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Article  |   October 2014
Speeded classification in simultaneous masking
Author Affiliations
  • Frouke Hermens
    School of Psychology, University of Aberdeen, Aberdeen, UK
    frouke.hermens@gmail.com
  • Aidan Bell
    School of Psychology, University of Aberdeen, Aberdeen, UK
Journal of Vision October 2014, Vol.14, 6. doi:10.1167/14.6.6
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      Frouke Hermens, Aidan Bell; Speeded classification in simultaneous masking. Journal of Vision 2014;14(6):6. doi: 10.1167/14.6.6.

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Abstract

In simultaneous masking, flanking elements impair performance on a visual target. Previous studies on simultaneous masking have predominantly used discrimination threshold estimation to quantify performance on the target. Results based on thresholds suggest that an important factor in simultaneous masking is the strength of grouping between the target and the flankers. Recently Panis and Hermens (2014) showed that error rates in a speeded discrimination task, using the same simultaneous masking paradigm, provide a very similar pattern of results compared to thresholds from previous studies. In contrast, response times were found to deviate from the pattern in the error rates in some of the conditions, possibly providing a method to tap into low-level visual processes within the same paradigm. However, only a small number of masks was used, and it is therefore unclear to what extent differences can be found between thresholds, error rates, and response times. Here, we address this issue by examining speeded classification performance on a vernier target for a broad range of simultaneous mask layouts. Results suggest that thresholds and error rates are strongly associated, and that response times generally show the same pattern of results, although to a slightly weaker extent. We suggest that masking strength, defined by either measure, appears to be linked to target-flanker grouping rather than to low-level interactions.

Introduction
Contextual elements have been shown to influence the percept of a visual target (e.g., Herzog & Fahle, 2002; Li, Thier, & Wehrhahn, 2000; Zipser, Lamme, & Schiller, 1996). One striking example is simultaneous masking, where flanking elements—presented together with a visual target—strongly impair the ability to report features of the target (e.g., Hermens, Herzog, & Francis, 2009; Malania, Herzog, & Westheimer, 2007). Simultaneous masking is a special case of visual masking (Breitmeyer & Ogmen, 2006), with forward masking referring to the presentation of the mask before the target, backward masking to the mask presented after the target, and simultaneous masking to the situation in which the mask is presented simultaneously with the target. Simultaneous masking is also related to crowding (Levi, 2008; Whitney & Levi, 2011), with the target and the mask predominantly presented in peripheral vision, while in simultaneous masking, both stimuli are typically presented at fixation. 
Although some of the effects of simultaneous masking appear to occur at a relatively low level of visual processing (e.g., Saarela & Herzog, 2008), there are indications that higher level mechanisms may be involved. In particular, research by Herzog and colleagues (Hermens et al., 2009; Malania et al., 2007; Sayim, Westheimer, & Herzog, 2008, 2010) has suggested that the spatial grouping of the target with the flanking elements influences the strength of masking. For example, when a target vernier was flanked by arrays of same length elements, offset discrimination performance on the target was strongly impaired. However, when either longer or shorter flanking elements were used, excellent performance on the target was obtained (Malania et al., 2007). The high performance for the short flankers can be explained on the basis of spatial pooling (Badcock & Westheimer, 1985; Parkes, Lund, Angelucci, Solomon, & Morgan, 2001; Pelli, Palomares, & Majaj, 2004; Wilkinson, Wilson, & Ellemberg, 1997) or lateral inhibition (Solomon, Felisberti, & Morgan, 2004; Tadin, Lappin, Gilroy, & Blake, 2003; Westheimer & Hauske, 1975). These explanations, however, fail to account for the high performance for the longer flankers relative to the same-length flankers. The reason is that they exert a similar, if not stronger, influence on the vernier compared to same-length flankers either in terms of spatial pooling or lateral inhibition. Further evidence against these low-level mechanisms was provided by the decrease in masking strength when increasing the number of short flankers, whereas spatial pooling and lateral inhibition predict no effects of additional flankers. For these reasons, the data by Malania et al. (2007) suggest that spatial grouping with the target vernier, which is arguably strongest when target and flankers are of the same length and when there are many flankers, explains the results. This conclusion was supported by comparing the results with participants' ratings of how strongly the vernier target stood out from the surrounding verniers. The role of perceptual grouping was also supported by the finding that with only one flanking aligned vernier on each side (resulting in fewer elements to group), only small differences were found between the short and same-length flankers (Malania et al., 2007). Further evidence for the grouping account was obtained for grouping by color (Sayim et al., 2008) and by creating shapes from the flanking elements (Sayim et al., 2010). 
These results suggest that thresholds, as a measure of performance in simultaneous masking, are dictated by higher level visual processes (i.e., the perceptual grouping between the target and the mask). It would, however, be interesting if a method could be developed that could tap in both lower-level (e.g., spatial pooling, lateral inhibition) and higher order processes simultaneously. A suggestion for such a method was offered in the work by Panis and Hermens (2014), who applied a simultaneous masking paradigm similar to Malania and colleagues (2007), in which vernier offset discrimination was examined for arrays of half-length (“short”), same-length, and double-length (“long”) flankers. Their experiments were set up to examine the time-course of these contextual influences on vernier discrimination. Instead of applying a staircase method to examine responses in terms of vernier offset discrimination thresholds, Panis and Hermens (2014) adopted a speeded offset discrimination task (cf., Figure 1a) using a fixed target offset size and analyzed the results using survival analysis. To be able to use this latter analysis, they presented a limited number of stimulus conditions (same length flankers, short flankers, long flankers; right column of Figure 2a) many times, so that reaction time distributions and hazard functions could be analyzed. Interestingly, the average data in their experiment suggest that while error rates in speeded classification showed a pattern consistent with a perceptual grouping account, average response times suggest a pattern of results consistent with low-level accounts. These results therefore suggest that speeded offset discrimination could be used as a method to simultaneously examine both low-level and high-level visual processes underlying simultaneous masking. By considering response times, low-level processes could be revealed, and by examining error rates in the same task, higher-level grouping aspects are considered. 
Figure 1
 
(a) Stimulus sequence. Each trial started with four white corner elements on a dark background for 800 ms, followed by the vernier target with flankers in the center (4 same-length flankers shown) for 208 ms (Experiments 1 through 3) or 14 ms (Experiment 3). A blank screen followed until the response of the participant. Feedback was presented afterwards for 500 ms in the form of four red corner elements for an incorrect response and four green corner elements for a correct response. (b) Stimulus dimensions in degrees and arcmin of visual angle for the 2 m viewing distance used in most conditions (in reverse contrast). Approximate dimensions for the 52 cm viewing distance in Experiment 3 can be obtained by multiplying the values by 3.85.
Figure 1
 
(a) Stimulus sequence. Each trial started with four white corner elements on a dark background for 800 ms, followed by the vernier target with flankers in the center (4 same-length flankers shown) for 208 ms (Experiments 1 through 3) or 14 ms (Experiment 3). A blank screen followed until the response of the participant. Feedback was presented afterwards for 500 ms in the form of four red corner elements for an incorrect response and four green corner elements for a correct response. (b) Stimulus dimensions in degrees and arcmin of visual angle for the 2 m viewing distance used in most conditions (in reverse contrast). Approximate dimensions for the 52 cm viewing distance in Experiment 3 can be obtained by multiplying the values by 3.85.
Figure 2
 
Stimuli and results from Experiment 1. (a–c) Flanker configurations and results examining the influence of the number and height of the flankers (see Malania et al., 2007). (d–f) Flanker configurations and results examining the influence of the number of same length flankers (see Manassi et al., 2012, who measured thresholds for peripherally presented stimuli). (g–i) Flanker configurations and result examining the role of indicators of the target position.
Figure 2
 
Stimuli and results from Experiment 1. (a–c) Flanker configurations and results examining the influence of the number and height of the flankers (see Malania et al., 2007). (d–f) Flanker configurations and results examining the influence of the number of same length flankers (see Manassi et al., 2012, who measured thresholds for peripherally presented stimuli). (g–i) Flanker configurations and result examining the role of indicators of the target position.
The distinction between response times and error rates in the study by Panis and Hermens (2014), however, was based on a single condition (only for the long flanker condition response times and error rates diverged from the pattern set by the other conditions). It is therefore unclear whether the dissociation between response times and error rates is unique to this condition, or whether it can be found across a range of different stimulus configurations. It would be particularly important to determine whether the conditions for which the two measures (response times and error rates) show dissociated results, are exactly those conditions for which predictions of low-level (e.g., spatial pooling, lateral inhibition) and higher-level (e.g., spatial grouping) accounts differ. 
The present study was designed to address this issue by examining response times and error rates for a broad range of spatial configurations of the simultaneous mask. We chose an exploratory approach, in which we tested a broad range of configurations, to allow for an alternative situation in which neither account could explain the results, but in which still some conclusions could be drawn about the possible underlying mechanisms of spatial aspects in simultaneous masking. Three experiments were conducted. Experiment 1 applied a broad range of masks inspired by Malania et al. (2007), testing the influence of the strength of grouping between the target and the flankers. Experiment 2 used a range of masks inspired by Malania et al. (2007) and Ghose, Hermens, and Herzog (2012), examining the influence of the regularity of the overall target-mask configuration. Because the results of these two experiments were at odds with the critical condition from the study by Panis and Hermens (2014) (the long flanker condition), a third experiment examined a few possible reasons for this lack of replication. 
General methods
Participants
Participants (average age = 20.7 years, 31 female and 21 male) were the authors (Experiments 2 and 3) and students from the University of Aberdeen (all experiments), recruited via an online research participation system or by word of mouth, participating either in return for course credit or with reimbursement. All participants reported normal or corrected-to-normal vision. Before taking part, they all signed an informed consent for the study that was approved by the local ethics committee. 
Apparatus
Participants were tested in a quiet, dimly lit experimental room. They were seated at either 2 m (Experiments 1, 2, and 3, see also Malania et al., 2007) or 52 cm (Experiment 3, see also Panis & Hermens, 2014) from a 24-in. wide-screen Silicon Graphics computer monitor (1920 × 1080 pixels, set at a refresh rate of 72 Hz). Stimulus presentation was controlled by a Dual Core PC (replaced by a similar PC after participant 10 in Experiment 3, due to hardware failure), using the OpenSesame software package (Mathôt, Schreij, & Theeuwes, 2012) under the Lubuntu (version 13.10) operating system. A USB number pad, extended by a USB 2.0 cable was used to record participants' responses. 
Stimuli
Each trial started with four corner elements on a virtual rectangle measuring 10.05° (width) by 4.09° (height; illustrated in Figure 1a). Corner elements themselves were 0.26° wide and tall, and presented in white (79.5 cd/m2) on a dark background (0.11 cd/m2). The use of the corner elements was inspired by the work in the Herzog lab (e.g., Hermens, Scharnowski, & Herzog, 2009; Malania et al., 2007). It provides participants with a temporal cue to the impending onset of the target and a spatial cue to the center of the image without forwardly masking the target. The fixation stimulus was followed by the target and mask. The vernier target's size on the screen was kept constant throughout the experiment, which extended 19.9 arcmin by 0.50 arcmin per segment at the standard viewing distance of 2 m (Figure 1b). The standard horizontal offset between the elements was 0.99 arcmin, which was halved or doubled, depending on performance of the participant in the first set of trials. Flankers were presented at a distance of 8.0 arcmin from the center of the vernier target, and the same distance was used for the spacing between flankers. The vernier target and mask elements were presented in white on a dark background, except for some mask elements in Experiment 2, which were presented in half contrast values, resulting in gray-looking (16.6 cd/m2) elements. 
Design
Each experiment involved participants responding to a target vernier surrounded by two or more flankers (except for the vernier-only condition, in which the vernier was presented in isolation). Various configurations of flanker layouts were used, which were randomly interleaved across the trials in the experiment. In Experiment 3, different presentation durations and viewing distances were used, which were presented in a blockwise manner. On each trial, the target vernier could be offset to the left or right, and equal numbers of left and right offset targets were used, whose order was randomized for each participant along with the conditions. 
Procedure
Participants were seated at a distance of 2 m (Experiments 1, 2, and some conditions in Experiment 3) or 52 cm (short viewing distance in Experiment 3) from the computer monitor and provided a USB number pad for their responses. The stimulus sequence is illustrated in Figure 1a. Each trial started with four white corner elements followed by the target and mask presented until the first refresh after 200 ms (208 ms for the 72 Hz screen that we used; Experiments 1, 2, and some conditions in Experiment 3), or approximately 14 ms (1 refresh of the screen at 72 Hz; some conditions of Experiment 3). Participants were asked to report the position of the lower segment of the vernier (left or right) with respect to the top segment as quickly and accurately as possible by pressing the 4 key (left) or the 6 key (right) on the keypad. Feedback was provided after each trial with the corner elements returning in red (incorrect response) or green (correct response) for 500 ms. Participants started with a practice block, in which verniers were always presented in isolation with various offsets to ensure that participants understood the task. After these practice trials, the experiment started. After the first 35 trials of the experiment, feedback on the overall error rate and average response time was provided. Based on the accuracy reported during this feedback, the experiment was either continued (accuracy around 75%, exact thresholds set for each experiment separately), or restarted with half the offset (for high performance) or double the offset (for low performance) for the target vernier. After each subsequent 100 trials, further feedback on accuracy and average response times was provided and an opportunity to take a break. After completing the experiment, which typically took 35 to 40 minutes, participants were debriefed about the purpose of the study. 
Data analysis
Accuracy and median response times across correct responses were computed for each stimulus condition. We also computed average response times after filtering the response times for outlier data, but as this analysis provided very similar patterns of results to the median response times, only the medians will be reported. To examine statistical significance of differences across conditions, univariate repeated measures ANOVAs (Greenhouse-Geisser corrected where appropriate) and t tests will be reported. For sets of post hoc comparisons, Bonferroni corrections will be applied to keep the overall type I error rate for the set equal to 0.05. Note that the critical value rather than the computed p values will be adjusted. Because scatterplots comparing different measures suggested linear trends in most instances, Pearson's correlations were used. 
Simulations
Previous work has suggested that a lateral inhibition and excitation account, while successful in explaining backward masking (Hermens, Luksys, Gerstner, Herzog, & Ernst, 2008) and feature fusion (Hermens et al., 2009) data, may not be able to account for simultaneous masking data (Panis & Hermens, 2014). We used the broad range of mask layouts in the present experiments to verify this failure to predict performance in simultaneous masking. To this end, the model described in detail in Hermens et al. (2008) was presented with each of the masks for 60 ms (the read-out time in the model; meaning that presenting the masks for longer to the model does not make a difference). For the simulations, we left the parameter settings of the model (as specified in Hermens et al., 2008) intact, and computed the overlap of the neural activity at the standard read-out time (60 ms after target onset) with the vernier as a measure of predicted performance (see also Hermens et al., 2008). We also tried comparing the target related activity with that for an oppositely offset vernier (representing an error response, as in Hermens et al., 2009), but this yielded very similar results. We also tested the assumption that the target offset could introduce additional centers of activity in the network inconsistent with the actual offset size used in the experiment (the grid density for the simulations did not allow to simulate the actual offset size). To examine whether predictions of the model critically depended on the target offset size used for the simulations, we tried various offset sizes (zero pixels, one pixel, two pixels to each side). Very similar data fits were obtained across offset sizes, and therefore, the standard offset for previous simulations (two pixels to each side, Hermens et al., 2008, 2009) will be reported. The outcomes of these simulations will be provided after Experiment 2, allowing the pooling of the data of the first two experiments for the evaluation of model performance. 
Experiment 1
The first experiment examined, for a broad range of simultaneous mask layouts, to which extent response times and error rates are dissociated, with the aim to determine whether the two measures probe into different underlying visual processes. 
Methods
Seventeen participants (aged between 18 and 25 years, six male) took part in the first experiment. For 12 participants, whose performance was above 65% but below 85% after the first 35 experimental trials, the standard vernier offset size (Figure 1) was used. Another two completed the experiment with half the standard offset, while the remaining three participants completed the experiment with a double target offset size. The masks, together with the vernier targets (right offset shown), are illustrated in Figure 2a, d, and g in reverse contrast. Each masking condition was presented 48 times (24 times with a left offset, 24 times with a right offset), and results were pooled across these two offset directions. 
Results
The main aim of Experiment 1 was to determine the association (or dissociation) between response times (RTs) and error rates for a broad range of simultaneous mask configurations. Before plotting this association, we first examine the effects of the various spatial configurations of the simultaneous mask (Figure 2). Shown are the effects of the number (2 or 16) of and length (short, same-length, long) of the flankers (Figure 2b and c), the effect of the number of same length flankers (Figure 2e and f), and the effect of local increases and indicators of the target location (Figure 2h and i). 
For two-flanker masks, double length flankers result in better performance (short RTs and low error rates), while for 16-flankers, the weakest performance is found for the same-length flankers. Paired samples t tests revealed significantly faster response times for two long compared to two short flankers (p = 0.0040), while the other comparisons on the response times did not survive the Bonferroni correction (for three comparisons). Further paired comparisons showed lower error rates for two long flankers compared to same-length and short flankers (both p-values < 0.001). For 16-flankers, lower error rates were found for the short compared to the same-length flankers (p < 0.001) and for long compared to same-length flankers (p < 0.001). 
A second manipulation involved the number of same-length flankers (Figure 2d through f), inspired by Manassi, Sayim, and Herzog (2012). It may be expected that adding more same-length flankers leads to a stronger grouping between the flankers and the target and, therefore, to worse performance. For peripherally presented stimuli and variable vernier offsets (used for threshold estimation), however, Manassi et al. (2012) did not find such a decrement. This outcome was confirmed by the response times in the present study, F(4, 64) = 0.82, p = 0.52, Display FormulaImage not available = 0.049, but not by the error rates, F(4, 64) = 6.96, p < 0.001, Display FormulaImage not available = 0.30. Paired planned comparisons between subsequent flanker numbers showed an increase in error rates between two and four flankers, t(16) = 5.35, p < 0.001.  
Finally, the role of pointers to the location of the target vernier and the role of local irregularities were examined (Figure 2g through i). Pointers toward the position of the target are expected to reduce uncertainty about where to attend and, therefore, may lead to better performance on the target. Previous results in peripheral vision, however, showed no effect of such pointers (Manassi et al., 2012). Two shape manipulations were tested, with increasing (“butterfly” shape) and decreasing flanker (“diamond shape”) length (Figure 2g). Neither of these manipulations were found to affect performance, with response times, F(2, 32) = 2.16, p = 0.13, Display FormulaImage not available = 0.12; and error rates: F(2, 32) = 0.47, p = 0.63, Display FormulaImage not available = 0.029, in agreement with Manassi et al. (2012). We then tested the effects of a local irregularity, created by single long flankers adjacent to the target (P1DL). This mask led to significantly lower error rates compared to the 16 same-length flankers, t(16) = 6.24, p < 0.001, and similar error rates as for 16 long flankers, t(16) = 1.57, p = 0.14), suggesting that increasing the length of the nearest flanker is sufficient to reduce grouping. Response times, in contrast, showed better performance (faster response times) for 16 long flankers compared to one double length adjacent pair of flankers, t(16) = 3.68, p = 0.0020, and no difference between 16 same-length flankers and a single pair of long flankers, t(16) = 0.40, p = 0.69, so the overall influence of the local irregularity on performance is unclear.  
Comparison of response times, error rates, and thresholds
While it may be expected that response times, error rates, and offset discrimination thresholds all provide a measure of performance on the vernier target, previous results have suggested that while thresholds and error rates are associated, there may be masks for which response times and error rates are dissociated (Panis & Hermens, 2014). To examine for which masks such a dissociation exists, Figure 3 plots the different measures against each other. Figure 3a plots response times against error rates, and for the masks that were also used by Malania et al. (2007), Figure 3b and c plots thresholds against error rates and thresholds against response times. Note that thresholds in these plots are from Malania et al. (2007), meaning that they were collected in a staircase, blocked-presentation procedure, using slightly different stimulus dimensions, different equipment, without an instruction on response times, across fewer participants, but with many more trials per participant. The stimuli associated with the different codes in the data plots are shown in Figure 3d. The present comparison only includes the data by Malania et al. (2007), so that a comparison is obtained between foveal stimuli only (i.e., no comparison was made with Manassi et al., 2012, where stimuli were presented peripherally). 
Figure 3
 
Examining the association between error rates, response times (both from the present study), and thresholds (Malania et al., 2007). (a) Error rates plotted against response times, both from the present study. (b) Error rates from the present study plotted against thresholds from Malania et al. (2007). (c) Error rates from the present study plotted against thresholds from Malania et al. (2007). (d) Illustrations of the mask configurations indicated by the labels in the data plots. The horizontal and vertical lines around each data point show the standard error of the mean across participants. The title of each subplot shows the correlation.
Figure 3
 
Examining the association between error rates, response times (both from the present study), and thresholds (Malania et al., 2007). (a) Error rates plotted against response times, both from the present study. (b) Error rates from the present study plotted against thresholds from Malania et al. (2007). (c) Error rates from the present study plotted against thresholds from Malania et al. (2007). (d) Illustrations of the mask configurations indicated by the labels in the data plots. The horizontal and vertical lines around each data point show the standard error of the mean across participants. The title of each subplot shows the correlation.
The data plots show approximately linear associations between the three measures. A fairly close relation between error rates and response times is found, confirmed by a significant correlation, r = 0.78, df = 11, p = 0.002, although part of this correlation may be due to the vernier stimulus. After removal of this condition, however, the correlation remains significant, r = 0.67, df = 10, p = 0.016). This outcome suggests that the dissociation observed earlier (Panis & Hermens, 2014) does not extend to a broad range of spatial layouts, and therefore, response times and error rates may be probing the same underlying mechanisms. 
Interestingly, a very high correlation is found between thresholds from the Malania et al. (2007) study and the error rates of the present study, r = 0.95, df = 7, p < 0.001, despite the many differences between the studies, including a large difference in the number of trials per data point (160 vs. 48), a large difference in the number of participants (5 vs. 17), the use of a staircase procedure versus a fixed vernier offset size, and a blocked versus a mixed presentation. Response times, in contrast, are less strongly correlated with thresholds (but still significantly, r = 0.76, df = 7, p = 0.018). These results together suggest that performance in a speeded discrimination task provides a viable alternative to estimate the perceptual influence of the spatial layout of simultaneous masks, weakening the need of using an adaptive staircase procedure, threshold estimation, high spatial resolution displays, and long testing times per participant. 
Experiment 2
Experiment 1 investigated the role of perceptual grouping on response times and accuracy in a speeded vernier offset discrimination paradigm. In Experiment 2, the role of mask regularity is investigated. The masks used in this experiment were inspired by past studies by Hermens and Herzog (2007) and Ghose, Hermens, and Herzog (2012), who applied the masks (with an aligned vernier at the center) in a backward masking paradigm. These studies suggested that more regular masks lead to weaker masking. By applying the masks in a simultaneous masking paradigm, the opposite relationship is expected. While regular backward masks may be easily discounted by the visual system, regular masks may bind strongly with the central target vernier in a simultaneous masking paradigm. Experiment 2 also repeats the conditions from Panis and Hermens (2014) so that, when pooled across experiments, data across a larger set of participants is obtained. 
Methods
Seventeen new participants (the two authors and fifteen students from the University of Aberdeen, mean age 19.5 years, 11 female) took part in Experiment 2. Participating students were all naive to the purpose of the experiment. Masks were varied in regularity by introducing irregular elements, as shown in Figure 5f. Elements were added incrementally (“multiple conditions”), or they were shifted in their position with respect to the target (“single conditions”; Ghose et al., 2012; Hermens & Herzog, 2007). Four different variations of irregular elements were used: Double length (Ghose et al., 2012; Hermens & Herzog, 2007), half-length elements, half-contrast (approximately one-fourth luminance) elements (Ghose et al., 2012) and gap elements (Ghose et al., 2012). The main conditions from Panis and Hermens (2014, 16 same-length, half-length, and double-length flankers, and the vernier by itself were also included. Each condition was presented 26 times (13 times with a left offset target vernier, and 13 times with a right offset vernier; results pooled), and the order of the stimuli was randomized for each participant. As Experiment 2 proved to be more frustrating to participants, the threshold for doubling the target vernier offset was lowered to 73%. Ten of the 17 participants completed the experiment at this double target vernier offset, and none of the participants completed it at the half-offset size. 
Figure 4
 
Flanker configurations (right) and results (left) in Experiment 2, in which the role of different types of irregular elements was investigated. The examples on the right show a subset of the stimuli, namely the stimuli with irregularities at positions P3 (“single”) and P1+P3 (“multiple”). The full set can be found in Figure 5f. Single and multiple irregular elements were used, and irregularities in length (double length, half length) as well as contrast (half contrast, gap elements) were examined. In addition, the three 16-flanker masks from Experiment 1 and Panis and Hermens (2014) were repeated. The data plots show the median response times and error rates across conditions. The 16 same-length flanker mask (labeled as “Std,” cf., Hermens & Herzog, 2007) data was used for final single condition (i.e., a mask with the irregular element outside the mask). The P1+P3+P5+P7 mask is labeled as “EvSec” (“every second,” Hermens & Herzog, 2007) to indicate that every second element was irregular, making the mask globally regular. The error bars show the standard error of the mean.
Figure 4
 
Flanker configurations (right) and results (left) in Experiment 2, in which the role of different types of irregular elements was investigated. The examples on the right show a subset of the stimuli, namely the stimuli with irregularities at positions P3 (“single”) and P1+P3 (“multiple”). The full set can be found in Figure 5f. Single and multiple irregular elements were used, and irregularities in length (double length, half length) as well as contrast (half contrast, gap elements) were examined. In addition, the three 16-flanker masks from Experiment 1 and Panis and Hermens (2014) were repeated. The data plots show the median response times and error rates across conditions. The 16 same-length flanker mask (labeled as “Std,” cf., Hermens & Herzog, 2007) data was used for final single condition (i.e., a mask with the irregular element outside the mask). The P1+P3+P5+P7 mask is labeled as “EvSec” (“every second,” Hermens & Herzog, 2007) to indicate that every second element was irregular, making the mask globally regular. The error bars show the standard error of the mean.
Figure 5
 
(a) Scatter plot comparing response times and error rates from Experiment 2, both from simultaneous masking. (b) Comparison of response times in simultaneous masking (present Experiment 2) and thresholds in backward masking (data from Ghose et al., 2012). (c) Comparison of error rates in simultaneous masking (present Experiment 2) and thresholds (data from Ghose et al., 2012). A subsection of the mask labels are included in the plot to mark the outmost mask of each data cloud. The titles of the subplots show the correlations. Horizontal and vertical lines behind data points show the standard error of the mean across participants. (d) Modeling results. The scatter plot shows the association between target-related activity in the excitatory layer of the network at read-out time (60 ms after target onset), and the error rates observed in Experiments 1 and 2. (e & f) Stimulus pictures for the two experiments, providing the meaning of the labels in the graphs.
Figure 5
 
(a) Scatter plot comparing response times and error rates from Experiment 2, both from simultaneous masking. (b) Comparison of response times in simultaneous masking (present Experiment 2) and thresholds in backward masking (data from Ghose et al., 2012). (c) Comparison of error rates in simultaneous masking (present Experiment 2) and thresholds (data from Ghose et al., 2012). A subsection of the mask labels are included in the plot to mark the outmost mask of each data cloud. The titles of the subplots show the correlations. Horizontal and vertical lines behind data points show the standard error of the mean across participants. (d) Modeling results. The scatter plot shows the association between target-related activity in the excitatory layer of the network at read-out time (60 ms after target onset), and the error rates observed in Experiments 1 and 2. (e & f) Stimulus pictures for the two experiments, providing the meaning of the labels in the graphs.
Results
Figure 4 shows the median correct response times and error rates in Experiment 2 for each of the irregularity manipulations (top data plots) and the repeated main conditions of Experiment 1 (bottom panel), with example stimulus configurations shown to the right. For masks with double length elements, higher error rates were found in the single compared to the multiple conditions: main effect, F(1, 16) = 8.28, p = 0.011, Display FormulaImage not available = 0.34. Response time effects varied with both the position and the number (single vs. multiple) of long elements: interaction, F(2, 32) = 11.1, p < 0.001, Display FormulaImage not available = 0.41. Post hoc ANOVAs suggest that the effects of the position of the flankers just fall short of significance after Bonferroni correction for two comparisons: single, F(3, 48) = 2.82, p = 0.049, Display FormulaImage not available = 0.15; multiple, F(3, 48) = 3.32, p = 0.027, Display FormulaImage not available = 0.17. Masks with half-length flankers showed larger numbers of errors for multiple elements compared to single elements: main effect, F(1, 16) = 5.74, p = 0.029, Display FormulaImage not available = 0.26, no interaction. The position of the elements marginally influenced the error rate: main effect, F(2, 32) = 3.21, p = 0.053. Response times were both influenced by the position and number (single or multiple) of half-length flankers: interaction, F(1.73, 27.7) = 6.48, p = 0.007, Display FormulaImage not available = 0.29. For single elements, the position of the irregular element significantly influenced response times, F(3, 48) = 7.83, p < 0.001, Display FormulaImage not available = 0.33. This was not the case for multiple elements, F(1.98, 31.6) = 2.74, p = 0.080, Display FormulaImage not available = 0.15.  
For the half contrast irregular elements, error rates were higher in the single than in the multiple conditions: main effect, F(1, 16) = 55.7, p < 0.000, Display FormulaImage not available = 0.78, but no influence of the position of the elements was found: main effect, F(2, 32) = 1.13, p = 0.37, no interaction. Similar findings were obtained for response times, with faster responses for single than for multiple elements: main effect, F(1, 16) = 13.1, p = 0.002, Display FormulaImage not available = 0.45, and a marginal influence of the position of the elements: main effect, F(1.39, 22.3) = 3.64, p = 0.057, no interaction. The pattern of results was similar for masks with gaps. Error rates were higher for single than for multiple gaps: main effect, F(1, 16) = 41.63, p < 0.001, Display FormulaImage not available = 0.72, without an effect of the position of these gaps: main effect, F(2, 32) = 0.51, p = 0.61, no interaction. Response times were faster for single gaps: main effect, F(1, 16) = 11.48, p = 0.004, Display FormulaImage not available = 0.42, which were influenced by the position of the gap(s), F(2, 32) = 4.89, p = 0.014, Display FormulaImage not available = 0.23, no interaction.  
For the three repeated conditions from Experiment 1 (bottom row of Figure 4), the same pattern of results was found. Error rates were significantly different across the three masks, F(2, 32) = 21.5, p < 0.001, Display FormulaImage not available = 0.57, with significant differences between the same-length and half-length masks, t(16) = 4.75, p < 0.001, and between the same-length and double-length masks, t(16) = 5.61, p < 0.001, but not between the double-length and half-length masks, t(16) = 1.97, p = 0.067. In contrast, response times did not show any significant differences between the three masks, F(2, 32) = 2.28, p = 0.12, Display FormulaImage not available = 0.13.  
Comparison of response times, error rates and thresholds
In backward masking, performance on the target has been shown to be more strongly impaired if the mask is irregular (Hermens & Herzog, 2007). Irregular structures may be strong masks, because they are more difficult to process and therefore interfere more with the target processing. In simultaneous masking, regular masks may strongly group with the target, and therefore regular structures may be stronger masks. These two observations lead to a predicted inverse association between performance on backward masking and on simultaneous masking for the same masks. This possible inverse association is examined in Figure 5, where response times and error rates from Experiment 2 are compared to thresholds (Ghose et al., 2012). 
In agreement with Experiment 1, a highly significant correlation is found between error rates and response times, r = 0.86, df = 26, p < 0.001, supporting the conclusion that both measures tap into the same underlying processes. However, no significant correlations were found between thresholds (backward masking) and response times (simultaneous masking), r = 0.19, df = 17, p = 0.44, and between thresholds (backward masking) and error rates (simultaneous masking), r = −0.10, df = 17, p = 0.68, arguing against the hypothesis put forward that mask regularity effects are inversely related in simultaneous and backward masking. 
Computational modeling
The effects of the spatial layout of the mask in backward masking could be explained in terms of lateral neural interactions, implemented as a neural network model (Hermens et al., 2008). Lateral interactions between neighboring neurons in the model suppress activity inside regular structures, while irregular elements (such as edges next to gaps) are highlighted. These highlighted irregular elements interfere with processing of the target, particularly if they are located near the target. Similar processes may be at work in simultaneous masking, leading to the prediction that the information of a target embedded in same-length flankers is suppressed by the surrounding elements. This is indeed what was found when simulations were performed with the model (Panis & Hermens, 2014). In contrast, the model could not explain the weak interference of the double-length flankers. Lateral interactions between neurons coding for the long lines suppressed activity at the target site, resulting in a weak target signal. The question then arises whether the double length mask is unique with respect to the failure of the model to explain its effects. To examine this issue, simulations were performed across all masks of Experiments 1 and 2
Figure 5d plots target-related activity in the excitatory layer of the neural network as a measure of predicted performance (Hermens et al., 2008, 2009; Panis & Hermens, 2014) against error rates in the two experiments. If the model correctly predicts observed performance, a strong negative correlation between target-related activity (the more, the better performance) and error rates (the higher, the worse performance) would be predicted. The data show the predicted negative correlation, r = −0.50, p < 0.001, but despite it being significant, it is rather weak. Masks that deviate from the negative trend in the data plot are the double-length masks (lower error rates than predicted), and various half-length masks from Experiment 2 (higher error rates than predicted). These results suggest that the failure of the model to explain the 16 long-flankers condition is not an isolated case. 
Experiment 3
Experiments 1 and 2 did not replicate the differential pattern of response times found by Panis and Hermens (2014). Instead, they found the same pattern of results for error rates and response times (although the effect sizes appear to be low for response times). Experiment 3 aims to examine this replication failure in more detail, because the present data seem to suggest that response times and error rates do not tap into different underlying processes, contrary to what the data by Panis and Hermens (2014) suggested. Experiments 1 and 2 used a procedure similar to that used by Malania et al. (2007), with participants viewing the screen at a distance of 2 m and stimuli presented for 200 ms. In the experiments by Panis and Hermens (2014), a much shorter viewing distance (57 cm), and a shorter presentation duration (one screen refresh was used). Our initial assumption was that these factors do not influence the results, but we then realized that this assumption should be evaluated experimentally. In Experiment 3, we therefore varied the viewing distance and presentation duration to examine the influence of these factors. 
Methods
Eighteen participants, including the two authors (average age = 21.2 years, eight female), took part in Experiment 3. Vernier offset was adjusted after 35 trials if performance was well above 75% (for some participants in the 208 ms conditions; offset decreased) or well below 75% performance (for some participants in the 14 ms presentation condition; offset increased). Participants conducted four blocks in which the three 16-flanker masks (same length, double length, half length, see Figure 2) were each presented 70 times (35 times with a left offset and 35 times with a right offset target vernier). The four blocks changed two variables orthogonally: viewing distance (2 m vs. 52 cm) and presentation duration (208 ms vs. 14 ms). Because the physical size of the stimuli on the screen was kept constant, this meant that at the short viewing distance, the stimuli were larger in angular size (see Figure 1). The order of the four blocks were counterbalanced across participants, but keeping the two short and the two long viewing distances together, so that participants did not have to move their seat too often. 
To compare the results in Experiment 3 with those by Panis and Hermens (2014) and those from Experiments 1 and 2, a standardized measure of the effect size (Hedges' g) of the difference between same-length and half-length flankers and between same-length and double-length flankers was computed using the MATLAB (MathWorks, Inc., Natick, MA) Measures of Effect Size Toolbox (Hentschke & Stüttgen, 2011). This toolbox also provides 95% confidence intervals of the effect size, calculated using a bootstrap method (using 10,000 samples per interval). In order to pool the different effect size and confidence intervals, weights were assigned to each effect size on the basis of each confidence interval (weights were the inverse of the square of the width of the confidence divided by 4, as a proxy of the variance normally used in meta-analysis, taking into account the sometimes highly asymmetric confidence intervals). 
Results
Median correct response times and error rates are shown in Figure 6a through h. Response times and error rates in these plots suggest a similar pattern of results as in Experiments 1 and 2, contrasting the findings by Panis and Hermens (2014). To assess these results statistically, a repeated measures ANOVA was used to compare the influence of the flanker length, viewing distance, and presentation duration. Error rates showed significant main effects of flanker length, F(2, 34) = 69.5, p < 0.001, Display FormulaImage not available = 0.81, viewing distance, F(1, 17) = 40.8, p < 0.001, Display FormulaImage not available = 0.71, and presentation duration, F(1, 17) = 11.1, p = 0.004, Display FormulaImage not available = 0.40, in the absence of any significant interactions (smallest p-value of 0.082 for the viewing distance by flanker length interaction). This means that, while viewing distance and presentation duration influenced the number of errors, the pattern of results across mask layouts was not influenced. Response times showed a similar pattern of results, but only the main effect of viewing distance, F(1, 17) = 8.89, p = 0.008, Display FormulaImage not available = 0.34, reached significance, whereas flanker length, F(1.05, 17.8) = 3.60, p = 0.072, and presentation duration, F(1, 17) = 3.88, p = 0.065, did not significantly affect response times. Results of the pairwise comparisons are shown in Figure 6, with all p-values smaller than 0.05 shown, suggesting strong and significant effects between conditions on error rates, but many of the comparisons of response times fail to reach significance after applying a Bonferroni correction for the three comparisons per graph.  
Figure 6
 
(a–h) Response times and error rates in Experiment 3, where three flanker types were used (16 half-length, 16 same-length, and 16 double-length), in combination with two viewing distances and two presentation durations, as indicated in the titles of the various subplots. The horizontal dashed line indicates performance on the vernier-only condition. Error bars show the standard error of the mean across participants. (i) Stimulus pictures. (j) Comparison of the effect sizes across the different experiments, showing Hedges' g (with 95% confidence intervals) for the comparisons between same-length (SL) and half-length (HL), and between the same-length (SL) and double-length (DL) flanker conditions. P&H14 refers to the Panis and Hermens (2014) study, Exp1 to the present Experiment 1, Exp2 to the present Experiment 2, Exp3-1 to the short-distance, short-presentation-duration condition of Experiment 3, Exp3-2 to the long-distance, short-presentation-duration condition of Experiment 3, Exp3-2 to the short-distance, long-presentation-duration condition of Experiment 3, and Exp3-4 to the long-distance, long-presentation-duration condition of Experiment 3. The bottom line shows the pooled effect size across studies, weighting the individual effect sizes and confidence intervals on the basis of the width of the confidence interval (higher weight for smaller confidence intervals).
Figure 6
 
(a–h) Response times and error rates in Experiment 3, where three flanker types were used (16 half-length, 16 same-length, and 16 double-length), in combination with two viewing distances and two presentation durations, as indicated in the titles of the various subplots. The horizontal dashed line indicates performance on the vernier-only condition. Error bars show the standard error of the mean across participants. (i) Stimulus pictures. (j) Comparison of the effect sizes across the different experiments, showing Hedges' g (with 95% confidence intervals) for the comparisons between same-length (SL) and half-length (HL), and between the same-length (SL) and double-length (DL) flanker conditions. P&H14 refers to the Panis and Hermens (2014) study, Exp1 to the present Experiment 1, Exp2 to the present Experiment 2, Exp3-1 to the short-distance, short-presentation-duration condition of Experiment 3, Exp3-2 to the long-distance, short-presentation-duration condition of Experiment 3, Exp3-2 to the short-distance, long-presentation-duration condition of Experiment 3, and Exp3-4 to the long-distance, long-presentation-duration condition of Experiment 3. The bottom line shows the pooled effect size across studies, weighting the individual effect sizes and confidence intervals on the basis of the width of the confidence interval (higher weight for smaller confidence intervals).
Experiments 1 to 3 all examined response times (and error rates, but these show clear effects) between short, same-length and long flankers. These results can now be combined to examine the overall effect size and significance of the difference between the flanker conditions. Effect sizes are shown in Figure 6j, where Hedges' g is plotted for the same-length versus half-length (SL–HL) and the same-length versus double-length (SL–DL) comparisons (in combination with the 95% confidence interval of this measure). For a better comparison across studies, we used the original data from Panis and Hermens (2014) and computed median response times (whereas in the original study, mean response times on filtered data were used). The effect sizes suggest that while the effect size for the SL–HL comparison in the study by Panis and Hermens (2014) was in the top of the range, the effect size for the SL–DL comparison was at the bottom of the range. The bottom of the plots in Figure 6j show an estimate of the pooled effect size and confidence interval (weighting based on the width of the confidence intervals), which suggests that, while the effect size for the half length comparison was larger than that of the double length comparison, both effect sizes were significantly different from zero (no overlap of confidence interval with zero). The repetition of the 16-flankers conditions across experiments (with different participants, except for the authors) also allows for a statistical test on the differences with a much larger sample size (50 participants; 2 m viewing distance and 208 ms presentation) than in the Panis and Hermens (2014) study (with only 13 participants in the analysis). Paired samples t tests on the basis of the present three experiments show significant differences in response times between the same-length and half-length conditions, t(49) = 7.36, p < 0.0001, and the same-length and double-length conditions, t(49) = 3.64, p < 0.001. As Experiment 3 did not show an effect of the viewing distance and the presentation duration, the lack of a difference between the same-length and double-length flankers in the Panis and Hermens (2014) study may have been due to a lack of statistical power. 
General discussion
Studies of simultaneous masking, where a target is embedded in an array of flankers and presented at fixation, have suggested that the strength of the mask is determined by how strongly the target groups with the flanking elements (Malania et al., 2007; Sayim et al., 2010, 2008; Sayim, Westheimer, & Herzog, 2011). A recent study, in which a speeded classification paradigm was used to study simultaneous masking, suggested that error rates in such a paradigm reveal grouping effects, while response times may provide an indication of more low-level visual processes (Panis & Hermens, 2014). This tentative conclusion, however, was based on a single condition in one of the experiments. The present study therefore aimed to verify these results using a much broader range of mask layouts. Three experiments were conducted. The first experiment investigated the role of grouping between the target and the flankers, while the second experiment examined the role of the regularity of the structure of the mask. Because these two experiments failed to replicate the original finding by Panis and Hermens (2014) that led to the speculation of dissociated response times and error rates, a third experiment examined the relevant conditions in more detail. The results suggest that response times and error rates are closely related, and that they are both related to the strength of grouping between the target and the flanking elements, in agreement with earlier studies (Malania et al., 2007; Sayim et al., 2008, 2010, 2011). 
In the first experiment, the influence of spatial grouping was examined by varying the length and the number of flankers. In agreement with earlier observations (Malania et al., 2007), the pattern of results suggest that both error rates and response times are influenced by the spatial grouping between the target and the flankers (see Malania et al., 2007; Manassi et al., 2012, for measures of how strongly the vernier stands out from the surround). Error rates were found to vary less across participants and yield more reliable differences between conditions than response times, with fewer participants needed to achieve significant differences. Moreover, error rates were more strongly related to previously obtained thresholds (Malania et al., 2007). The observed influences of grouping on simultaneous masking are consistent with effects in feature fusion, in which the target vernier may form a joint percept with an oppositely offset vernier in the mask (Hermens et al., 2009; Hermens, Scharnowski, & Herzog, 2010). For example, a vernier fuses with a subsequently presented antioffset vernier when this second vernier is embedded in an array of aligned verniers (i.e., no grouping between the second vernier and its flankers takes place). In contrast, no fusion takes place when the subsequently presented antivernier is embedded in an array of antioffset verniers (grouping). Similar effects of grouping between the target and the mask were found by Hermens et al. (2009), who combined simultaneous masking with backward and forward masking. A vernier target, embedded in an array of same-length flankers, was masked by a spatially overlapping aligned vernier, only when the interval between the single aligned vernier and the target flanker combination was large. At a zero stimulus-onset asynchrony, the single aligned vernier grouped with the arrays of same-length flankers and the target vernier was released from masking. 
Experiment 1 provides further support for the conclusion that the failure to report the offset of the target is not due to a failure to locate the target (Manassi et al., 2012). We used increasing and decreasing length manipulations (creating butterfly and diamond shaped target-mask combinations; Experiment 1) to reveal to the participants where the target was located. As before, these manipulations did not improve performance on the target. An effect that we did not fully replicate from the previous study in peripheral vision (Manassi et al., 2012) is the effect of the number of same-length flankers. We found a significant increase in errors when increasing the number of flankers from one on each side to two of each side, suggesting that at least five elements are needed to create a group. The difference in results maybe due to how the stimuli were presented (in the fovea or in the periphery) or the speed with which participants had to respond (speeded classification vs. a focus on response accuracy). 
Experiment 2 investigated the effects of mask regularity on simultaneous masking performance. Complementing previous results from a backward masking paradigm (Ghose et al., 2012; Hermens & Herzog, 2007), the regularity of the mask was found to influence performance in a simultaneous masking paradigm. Also, in agreement with the backward masking observations, differences were found between the effects of single and multiple irregular elements, and between different types of irregular elements (double-length, half-length, gap, and half-contrast elements). Generally, single elements (not leading to grouping) yielded higher error rates than the multiple conditions (leading to stronger grouping, particularly when the number of elements was increased). The exact pattern of results, however, was different across the two paradigms. While the double length conditions showed the predicted inverse pattern across the two studies, the gap conditions showed a similar pattern (not an inverse pattern) across studies, except for the ordering between single and multiple conditions. The half-length conditions, which were not tested before, show an opposite pattern of the other manipulations, with single conditions leading to lower error rates than multiple conditions. While previous work (Ghose et al., 2012) has shown that different types of irregularities (e.g., double-length, gap) have different influences on the masking strength, it is unclear why this is the case. It is also unclear, at this stage, why the predicted inverse pattern for simultaneous masking did not occur. Experiment 2, however, confirmed the strong association between response times and error rates found in Experiment 1
Experiments 1 and 2 repeated the three conditions in Panis and Hermens (2014), but failed to replicate the pattern of results in the response times. The present experiments used a setup similar to past studies (Malania et al., 2007; Sayim et al., 2008, 2010, 2011), but differed in the viewing distance and presentation duration from Panis and Hermens (2014). To examine whether these factors are important, Experiment 3 repeated the three conditions at different viewing conditions and with different viewing times. Although the two factors influenced the overall error rates, they did not influence the pattern of results, meaning that viewing distance and presentation duration could not explain the failure to replicate. By pooling the data across the three experiments, significant differences were found for both the same-length versus half-length and same-length versus double-length comparisons. The effect sizes were fairly small, suggesting that the failure to replicate the original pattern of results may have been due to a lack of statistical power. Interestingly, the finding in Experiment 3 that the pattern of results was independent of the viewing distance is also at odds with predictions of the lateral neural network model of backward masking (Hermens et al., 2008, 2009). The model uses fixed interaction kernel widths and therefore would predict an influence of the angular size of the stimuli, which was varied by varying the viewing distance while keeping the size of the stimuli on the screen constant. 
Further problems for the model to account for simultaneous masking were found when simulating the results of Experiments 1 and 2 (see also Panis & Hermens, 2014). In particular, the influences of double-length flankers and certain gap and half-luminance flanker configurations were not well predicted. However, this does not imply that any type of lateral interactions cannot explain simultaneous masking effects. Future work will need to establish whether other versions of the model (applying different parameter settings) can account for the data (provided that these new versions can also account for the backward masking data). A more fundamental problem of the model is that predictions are strongly dependent on the angular size of the stimuli (because the model uses fixed kernel sizes), while the present data (Experiment 3) suggest that performance is largely independent of this factor. Furthermore, the model does not provide a mechanism to account for response time, which could possibly require the implementation of a two-stage process (Rüter, Marcille, Sprekeler, Gerstner, & Herzog, 2012). Alternative accounts may be provided by models simulating figure–ground segmentation (Francis, 2009) or models designed to explain flanker interference (e.g., Dayan & Solomon, 2010). 
Experiment 3 controlled for almost all differences in the present study and the work by Panis and Hermens (2014). One factor, however, was different between the studies. While in Panis and Hermens (2014) participants were instructed not to respond when uncertain (but aim to achieve around 90% responses), participants in the present study always responded. Nonresponses in Panis and Hermens (2014), however, were infrequent (around 3%), and were discarded from the average data. One could argue that the instruction to sometimes not respond may have influenced how participants respond overall (3% of the data are less likely to influence median response times); however, such effects would be expected to influence all conditions. Because Panis and Hermens (2014) found larger differences for the same-length and short flanker comparison, but smaller differences for the same-length and long flanker comparison, compared to the present study, it is unlikely that the “do not always respond” instruction caused the differences in the pattern of results. Further support for such a conclusion is provided by Experiment 2 from Panis and Hermens (2014) showing a significant same-length versus double-length flanker difference when spatially offset flankers were used. 
The present data have implications for how simultaneous masking experiments may be performed in the future. Up to now, many of these experiments have used staircase procedures to obtain a measure of performance (Malania et al., 2007; Sayim et al., 2008, 2010, 2011). In these procedures, the offset size of the vernier target is varied according to a staircase procedure, with each mask configuration tested in a separate block. At the end of the block, a psychometric function is fitted to all data in the block and the vernier offset size required for a level of 75% correct responses is estimated (the threshold). This method places some constraints on the experimental setup and the time required from each participant. First, because vernier offset discrimination performance is often very high, the stimuli should be presented with sufficient spatial resolution. This means that either the participant must be viewing the screen from a large distance, or the screen should have a high spatial resolution. Second, threshold estimation requires a certain number of trials (typically, 80 trials are used per threshold), which means that either testing time will be long, or that only a few conditions can be directly compared. Thresholds are typically estimated in separate blocks. Although it is possible to interleave staircases, this would render each block very long. By using blocked presentations, however, participants may develop strategies to focus on particular aspects of the display to optimize task performance. Depending of the aim of the study, this may or may not be a desired effect. Our present data, in conjunction with those from Panis and Hermens (2014), suggest that error rates in a speeded vernier discrimination task may provide a good alternative to this traditional method. 
Conclusion
In our experiments, we found a strong association between response times and error rates in a simultaneous masking paradigm, suggesting that both measures tap into the same underlying processes. The strong association between the error rates in the present experiments and thresholds from previous experiments, suggests that the speeded classification paradigm may provide an alternative method to measure the influence of the spatial layout of the mask in simultaneous masking. 
Acknowledgments
We thank Jim Urquhart for technical support. 
Commercial relationships: none. 
Corresponding author: Frouke Hermens. 
Email: frouke.hermens@gmail.com. 
Address: School of Psychology, University of Aberdeen, Aberdeen, UK. 
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Figure 1
 
(a) Stimulus sequence. Each trial started with four white corner elements on a dark background for 800 ms, followed by the vernier target with flankers in the center (4 same-length flankers shown) for 208 ms (Experiments 1 through 3) or 14 ms (Experiment 3). A blank screen followed until the response of the participant. Feedback was presented afterwards for 500 ms in the form of four red corner elements for an incorrect response and four green corner elements for a correct response. (b) Stimulus dimensions in degrees and arcmin of visual angle for the 2 m viewing distance used in most conditions (in reverse contrast). Approximate dimensions for the 52 cm viewing distance in Experiment 3 can be obtained by multiplying the values by 3.85.
Figure 1
 
(a) Stimulus sequence. Each trial started with four white corner elements on a dark background for 800 ms, followed by the vernier target with flankers in the center (4 same-length flankers shown) for 208 ms (Experiments 1 through 3) or 14 ms (Experiment 3). A blank screen followed until the response of the participant. Feedback was presented afterwards for 500 ms in the form of four red corner elements for an incorrect response and four green corner elements for a correct response. (b) Stimulus dimensions in degrees and arcmin of visual angle for the 2 m viewing distance used in most conditions (in reverse contrast). Approximate dimensions for the 52 cm viewing distance in Experiment 3 can be obtained by multiplying the values by 3.85.
Figure 2
 
Stimuli and results from Experiment 1. (a–c) Flanker configurations and results examining the influence of the number and height of the flankers (see Malania et al., 2007). (d–f) Flanker configurations and results examining the influence of the number of same length flankers (see Manassi et al., 2012, who measured thresholds for peripherally presented stimuli). (g–i) Flanker configurations and result examining the role of indicators of the target position.
Figure 2
 
Stimuli and results from Experiment 1. (a–c) Flanker configurations and results examining the influence of the number and height of the flankers (see Malania et al., 2007). (d–f) Flanker configurations and results examining the influence of the number of same length flankers (see Manassi et al., 2012, who measured thresholds for peripherally presented stimuli). (g–i) Flanker configurations and result examining the role of indicators of the target position.
Figure 3
 
Examining the association between error rates, response times (both from the present study), and thresholds (Malania et al., 2007). (a) Error rates plotted against response times, both from the present study. (b) Error rates from the present study plotted against thresholds from Malania et al. (2007). (c) Error rates from the present study plotted against thresholds from Malania et al. (2007). (d) Illustrations of the mask configurations indicated by the labels in the data plots. The horizontal and vertical lines around each data point show the standard error of the mean across participants. The title of each subplot shows the correlation.
Figure 3
 
Examining the association between error rates, response times (both from the present study), and thresholds (Malania et al., 2007). (a) Error rates plotted against response times, both from the present study. (b) Error rates from the present study plotted against thresholds from Malania et al. (2007). (c) Error rates from the present study plotted against thresholds from Malania et al. (2007). (d) Illustrations of the mask configurations indicated by the labels in the data plots. The horizontal and vertical lines around each data point show the standard error of the mean across participants. The title of each subplot shows the correlation.
Figure 4
 
Flanker configurations (right) and results (left) in Experiment 2, in which the role of different types of irregular elements was investigated. The examples on the right show a subset of the stimuli, namely the stimuli with irregularities at positions P3 (“single”) and P1+P3 (“multiple”). The full set can be found in Figure 5f. Single and multiple irregular elements were used, and irregularities in length (double length, half length) as well as contrast (half contrast, gap elements) were examined. In addition, the three 16-flanker masks from Experiment 1 and Panis and Hermens (2014) were repeated. The data plots show the median response times and error rates across conditions. The 16 same-length flanker mask (labeled as “Std,” cf., Hermens & Herzog, 2007) data was used for final single condition (i.e., a mask with the irregular element outside the mask). The P1+P3+P5+P7 mask is labeled as “EvSec” (“every second,” Hermens & Herzog, 2007) to indicate that every second element was irregular, making the mask globally regular. The error bars show the standard error of the mean.
Figure 4
 
Flanker configurations (right) and results (left) in Experiment 2, in which the role of different types of irregular elements was investigated. The examples on the right show a subset of the stimuli, namely the stimuli with irregularities at positions P3 (“single”) and P1+P3 (“multiple”). The full set can be found in Figure 5f. Single and multiple irregular elements were used, and irregularities in length (double length, half length) as well as contrast (half contrast, gap elements) were examined. In addition, the three 16-flanker masks from Experiment 1 and Panis and Hermens (2014) were repeated. The data plots show the median response times and error rates across conditions. The 16 same-length flanker mask (labeled as “Std,” cf., Hermens & Herzog, 2007) data was used for final single condition (i.e., a mask with the irregular element outside the mask). The P1+P3+P5+P7 mask is labeled as “EvSec” (“every second,” Hermens & Herzog, 2007) to indicate that every second element was irregular, making the mask globally regular. The error bars show the standard error of the mean.
Figure 5
 
(a) Scatter plot comparing response times and error rates from Experiment 2, both from simultaneous masking. (b) Comparison of response times in simultaneous masking (present Experiment 2) and thresholds in backward masking (data from Ghose et al., 2012). (c) Comparison of error rates in simultaneous masking (present Experiment 2) and thresholds (data from Ghose et al., 2012). A subsection of the mask labels are included in the plot to mark the outmost mask of each data cloud. The titles of the subplots show the correlations. Horizontal and vertical lines behind data points show the standard error of the mean across participants. (d) Modeling results. The scatter plot shows the association between target-related activity in the excitatory layer of the network at read-out time (60 ms after target onset), and the error rates observed in Experiments 1 and 2. (e & f) Stimulus pictures for the two experiments, providing the meaning of the labels in the graphs.
Figure 5
 
(a) Scatter plot comparing response times and error rates from Experiment 2, both from simultaneous masking. (b) Comparison of response times in simultaneous masking (present Experiment 2) and thresholds in backward masking (data from Ghose et al., 2012). (c) Comparison of error rates in simultaneous masking (present Experiment 2) and thresholds (data from Ghose et al., 2012). A subsection of the mask labels are included in the plot to mark the outmost mask of each data cloud. The titles of the subplots show the correlations. Horizontal and vertical lines behind data points show the standard error of the mean across participants. (d) Modeling results. The scatter plot shows the association between target-related activity in the excitatory layer of the network at read-out time (60 ms after target onset), and the error rates observed in Experiments 1 and 2. (e & f) Stimulus pictures for the two experiments, providing the meaning of the labels in the graphs.
Figure 6
 
(a–h) Response times and error rates in Experiment 3, where three flanker types were used (16 half-length, 16 same-length, and 16 double-length), in combination with two viewing distances and two presentation durations, as indicated in the titles of the various subplots. The horizontal dashed line indicates performance on the vernier-only condition. Error bars show the standard error of the mean across participants. (i) Stimulus pictures. (j) Comparison of the effect sizes across the different experiments, showing Hedges' g (with 95% confidence intervals) for the comparisons between same-length (SL) and half-length (HL), and between the same-length (SL) and double-length (DL) flanker conditions. P&H14 refers to the Panis and Hermens (2014) study, Exp1 to the present Experiment 1, Exp2 to the present Experiment 2, Exp3-1 to the short-distance, short-presentation-duration condition of Experiment 3, Exp3-2 to the long-distance, short-presentation-duration condition of Experiment 3, Exp3-2 to the short-distance, long-presentation-duration condition of Experiment 3, and Exp3-4 to the long-distance, long-presentation-duration condition of Experiment 3. The bottom line shows the pooled effect size across studies, weighting the individual effect sizes and confidence intervals on the basis of the width of the confidence interval (higher weight for smaller confidence intervals).
Figure 6
 
(a–h) Response times and error rates in Experiment 3, where three flanker types were used (16 half-length, 16 same-length, and 16 double-length), in combination with two viewing distances and two presentation durations, as indicated in the titles of the various subplots. The horizontal dashed line indicates performance on the vernier-only condition. Error bars show the standard error of the mean across participants. (i) Stimulus pictures. (j) Comparison of the effect sizes across the different experiments, showing Hedges' g (with 95% confidence intervals) for the comparisons between same-length (SL) and half-length (HL), and between the same-length (SL) and double-length (DL) flanker conditions. P&H14 refers to the Panis and Hermens (2014) study, Exp1 to the present Experiment 1, Exp2 to the present Experiment 2, Exp3-1 to the short-distance, short-presentation-duration condition of Experiment 3, Exp3-2 to the long-distance, short-presentation-duration condition of Experiment 3, Exp3-2 to the short-distance, long-presentation-duration condition of Experiment 3, and Exp3-4 to the long-distance, long-presentation-duration condition of Experiment 3. The bottom line shows the pooled effect size across studies, weighting the individual effect sizes and confidence intervals on the basis of the width of the confidence interval (higher weight for smaller confidence intervals).
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