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. 2023 Dec 18;70(4):249–256. doi: 10.1027/1618-3169/a000594

The Beep-Speed Illusion Cannot Be Explained With a Simple Selection Bias

Hauke S Meyerhoff 1,2,*, Nina A Gehrer 3, Christian Frings 4
PMCID: PMC10929686  PMID: 38105748

Abstract

Abstract: An object appears to move at higher speed than another equally fast object when brief nonspatial tones coincide with its changes in motion direction. We refer to this phenomenon as the beep-speed illusion (Meyerhoff et al., 2022, Cognition, 219, 104978). The origin of this illusion is unclear; however, attentional explanations and potential biases in the response behavior appear to be plausible candidates. In this report, we test a simple bias explanation that emerges from the way the dependent variable is assessed. As the participants have to indicate the faster of the two objects, participants possibly always indicate the audio-visually synchronized object in situations of perceptual uncertainty. Such a response behavior potentially could explain the observed shift in perceived speed. We therefore probed the magnitude of the beep-speed illusion when the participants indicated either the object that appeared to move faster or the object that appeared to move slower. If a simple selection bias would explain the beep-speed illusion, the response pattern should be inverted with the instruction to indicate the slower object. However, contrary to this bias hypothesis, illusion emerged indistinguishably under both instructions. Therefore, simple selection biases cannot explain the beep-speed illusion.

Keywords: audio-visual illusion, audio-visual attention, audio-visual coincidence, perceived speed, response bias

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Every waking moment, an endless stream of sensory information exceeding human capacity limitations competes for attentional selection for further processing (Lavie, 1995; Meyerhoff et al., 2017; Yantis, 1993). Beyond determining which information is available for conscious processing (Simons & Levin, 1997), attentional processing also influences the way how selected information is processed. At the neural level, an increased firing rate of neurons has been observed for cortical structures representing attended rather than unattended areas in the visual field (Martınez-Trujillo & Treue, 2002; Reynolds et al., 2000). At the phenomenological level, however, it has been controversially discussed whether attentional allocation correspondingly intensifies the percept of a stimulus (Carrasco et al., 2004; see Carrasco & Barbot, 2019, for a review) or not (e.g., Prinzmetal et al., 1997; Schneider & Komlos, 2008).

Within this debate, Carrasco et al. (2004) reported a remarkable experiment in which they asked participants to judge the orientation of the one of two presented Gabor patches that appeared to be higher in contrast. They observed that cueing transient attention toward one of the Gabor patches increased the proportion with which the orientation of this patch was reported. From this pattern of results, Carrasco et al. concluded that the temporary allocation of visual attention has an intensifying effect on contrast perception. Beyond contrast, similar intensifications of visual properties have also been reported for spatial frequency (Gobell & Carrasco, 2005) and motion speed (Turatto et al., 2007). Subsequent research, however, has challenged the perceptual explanation but merely attributed the effect to decisional biases. Supporting evidence for decisional effects that might have affected response behavior in the experiments of Carrasco et al. (2004) emerges from studies demonstrating that response behavior varies across different task instructions (Schneider & Komlos, 2008; Schneider & Malik, 2021; Valsecchi et al., 2010) as well as showing that the intensified contrast is most pronounced in situations with high perceptual uncertainty (Itthipuripat et al., 2019; Kerzel et al., 2010).

While all the aforementioned studies used peripheral visual cues to guide attention toward the cued location, visual attention could also be guided by auditory cues. For instance, Störmer et al. (2009) reported that a spatially informative tone preceding the presentation of two Gabor patches could elicit a similar effect as a visual cue in the study of Carrasco et al. (2004). In other words, the attentional guidance by the spatial tones also seemingly increased the perceived contrast of the Gabor patch at the cued location. Besides preceding spatially informative tones such as in the study of Störmer et al. (2009), several findings from multimodal studies suggest that pure temporal coincidence of spatially uninformative tones and changes in the visual display could also attract visual attention. For instance, van der Burg et al. (2008; see also van der Burg et al., 2011) showed that coincidence between a spatially uninformative tone and an irrelevant color change in a visual search task substantially reduced the search slope (i.e., the increase in response latencies with increasing search load). Similarly, Staufenbiel et al. (2011) reported that visual direction changes of moving objects could be identified more efficiently when they coincide with a brief spatially uninformative tone.

In a recent study, we observed an audio-visual illusion that suggests that attentional guidance by audio-visual coincidence also might be capable of intensifying visual percepts (Meyerhoff et al., 2022). In this study, we presented two objects that moved about the screen occasionally changing their direction of motion. Between the trials, we varied the motion speed of one of the objects and asked the participants to indicate the object which they perceived as moving faster. Critically, a brief nonspatial tone coincided with the direction changes of the object that moved at the same speed in every trial (we call this the audio-visual object), whereas no such coincidence was present for the object for which we manipulated speed across trials (we call this the visual object). Borrowing measures from psychophysics (in this terminology, the audio-visual object served as standard, whereas the visual object served as comparison), we observed a shift in the point of subjective equality (PSE). This shift signaled that the visual object needed to move approximately 5% faster than the audio-visual object to appear moving at the same speed (i.e., have the same probability to be indicated as moving faster). The same illusion emerged when eye movements were controlled for, ruling out differential speed processing between central and peripheral visions as a potential explanation (e.g., Hassan et al., 2016). Because we observed a similar modulation of perceived object speed when we used (peripheral) visual cues to guide spatio-visual attention to one of the objects (see Lu & Zhou, 2005), we considered attentional guidance to be responsible of the shift in the PSE. Similar to the allocation of attention on contrast perception in the visual domain (e.g., Carrasco et al., 2004; Schneider & Komlos, 2008), it remains unclear whether the beep-speed illusion emerges from perceptual (i.e., a change in the percept; see Carrasco et al., 2004) or decisional (i.e., a change in the interpretation of the otherwise identical percept; see Schneider & Komlos, 2008) processing. Whereas this question is highly theoretically relevant, there is one further alternative explanation that would render the beep-speed illusion rather pointless.

We refer to this alternative explanation as the selection bias hypothesis. Consider the following scenario: A participant in the experiment perceives both discs as moving at the same speed in a particular trial. Due to the two-alternative forced-choice procedure, the participant needs to indicate one of the objects as moving faster than the other anyway. Typically, one would expect that the participant guesses in such a scenario which would leave the PSE unaffected. However, the participants might become aware that there is a synchronized audio-visual object. If the participant would simply select this object at the end of the trial (instead of guessing), a shift in the PSE would be observable, which might be misinterpreted as an illusory increase in perceived speed. Similar selection biases have been discussed for the presence of peripheral cues in purely visual studies on the effect of attention on object appearance (Anton-Erxleben et al., 2007; Carrasco et al., 2004; Turatto et al., 2007). Obviously, such a process would rather be an artifact than a theoretically relevant mechanism.

In the present paper, we therefore aimed at ruling out the selection bias hypothesis. More specifically, we tested whether participants simply select the audio-visually synchronized object in situations of perceptual uncertainty. The main reason why this simple selection bias cannot be ruled out with the experiments in our previous study (Meyerhoff et al., 2022) is that we always instructed our participants to indicate the object that appeared to move faster than the other. Therefore, a simple selection bias favoring the audio-visual object would mimic the result pattern of theoretically more relevant perceptual or decisional explanations and thus undermine the relevance of the beep-speed illusion for exploring the effects of attention on perceptual phenomenology. To rule out the selection bias hypothesis, we manipulated the task instructions. More specifically, inspired by previous research on object appearance within the visual domain (Anton-Erxleben et al., 2007; Carrasco et al., 2004; Turatto et al., 2007), we reversed the task instructions. In one block of the experiment, the participants indicated the object which appeared to move faster. This condition replicates the original report of the beep-speed illusion. In the other block, the participants were instructed to indicate the object which appeared to move slower. The order of the task instructions was counterbalanced between participants. In the condition with the instruction to indicate the faster object, we expect to replicate the original report of the beep-speed illusion which would be a shift of the PSE, indicating that the audio-visual object appeared to move faster than the visual object. With regard to the instruction to indicate the slower object, however, we should observe the inverse result pattern if the selection bias hypothesis can account for the shift of the PSE. This is because the participants should select the audio-visual object as the last attended object, irrespective of the task instructions. In contrast, if the shift of the PSE is equally pronounced in the direction of perceiving faster motion of the audio-visual object in both instruction conditions, this would likely rule out the simple selection bias hypothesis.

Methods

The experiment has been pre-registered at the Open Science Framework (OSF). The pre-registration is available at https://osf.io/dzf2b. All materials, raw data, and analysis scripts, which are necessary to replicate the experiment or the results of the analysis, are available at https://osf.io/txbqy/. A demonstration video of the beep-speed illusion is available at https://www.iwm-tuebingen.de/public/realistic_depictions_lab/beep_speed_illusion.

Participants

Following our pre-registration, 50 participants completed the online experiment. We recruited our participants from our regular pool of students (i.e., the same population that would normally come to the lab). Each participant received an individual link to participate in the experiment and had to send back a completion code when finished. In return for their participation (approx. 30 min), the participants received a 5€ voucher of a big online marketplace. The experimental procedure was ethically approved by the institutional review board of the Leibniz-Institut für Wissensmedien, Tübingen. All participants provided informed consent prior to testing. The data of one participant were not stored on the server, one participant maintained to indicate the faster object, irrespective of the change in the instruction, and data from three further participants were excluded (see the Results section for details). The final sample therefore consisted of 45 students (32 female, 12 male, one diverse; 19–59 years). Within this final sample, 22 participants started with the block in which they were instructed to indicate the faster of the two moving objects, whereas the remaining 23 participants started with the block in which they were instructed to indicate the slower of the two moving objects.

Our motivation for this rather large sample size (for this kind of research) emerged from the following considerations. There are two relevant effect sizes for our study. The first one is the effect size of the beep-speed illusion itself (i.e., the deviation of the point of subjective equality from the point of objective equality). In our initial report of the beep-speed illusion, the lowest corresponding effect size in three experiments was dz = 0.77. Based on this effect size, we used G*Power (Faul et al., 2007) to calculate a recommended sample size with a power of (1 − β) > .95 at α = .05 (two-tailed). The recommended sample size was a minimum of 24 participants. However, the initial experiments on the beep-speed illusion were lab-based, whereas this experiment was conducted online (due to the COVID-19 pandemic). We therefore decided to increase this number to 50 participants to compensate for potential exclusions, technical problems, and potentially weaker manifestations of the illusion in an online environment.

The second relevant effect size for our study is the difference in the magnitude of the beep-speed illusion between the blocks with different response instructions (i.e., indicate the faster vs. indicate the slower moving object). There were no existing data which we could use to calculate power for this effect. However, the simple selection bias hypothesis suggests a reversal of the beep-speed illusion in the block in which participants indicate the slower object. Therefore, we have calculated such a scenario with the data from our initial report of the beep-speed illusion (i.e., considering a second condition with an inverted sign of the beep-speed illusion). This calculation suggests an effect size of dz = 1.56. This effect is larger than the presence of the beep-speed illusion itself (suggested sample size of eight participants) and therefore did not further contribute to the sample size considerations.

Apparatus

The experiment was coded in JavaScript using the PsychoPy3 libraries (Peirce, 2007). The experiment was run on the pavlovia.org servers (https://pavlovia.org/). All participants used their personal computer or notebook to complete the experiment (either in the Firefox or in the Chrome browser). The auditory stimuli were administered either by loudspeakers or headphones depending on the individual setup of the participants. Before the start of the actual experiment, the participants were able to adjust their sound setup (repeatably if necessary) so that they could clearly hear the tones that were presented in the experiment.

Stimuli and Procedure

Given the to-be-expected variability in the screen sizes, we coded all stimulus sizes relative to the height of the window using the corresponding PsychoPy3 functions (i.e., a value of 1 corresponded to the full height of the window). As our experiments were presented in full-screen mode, this matched with the height of the monitor. We chose all stimulus sizes so that they roughly correspond to the values of the initial report of the beep-speed illusion (Meyerhoff et al., 2022) if the experiment would be presented on a 23″ monitor at a viewing distance of 60 cm. In this scenario, a height of one would approximately correspond to 28° of visual angle (see Figure 1).

Figure 1. Schematic illustration of the stimulus display and the task. The two objects moved changing their motion directions occasionally (fading indicates motion history). For the audio-visual object (depicted left in this example), the changes in motion direction coincided with a brief tone. The speed of the visual object (depicted right) varied across trials to obtain the point of subjective equality for faster/slower judgments.

Figure 1

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Figure 2. Illustration of the results in the block in which participants indicated the faster moving object (upper panel) and the block in which the participants indicated the slower moving object (lower panel). Block order was counterbalanced across participants. The black dots illustrate group mean data; the error bars indicate within-subject confidence intervals. The dashed lines illustrate individual fits of the psychometric functions. Points of subjective equality (dotted lines) larger than 1 (solid line) signal the presence of the illusory increase in speed of the audio-visual object.

Figure 2

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The visual display consisted of two white discs (0.014 heights in diameter) that moved against a black background. To keep the discs in spatially distinguishable locations, each of the discs moved inside an invisible square of 0.48 × 0.48 heights that were located to the left and the right of the center of the screen (separated by 0.05 heights). The object motion consisted of three intervals of 1,000 ms. In each of these intervals, both objects changed their direction of motion with an angular difference between the old and new motions between 60° and 120°. The only spatial restriction for the motion paths was that no object was allowed to touch any of the borders of the invisible squares. Additionally, there were two temporal restrictions. First, there was a minimum interval of 250 ms between any direction changes. Second, no direction change could appear in the first or final 250 ms interval of each trial. The trials were generated offline. To eliminate any potential influences of the motion paths, we generated a new set of trials for each participant. Additionally, we presented each trial four times to each participant, once in each hemifield (i.e., right and left sides of the screen) in each instruction condition (i.e., indicate faster vs. slower object).

The motion speed of one of the objects was 0.11 heights/s. A brief nonspatial tone (500 Hz, 60 ms) coincided with the direction changes of this object. We therefore refer to this object as the audio-visual object. The remaining object moved without coinciding tones. We therefore refer to this object as the visual object. The speed of the visual object varied between the trials (0.03 heights/s, 0.08 heights/s, 0.09 heights/s, 0.10 heights/s., 0.11 heights/s, 0.12 heights/s, 0.13 heights/s, 0.14 heights/s, and 0.19 heights/s). For the sake of simplicity, we converted these speed values as relative to the speed of the audio-visual object (i.e., 0.27, 0.73, 0.82, 0.91, 1, 1.09, 1.18, 1.27, and 1.73). At the end of the motion interval, the discs disappeared from the screen, and the participants provided their response by pressing the X key (for the object moving on the left side) or the M key (for the object moving on the right side). There were two different instruction conditions. The participant either responded to the object which they perceived to move faster or the object which they perceived to move slower. The instruction condition was manipulated within subjects. Each participant completed four blocks of 36 trials (preceded by 10 practice trials) within one of the instruction conditions before switching to the remaining instruction condition for another four blocks of 36 trials (again preceded by 10 practice trials).

Results

For the analysis, we first recoded the binary responses of our participants (i.e., left/right object moving faster/slower) into a binary value indicating whether the participants indicated the audio-visual object as moving faster than the visual object. Following our pre-registration, we then checked for each participant in each condition whether the responses varied with the objective differences in the speed of the visual object (otherwise this would indicate random response behavior). To do so, we fitted the binary variable indicating whether the participants reported the audio-visual object to move faster than the visual object using generalized linear models with logit linking functions. We fitted two models for each participant and condition. The first model only included an intercept representing the general tendency to mark the audio-visual object as moving faster. The second model included the intercept and a slope for the objective speed of the visual object. For all participants and in each condition, the model with the slope explained the data significantly better (i.e., the increase in explained variance was worth adding the additional parameter). This model check revealed that one participant persisted to indicate the faster object (which was the task for this participant in the first block) in the block with the instruction to indicate the slower object. We excluded the data from this participant as this likely emerged from not reading the instruction of the second block. For the remaining participants, the model check confirmed that they varied their responses in accordance with the objective differences in the speed of the visual object and thus likely followed the task instructions. From the models with the slope parameter, we then calculated the point of subjective equality (i.e., the speed value of the visual object at which both objects appear to move at the same speed) for each participant and each instruction condition. For three of the participants, one of the two PSEs deviated more than 3 SD from the group mean of the corresponding condition. We therefore excluded the data from these participants for the further analysis.1

Beep-Speed Illusion (Confirmatory)

Following our pre-registration, we first analyzed how the coinciding tones affected perceived object speed in both instruction conditions. We therefore used one sample t-tests to investigate whether (and how) the beep-speed illusion emerges under both instruction conditions. To estimate confidence intervals of all reported effect sizes, we used a bootstrapping procedure with 10,000 iterations.

We observed the beep-speed illusion in both instruction conditions. In the condition in which the participants indicated the faster of the two objects, we observed a shift of the PSE toward an increased speed of the visual object, M = 1.06 (SD = 0.06). In other words, the visual object had to move approximately 6% faster than the audiovisual object to appear to be equally fast. This shift of the PSE is significant, t(44) = 6.44, p < .001, dz = 0.96, 95% CI [0.72, 1.29]. In the condition in which the participants indicated the slower one of the two objects, we observed an almost equal shift of the PSE, M = 1.08 (SD = 0.06). In other words, the visual object had to move approximately 8% faster than the audiovisual object to appear to be equally fast. This shift of the PSE also was significant, t(44) = 8.94, p < .001, dz = 1.33, 95% CI [0.97, 1.91]. A direct comparison of the PSEs in both instruction conditions revealed no evidence for a potential difference, t(44) = 1.59, p = .119.

Just Noticeable Differences (Exploratory)

Beyond the PSEs, we also extracted the just noticeable differences (JND; i.e., the difference in speed of the visual object between the 50% and 75% thresholds). The JND values for the block in which participants indicated the faster object, M = 0.21, SD = 0.12, and the block in which participants indicated the slower object, M = 0.22, SD = 0.09, did not differ from another, t(44) = .72, p = .473.

Effect of Task Order (Exploratory)

Because we counterbalanced the order of the instruction conditions in a blocked design, we conducted an exploratory analysis to rule out that there are effects of the order of the blocks, which would prevent a straightforward interpretation of the results. We therefore analyzed the PSEs using an ANOVA for mixed designs with instruction conditions as a within-subject factor and the order of the instruction conditions as a between-subject factor. This analysis provided no evidence for a relevant influence of the task order. Neither the main effect of the order, F(1, 43) < 1, nor the main effect of the instruction, F(1, 43) = 2.53, p = .118 (replicating the result from the t-test above), nor the interaction with the order and the instruction, F(1, 43) = 1.18, p = .284, reached significance (see Table 1).

Table 1. M (SD) data for the analysis of the task order.

Instruction condition Order
Faster first Slower first
M (SD) M (SD)
Note. M = mean; SD = standard deviation.
Faster 1.06 (0.06) 1.06 (0.06)
Slower 1.06 (0.06) 1.09 (0.06)
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Discussion

The results of the present experiment replicate and extend the original beep-speed illusion (Meyerhoff et al., 2022). Our participants reported the audio-visual object as seemingly moving faster, irrespective of the task instructions. That is, in the condition in which they were instructed to indicate the faster moving object, they selected the audio-visual object, whereas they selected the visual object in the condition in which they were asked to indicate the slower moving object. The most important implication of this finding is that participants do not simply respond with the last attended object (i.e., the audio-visual object), as suggested by the rather simplistic selection bias hypothesis. Ruling out this alternative explanation was relevant as it would reflect an experimental artifact rather than a theoretically interesting process. A further rather methodological issue that needs to be considered is that the objective differences (i.e., 0.5°/s per step) in the speed manipulation do not necessarily have to match with the corresponding perceptual spacing. For instance, if the perceived differences in speed would be larger for decreasing speeds than increasing speeds of the visual object, a similar shift in the PSE would emerge even in the absence of an illusion.2 There are two observations that seem to rule out this alternative explanation (at least for the range of speed values that we used in the present study). First, the visual inspection of our results in the present study suggests that the fitted curves are symmetrical rather than systematically biased to decreasing or increasing speeds. Second, using similar speed values, we observed no shift in the PSE in a condition in which the beep was replaced by a flashing frame in our initial report of the beep-speed illusion (Meyerhoff et al., 2022, Experiment 2). Unequal perceptual spacing, however, would predict a shift in the PSE in this experiment as well. Taken together, our findings therefore highlight the importance of investigating the origin of the recently reported beep-speed illusion as it cannot be attributed to simple methodological constrains.

In analogy to the research on visually guided attention, there are two plausible candidate mechanisms that might elicit the beep-speed illusion. The first candidate is that the cross-modally induced allocation of attention intensifies the speed percept. This suggestion is in agreement with the above reviewed reports that suggest that transient attention intensifies percepts along multiple stimulus dimensions, including contrast (e.g., Anton-Erxleben et al., 2011; Carrasco et al., 2004), spatial frequency (Gobell & Carrasco, 2005), or object and gap size (Anton-Erxleben et al., 2007; Gobell & Carrasco, 2005; Kirsch et al., 2018; for further examples, see Carrasco & Barbot, 2019). It seems noteworthy that previous research has already ruled out eye movements as a potential origin of the differences in perceived speed (Hassan et al., 2016) as the beep-speed illusion emerges equally strong with enforced central fixation (Meyerhoff et al., 2022). The second candidate is that the allocation of attention alters decisional criteria rather than perception. This suggestion receives support from the observation that illusory intensifications of percepts vary remarkably across different paradigms (Schneider, 2011; Schneider & Komlos, 2008; but see Anton-Erxleben et al., 2011). For the beep-speed illusion, such a decisional bias might arise from the possibility that the participants experience the objects as moving identically fast. Because they are forced to decide which one moves faster (two-alternative forced-choice paradigm), they might search for other cues indicating speed, such as the coinciding sound. Thus, exploring the beep-speed illusion across various paradigms would be highly informative for distinguishing between perceptual processing and decisional processing. Of most interest would be a paradigm in which the participants could also select the response that both objects appear to move equally fast or a paradigm in which the participants judge whether the objects are moving at equal or different speeds. Such an approach would be helpful for distinguishing perceptual and decisional processing (Schneider & Komlos, 2008), as well as investigating whether the magnitude of the beep-speed illusion exceeds the threshold of conscious awareness (see Valsecchi et al., 2010). One particular strength of the beep-speed illusion for further understanding the effect of attentional allocation on perception is that it does not require a visual cue for the attentional guidance so that cue-target interactions (Schneider, 2006) do not further complicate the interpretation of the results. Furthermore, the beep-speed illusion emerges with fully visible stimuli so that biases emerging from perceptual uncertainty are unlikely (see Itthipuripat et al., 2019).

Conclusion

We showed that the beep-speed illusion does not emerge from an experimental artifact, namely that participants do not select the audio-visual object, irrespective of task instructions. As such, the present experiment rules out the simplest of the possible response biases (and the one which would remove the theoretical relevance from the beep-speed illusion). Against the background of our findings, the new beep-speed illusion is a valid tool to investigate direct effects of the allocation of attention on visual perception.

Open Data: The experimental script, raw data, and the script for the analyses of this study are available at https://osf.io/txbqy/ (Meyerhoff et al., 2023). The formal pre-registration of the experiment is available at https://osf.io/dzf2b/ (Meyerhoff, 2022).

Funding Statement

Funding: Open access publication enabled by the University of Erfurt.

Footnotes

1

We forgot to pre-register this exclusion criterion. Nevertheless, we excluded these data points in accordance with common scientific practice as well as our own previous work on the beep-speed illusion (Meyerhoff et al., 2022). To make sure that this has no effect on the interpretation of our results, we reran all analyses with the data from all 49 participants (i.e., including outliers). There were no changes in the significance of any reported effect.

2

We thank an anonymous reviewer for bringing this alternative explanation to our attention.

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