For each participant, the mean number and the standard deviation of perceived flashes were calculated for each condition, and in many of the experiments, participants also reported perceived location of the flashes; these data were aggregated based on how many flashes participated on a given trial. In several cases, assumptions underlying parametric statistics were violated, so throughout our analyses, we used non-parametric statistics to test for differences between conditions. Initial data processing was conducted using MATLAB; statistical analyses were conducted using SPSS statistics. When recommended by SPSS (due to small number of cases), we used exact p-values based on the binomial distribution. To facilitate comparisons across experiments, we reported the standardized test statistic z wherever possible. Data are available via the Open Science Framework .

Part 1: Illusory Audiovisual (AV) rabbit

Experiment 1.1 Illusory flashes (N = 7) (Block 1). The first step in investigating the Illusory AV Rabbit is to show that an illusory flash is perceived due to the presence of a beep, when that beep is preceded and followed by flash-beep pairs. Therefore, in the first experiment participants recorded the number of flashes perceived when a variety of beep-flash stimuli are presented (further experimental parameters are described in the methods section). Fig 3A shows that the Illusory AV Rabbit (3b2f) stimulus caused participants to report perceiving more flashes (Mdn = 2.52, M = 2.64, SD = 0.31) than an identical stimulus without the second unpaired beep (2b2f) (Mdn = 2.04, M = 2.10, SD = 0.15). Both conditions showed significant deviations from normality using the Shapiro-Wilk test, thus we used the Related-Samples Wilcoxon Signed Rank Test to compare these conditions. This difference was statistically significant (z = 2.536, p = 0.011, r = 0.634). Therefore, the presence of an unpaired beep (preceded and followed by flash-beep pairs), is causing an illusory flash in the Illusory AV Rabbit (3b2f) stimulus. This result was replicated by Experiment 1.2, 1.3, 1.4 (different participants), and 1.5, which have different designs and goals but repeat the 3b2f (rabbit) and 2b2f conditions. PPT PowerPoint slide

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larger image TIFF original image Download: Fig 3. Illusory AV rabbit results. Fig 3A plots the number of flashes perceived for several beep and flash stimuli presented in Experiment 1.1. Fig 3B shows the confidence rating reported for perceiving three flashes for the Illusory AV Rabbit stimulus in comparison to non-illusory stimuli. Fig 3C plots the reported flash locations (in centimeters) across participants for the Illusory AV Rabbit stimulus, when three flashes are reported. Error bars are standard deviation. https://doi.org/10.1371/journal.pone.0204217.g003 To further obtain converging statistical evidence, we conducted several additional analyses. The difference between the number of flashes perceived in the 0b2f (Mdn = 2.24, M = 2.34, SD = 0.31) and the 2b2f conditions was not statistically significant (z = 1.825, p = 0.068, r = 0.456). We also conducted one-sample Wilcoxon Signed Rank Tests to compare each of the three tested conditions to the veridical value of two flashes; in all three cases, the difference in perceived flashes was statistically significant (3b2f: z = 2.536, p = 0.011, r = 0.0897; 0b2f: z = 2.371, p = 0.018, r = 0.838; 2b2f: z = 2.032, p = 0.042, r = 0.718). Finally, in order to confirm that the illusion strength was not substantially modulated by repetitive experiences of the illusion we investigated if the illusory strength significantly varied over the experimental duration (i.e. repetitions of trials). To test this, a direct comparison of the first and last 50 trials (1/3 of the trials) for the Illusory AV Rabbit (3b2f) condition was performed using the Related-Samples Wilcoxon Signed Rank Test. There was no significant difference between the first and last third of the trials for the 3b2f Illusory AV Rabbit condition (z = 0.676, p = 0.499, r = 0.169) or for the 2b2f condition (z = 0.000, p = 1.000, r = 0.000); however, there was a significant difference for the 0b2f condition (z = 2.383, p = 0.017, r = 0.596), such that more flashes were reported in the first 50 trials (Mdn = 2.35, M = 2.46, SD = 0.39) than in the last 50 trials (Mdn = 2.11, M = 2.24, SD = 0.32).

Experiment 1.2: Illusory rabbit location (N = 7–8) (Block 2). Analysis of the reported number of flashes perceived by each participant replicated the original effect described in Experiment 1.1; participants reported seeing more flashes in the 3b2f condition (Mdn = 2.54, M = 2.54, SD = 0.34) than in the 2b2f (Mdn = 2.00, M = 2.05, SD = 0.07) or 0b2f (Mdn = 2.18, M = 2.20, SD = 0.19) conditions, though fewer than in the 3b3f condition (Mdn = 2.89, M = 2.81, SD = 0.24). We used the Related-Samples Wilcoxon Signed Rank Test to compare the 2b2f and 3b2f conditions, as these were the critical conditions for replicating our effect. The difference between the 3b2f and 2b2f conditions was statistically significant, (z = 2.366, p = 0.018, r = 0.592). While the first experiment showed that an illusory flash is perceived in the Illusory AV Rabbit (3b2f), it did not indicate where that flash is located. This second experiment asks participants to report the number of flashes and then the locations of each of the flashes perceived. The trials in which three flashes were perceived for the Illusory AV Rabbit (3b2f), were used to generate a distribution of locations reported for each flash (Fig 3C). The veridical flashes were located at positions of −1.42, and 1.42 degrees. Of the eight participants who took part in this experiment, one participant did not ever report seeing the illusory flash (this participant also reported seeing only two flashes on the majority of trials in which three physical flashes were presented), and thus only data from the other seven participants was analyzed for location. For each of the other participants, the mean reported location of each flash was calculated for each condition. When three flashes were reported, the reported positions of the first and third flashes were shifted substantially away from the center, while the second flash was perceived to be located in the approximate center of the two physical flashes. The median reported position (across observers) for the first flash was -2.40 degrees (M = –2.63 degrees, SD = 1.19 degrees), the median reported position for the second flash was −0.15 degrees (M = -0.50 degrees, SD = 0.97 degrees), and the mean reported position for the third flash was 2.29 degrees (M = 2.47 degrees, SD = 0.96). We used the Jonckheere-Tempstra test, which allows testing for an ordered pattern of medians. This test does not take into account repeated measures, and thus is overly conservative for our design, but repeated measures tests such as Friedman’s ANOVA do not allow testing for a particular hypothesis about order. In this case, we hypothesized that the second flash would be perceived in between the veridical flashes. For center-to-right motion, each flash was perceived further to the right than the prior flash (z = 4.478, p < 0.001, r = 0.978), with all pairwise comparisons significant. Thus, we conclude that the second flash was perceived to appear at a different location from, and in between the first and third locations. This is suggestive that the Illusory AV Rabbit is postdictive in mechanism, as the third flash is not shown until after the second stimulus is finished. We conducted several additional analyses. The first of these analyses compared the reported locations of the first and last flashes in the 3b2f condition in which an illusion was perceived with those in which an illusion was not perceived. One participant saw the illusion on every 3b2f trial, and thus was excluded from this analysis. Every one of the six remaining participants showed the same pattern of responses: reporting the first and last flash as further from the center on trials in which they experienced an illusion than trials on which they didn’t experience an illusion (see Table 1). Using the Related Samples Wilcoxon Signed Rank Test to compare the locations, we found the difference was statistically significant (z = 2.524, p = 0.031, r = 0.729). PPT PowerPoint slide

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larger image TIFF original image Download: Table 1. Experiment 1.2 illusory rabbit location. https://doi.org/10.1371/journal.pone.0204217.t001 Additional data analyses are included in the supplemental information.

Experiment 1.3: Prior knowledge of stimuli direction with location: A critical test for postdictiveness (N = 8) (Block 3). For the number of flashes reported, the results were again consistent with that of Experiment 1.1; participants often reported seeing three flashes in the 3b2f conditions (for center-to-left motion, Mdn = 2.80, M = 2.69, SD = 0.34 and for center-to-right motion, Mdn = 2.73, M = 2.63, SD = 0.35), more frequently than in the 2b2f conditions (for center-to-left motion, Mdn = 2.03, M = 2.04, SD = 0.05 and for center-to-right motion, Mdn = 2.00, M = 2.05, SD = 0.08) and the 0b2f conditions (for center-to-left motion, Mdn = 2.27, M = 2.29, SD = 0.23 and for center-to-right motion, Mdn = 2.20, M = 2.27, SD = 0.21). Comparisons were made using the Related-Samples Wilcoxon Signed Rank Test; for both directions, significantly more flashes were perceived in the 3b2f conditions than in the 2b2f conditions (all p < 0.05). In order to prevent prediction of the final flash location in the Illusory AV Rabbit, we randomized the direction that the flashes moved. In Experiment 1.3, participants reported the number of flashes perceived, and indicated the locations of those flashes, similar to Experiment 1.2. Table 2 indicates the mean reported location of each flash (averaged across observers) for the trials in which participants reported seeing three flashes (Table 1). Note that the veridical locations of the first and final flash were at 0 and +/- 2.84 degrees. PPT PowerPoint slide

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larger image TIFF original image Download: Table 2. Experiment 1.3 Prior knowledge of stimuli direction with location. https://doi.org/10.1371/journal.pone.0204217.t002 Participants reported that the middle flash of the Illusory AV Rabbit (2b3f) was perceived between the first and last flash, independent of the direction of flash movement. As with Experiment 1.2, we used the Jonckheere-Tempstra test, which allows testing for an ordered pattern of medians. This test does not take into account repeated measures, and thus is overly conservative for our design, but repeated measures tests such as Friedman’s ANOVA do not allow testing for a particular hypothesis about order. In this case, we hypothesized that the second flash would be perceived in between the veridical flashes. For center-to-right motion, each flash was perceived further to the right than the prior flash (z = 4.867, p < 0.001, r = 0.993), with all pairwise comparisons significant. Similarly, for center-to-left motion, each flash was perceived further to the left than the prior flash (z = -4.444, p < 0.001, r = -0.907), with all pairwise comparisons significant. Therefore, even when the location of the final flash is unpredictable, the second illusory flash is perceived between the final and first flashes. This direction randomization further verifies that postdiction rather than prediction generates the Illusory AV Rabbit. Additional data analyses are included in the supplemental information.

Experiment 1.4: Eccentricity variation of the illusory AV rabbit (N = 5) (Block 4). It is interesting to investigate if changes to the eccentricity of the visual stimulus impact the strength of the Illusory AV Rabbit, as it does in similar illusions (such as the double flash illusion) [18, 19]. We tested this hypothesis by varying the eccentricity of the flash location between three locations (Near ~ 4 degrees, Middle ~ 10 degrees, Far ~ 16 degrees), where an increase in eccentricity may decrease the visual signal to noise ratio. Participants reported the number of flashes perceived. At all eccentricities, the Illusory AV Rabbit replicated successfully in this new group of participants. We used the Related-Samples Wilcoxon Signed Rank Test to separately test for the effect at each eccentricity by comparing the 3b2f conditions to the 2b2f conditions, and found significant differences in all three cases (all p < 0.05), confirming the replication of the illusion. We used Friedman’s ANOVA to test for differences in the effect size by examining the number of flashes perceived in the 3b2f condition perceived at each of the three locations; we found that, although there was a trend of increased illusion strength at the farthest distance (near Mdn = 2.86 reported flashes, M = 2.64 reported flashes, SD = 0.41; middle Mdn = 2.80 reported flashes, M = 2.79 reported flashes, SD = .28; far Mdn = 3.00 reported flashes, M = 2.88 reported flashes, SD = 0.25), the differences were not statistically significant, X2 F (2) = 3.263, p = 0.196. These results indicate that the Illusory AV Rabbit could be resistant to change across eccentricity (within the tested range); if true this would draw an interesting contrast to similar illusions (such as the double flash illusion) which alter with eccentricity [18, 19]. Additional experiments with participant gaze verified by eye-tracking would further clarify the impact of eccentricity.