U) judgments arise when D is large and positive (D > d2), and ‘‘simultaneous” (S) judgments arise when d1 6 D 6 d2. The probabilities pD, pS, and pU of these judgments vary with Dt as

pD ðDtÞ ¼ Fðd1 ; DtÞ;

ð5Þ

pS ðDtÞ ¼ Fðd2 ; DtÞ  Fðd1 ; DtÞ;

ð6Þ

pU ðDtÞ ¼ 1  Fðd2 ; DtÞ;

ð7Þ

with

Z Fðd; DtÞ ¼

d

1

( f ðz; DtÞ dz ¼

1 2

exp½kðd  DtÞ

if d 6 Dt

1  exp½kðd  DtÞ if d > Dt 1 2

:

ð8Þ

In SJ tasks, U and D judgments are aggregated into the category of non-simultaneous judgments and the psychometric function for S responses in SJ tasks is

WSJ ðDtÞ ¼ pS ðDtÞ:

ð9Þ

Red curves in the right panels in the bottom parts of Fig. 1a and b show the resultant shape of WSJ under the additional assumptions in each case (i.e., the form of the distribution of perceived-onset differences and the location of the decision boundaries d1 and d2). In TOJ tasks, where observers must give U or D responses even when they judge simultaneity, a guessing (response bias) parameter n describes the probability with which the observer gives a U response on a trial that resulted in an S judgment. Then, the psychometric function for U responses in TOJ tasks is

WTOJ ðDtÞ ¼ npS ðDtÞ þ pU ðDtÞ:

ð10Þ

Blue curves in the right panels in the bottom parts of Fig. 1a and b illustrate how WTOJ may vary in shape relative to WSJ, with an additional source of variation arising from the value of parameter n (see also Fig. 1 in Diederich & Colonius, 2015).

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Fig. 1. IC model of timing judgments and resultant psychometric functions in SJ and TOJ tasks for two sample distributions of perceived onsets (top panels in parts a and b) and several sample locations for the decision boundaries (lower panels in each part). Compared to part b, part a assumes perceived onsets that occur earlier and with less variability. The distribution of perceived-onset differences (left panels in the three bottom rows in either part) is thus narrower and taller in part a compared to part b. Vertical lines in the same panels indicate sample partitions of decision space that render the three possible timing judgments in a trial (see labels at the top of each region). In the first row, these boundaries are symmetrically placed about D = 0 (at D = d1 = 60 and D = d2 = 60), defining a narrow central region; in the second row, boundaries are also symmetrically placed (d1 = 130 and d2 = 130) but the central region is broader; in the third row, the central region has the same width as in the first row but it is asymmetrically placed about D = 0 (d1 = 10 and d2 = 110). The right panels in each row in parts a and b show the resultant psychometric function WSJ in an SJ task (red curve) and WTOJ in a TOJ task for three sample values of the response bias parameter n. Circles on the curves at Dt = 50 ms denote the probability arising from the partition in the corresponding panel on the left. Note that, in all cases, the location of the peak of WSJ (dotted vertical line) matches the location of the 50% on WTOJ (crossing with the dotted horizontal line) only when n = 0.5. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Note that perceptual processes differ across Fig. 1a and b (as given by the distributions of perceived onsets illustrated in the top panels) but the shapes of the resultant psychometric functions WTOJ and WSJ are not only determined by those perceptual processes: These shapes vary within Fig. 1a and within Fig. 1b. Consider WSJ (red curves) in the bottom part of either Fig. 1a or Fig. 1b. Compared to the shape of WSJ in the first row, a broader region for ‘‘simultaneous” judgments in decision space makes WSJ taller and broader (second row) whereas a shifted region of the same width merely displaces WSJ laterally (third row). Because the shape of a psychometric function has multiple determinants, observed differences in shape across conditions cannot be attributed to differences in perceptual processes if non-perceptual determinants have not been separated out. Estimating IC model parameters from the data accomplishes such separation. Several characteristics of psychometric functions under the model are worth stressing in this respect. First, the height of WSJ and the sharpness of its peak are solely determined by the distance between d1 and d2 (i.e., the breadth of the region for ‘‘simultaneous” judgments in decision space); this breadth also affects the range of variation of the lateral shift of WTOJ relative to WSJ across changes in parameter n. Second, and with the given height of WSJ and the sharpness of its peak, the rate of its drop-off on either side is solely determined by the spread of the distribution of perceived onsets. This rate (and, correspondingly, the steepness of WTOJ) is invariant across variations in the location of d1 and d2: Psychometric functions in the bottom parts of Fig. 1a or Fig. 1b are identical in this respect across the three cases, but they are shallower in Fig. 1b compared to Fig. 1a. Third, the peak of WSJ, which is the conventional PSS estimate in SJ tasks, occurs at (d1 + d2)/2 and, thus, it is affected by a potential decisional bias by which d1 and d2 are asymmetrically located with respect to D = 0 (as in the bottom row in Fig. 1a and b). In turn, the location of the 50% point on WTOJ, which is the conventional TOJ estimate of the PSS, is greatly affected by n and can occur anywhere within a relatively broad area around the location of the peak of WSJ; conventional SJ and TOJ estimates of the PSS match only when n = 0.5 (see the red curve and the dashed blue curve in each of the panels in the bottom parts of Fig. 1a and b). Finally, JND estimates from TOJ tasks are severely affected by the value of the response bias parameter n, as this affects greatly the distance between the 25% and 75% points on WTOJ that are conventionally used to define the JND. The IC model must be amended to cover realistically the mapping of judgments onto responses, a process during which errors can be made (see García-Pérez & Alcalá-Quintana, 2012a, 2012b, 2015). The final psychometric functions in SJ and TOJ tasks thus become

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WSJ ðDtÞ ¼ eDðSJÞ pD ðDtÞ þ ð1  eSðSJÞ ÞpS ðDtÞ þ eUðSJÞ pU ðDtÞ; ðTOJÞ pD ðDtÞ D

WTOJ ðDtÞ ¼ e

ðTOJÞ ÞpU ðDtÞ; U

þ npS ðDtÞ þ ð1  e

ð11Þ ð12Þ

where each e reflects the probability of misreporting the judgment indicated by its subscript under the task indicated in its parenthetical superscript. Note that Eqs. (9) and (10) obtain in the absence of response errors (i.e., when all es are zero). As will be seen below, evidence of response errors is sometimes large, which further affects observed performance via response processes that are unrelated to timing judgments. In sum, the IC model describes performance in SJ and TOJ tasks involving identical stimuli with a unique timing parameter (k) and with decisional and response parameters (d1, d2, n, and the various es) that may vary across tasks. All of these parameters or a subset of them might differ across conditions (e.g., for stimuli presented in the LVF or in the RVF). 3. Testing approach The foregoing discussion attests to the fact that differences in performance can occur as a result of decisional and response factors even when timing processes are identical (see the several resultant shapes for WSJ and WTOJ in the bottom part of Fig. 1a or in the bottom part of Fig. 1b, which are caused only by decisional and response factors). With respect to the issue addressed by Matthews and Welch (2015), it might be that timing processes are identical in the LVF and in the RVF and that the observed differences in performance are due to differences in decisional and response factors. If such were the case, and considering potential individual differences in timing processes, one would expect psychometric functions involving the same k in both hemifields on a subject-by-subject basis, but showing also the effects of decisional and responses processes that may vary across hemifields. In contrast, if timing processes differed across hemifields, psychometric functions would call for a different k in each hemifield. In other words, in the former case, WSJ and WTOJ should vary across hemifields for each observer in some of the forms illustrated in the bottom part of, e.g., Fig. 1a (but with individual differences in all parameters); in contrast, in the latter case, WSJ and WTOJ should vary across hemifields as they vary across Fig. 1a and b (allowing also for individual differences). We tested explicitly the hypothesis of identity of timing processes in both hemifields by checking the extent to which the assumption of a common value for the timing parameter k can fit the data from each individual observer across hemifields and tasks. We retrieved the raw data provided by Matthews and Welch (2015) as Supplementary Information and estimated model parameters for each observer under the stated constraint. The model was fitted using a fortran version of the software in Alcalá-Quintana and García-Pérez (2013), which was modified to implement the constraint. Decisional and response parameters (d1, d2, n, and the es) were still allowed to vary freely across tasks and hemifields. Non-null values for the es were not pre-assumed but tested for suitability (see Alcalá-Quintana & García-Pérez, 2013). A poor fit, in the form of fitted curves failing to follow the path of the data and significant goodness-of-fit statistics, would provide evidence against the hypothesis of common timing processes. The joint fit involves somewhere between 11 parameters (when all es are null) and 21 parameters (when all es are non-null) per observer. The seemingly large number of parameters is caused by the presence of four conditions (two tasks in each of two hemifields), but this number is much smaller than needed under a conventional analysis that fits psychometric functions separately for each task in each visual hemifield: Each individual SJ function requires three parameters and each individual TOJ function requires four parameters, for a total of 28 parameters per observer under a conventional approach. Although the fit of the model in these conditions was remarkably good (see the next section), we also fitted the IC model to data from each hemifield separately, thus allowing estimates of k to attain different values in each hemifield. This strategy adds a further free parameter but it could also result in a better fit. This was not the case and, hence, those results will not be presented in full detail. 4. Results Fig. 2 shows data and fitted psychometric functions for each observer in each task and in each hemifield in the main experiment of Matthews and Welch (2015), including also a summary panel for data aggregated across observers and fitted curves also averaged across observers. Parameter estimates and goodness-of-fit measures are appended as Supplementary Information. At a = 0.05, the likelihood-ratio G2 goodness-of-fit statistic was not significant for any observer. Model curves follow the path of the data remarkably closely except in the occasional cases in which noisy data do not so allow. Thus, observed performance in both tasks and in both hemifields is compatible with unique timing processes captured by parameter k, with the participation of task-dependent decisional and response processes that vary across hemifields (as discussed below). Across observers, estimates of 1/k ranged from 16.32 to 61.04 with an average of 23.10 and a standard deviation of 9.78. A comparison of the panel for any given observer in Fig. 2a (LVF) with the corresponding panel in Fig. 2b (RVF) reveals that the data support the common drop-off rate of WSJ across hemifields arising from a common k, whereas differences in the overall shape of WSJ across hemifields is captured by decisional parameters affecting the sharpness of the peak (compare, e.g., differences in this respect across hemifields for observer #6) or by error parameters (compare, e.g., the left sides of WSJ for observer #1 in the LVF and in the RVF). TOJ data also support a common steepness across hemifields (and also across tasks),

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Fig. 2. Data and fitted psychometric functions under SJ (red data points and curves) and TOJ tasks (blue data points and curves) for each individual observer (label in the top left corner in each panel) in the main experiment of Matthews and Welch (2015) for presentations in the LVF (a) and in the RVF (b). The grayed panel at the bottom right in each part shows aggregated data across observers and average fitted psychometric functions. The ordinate reflects the proportion of ‘‘simultaneous” responses in the SJ task and the proportion of ‘‘upward” responses (i.e., orientation changed first in the bottom part of the display) in the TOJ task. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

although the presence of an intermediate region of reduced slope (caused by a response bias parameter valued near 0.5; see Fig. 1) occludes this characteristic. Also clear across panels in Fig. 2 is an apparent inconsistency in the form that identification of temporal order (in the TOJ task) does not always seem possible at SOAs for which SJ data reflect instead errorless identification of asynchrony (compare, e.g., SJ and TOJ data from observer #1 at the two largest positive asynchronies in either hemifield). This inconsistency sometimes varies across hemifields: See, e.g., the inconsistent SJ and TOJ data for observer #14 at negative asynchronies in the LVF coupled with a mild inconsistency at the two largest positive asynchronies also in the LVF in comparison with a reverse pattern in the RVF. Further commentary on these inconsistencies and their potential cause is deferred to Section 5. It is also important to note that, despite the common (intra-individual) timing processes revealed by this analysis in both hemifields, differences in decisional and response processes across hemifields (discussed below) contribute to rendering the overall differences reported by Matthews and Welch (2015) and corroborated in the panels for average data in Fig. 2 here. If average data in those panels were replotted in the form of proportion correct (for TOJ data) or d0 (for SJ data), both measures would be higher in the LVF.1 Fitting the data under the alternative approach that allows the timing parameter k to vary across hemifields did not result in a better fit. Fitted psychometric functions remained virtually identical to those shown in Fig. 2 and estimates of 1/k in the LVF averaged 25.07 with a standard deviation of 11.85 whereas estimates of 1/k in the RVF averaged 26.80 with a standard deviation of 12.97 (Cohen’s dz: 0.12). A Bradley–Blackwood test (Bradley & Blackwood, 1989) did not reject the joint null hypothesis of equality of means and variances in both hemifields (F2,19 < 1). Then, even when the timing parameter is estimated separately in each hemifield, estimates do not differ meaningfully or significantly between hemifields.

1 It should be noted that Matthews and Welch (2015) computed d0 incorrectly, as they used equations that are only valid for yes–no tasks. We checked that properly computed estimates with the equations that hold for SJ tasks nevertheless do not change this result, as d0 is always a monotonic transformation of proportion correct (even when incorrect equations are used).

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Fig. 3 shows data and fitted psychometric functions for each observer in each task and in each hemifield in the luminance transient control experiment of Matthews and Welch (2015), including also summary panels. Parameter estimates and goodness-of-fit measures are appended as Supplementary Information. In comparison to data from the main experiment (Fig. 2), these data are noisier, suggest shallower psychometric functions, and show substantial evidence of response errors across the board. The IC model nevertheless provided a remarkable account of the data on the assumption that timing processes do not differ across hemifields. At a = 0.05, the G2 statistic was significant only for observer #3 and model curves follow the path of the data remarkably closely even in this case. Thus, also in this experiment, observed performance does not rule out identical timing processes in both hemifields. Estimates of 1/k now ranged from 49.43 to 112.08 across observers with an average of 64.27 and a standard deviation of 18.84. In comparison with analogous measures reported earlier for the main experiment (which involved a different sample of observers), the accuracy with which the temporal occurrence of orientation changes can be detected and compared seems severely disrupted in both hemifields when Gabor patches are flickering. This was corroborated by a two-sided Welch’s t-test for means (t24.58 = 8.13, p < 0.001, Cohen’s ds: 2.81). If identical timing processes in both tasks and hemifields cannot be ruled out, the question arises as to how decisional and response processes account for the observed differences in performance. Fig. 4 shows scatter plots of the relevant decisional and response parameters in the main experiment (top row) and in the luminance transient control experiment (bottom row). Consider the top row first, for the main experiment in which raw data were substantially less noisy (see Fig. 2). The top panel in Fig. 4a shows the estimated width, d2  d1, of the central region in decision space (see Fig. 1) in the RVF against the estimated width in the LVF, separately for the SJ task (red symbols) and the TOJ task (blue symbols). For both tasks, data points tend to lie above the diagonal identity line, implying that the central region tends to be broader in the RVF than in the LVF. There are also noticeable differences in these widths across tasks, with TOJ performance implying broader central regions than SJ performance. A 2  2 ANOVA with hemifield (LVF and RVF) and task (SJ and TOJ) as repeated-measures factors and width as the dependent variable revealed significant main effects of hemifield (F1,20 = 7.26, p = 0.014, g2p = 0.27) and task (F1,20 = 38.11, p < 0.001, g2p = 0.66) with no interaction (F1,20 = 3.23, p = 0.087, g2p = 0.14). The first and second rows in the bottom part of Fig. 1a or b reveal how differences in width produce differences in performance in the SJ task (compare the resultant red psychometric functions in those cases) and in the TOJ task (compare the resultant blue psychometric functions for any given value of n in those cases).

Fig. 3. Data and fitted psychometric functions under SJ (red data points and curves) and TOJ tasks (blue data points and curves) for each individual observer (label in the top left corner in each panel) in the luminance transient control experiment of Matthews and Welch (2015) for presentations in the LVF (a) and in the RVF (b). The grayed panel at the bottom right in each part shows aggregated data across observers and average fitted psychometric functions. The ordinate reflects the proportion of ‘‘simultaneous” responses in the SJ task and the proportion of ‘‘upward” responses (i.e., orientation changed first in the bottom part of the display) in the TOJ task. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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Fig. 4. Scatter plots of estimated width (a) and center location (b) of the ‘‘simultaneous” region in decision space across hemifields, and of response bias in the TOJ task (c) also across hemifields in the main experiment of Matthews and Welch (2015) (top row) and in their luminance transient control experiment (bottom row). Red symbols depict individual estimates from the SJ task; blue symbols depict individual estimates from the TOJ task. In each panel, the oblique dashed line is the identity line (note that the horizontal and vertical ranges and scales are identical in the top and bottom panels except in b). Overlaid crosses sketch the distribution of the data from each task. The two arms of each cross meet at the coordinates of the mean of each variable and the length of each arm spans the range from one standard deviation below the mean to one standard deviation above it. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

The top panel in Fig. 4b shows an analogous scatter plot, now using estimates of the location of the center of the region for ‘‘simultaneous” judgments in decision space, given by (d1 + d2)/2 (see Fig. 1). A region centered away from D = 0 (as depicted in the bottom row of Fig. 1) reflects a decisional bias towards one of the temporal orders and produces differences in performance for positive and negative asynchronies of the same magnitude. No evidence to this effect was actually observed in the raw data (see Fig. 2). Consistent with it, red symbols (for the SJ task) in the top panel of Fig. 4b are tightly clustered around the origin with no sign of systematic differences between hemifields; the same holds for the TOJ task (blue symbols), although data points are more broadly scattered around the origin. A 2  2 ANOVA with hemifield (LVF and RVF) and task (SJ and TOJ) as repeated-measures factors and center location as the dependent variable revealed no significant main effects of hemifield (F1,20 < 1, g2p < 0.01) or task (F1,20 < 1, g2p < 0.01) and no interaction (F1,20 < 1, g2p < 0.01). In other words, large individual differences are observed in decisional bias along with a broader range of decisional bias in the TOJ task compared to the SJ task, but no systematic differences in decisional bias are apparent between hemifields. Finally, the top panel in Fig. 4c shows a scatter plot of response bias (in the TOJ task) in the RVF against response bias in the LVF, given by the estimated value of parameter n. Recall that this parameter reflects the observer’s propensity to give an ‘‘upward” response upon ‘‘simultaneous” judgments in the TOJ task. The scatter plot shows no evidence of differences in response bias between hemifields. The bottom row of Fig. 4 shows analogous scatter plots for the luminance transient control experiment. As expected for noisy raw data (see Fig. 3), the variability of estimates is much larger and the overall picture is less clear. The results reveal again a clear difference between SJ and TOJ tasks as regards the width of the central region in decision space with not-soclear differences in this respect between hemifields (bottom panel in Fig. 4a), little difference across tasks or hemifields in the location of the center of that region (bottom panel in Fig. 4b), and weak signs of higher response bias in the RVF than in the LVF (bottom panel in Fig. 4c). Further statistical analyses were not conducted because their results would not be dependable given the small sample size and the large variability. 5. Discussion Performance in any psychophysical task is determined by the interplay of perceptual, decisional, and response processes. Observed differences in performance across stimuli, tasks, or experimental manipulations cannot be unequivocally attributed to perceptual components without an analysis that separates out the individual contribution of each component (GarcíaPérez & Alcalá-Quintana, 2013). Application of this model-based strategy in other areas of psychophysics has shown that observed differences in performance across tasks reflect the influence of task-dependent decisional and response processes operating on the output of sensory processes that are invariant across tasks (Allik, Toom, & Rauk, 2014; García-Pérez & Peli, 2014). Using a model of timing judgments that shares these characteristics, we have separated timing, decisional, and response components in the data reported by Matthews and Welch (2015), which further allows for an explicit test of differences in the operation of each of these components in the LVF and in the RVF. The model gave an excellent account of the

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data (see Figs. 2 and 3) under the assumption that the operation of the timing component is invariant in the LVF and in the RVF, with observed differences in performance between hemifields and also between SJ and TOJ tasks resulting only from differences in decisional components: The region for ‘‘simultaneous” judgments in decision space is broader in the RVF than in the LVF and it is also broader under TOJ tasks than under SJ tasks. This result was clear for data from the main experiment of Matthews and Welch, although it was not clearly apparent for the noisier data from their luminance transient control experiment. The fact that the data support unique timing processes governed by a common parameter k in both hemifields suggests that perceived onsets have the same distribution in both cases and, hence, that the speed of neural processing (up to the decision center for timing judgments) does not vary between hemifields. A more direct test of differences in perceived onsets for stimuli presented in the LVF or in the RVF comes from studies in which each stimulus in the pair is presented in a different hemifield. Some studies in which this direct comparison was used reported significant differences in performance when the leading stimulus is presented in the LVF vs. the RVF (see references to this effect in Matthews & Welch, 2015), but other studies have reported little or no differences (see Capa, Duval, Blaison, & Giersch, 2014; Kelly & Matthews, 20112; Lalanne, van Assche, & Giersch, 2012; Lalanne, van Assche, Wang, & Giersch, 2012). These contradictory results seem to reveal again the inadequacy of observed performance as an outcome measure without differentiating the contributions of timing, decisional, and response processes. Indeed, an analysis of the data reported by Capa et al. (2014) under the IC model concurred with the present results in indicating that perceived onsets in the LVF and in the RVF have identical distributions (see García-Pérez & Alcalá-Quintana, 2015). Besides common timing processes in both hemifields, our analyses revealed that the breadth of the central region for ‘‘simultaneous” judgments in decision space (see Fig. 1) is significantly larger in the RVF than in the LVF. A broader central region in decision space implies that stronger evidence (i.e., a larger perceived-onset difference) is needed at the decision center to perceive asynchrony. This decisional requirement is independent of the timing parameter k (compare the first and second rows in the bottom parts of Fig. 1a and b) and reflects only the resolution at which the decision center operates. The picture that emerges from our analysis is, then, that targets are not perceived any sooner in the LVF than in the RVF although differences in perceived onsets in the RVF need to be larger than in the LVF for observers to judge asynchrony. This result places the origin of the LVF advantage at the decision stage, which is consistent with a statement by Matthews, Vawter, and Kelly (2012) to the effect that the LVF advantage in an SJ task occurs at a late stage (after stimulus detection).3 Our results further show that the LVF advantage occurs also at the decision stage in TOJ tasks. In the absence of direct evidence, it is unclear whether these differences at the decision stage reflect attentional influences but, certainly, such influences do not produce a prior entry effect given that parameter k did not differ across hemifields in our analyses. The functional resolution (i.e., the breadth of the central region in decision space) with which observers make judgments also differed by our analyses between SJ and TOJ tasks in analogous ways in both hemifields. Although this result has no bearing on the issues addressed by Matthews and Welch (2015), it suggests an interesting issue with potential implications for data collection in timing studies. Contrary to the present results, the analysis of some data sets revealed instead that the central region is narrower in TOJ tasks than in SJ tasks (García-Pérez & Alcalá-Quintana, 2012a). This was interpreted as indicating that observers refrain from working at their limiting resolution in SJ tasks, perhaps because the ‘‘simultaneous” response option offers a refuge. TOJ tasks do not offer this refuge and observers must use the weakest piece of evidence available to them to avoid guessing a temporal-order response. The current opposite finding of a narrower central region in SJ tasks compared to TOJ tasks was also systematically observed in the analysis of a large number of other data sets (see García-Pérez & Alcalá-Quintana, 2015), demanding an alternative interpretation that we conjecture next. The IC model assumes that only three judgments are possible. An SJ task covers them adequately (although not exhaustively) because judgments of temporal order in any direction are legitimately reported as non-simultaneous responses. The TOJ task, on the other hand, does not give an adequate coverage because judgments of simultaneity must be randomly (mis) reported as temporal-order responses in one direction or the other. The ternary simultaneity judgment task (SJ3) blends SJ and TOJ tasks by providing a response option for each possible judgment and the utility of this task has been demonstrated (Kohlrausch, van Eijk, Juola, Brandt, & van de Par, 2013; Kuling, van Eijk, Juola, & Kohlrausch, 2012; Ulrich, 1987; van Eijk, Kohlrausch, Juola, & van de Par, 2008). Yet, observers may experience that presentations were not simultaneous and still be unable to identify their order. Anecdotal evidence on this fourth judgment category comes from observers’ spontaneous reports but also from asynchronous audiovisual speech streams: The asynchrony is clearly noticeable even when it is small, but identifying whether audio leads or lags video is often very difficult if not impossible. Fig. 5a shows a plausible partition of decision space that renders these four judgments. Extra regions flanking the central region are associated with this fourth judgment, reflecting perceived-onset differences that are sufficiently large to judge asynchrony but not enough to identify temporal order. These regions may also have different widths on the negative and positive sides, as illustrated in Fig. 5a. These extra regions do not have any effect in SJ tasks because they are still associated with non-simultaneous judgments; in contrast, in TOJ tasks, these regions also result in guesses because temporal order has not been identified. The existence of this fourth judgment renders a functionally broader 2 The applicable results for the present discussion are to be found in their Fig. 3, which shows that average d0 and average miss and false-alarm rates in an SJ task are nearly identical when changes in orientation occur for stimuli presented in the same hemifield and when they occur for stimuli presented in different hemifields. 3 We thank Dr. Nestor Matthews for drawing our attention to that statement.

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Fig. 5. Modified IC model of timing judgments. (a) Partition of decision space, with two additional regions flanking the central region for ‘‘simultaneous” judgments and reflecting perceived-onset differences sufficiently large to perceive non-simultaneity but not enough to perceive temporal order. (b) Resultant psychometric functions in SJ tasks (red curve) and TOJ tasks for different values of the response bias parameter n (blue curves). Functionally, SJ performance is governed by the two inner boundaries at d2 and d3 whereas TOJ performance is governed by the two outer boundaries at d1 and d4. As a result, the implied central region for ‘‘simultaneous” judgments is broader in TOJ tasks than it is in SJ tasks (i.e., d4  d1 > d3  d2). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

central region in the TOJ task, producing the inconsistencies described earlier: Judgments of non-simultaneity without an identifiable temporal order may be responsible for imperfect identification of temporal order at SOAs where SJ performance is much more accurate or even errorless (see Fig. 5b). Experimental studies are underway to search for direct evidence of four judgment categories using a four-response simultaneity judgment task (SJ4), where a separate response option is provided for observers to report each of these four judgments. Acknowledgments This research was supported by Grant PSI2012-32903 from Ministerio de Economía y Competitividad (Spain). Parts of the computations were carried out on EOLO, the MECD- and MICINN-funded HPC of Climate Change at Moncloa Campus of International Excellence, Universidad Complutense. We thank N. Matthews and L. Welch for making their data available. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.concog. 2015.08.004. References Alcalá-Quintana, R., & García-Pérez, M. A. (2013). Fitting model-based psychometric functions to simultaneity and temporal-order judgment data: Matlab and R routines. Behavior Research Methods, 45(4), 972–998. http://dx.doi.org/10.3758/s13428-013-0325-2. Allik, J., Toom, M., & Rauk, M. (2014). Detection and identification of spatial offset: Double-judgment psychophysics revisited. Attention, Perception, and Psychophysics, 76(8), 2575–2583. http://dx.doi.org/10.3758/s13414-014-0717-0. Bradley, E. L., & Blackwood, L. G. (1989). Comparing paired data: A simultaneous test for means and variances. American Statistician, 43(4), 234–235. http:// dx.doi.org/10.1080/00031305.1989.10475665. Capa, R. L., Duval, C. Z., Blaison, D., & Giersch, A. (2014). Patients with schizophrenia selectively impaired in temporal order judgments. Schizophrenia Research, 156(1), 51–55. http://dx.doi.org/10.1016/j.schres.2014.04.001. Colonius, H., & Diederich, A. (2011). Computing an optimal time window of audiovisual integration in focused attention tasks: Illustrated by studies on effect of age and prior knowledge. Experimental Brain Research, 212, 327–337. http://dx.doi.org/10.1007/s00221-011-2732-x. Diederich, A., & Colonius, H. (2015). The time window of multisensory integration: Relating reaction times and judgments of temporal order. Psychological Review, 122(2), 232–241. http://dx.doi.org/10.1037/a0038696. García-Pérez, M. A., & Alcalá-Quintana, R. (2012a). On the discrepant results in synchrony judgment and temporal-order judgment tasks: A quantitative model. Psychonomic Bulletin and Review, 19(5), 820–846. http://dx.doi.org/10.3758/s13423-012-0278-y. García-Pérez, M. A., & Alcalá-Quintana, R. (2012b). Response errors explain the failure of independent-channels models of perception of temporal order. Frontiers in Psychology, 3, 94. http://dx.doi.org/10.3389/fpsyg.2012.00094. García-Pérez, M. A., & Alcalá-Quintana, R. (2013). Shifts of the psychometric function: Distinguishing bias from perceptual effects. Quarterly Journal of Experimental Psychology, 66(2), 319–337. http://dx.doi.org/10.1080/17470218.2012.708761. García-Pérez, M. A., & Alcalá-Quintana, R. (2015). Converging evidence that common timing processes underlie temporal-order and simultaneity judgments: A model-based analysis. Attention, Perception, and Psychophysics, 77, 1750–1766. http://dx.doi.org/10.3758/s13414-015-0869-6. García-Pérez, M. A., & Peli, E. (2014). The bisection point across variants of the task. Attention, Perception, and Psychophysics, 76(6), 1671–1697. http://dx.doi. org/10.3758/s13414-014-0672-9. Heath, R. A. (1984). Response time and temporal order judgement in vision. Australian Journal of Psychology, 36, 21–34. http://dx.doi.org/10.1080/ 00049538408255075. Keetels, M., & Vroomen, J. (2012). Perception of synchrony between the senses. In M. M. Murray & M. T. Wallace (Eds.), The neural bases of multisensory processes (pp. 147–177). Boca Raton, FL: CRC Press. Kelly, J. G., & Matthews, N. (2011). Attentional oblique effect when judging simultaneity. Journal of Vision, 11(6), 1–15. http://dx.doi.org/10.1167/11.6.10 (10). Kohlrausch, A., van Eijk, R., Juola, J. F., Brandt, I., & van de Par, S. (2013). Apparent causality affects perceived simultaneity. Attention, Perception and Psychophysics, 75(7), 1366–1373. http://dx.doi.org/10.3758/s13414-013-0531-0. Kuling, I. A., van Eijk, R. L. J., Juola, J. F., & Kohlrausch, A. (2012). Effects of stimulus duration on audio-visual synchrony perception. Experimental Brain Research, 221(4), 403–412. http://dx.doi.org/10.1007/s00221-012-3182-9.

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