Two components in IOR: evidence for response bias and perceptual processing delays using the SAT methodology

Zhao, Yuanyuan; Heinke, Dietmar; Ivanoff, Jason; Klein, Raymond M.; Humphreys, Glyn W.

doi:10.3758/s13414-011-0181-z

Two components in IOR: evidence for response bias and perceptual processing delays using the SAT methodology

Published: 26 July 2011

Volume 73, pages 2143–2159, (2011)
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Two components in IOR: evidence for response bias and perceptual processing delays using the SAT methodology

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Yuanyuan Zhao¹,
Dietmar Heinke¹,
Jason Ivanoff²,
Raymond M. Klein³ &
…
Glyn W. Humphreys¹

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Abstract

Inhibition of return (IOR) occurs when reaction times (RTs) are slowed to respond to a target that appears at a previously attended location. We used the speed–accuracy trade-off (SAT) procedure to obtain conjoint measures of IOR on sensitivity and processing speed by presenting targets at cued and uncued locations. The results showed that IOR is associated with both delays in processing speed and shifts in response criterion. When the target was briefly presented, the results supported a criterion shift account of IOR. However, when the target was presented until response, the evidence indicated that, in addition to a response bias effect, there was an increase in the minimal time required for information about the target to accumulate above chance level. A hybrid account of IOR is suggested that describes effects on both response bias and perceptual processing.

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The visual environment contains multiple stimuli that cannot be responded to at once. As a consequence, attentional mechanisms are required to select the behaviourally relevant stimuli and to filter out stimuli that are less relevant to our goals. One classical experimental approach used to study visual attention is to use spatial cueing to bias attention towards or away from a target (Posner & Cohen, 1984). In this procedure, participants typically see a spatial cue either to the left or right side of fixation, followed by a target either at the same location as the cue or on the opposite side. Participants are asked to press a key as soon as they detect the target. When there are relatively short time intervals (SOAs) between the cue and the target, reaction times (RTs) are faster when the target and the cue are at the same location, as compared to when these stimuli appear on opposite sides. However, when the time interval between the cue and target is increased, this facilitatory effect of cueing is usually reversed: Participants are slower to respond when the target and cue appear at the same location than when they appear on opposite sides. Posner, Rafal, Choate, and Vaughan (1985) termed this the inhibition of return (IOR) effect.

One (standard) interpretation of these results is that the early facilitation effect reflects the fast, reflexive orienting of attention towards the sudden appearance of the cue, which leads to more efficient processing of targets at that location (Folk, Remington, & Johnston, 1992; Posner, 1980; Posner & Cohen, 1984; Yantis & Hillstrom, 1994; Yantis & Jonides, 1984). However, the nature of the later IOR effect remains unclear, with arguments having been made that IOR reflects either impaired perceptual processing (e.g., Cheal, Chastain, & Lyon, 1998; Handy, Jha, & Mangun, 1999; Lupiáñez, Milan, Tornay, Madrid, & Tudela, 1997; Prime & Ward, 2004) or a change in response criterion to stimuli at the cued location (e.g., Ivanoff & Klein, 2001, 2003, 2004; Klein & Taylor, 1994), or both (Ivanoff & Klein, 2006). In this article, we aim to examine these two aspects of IOR using the speed–accuracy trade-off (SAT) methodology.

To assess IOR, we took a signal detection theory (SDT) approach. SDT separates processing of stimuli into two stages: a perceptual-coding stage and a decision stage (Green & Swets, 1966; Swets, Green, Getty, & Swets, 1978). Crucially, the participant’s sensitivity to the stimulus can be measured with the d′ metric, and the bias for responding in a particular direction may be determined with c, the decision criterion metric (Macmillan & Creelman, 2005). Both measurements are influenced by several factors, including the quality of the stimuli and the length of time available for stimulus classification. Especially important for this article is the fact that the timing of the response to a stimulus reflects the monotonically increasing quality of perceptual encoding based on continued accumulation of information about the target, leading to the well-established SAT function (Reed, 1973; Wickelgren, 1977). Figure 1 illustrates three hypothetical SAT functions that might underlie the IOR effect. Within the framework of SDT, the IOR effect can be explained in at least two ways. One possibility is that IOR influences perceptual coding, with perceptual sensitivity to the target being impaired. For example, the maximal amount of information that can accrue from the time-limited presentation of the target may be less at regions affected by IOR (Fig. 1a). Alternatively, it may take longer to accumulate information about the target at the previously cued location (Fig. 1b). This is the attentional/perceptual account of IOR (cf. Handy et al., 1999; Ivanoff & Klein, 2006; Reuter-Lorenz, Jha, & Rosenquist, 1996). A second possibility is that IOR occurs because the criterion for the decision process is raised at the previously cued location—the criterion shift account (Ivanoff & Klein, 2001, 2003, 2004, 2006; see Fig. 1c). Crucially, these two accounts predict different effects of IOR on performance accuracy, even if similar effects are predicted on RTs. The criterion shift account holds that there is no difference in the accumulation of information at the cued and uncued locations, but that cueing generally slows RT when a decision criterion is applied (it is applied later to targets at cued locations). Because the decision criterion is applied later, there should be more perceptual information available when a decision is made (at least when the perceptual information remains available for report). It follows that there should be higher accuracy at the cued than at the uncued location. In contrast, the attentional/perceptual account suggests that accuracy should be lower at the cued location, since information accrual is delayed or the rate of accrual is slowed there. Importantly, there is support for both accounts in the literature. We first will review the studies supporting the attentional/perceptual account.

Lupiáñez et al. (1997) investigated IOR in a discrimination task. They found that both delayed RTs and reduced accuracy were elicited at cued as compared to uncued locations across a range of SOAs from 700 to 1,300 ms. Cheal et al. (1998) and Handy et al. (1999) also found decreased accuracy and delayed RTs when the cue shared the same location as the target. However, these studies used either masking or short target presentations, which might have led to a rapid loss of stimulus information. If response selection is delayed while stimulus information decays, performance may be less accurate under IOR conditions simply because of the greater decay of stimulus-based evidence over a longer period of time (see Ivanoff & Klein, 2001, 2006, for a similar argument). This argument is supported by Handy et al.’s (1999) study, where d′ was reported to decrease with longer RTs. In this study, for which participants were instructed to emphasise accuracy, they tended to respond more slowly and, interestingly, also with decreased accuracy.

Support for the criterion shift account of IOR comes from a series of studies by Ivanoff and colleagues (e.g., Ivanoff & Klein, 2001, 2003, 2004, 2006; Klein & Taylor, 1994). These studies reported a lower false alarm rate along with longer RTs for targets appearing at cued relative to uncued locations in both go/no-go and discrimination tasks. These authors argued that a lower false alarm rate implies a more conservative response criterion and therefore constitutes evidence for a criterion shift account of IOR. Although lower false alarms alone do not provide conclusive evidence for a criterion shift, as false alarms need to be considered together with the hit rate to properly measure criterion levels, c scores in these studies were highly related to false alarms, as generally no misses were found. It is noteworthy that in these studies, targets were presented until response, thereby avoiding effects of stimulus decay on performance—unlike studies supporting the perceptual account.

The present study aimed to go beyond the above studies by fully measuring the SAT function so as to derive the parameter estimates for the intercept, slope, and asymptotes, as suggested by Wickelgren (1977). This approach enables the time course of information accrual to be plotted while, at the same time, allowing the experimenter to control the relations between the speed and accuracy of responses. Importantly, the procedure also allows us to determine the time course of target processing for limited and unlimited presentation times together, since this procedure produces false alarms together with hits at a reasonable rate for both. Importantly, in the case of limited target presentation time, the procedure allows us to determine whether effects of information decay contribute to performance. Finally, we also manipulated the luminance of the cues to test the generality and robustness of our findings with respect to cue luminance.

The SAT methodology has previously been applied in a variety of areas in cognitive psychology, including attentional cueing (Carrasco & McElree, 2001; Giordano, McElree, & Carrasco, 2009) and memory (Reed, 1973). The cited studies showed that the relationship between processing time and accuracy can best be described with the so-called SAT function. The SAT function assumes that response accuracy increases with processing time in an exponential fashion (see Fig. 1 for illustrations, and the Results section of Exp. 1 for the mathematical formula). The function has three parameters. The intercept parameter indexes the point in time at which the increase begins and accuracy departs from chance level. The sensitivity asymptote specifies the maximal possible accuracy. Finally, the rate parameter describes the growth rate of accuracy over time. The combination of the intercept and rate parameters can be interpreted as describing the speed of information processing (e.g., Giordano et al., 2009). Note that alternative models such as the linear ballistic accumulation (LBA) model proposed by Brown and Heathcote (2008) can also successfully accommodate decision making and choice response time (e.g., Farrell, Ludwig, Ellis, & Gilchrist, 2010). In this model, evidence for alternative responses is independently accumulated in a linear manner, at different rates. Each accumulator begins with a starting amount of evidence, and a response is made when the first accumulator reaches the threshold. However, by fitting an SAT function here, we are able to compare our results to the results from similar studies using this method (e.g., Carrasco & McElree, 2001; Ivanoff & Klein, 2006).

Carrasco and McElree (2001) applied the SAT method to an investigation of the effect of spatial cueing on visual search. They found that cueing not only improved asymptotic sensitivity, but also accelerated the rate of information-processing speed at the cued location (at least at short cue–target SOAs). McCormick and Francis (2005) also found that spatial cueing improved processing speed at short SOAs. In contrast to these studies on early facilitatory cueing, Ivanoff and Klein (2006) explored IOR using of the SAT procedure. They examined sensitivity as a function of RT in both go/no-go and discrimination tasks using a time window procedure (Carrasco & McElree, 2001; Ivanoff & Klein, 2006; Wickelgren, 1977). Participants were required to respond within a 210-ms time window that occurred 120, 240, 360, or 480 ms after target presentation. In both tasks, IOR was observed in RTs across all but the longest time interval between the cue and the target (480 ms). This effect on RTs was accompanied by reduced d′ at the cued locations for all but the shortest time interval (120 ms). No effect of a criterion shift was found except at the shortest time interval, when the criterion was higher for targets at cued relative to uncued locations. Together, these findings support the perceptual as well as the criterion shift accounts of IOR. The authors suggested that, early on in target processing, when the quality of stimulus evidence is poor, IOR is initially implemented as a criterion shift that biases participants against responding to targets at cued locations. However, later in time, when the quality of stimulus evidence improves, IOR appears to act upon perception, reducing sensitivity to cued targets and slowing RTs. The design of Ivanoff and Klein’s (2006) study did not allow them to fit an SAT function, as they used only four intervals between target presentation and the response window. It is possible, however, that their effect on perceptual sensitivity could arise for at least two reasons—an effect on the asymptotic level of sensitivity at cued and uncued locations, or an effect on the time course of the buildup of perceptual information (see Fig. 1a and b for an illustration). The design of the present experiments overcomes this limitation by using seven time intervals ranging from 90 to 1,350 ms, to enable SAT functions to be plotted and asymptote and rate effects to be distinguished. In addition, Ivanoff and Klein (2006) used only unlimited target presentation times, yet different effects might emerge with short and prolonged target exposures. Here we will apply the time window procedure to both unlimited and limited target presentations to explore whether differences in target exposure contribute to the conflicting results found in the IOR literature. We used limited target presentation in the first experiment and fitted a single SAT function for the cued and uncued conditions (Fig. 1c). In Experiment 2, unlimited target presentations were used, and there was a delay in information processing for the cued relative to the uncued target (Fig. 1b). In addition, both experiments showed a more conservative criterion at the cued than at the uncued location.

Experiment 1: brief target presentation

In Experiment 1, a brief target presentation was used. With brief target presentations, Lupiáñez et al. (1997), Cheal et al. (1998), and Handy et al. (1999) all found evidence indicating an effect of IOR on perception, since accuracy increased at cued relative to uncued locations. However, their studies did not control for speed–accuracy trade-offs, nor did they determine the SAT function to assess the precise effect of IOR on performance. Our experimental procedure follows Ivanoff and Klein’s (2006) second experiment, the main differences being that Ivanoff and Klein (2006) had used an unlimited target presentation and four response windows. Here, we limited the presentation of the target and used seven response windows so that we were able to fit a complete SAT function. We also manipulated target luminance. Hunt and Kingstone (2003) and Reuter-Lorenz et al. (1996) reported that reductions in target luminance increased IOR. Target Luminance was manipulated as a between-subjects factor to test the generality of our findings and to assess whether there were differential effects of this factor across the SAT function.

Method

Participants

A group of 17 postgraduates participated (8 were tested with the bright target and 9 with the dim target), comprising 10 females and 7 males from 22 to 40 years of age, with a mean age of 28.5 years. The participants were from the psychology department of Dalhousie University, and they were naive as to the purpose of the study. The participants were paid Can$25 and took part in approximately two sessions of 70 min each, which were completed on different days within the same week. All participants reported normal or corrected-to-normal vision, and all except 3 were right-handed.

Apparatus

Stimulus presentation and data collection were performed using E-Prime 1.2. The stimuli were presented on a 17-in Viewsonic PT775 monitor controlled by a personal computer, and responses were polled from the standard keyboard.

Stimuli

The stimulus display (see Fig. 2) consisted of a fixation circle (68.86 cd/m²) subtending 0.6° in diameter and 0.07° thick, presented at the centre of the screen (background 0.82 cd/m²), and two outline boxes with asterisks (2.5 cd/m²) in the centres of the boxes, aligned horizontally to the left and right of the fixation cross. The distance between the fixation circle and the centre of each box was 7.1°. Each box had a 0.15°-thick frame and subtended 3.3° in height and 3.0° in width. Each asterisk was made from overlapping “×” and “+” signs; the “+” was 2.3° in length and 0.2° thick, and the “×” was 3.4° in length and 0.15° thick, with both elements containing the same number of pixels. The cue comprised a luminance increase of one of the box outlines to 123.69 cd/m² (for the bright cue) or 23.30 cd/m² (for the dim cue), each lasting 80 ms. The cue back to fixation comprised a thickening of the fixation circle to 0.15° for 100 ms. The target was a luminance increase of either the “+” or the “×” to 123.69 cd/m² (the bright target) or to 23.30 cd/m² (the dim target) for 80 ms.

Procedure

The experiment was conducted in a quiet, dimly lit room. Participants were given both written and oral instructions for the task, and were individually tested sitting at a distance of approximately 57 cm from the computer screen. RTs and response accuracy were recorded by the computer. The participants were instructed to maintain fixation throughout the experiment and not to make any eye movements. They were also told that cues were uninformative as to the location of the target.

The trial sequence is shown in Fig. 2. Each trial began with a blank 500-ms intertrial interval, not shown in Fig. 2. Following this, a display consisting of a central fixation circle and two peripheral boxes with asterisks in the middle was presented for 500 ms. Subsequently, one of the peripheral boxes was cued by increasing the luminance of the outline of the box for 80 ms. This increase was experienced as a flash. The cue comprised two levels of luminance changes. After the cue was removed, the fixation circle and the two boxes with asterisks were presented alone for 170 ms. A return cue was presented by enlarging the fixation circle for 100 ms to ensure that attention did not remain at the cued location. The fixation circle and two boxes with asterisks were then presented alone for 650 ms. Finally, the target was presented as a luminance increase of the “+” or the “×” in the left or the right box. Target presentation time was 80 ms and comprised two levels of luminance change. The targets, the “+” or “×,” appeared with equal frequency.

On each day, each of the seven target–tone onset asynchronies (TTOAs; 90, 180, 270, 360, 450, 900, or 1,350 ms) was presented in a separate block. Whether TTOAs are blocked or mixed appears to have little effect on the SAT function (Miller, Sproesser, & Ulrich, 2008). The order of the TTOAs was randomised. The tone (a high pitch) signalled a 210-ms response window in which participants were instructed to make the appropriate response. Half of the participants were instructed to make a keypress with the index finger of their left hand on the “Z” key and the middle finger on the “A” key, and the other half were instructed to use their right index finger on the “M” key and middle finger on the “K” key. Within each group, half were also instructed to press the index finger whenever “+” was presented and to press the middle finger whenever “×” was presented, or vice versa for the other half. Detection time for the target was measured from the target onset to response. If no response was made within the response window, an error tone (low pitch) was given at the end of each response window to inform participants; this provided no information about whether the responses were correct.

After the instructions had been understood, the participants were administered practice trials until they were able to perform the task correctly. The responses for these trials were not recorded.

Design

The experiment consisted of a 2 (cue luminance: bright/dim) × 2 (cue: cued/uncued) × 7 (TTOA: 90/180/270/360/450/900/1,350 ms) × 2 (target luminance: bright/dim) mixed design with Target as a between-subjects factor. The experiment consisted of 1,792 trials in total, which were divided into 14 blocks, and the first 16 trials of each block were excluded from analyses. Within each block, the trials were randomised with respect to trial type and were equally divided with respect to cue luminance, cue, SOA, and target location. Each of the experimental conditions contained 56 trials, with 28 trials using a target “+” and 28 trials with a target “×”.

Data analysis

Sensitivity was calculated as

$$ d\prime = z(H) - z(F), $$

(1)

where z(H) is the z score for correct responses to “+” (hits) and z(F) is the z score for incorrect responses to “×” (false alarm). Extreme values of hits and false alarms were treated by subtracting or adding .5 to the counts, respectively (log-linear transformation; Snodgrass & Corwin, 1988).

The criterion was given by

$$ c = - \left[ {z(H) + z(F)} \right]/2. $$

(2)

The criterion value in a discrimination task only indicates bias towards a particular response, either “+” or “×.” To determine additional evidence for a criterion shift, we used the following indirect measures: anticipations, response frequencies, and misses (see Ivanoff & Klein, 2006). Anticipations are the percentages of responses after target onsets but before the response signal. Response frequency refers to the percentage of responses within the response window (including correct and wrong responses). Misses are either responses made after the response window or failures to respond on a trial (time limit: 500 ms after the response signal). A more conservative criterion is reflected by an increase of misses and a decrease of anticipations. The IOR effect on RTs was measured based on a tone reaction time (tone RT) analysis. The tone RT is the time from the response signal (tone) to the response when a correct keypress occurred within the response window.

The dependent variables were analysed using ANOVAs, with the Greenhouse–Geisser correction applied when Mauchly’s test of sphericity was significant.

Results

The hit rate (response rate within the response window) was 79.05% on average, with a minimum of 68.62%. The accuracy rate of hits was 84.75% on average with a minimum of 75.87%. Figure 3 shows that d′ increased with increasing processing time. Hence, despite our use of a brief target presentation, information about the target increased rather than decayed as the TTOA was increased. Since the time course of d′ is very similar to that from other experiments employing the SAT methodology (e.g., Carrasco & McElree, 2001), we fitted the SAT function as suggested by Wickelgren (1977).

Fit of SAT function

We used the following mathematical description of the SAT function to fit the data of d′ for each TTOA condition and average processing time (TTOA plus RTs for correct responses) for that condition (Liu & Smith, 2009; Wickelgren, 1977):

$$ d\prime (t) = \left\{ {\begin{array}{*{20}{c}} {\lambda (1 - {e^{{ - (t - \delta )/\beta }}}),t > \delta } \hfill \\ {\quad \quad \;\;0\quad \quad \;\;,t \leqslant \delta } \hfill \\ \end{array}, } \right. $$

(3)

where λ is the asymptotic parameter reflecting the accuracy with maximal processing time, 1/β describes the rate at which accuracy grows from chance (d′ = 0) to asymptote, and δ is an intercept parameter indexing the discrete point in time when accuracy departs from chance.

We used a hierarchical model-testing scheme to find the most parsimonious SAT model for each participant (Carrasco & McElree, 2001; Giordano et al., 2009; Liu & Smith, 2009). The model selection procedure began with the full model, where each condition was modelled with a unique set of parameters. To find the simplest model, we used the G ² statistic (the difference in deviance values between two nested models; Liu & Smith, 2009). The maximum likelihood criterion was used to fit the models with MATLAB’S fminsearch (Liu & Smith, 2009). In addition, the resulting model was characterised with adjusted R ² (Dosher, Han, & Lu, 2004):

$$ {\text{adj}}\;{R^2} = 1 - \frac{{{{\sum {_{{i = 1}}^n({d_i} - {{\hat{d}}_i})} }^2}/(n - k)}}{{{{\sum {_{{i = 1}}^n({d_i} - \overline d )} }^2}/(n - 1)}}, $$

(4)

where d _i is the observed d′ values, $ {\hat{d}_i} $ is the predicted d′ values, $ \overline d $ is the mean of d′, n is the number of data points, and k is the number of free parameters.

To analyse the results across all participants, the parameters for each participant were entered into three separate three-way within-participants ANOVAs (Liu & Smith, 2009).

The final models produced an average adjusted R ² value of .930 across participants, with a minimum of .858. The parameters of asymptote, intercept, and slope in the final model for each participant were entered into three separate 2 × 2 × 2 ANOVAs with Cue Luminance (bright or dim) and Cue (cued or uncued) as within-subjects factors and Target Luminance (bright or dim) as a between-subjects factor. Figure 4 shows the means of the three sets of parameters.^{Footnote 1} There were no significant effects of any factor for any of the parameters [asymptote: cue, F(1, 15) = 0.20, p = .66; intercept: cue, F(1, 15) = 1.04, p = .32; 1/slope: cue, F(1, 15) < 0.001, p = .99]. Figure 3 illustrates the means of the curve-fitting procedure for d′ for each participant as a function of processing time, cue luminance, and cue. The mean data points for each condition are also shown. The pattern of the curve in Fig. 3 is consistent with pattern C in Fig. 1.

Tone RT

The mean tone RTs for each condition are shown at the top of Table 1. The tone RTs were entered into a 2 × 2 × 7 × 2 ANOVA with Cue Luminance (bright or dim), Cue (cued or uncued), and TTOA (90, 180, 270, 360, 450, 900, or 1,350 ms) as within-subjects factors and Target Luminance (bright or dim) as a between-subjects factor. The main effect of cue was significant, F(1, 15) = 52.69, p < .001: RTs were 4.74 ms faster in the uncued than in the cued condition. There was a Cue × TTOA interaction [F(6, 90) = 5.48, p < .001], reflecting greater IOR at early TTOAs. The main effect of TTOA was significant [F(6, 90) = 25.19, p < .001], indicating decreasing then increasing (a U-shaped function) RTs across the TTOAs. There was also a significant Cue Luminance × Target Luminance interaction [F(1, 15) = 4.77, p < .05] (Fig. 5). When the target was dim, RTs were slowed following the bright cue (131.28 ms) relative to the dim cue (129.10 ms); however, the data went in the opposite direction when the target was bright (bright cue, 125.85 ms; dim cue, 126.51 ms). None of the other main effects or interactions reached significance (all ps > .1).

Table 1 Mean tone RTs, d′, percentages of anticipations, percentages of response frequencies, percentages of misses, and criterion for each condition in Experiment 1

Full size table

We conducted separate ANOVAs with Cue Luminance and Cue as factors at each TTOA.^{Footnote 2} Figure 6 shows the mean IOR (positive values indicate IOR) for each combination of cue luminance and TTOA (the between-subjects factor of Target Luminance was merged for all of the figures). There were significant IOR effects at TTOAs of 90 ms [magnitude 8.21 ms; F(1, 16) = 19.45, p < .001], 180 ms [magnitude 13.67 ms; F(1, 16) = 31.22, p < .001], and 270 ms [magnitude 4.61 ms; F(1, 16) = 7.07, p < .05].

Sensitivity (d′)

Table 1 shows d′ for each condition. From the fitted SAT curve, it is clear that d′ reached ceiling before TTOA 900 ms. We therefore omitted TTOAs of 900 and 1,350 ms from the analyses. The same analysis was conducted in Experiment 2 below. The main effect of cue was significant [F(1, 15) = 7.38, p < .05]: d′ was 0.09 higher for targets at the cued than at the uncued location. There was also a significant TTOA main effect [F(4, 60) = 150.48, p < .001]; d′ increased as TTOA increased from 90 to 450 ms. None of the other main effects were reliable, and there were no interactions (all ps > .1).

Figure 7 shows the mean IOR in d′ for each combination of cue luminance and SOA (a positive value indicates a lower d′ at the cued location). Separate ANOVAs for Cue Luminance × Cue were performed at each TTOA. There was a significant main effect of cue at TTOA 180 ms [F(1, 16) = 6.67, p < .05], in that d′ was 0.30 higher for cued trials than uncued trials. There was also a significant main effect of cue luminance at TTOA 450 ms [F(1, 16) = 7.61, p < .05]; d′ was 0.24 higher for the bright cue than for the dim cue.

Anticipations

Anticipations (responses after target onsets but before the response signal) for each condition, presented as percentages, are shown in Table 1. The main effect of cue was significant [F(1, 15) = 5.01, p < .05]; anticipations were 0.78% lower for targets at the cued than at the uncued location. The main effect of TTOA was significant [F(2.92, 43.86) = 15.34, p < .001]; anticipations increased as the TTOA lengthened and were constant after a TTOA of 360 ms. Finally the Cue Luminance × Cue × Target Luminance interaction was also significant [F(1, 15) = 5.00, p < .05]. Anticipations were lower for targets at the cued than at the uncued location when the cue and target luminances were both dim, but not with the other luminance combinations. None of the other main effects were reliable, and there were no interactions (all ps > .08).

Separate ANOVAs with the factors Cue Luminance and Cue at each TTOA showed a significant cue main effect at TTOA 270 ms [F(1, 16) = 16.29, p < .001]: There were 2.84% fewer anticipations made to the cued than to the uncued location, in this case.

Response frequency

Table 1 shows the response frequencies (both correct and incorrect responses within the response window) as percentages in each condition. The main effect of TTOA was significant [F(3.08, 46.16) = 6.65, p < .001]. The response frequency was higher at TTOA 270 ms than at the other TTOAs. The Cue × TTOA interaction was also significant [F(6, 90) = 4.94, p < .001]. No other main effects or interactions were significant (all ps > .1).

Separate ANOVAs with the factors Cue Luminance and Cue were conducted for each TTOA. There was a significant main effect of cue at TTOA 90 ms [F(1, 16) = 11.48, p < .01]; 6.83% fewer responses were made to targets at the cued than at the uncued location. There were also main effects of cue at TTOA 270 ms [F(1, 16) = 4.64, p < .05]; there were 2.42% more responses to targets at the cued than at the uncued location.

Misses

The percentages of misses (responses after the response window or failures to respond on a trial) are also provided in Table 1. The main effect of cue was significant [F(1, 15) = 13.04, p < .01], with 1.68% more misses to targets at cued than at uncued locations. The main effect of TTOA was significant [F(3.01, 45.16) = 11.60, p < .001], with misses decreasing and then increasing as TTOA increased. In addition, the Cue × TTOA interaction was significant [F(3.57, 53.56) = 4.92, p < .01], as was the Cue × TTOA × Target Luminance interaction [F(6, 90) = 2.96, p < .05]. None of the other main effects or interactions reached significance (all ps > .1).

Separate ANOVAs with the factors Cue Luminance and Cue at each TTOA revealed the following: There were more misses at TTOA 90 ms [F(1, 16) = 12.07, p < .01] and TTOA 180 ms [F(1, 16) = 6.97, p < .05] to targets at cued as compared with uncued locations [effect sizes 6.62% and 3. 57%, respectively]. There was also a Cue Luminance × Cue interaction at TTOA 450 ms [F(1, 16) = 5.72, p < .05]. More misses were made to targets at cued than at uncued locations when the cues were bright; however, this effect was reversed when the cues were dim.

Criterion (c)

Finally, Table 1 shows the criterion measure for each condition. Criterion values reflect bias towards a particular response. The main effect of TTOA was significant [F(3.75, 56.28) = 3.03, p < .05], with c decreasing (from positive to negative values) as TTOA increased. There was a slightly greater bias to “+” rather than “×” at early TTOAs, but this was reversed at late TTOAs. None of the other main effects or interactions reached significance (all ps > .1).

Discussion

The results showed that the quality of target information as measured by d′ increased with increasing processing time (i.e., at longer TTOAs). This accrual of target information took place despite the brief target presentation, providing no evidence that target decay was a critical factor in this study. This time course for d′ is similar to those from previous experimental findings with the SAT methodology (e.g., Carrasco & McElree, 2001). Nevertheless, our curve-fitting procedure did not reveal significantly different parameters across the different experimental conditions; instead, all conditions followed the same SAT function.

There was evidence for IOR in terms of RTs, especially for short TTOA intervals (TTOAs of 90, 180, and 270 ms). These results are largely consistent with findings by Ivanoff and Klein (2006), who also demonstrated an IOR effect for early response windows. The results also showed a significant overall effect of cueing on d′, with greater sensitivity for targets at cued than at uncued locations. In the absence of any difference in the parameters of the SAT function, this pattern is consistent with the criterion shift account of IOR (see Fig. 1c). Also note that the results were largely robust to changes in cue and target luminance.

Converging evidence for a criterion shift was also found from the analysis of anticipations, response frequencies, and misses. Participants tended to make fewer anticipations and more misses to targets at the cued location than at uncued locations, particularly at short TTOAs. There were no cueing effects on the response frequency measures. This pattern of responses indicates that participants were more conservative when responding to targets at cued relative to uncued locations. Finally, the manipulation of cue and target luminance had little impact on the results.

The present evidence for a criterion shift account of IOR contradicts at least one conclusion of Ivanoff and Klein (2006), who found that d′ was significantly decreased at the cued as compared with the uncued location—a result consistent with a perceptual account of IOR. However, there is at least one major methodological difference between our study and that of Ivanoff and Klein (2006): Our target appeared for 80 ms, while theirs was presented until the response. In the next experiment, we will test whether this difference was responsible for the contrasting findings.^{Footnote 3}

Experiment 2: unlimited target presentation times

The second experiment investigated whether the target presentation duration was critical to the differences between our data and those of Ivanoff and Klein’s (2006). In this case, the target presentation time was unlimited, making our experiment essentially a replication of Ivanoff and Klein (2006), only with more TTOAs.