We present a simple reaction time (RT) versus temporal order judgment (TOJ) experiment as a test of the perception–action relationship. The experiment improves on previous ones in that it assesses for the first time RT and TOJ on a trial-by-trial basis, hence allowing the study of the two behaviors within the same task context and, most importantly, the association of RT to “correct” and “incorrect” TOJs. RTs to pairs of stimuli are significantly different depending on the associated TOJs, an indication that perceptual and motor decisions are based on the same internal response. Simulations with the simplest one-system model (J. Gibbon & R. Rutschmann, 1969) using the means and standard deviations of the RT to stimuli presented in isolation yield excellent fits of the mean RT to these increments when presented in sequence and moderately good fits of the RT when classified according to the TOJ categories. The present observation that the point of subjective simultaneity for stimulus pairs is systematically smaller than the difference in RT to each of the two increments in the same pairs pleads, however, in favor of distinct decision criteria for perception and action with the former below the latter. For such a case, standard one-system race models require that the internal noise associated with the TOJ be less than the one associated with the RT to the same stimulus pair. The present data show the reverse state of affairs. In short, data and simulations comply with “one-system–two-decision” models of perceptual and motor behaviors, while prompting further testing and modeling to account for the apparent discrepancy between the ordering of the two decisions.

*σ*

_{TOJ}

^{2}), with the latter being a measure directly related to observer's temporal order discrimination threshold. The equality of ΔRT and PSS is generally taken as direct evidence that motor and perceptual behaviors are determined by the same internal response and decision process (the one-system–one-decision hypothesis). For a sequence of two noninterfering signals, such a one-system–one-decision model also requires that

*σ*

_{TOJ}

^{2}be equal to the sum of the RT variances for each of the two stimuli (

*σ*

_{RT–S1}

^{2}+

*σ*

_{RT–S2}

^{2}). Instead, according to the two (parallel)-system hypothesis, neither ΔRT and PSS nor

*σ*

_{TOJ}

^{2}and

*σ*

_{RT–S1}

^{2}+

*σ*

_{RT–S2}

^{2}should be related.

*salience*: Adams & Mamassian, 2004;

*spatial frequency*: Barr, 1983; Tappe, Niepel, & Neumann, 1994;

*luminance rise times*: Jaśkowski, 1993;

*stimulus duration*: Jaśkowski, 1991, 1992). In particular, it was found that stimulus intensity affects ΔRT about twice more than it affects PSS (Jaśkowski, 1992; Jaśkowski & Verleger, 2000; Menendez & Lit, 1983; Roufs, 1974; but see Roufs, 1963). Such results were generally taken as supporting the two-independent-system view (Neumann, Esselmann, & Klotz, 1993; Steglich & Neumann, 2000; Tappe et al., 1994), but serial processing models positing distinct decision processes operating on the same internal response at different times have also been advocated. Sternberg and Knoll (1973), for example, proposed that RTs are triggered as the internal response evoked by the stimuli exceeds a motor threshold, whereas TOJs are based on the instant when the internal response reaches its peak value. More recently, Miller and Schwarz (2006) presented a one-system diffusion model with the motor triggering response level higher than the perceptual decision variable.

^{2}. Stimulus presentation and response recording were controlled using the Psychtoolbox (Brainard, 1997; Pelli, 1997) under Matlab.

*x*= ΔC or ΔO) were fitted with the exponential RT =

*c*

_{1}exp(−

*xc*

_{2}) +

*c*

_{3}(Barbur, Wolf, & Lennie, 1998), where

*c*

_{1},

*c*

_{2}, and

*c*

_{3}are free parameters. The high-salience increments used in the main experiment were chosen to be the ΔC or ΔO values for which the fitted RTs came within 5% of their asymptotic values for each observer. RTs to C and O increments were measured in separate blocks (of 500 trials each) repeated twice according to an ABBA sequence.

*SD*of the mean were excluded offline from further analysis. The 10 experimental blocks were run in a random order for each subject and were repeated three times. Hence, each experimental point (i.e., mean RT and percentage TOJ per SOA and per stimulus pair) was computed out of 150 trials.

*μ*) and standard deviations (

*σ*) specific to the given stimuli. Although simplistic, this model allows the computation of RT distributions to a pair of events, the TOJ psychometric functions (of the time interval between these events, SOA), as well as the RT distributions classified according to observers' TOJ (hereafter referred to as RT

_{TOJ}) with the same set of parameters. According to this one-system race model, the

*μ*and

*σ*parameters are directly available from the RT distributions measured for each observer and for each event when occurring in isolation.

^{1}In the present experiment, the two stimuli sequences were interleaved with trials where only one of the two stimuli occurred (see the Methods section) so that RT distributions, that is, their

*μ*and

*σ,*could be assessed for each isolated stimulus in each of the 10 experimental conditions out of 750 trials each.

*measured μ*and

*σ*variables (i.e., 4

*μ*and 4

*σ*values, i.e., 1

*μ*and 1

*σ*for each of the two increments and for each of the two stimulus attributes, C and O) is referred to as a 0-free-parameter model. A second analysis consisted in fitting the model separately to RT and RT

_{TOJ}data with

*μ*and

*σ*as free parameters. The fitting procedure provided either 8- or 32-free-parameters per observer. In the 8-free-parameter case, 4

*μ*and 4

*σ*values (see above) were used to fit RT and RT

_{TOJ}to the whole set of stimulus pairs (i.e., 10). In this case, as in the 0-free-parameter model, only one distribution (1

*μ*and

*σ*value) is associated to each stimulus, regardless of the experimental condition. The difference between the 0- and the 8-free-parameter fits is that, in the first case, the parameters are measured (the

*μ*and

*σ*of the RT distribution to single stimuli), and in the second case, they are fit to the data. For the 32-parameter fits, different

*μ*and

*σ*values were fitted to each of the 10 stimulus pairings, yielding a total of 4 (identical-stimuli conditions) × 2 (parameters) + 6 (different-stimuli conditions) × 4 (parameters) = 32 (the largest possible number of) free parameters. Fitted and measured

*μ*and

*σ*values were subsequently used to infer the parameters of the corresponding TOJ psychometric functions (of SOA), that is, their inflection points (PSS) and slopes (

*σ*

_{TOJ}). These inferred parameters were then compared with those obtained by fitting the raw TOJ with cumulative Gaussians. The fits were obtained via Monte Carlo simulations of random draws (500,000 per experimental condition and observer) from normally distributed distributions whose

*μ*and

*σ*were either given (0 free parameter) or adjusted for the best fit of the data (8- and 32-free-parameters).

*measured*(4

*μ*and 4

*σ*) parameters, their comparison with the 8

*free*parameters was meant as a qualitative evaluation of the extent to which RT distributions for single stimuli are good predictors, within the simplest one-system model framework, of the RT distributions to stimulus pairs and of the corresponding TOJ. The 32-free-parameter fits correspond to the upper goodness-of-fit bound provided by the simplest one-system model when all its parameters are set free. This upper goodness-of-fit bound could be used as a benchmark for testing future improvements of this simplest model. Significant differences between the 0- and 8-free-parameter fits, on the one hand, and between the latter two and the 32-free-parameter fits, on the other hand, would call into question the validity of the simplest one-system model and/or the independent processing of the two stimuli in a stimulus pair. The absence of a significant difference between the measured and fitted (8 and 32) parameters will instead sustain the validity of the former in predicting RT to stimulus pairs independently of their specific combinations.

^{2}computation

*R*

^{2}, for each observer as 1 − SSE/SST, where SSE is the sum of squares of errors of the predictions, that is, a measure of how close the points are to the regression line, and SST is the total sum of squares about the mean of the measured values. Accordingly,

*R*

^{2}can be negative when SSE is larger than SST, which means that the model describes the data less well than their mean (Neter, Kutner, Wasserman, & Nachtsheim, 1996). In the present case, SSE was computed relative to the major diagonal (slope of 1 and intercept of 0), that is, the perfect fit. It should be noted that this

*R*

^{2}index differs form the

*R*

^{2}of the simple linear regression analysis where the slope and intercept of the regression line are free parameters. The simple linear regression analysis yields higher

*R*

^{2}values but was discarded as the nonunit slope and nonzero intercept regression line makes no theoretical sense.

*μ*

_{RT}) and standard deviations (

*σ*

_{RT}) as a function of the O1–O2 SOA are shown in the top and bottom rows, respectively. Negative SOAs are for cases where O2 was presented before O1. Black curves are data fits obtained with the 0-free-parameter simple stochastic model, that is, based on the

*measured*RT distributions (

*μ*

_{RT}and

*σ*

_{RT}) to O1 and to O2 when presented in isolation (see the Model and data fits section). Red curves are the best fits of the 32-free-parameter stochastic model (i.e., with

*μ*

_{RT}and

*σ*

_{RT}for each of the two stimuli in the pair as free parameters). Data fits using only 8-free-parameters (i.e., with the same

*μ*

_{RT}and

*σ*

_{RT}for each of the four stimuli independently of how they were combined) lie somewhere in between the 0- and the 32-free-parameter fits.

*μ*

_{RT}and

*σ*

_{RT}tend asymptotically toward the respective values assessed for the first and last stimulus in the sequence when presented alone (horizontal lines in each panel); (b)

*μ*

_{RT}and

*σ*

_{RT}dips observed at short SOA result from probability summation over the stochastic internal responses evoked by the two stimuli (see Adams & Mamassian, 2004). Clearly, RT distributions to the O1–O2 (but also to the remaining nine) stimulus pair(s) as a function of SOA are satisfactorily predicted by the 0-free-parameter model with only marginal benefits brought about by the 32-free-parameter fits. As no systematic differences between data and fits were observed across the two attributes (C and O) and their combinations, further analyses of the goodness of fits were performed over all experimental conditions lumped together.

*σ*

_{RT}datum points (the variance of the variance of the data for each experimental condition) via time-consuming Monte Carlo simulations of an unworthy cost. As an alternative, Figure 3 displays for each

*absolute*SOA the average (over the four observers) coefficients of determination (

*R*

^{2}) between data and the 0-, 8-, and 32-free-parameter fits (black, light, and dark gray histogram bars, respectively) computed over

*μ*

_{RT}and

*σ*

_{RT}values lumped together ( Figure 3A) and over each of them separately ( Figures 3B and 3C). As noted above,

*μ*

_{RT}and

*σ*

_{RT}values for stimuli in a pair separated by large positive or negative SOA are bound to converge on the corresponding values assessed for each of these stimuli when presented alone (horizontal lines in Figure 2). Consequently, the

*R*

^{2}coefficients are also compelled to improve with ±SOA, as actually observed.

*R*

^{2}coefficients for the global RT distributions (

*μ*

_{RT}and

*σ*

_{RT}lumped together; Figure 3A) are no less than .70 (0-free-parameter fits) at 0 SOA and increase with absolute SOA. These correlations are mostly generated by the fits of the

*μ*

_{RT}data (

*R*

^{2}in between .77 and .98; Figure 3B) with the fits of the

*σ*

_{RT}data yielding systematically lower

*R*

^{2}(.58–.88; Figure 3C). Overall, Figure 3 supports the notion that RT distributions to sequential stimulations are predictable from the RT distributions to single stimuli (Adams & Mamassian, 2004). Not surprisingly, the goodness of the fits increases with the number of free parameters. In comparison with the

*R*

^{2}error bars across observers, however, this gain is relatively minor for the lumped and for the

*μ*

_{RT}data (Figures 3A and 3B) but not for the

*σ*

_{RT}data (Figure 3C) where the 32-free-parameter fits are better than the 0- and 8-free-parameter fits. Student

*t*tests between the measured (0-free-parameter) and the fitted (8- and 32-free-parameters) parameters do not yield a significant difference, either for the means, 0 versus 8:

*t*(15) = −1.17,

*p*= .260; 0 versus 32:

*t*(63) = −1.67,

*p*= .101, or for the standard deviations, 0 versus 8:

*t*(15) = 0.036,

*p*= .972; 0 versus 32:

*t*(63) = 0.695,

*p*= .493. Hence, within the framework of the simplest one-system model, measured and fitted

*μ*

_{RT}and

*σ*

_{RT}are statistically equivalent, which implies that allowing these parameters to vary with the different stimulus pairings is a useless endeavor.

*σ*

_{TOJ}) of the TOJ psychometric function (of SOA, hereafter referred to as Ψ functions) for an arbitrary stimulus pair can be inferred from the TOJ Ψ functions for other stimulus pairs given the assumptions underlying the present one-system model (a “consistency” test). This approach is similar but not equivalent to the one in the subsection above where distributions of RT to two-stimulus sequences were tested against predictions based on RT distributions to

*single*stimuli (0-free-parameter fits). It is similar in the sense that both approaches test predictions of the model but differs from the previous one in the specific way the consistency test was performed. Indeed, the TOJ task requires, by design, the presentation of

*two*stimuli, whereas RTs can be (and were) measured for both single and dual stimulations. The TOJ consistency issue was therefore grappled with via two independent analyses: one that tests the

*transitivity*of the measured PSS and one that tests the

*predictability*of the slopes of the TOJ Ψ functions obtained with nonidentical stimuli pairs from the Ψ functions assessed with identical stimuli pairs. As a first step for either of the two tests, percentages of “S1 seen first” responses as a function of SOA were fitted with cumulative Gaussians (constrained by their means,

*μ*

_{TOJ}—equivalent to the PSS—and by their standard deviations,

*σ*

_{TOJ}—equivalent to the slope of the Ψ function—for each of the 10 experimental conditions and for each observer). It must be noted that, by construction, the predictability of the RT distributions for stimulus pairs from the distributions for single stimuli ( Figure 3) necessarily involves an indirect test of their consistency as it implies the transitivity of their means and the summation of the RT variances for single stimuli when these stimuli are presented in pairs.

*given transitivity,*any PSS should be predictable from two other PSSs provided that the latter two are assessed with stimulus pairs sharing one stimulus and each of them sharing the to-be-predicted pair from one of the two remaining stimuli. For example, the PSS for the C1–C2 pair, PSS

_{C1–C2}= PSS

_{C1–O2}− PSS

_{C2–O2}. With four stimuli, there are four such different triplets as each of these four stimuli must be excluded once. The choice of the to-be-predicted PSS in a given PSS triplet is arbitrary.

_{M}= −0.06 PSS

_{P}+ 30.2, where subscripts M and P stand for “measured” and “predicted”),

*R*

^{2}= .003,

*t*(14) = 0.204,

*p*= .841. In substance, observers' PSSs are not consistent across experimental conditions, a variability frequently reported (e.g., Gibbon & Rutschmann, 1969; Jaśkowski, 1993, 1996, 1999) and consistently ignored. It may be due not only to cognitive factors (e.g., Frey, 1990; Schneider & Bavelier, 2003; Shore, Spence, & Klein, 2001) not intervening in the RT task but also to some high-level interactions between the two stimuli. Occasional transient fading of a low-saliency stimulus induced by a distant, higher saliency stimulus has been reported both in previous studies (Kanai & Kamitani, 2003) and by all four observers in the present experiments. Such interactions, however, do not seem to affect the RT distributions.

*i,*

*j*) in a pair are independent stochastic events, their combined variance

*σ*

_{ i, j}

^{2}is the sum of the two variances,

*σ*

_{ i}

^{2}+

*σ*

_{ j}

^{2}. Hence, for pairs of identical stimuli, the predicted

*σ*

_{ i}is given by the standard deviation of the fitted Ψ function,

*σ*

_{ i, i}, divided by

*σ*

_{ i, j}, were therefore computed as

*σ*

_{TOJ_M}= 0.954

*σ*

_{TOJ_P}+ 23.3),

*R*

^{2}= .295,

*t*(22) = 3.03,

*p*< .01, as it yields a slope not significantly different from 1,

*t*(22) = 0.144,

*p*= .44.

*μ*

_{RT}implies their transitivity), whereas the TOJ data are not.

*i,*

*j*) making up a sequential stimulus pair differ (ΔRT

_{ i, j}= RT

_{ i}− RT

_{ j}) and the PSS assessed for this same pair (PSS

_{ i, j}). According to the simplest one-system model (Gibbon & Rutschmann, 1969), the stimulus whose evoked internal response triggers the motor response must also be the one perceived first, with the difference between RT to each of the two events in a sequence (ΔRT) being equal to the SOA, entailing their simultaneous perception (PSS). This PSS–ΔRT relationship is shown in Figure 5A for all observers (different symbols) and for the six different-stimuli pairs.

^{2}An equivalent 1:1 relationship should also be observed between the measured slopes of the TOJ Ψ functions (

*σ*

_{TOJi,j}, where

*i*and

*j*are the two stimuli in a pair) and these same slopes as predicted from the standard deviations of the measured RT distributions to each of the stimuli in a pair (

*σ*

_{RTi}and

*σ*

_{RTj}). These predictions are given by

*R*

^{2}= .05,

*t*(22) = 1.11,

*p*= .279. The nonsignificance of this relation is probably due to the large dispersion of the data shown as triangles, the only ones to ever exceed the 95% prediction intervals (i.e., the intervals supposed to contain 95% of the datum points). Excluding this observer's data from the linear regression analysis does not change the parameters of the fitted regression line but yields a highly significant

*R*

^{2}(PSS = 0.474 ΔRT + 3.31),

*R*

^{2}= .411,

*t*(16) = 3.34,

*p*< .005, as frequently reported (Jaśkowski, 1992; Jaśkowski & Verleger, 2000; Menendez & Lit, 1983; Roufs, 1974). A binomial test on all data shows that most of these datum points are below the major diagonal,

*B*(6, 24),

*p*< .02, and above the 0 ordinate (PSS) point,

*B*(5, 24),

*p*< .01. This supports the notion that the PSSs are less affected by the difference between stimulus saliencies than ΔRT, in line with most previous studies that report a ΔRT:PSS ratio of about 2 (but see Roufs, 1963). Within the framework of a one-system model, this difference between ΔRT and PSS suggests that perceptual decisions are taken before motor ones.

*R*

^{2}coefficients (

*σ*

_{TOJ_M}= 1.46

*σ*

_{TOJ_P}− 2.16),

*R*

^{2}= .298,

*t*(38) = 4.01,

*p*< .001. A binomial test shows that most datum points lie above the major diagonal,

*B*(4, 40),

*p*< .001. This analysis (which, to the best of our knowledge, was never performed before) confirms once again the relationship between RT and TOJ tasks, while revealing a significantly higher variability associated with the latter (i.e., measured

*σ*

_{TOJ}> predicted

*σ*

_{TOJ}). Assuming that the noise of the evoked internal response increases with its magnitude over time (e.g., Gold & Shadlen, 2001; Luce, 1986; Smith & Ratcliff, 2004), one may speculate that this larger variance associated with the TOJ task reflects the existence of a perceptual criterion above the motor criterion (see also Miller & Schwarz, 2006), a conclusion opposite to the one based on ΔRT–PSS differences.

*σ*

_{TOJ}) and their values predicted from the RT distributions (ΔRT and

*σ*

_{RT}) substantiate the notion that motor (RT) and perceptual (TOJ) behaviors are (at least partly) based on the same internal response. However, the fact that data and predictions do not lie along unitary slope lines calls into question the validity of the one-system, one-decision model and suggests instead distinct decision processes for the two tasks. The data analysis below strengthens this analysis.

_{TOJ}), namely, “S1 seen first” and “S2 seen first”.

^{3}This feature is the main methodological improvement of the present study over previous ones. Figure 6 displays once more the data sample of Figure 2 (means and standard deviations of the RT distributions for the O1–O2 pair in the top and bottom rows, respectively; circles) and their 0- and 32-free-parameter fits (black and red curves, respectively) classified this time according to the “O1 seen first” (open circles and dotted curves) and “O2 seen first” (solid circles and curves) TOJ categories. Note that “O1 seen first” and “O2 seen first” responses are in agreement with the physical temporal display for negative and positive SOAs, respectively. From the perspective of the simplest one-system model, for O2 to be seen first despite being presented second (−SOA), it must be that the arrival time of its evoked response at the decision stage is delayed in average relatively to the arrival time of the response evoked by O1 (for the same −SOA). The same logic holds true for “O1 seen first” responses and +SOAs. Hence, provided that TOJs and RTs are both based on the same internal response, one expects that, overall, RTs associated with “wrong” TOJs be longer than those associated with “correct” TOJs (see Footnote 3). Moreover, the difference between the two RT

_{TOJ}types should increase with the absolute physical delay between the two stimuli. Mean RT

_{TOJ}and their fits in the top panels of Figure 6 sustain these observations and thereby the notion that motor and perceptual behaviors are most likely based on the same (or on strongly correlated) internal response(s). An equivalent account of the dependency on SOA of the standard deviation associated with “correct” and “wrong” RT

_{TOJ}(bottom panels of Figure 6) is less intuitive

^{4}and also less backed up by the data.

*R*

^{2}between the 0-, 8-, and 32-free-parameter fits of the measured

*μ*

_{RT}and

*σ*

_{RT}classified according to TOJ and the data were assessed as before over the whole data set (10 stimulus pairs) and for each observer (see the Methods section). Figure 7 presents the average (over the four observers)

*R*

^{2}for each set of free-parameter fits (black, light, and dark gray histogram bars for 0-, 8-, and 32-free-parameters, respectively) with

*μ*

_{RT}and

*σ*

_{RT}values lumped together ( Figure 7A) and over each of them separately ( Figures 7B and 7C). The global fits yield

*R*

^{2}values ranging from .77 to .23 for 0 and ±100 ms SOA, respectively. Once again, these correlations are mainly contributed to by the partial

*μ*

_{RT}fits (

*R*

^{2}ranging from about .7 to .4 for 0 to ±100 ms SOA, respectively; Figure 7B), with

*R*

^{2}for the partial

*σ*

_{RT}fits below .12 for the nonzero SOA ( Figure 7C).

^{5}As for the fits of the RT distributions noncontingent on observers' TOJ ( Figure 3), the goodness of the present fits increases with the number of free parameters, but the improvement is negligible relatively to the error bars across observers. Compared to those fits, the present

*R*

^{2}coefficients are globally lower, and instead of increasing, they decrease with absolute SOA. The latter discrepancy is at least partly due to the progressive decrease with the absolute SOA of the number of trials on which the estimated

*μ*

_{RT_TOJ}and

*σ*

_{RT_TOJ}values are based. Indeed, as the absolute SOA increases, the number of reports “seen first” for the second stimulus in the physical sequence decreases so that the assessment of the corresponding

*μ*

_{RT_TOJ}and

*σ*

_{RT_TOJ}values gets progressively less reliable. Most certainly, additional factors related to the variability of the TOJ should also account for the lower

*R*

^{2}coefficients in this TOJ-contingent RT analysis.

- In contrast, as already documented in the literature, the PSSs of the TOJ Ψ functions ( Figure 4A) show large scatters with little consistency (i.e., transitivity) across experimental conditions. This result contrasts with the standard deviations of the TOJ Ψ functions, which are consistent across observers and experimental conditions ( Figure 4B). This pattern of results is compatible with the idea that TOJs are biased in a nonsystematic, idiosyncratic manner (Gibbon & Rutschmann, 1969).
- Also in agreement with the literature and contrary to the simplest one-system model's prediction, the difference between RT (ΔRT) to each of the two events used in the 10 stimulus pairings is typically two times larger than the PSS for these same stimulus pairs ( Figure 5A).
- Without precedence in the literature, the present data analysis also indicates that the slopes of the TOJ Ψ functions are typically shallower (i.e., larger standard deviations) than those inferred from the RT variability ( Figure 5B); this observation, which is tantamount to the fact that perceptual decisions are noisier than motor decisions, suggests that perceptual decisions are taken after (and relatively to a higher criterion than) the motor decisions.
- Despite the abovementioned inconsistencies between RT and TOJ, all observers show distinct RT functions of SOA depending on the associated TOJ. This excludes the possibility of these responses being performed by two independent subsystems and is regarded as the main finding of the present study.
- Finally, no qualitative differences related to the nature of the stimuli (i.e., contrast vs. orientation increments) were observed, supporting the generality of the above observations.

*automatic*response behavior and, as such, are independent of stimulus context and of subjective decisional factors (Waszak & Gorea 2004; Waszak, Gorea, & Cardoso-Leite, in revision).

^{6}Instead, perceptual decisions are presumably referenced to a context-dependent criterion as defined by standard Signal Detection Theory (SDT; Green & Swets, 1966). According to SDT, the setting of a perceptual criterion results from a subjective optimization process (e.g., maximizing the number of correct responses) contingent on the observer's knowledge of the noise associated with a given task/stimulus and on contextual factors such as stimulus' a priori probability and payoff. Accordingly, TOJs (but not RTs) have been shown to comply with temporal Bayesian calibration whereby subjects use all the available information (sensory and contextual) to infer the physical onsets of the stimuli (Miyazaki, Yamamoto, Uchida, & Kitazawa, 2006). By contrast, inasmuch as observers' motor task does not require the maximization of the correct responses (but rather the minimization of their RTs), the motor threshold is presumably set as low as possible irrespective of the processing context (Sternberg & Knoll, 1973).

^{3}TOJ is a subjective task so that the PSS derived for unequal saliency stimuli need not and in fact do not correspond to the physical simultaneity of the stimuli onsets (i.e., 0 SOA). As a consequence, the classification of TOJ as “correct” versus “incorrect” is meaningless under such conditions.

^{4}The model assumes that the decision “S1 seen first” is a nonlinear operation (minimum of two values). The probability density function resulting from the minimum of two Gaussian random variables is thus not necessarily Gaussian and clearly depends on the separation between the two Gaussian distributions.

^{5}Histograms for the 66- and 100-ms SOA in Figure 7A are missing because the corresponding

*R*

^{2}values are negative and, thus, outside the plot's range.

^{6}The concept of an automatic process has been and still is an object of frantic debate (see Pashler, 1998, chapter 8). For the purpose of this discussion, we go along with (Waszak and Gorea's 2004) proposal that simple RTs are “automatic” in the sense that they are triggered once an internal response exceeds a

*fixed*motor

*threshold*as opposed to a contextually dependent perceptual

*criterion*(as defined by

*high-threshold*and

*signal detection*theories; Green & Swets, 1966).