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Article  |   July 2016
Dyslexics' usage of visual priors is impaired
Author Affiliations
  • Sagi Jaffe-Dax
    Edmond and Lily Safra Center for Brain Sciences, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Jerusalem, Israel
    sagi.jaffe@mail.huji.ac.il
  • Itay Lieder
    Edmond and Lily Safra Center for Brain Sciences, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Jerusalem, Israel
    itay.lieder@mail.huji.ac.il
  • Tali Biron
    Department of Neurobiology The Hebrew University of Jerusalem, Edmond J. Safra Campus, Jerusalem, Israel
    tali.biron@gmail.com
  • Merav Ahissar
    Edmond and Lily Safra Center for Brain Sciences, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Jerusalem, Israel
    Department of Psychology, The Hebrew University of Jerusalem, Mt. Scopus Campus, Jerusalem, Israel
    msmerava@gmail.com
Journal of Vision July 2016, Vol.16, 10. doi:10.1167/16.9.10
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      Sagi Jaffe-Dax, Itay Lieder, Tali Biron, Merav Ahissar; Dyslexics' usage of visual priors is impaired. Journal of Vision 2016;16(9):10. doi: 10.1167/16.9.10.

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Abstract

Human perception benefits substantially from familiarity, via the formation of effective predictions of the environment's pattern of stimulation. Basic stimulation characteristics are automatically retrieved and integrated into our perception. A quantitatively measurable manifestation of the integration of priors is known as “contraction to the mean”; i.e., perception is biased toward the experienced mean. We previously showed that in the context of auditory discrimination, the magnitude of this bias is smaller among dyslexic individuals than among good readers matched for age and general reasoning skills. Here we examined whether a similarly reduced contraction characterizes dyslexics' behavior on serial visual tasks. Using serial spatial frequency discrimination tasks, we found that dyslexics' bias toward the experiment's mean spatial frequency was smaller than that observed for the controls. Thus, dyslexics' difficulties in automatic detection and integration of stimulus statistics are domain-general. These difficulties are likely to impede the acquisition of reading expertise.

Introduction
Dyslexia is a persistent difficulty in acquisition of proficient reading skills. It is a specific deficit in the sense that dyslexics' general reasoning skills are within the normal range of the population of good readers or above (Snowling, 2000). Thus, their reading difficulty cannot be considered a consequence of a broad cognitive difficulty. Nevertheless, dyslexics' difficulties span a range of language-related skills (Snowling & Melby-lervåg, 2016), whose common denominator is still controversial (Ramus & Ahissar, 2012). Dyslexics have persistent difficulties in manipulating speech sounds (phonological awareness) and in fast serial naming of highly familiar symbols (rapid automatized naming; Wolff, Michel, & Ovrut, 1990). Their poor working memory has also been amply documented in the verbal domain (Snowling, 2000) but only sparsely studied and not well understood for nonverbal stimuli (e.g., Banai & Ahissar, 2004, 2006). 
Dyslexic individuals perform worse than than adequate readers on a range of serial perceptual discrimination tasks (e.g., Ahissar, Protopapas, Reid, & Merzenich, 2000; Hämäläinen, Salminen, & Leppänen, 2013; McAnally & Stein, 1996; Temple et al., 2000; Witton et al., 1998). These tasks necessarily rely on perceptual memory for stimulus retention during the interstimulus interval (ISI; Pasternak & Greenlee, 2005). In most situations, the load of online retention is aided by longer-term priors, based on either recent or earlier acquired priors. For example, when a specific stimulus is used as a reference that repeats across trials, this reference is used as a prior (internal anchor) to improve performance (Nahum et al., 2010). Dyslexics benefit less from such references (perceptual anchors) than controls (Ahissar, 2007; Ahissar, Lubin, Putter-Katz, & Banai, 2006; Oganian & Ahissar, 2012). Consequently, making accurate comparisons is even more demanding. In particular, it is difficult to determine whether dyslexics' explicit retention is impaired or whether only their ability to reduce some of this retention load by reliance on priors is impaired. 
Serial discrimination tasks place an asymmetric load on sequentially presented stimuli. The stimulus presented first has the highest memory load because it needs be retained until the subsequent stimulus is presented. Hence, relying on priors to compensate for noisy representations is crucial for this stimulus. Priors can be utilized to modify noisy representations into “more likely” stimuli, those based on previous exposures that led to the formation of priors. The integration of priors has been modeled computationally in the context of auditory perception for signal detection tasks (Treisman & Williams, 1984) and recently for two-tone frequency discrimination (Raviv, Ahissar, & Loewenstein, 2012; Raviv, Lieder, Loewenstein, & Ahissar, 2014; reviewed in Bausenhart, Bratzke, & Ulrich, 2016). Raviv et al.'s (2012) model asserts that participants do not compare the representations of the first and second tones as requested to do and as they do introspectively. Rather, they compare the representation of the second tone to the integrated representation of the first tone with the estimated mean (prior) of previous stimuli. Thus, the representation of the first tone is contracted toward the mean of previous trials, and when this contraction is in the direction of the correct response, the success rate will increase. 
The “contraction to the mean” was first described more than a century ago when it was reported that individuals tended to choose a probe card that was too large when the memorized card was small compared to the other cards used in the experiment whereas the opposite behavior was observed when the memorized card was relatively large (Hollingworth, 1910). This type of bias was also found in delayed discrimination tasks, in which in each trial two consecutive stimuli are compared with respect to some chosen feature (Woodrow, 1933). Similar to observations for cards, subjects tended to overestimate the compared feature for the first of the two stimuli when it was small and underestimate it when it was large, effectively “contracting” it toward the mean of the distribution. As described above, the larger contraction of the first stimulus is explained in the Bayesian framework as stemming from its noisier representation by the time the second stimulus is presented. 
In sequential comparison tasks, contraction of the first stimulus toward the mean may either lead to increasing the perceived difference between the two stimuli or decreasing it. Accordingly, trials can be divided into those in which contraction increases the perceived difference between the two stimuli, hence increasing success rate (Bias+), and trials in which contraction decreases the perceived difference and decreases the success rate (Bias−). As illustrated in Figure 1B, trials in which the first stimulus is closer to the mean than the second stimulus benefit from this contraction whether both stimuli are above or below the mean (Bias+). In a complementary manner, trials in which the second stimulus is closer to the mean lose out from this contraction (Bias−; whether both are above or both are below the mean). The magnitude of the contraction can be quantified as the difference in performance on these two types of trials. 
Figure 1
 
Schematic illustrations of the sequential spatial frequency discrimination task and contraction toward the mean. (A) The temporal structure of a single trial. The first grating was presented for 250 ms, followed by an ISI of 500 ms. The second grating was presented for 250 ms. The observer was requested to indicate which of the two gratings had the higher spatial frequency (density). (B) The contraction bias division to trial types. The middle plot illustrates the distribution of single trials in the frequency plane (the frequencies of the first and second grating in each trial, respectively) for a typical subject. Each green dot denotes the pair of stimuli in a single trial. This plane illustrates the ranges of the different trial types. In Bias+ trials, the frequency of the first grating stimulus was closer to the mean frequency; thus, contraction of its representation toward the mean increased the perceived difference between the two gratings and consequently improved performance. In Bias− trials, the first grating was farther from the mean; thus, contraction of its representation toward the mean frequency decreased the perceived difference between the gratings and hampered performance.
Figure 1
 
Schematic illustrations of the sequential spatial frequency discrimination task and contraction toward the mean. (A) The temporal structure of a single trial. The first grating was presented for 250 ms, followed by an ISI of 500 ms. The second grating was presented for 250 ms. The observer was requested to indicate which of the two gratings had the higher spatial frequency (density). (B) The contraction bias division to trial types. The middle plot illustrates the distribution of single trials in the frequency plane (the frequencies of the first and second grating in each trial, respectively) for a typical subject. Each green dot denotes the pair of stimuli in a single trial. This plane illustrates the ranges of the different trial types. In Bias+ trials, the frequency of the first grating stimulus was closer to the mean frequency; thus, contraction of its representation toward the mean increased the perceived difference between the two gratings and consequently improved performance. In Bias− trials, the first grating was farther from the mean; thus, contraction of its representation toward the mean frequency decreased the perceived difference between the gratings and hampered performance.
Contraction bias in serial comparison tasks has been observed in the visual (Ashourian & Loewenstein, 2011; Fischer & Whitney, 2014; Lages & Treisman, 1998; Liberman, Fischer, & Whitney, 2014), auditory (Lu, Williamson, & Kaufman, 1992; Raviv et al., 2012; Treisman & Williams, 1984), and tactile (Hairston & Nagarajan, 2007) modalities and was even observed in tactile velocity discrimination tasks in rats (Fassihi, Akrami, Esmaeili, & Diamond, 2014) and vibro-tactile discriminations in monkeys (Romo, Hernández, Zainos, Lemus, & Brody, 2002). 
In the context of two-tone frequency discrimination, it was recently found that dyslexics' contraction bias is substantially smaller than controls' (Jaffe-Dax, Raviv, Jacoby, Loewenstein, & Ahissar, 2015). Importantly, the magnitude of the contraction bias differed across individuals even within the general population of good readers. Individuals contract in a way that is consistent with their noise level. Specifically, individuals who are noisier within the trial contract more to the average of previous trials. Given their level of noise, dyslexics underweight previous trial statistics and can therefore compensate less for their within-trial noise levels. Event-related potential measures collected when listeners were watching a silent movie suggest that dyslexics' deficit resides in the lesser sensitivity of their automatic memory mechanisms to recent statistics. 
Here we inquired whether dyslexics' reduced usage of perceptual priors would also be manifested on serial visual tasks. Previous work has shown that dyslexics' difficulty in visual discrimination tasks is restricted to sequential protocols, but their performance is intact on simultaneously presented stimuli (Ben-Yehudah & Ahissar, 2004; Ben-Yehudah, Sackett, Malchi-Ginzberg, & Ahissar, 2001). However, these visual studies only used typical protocols in which one of the stimuli in each pair is constant across trials (reference) and the other (target) is randomly drawn from a limited range (target). Hence, serial comparisons could be aided by priors (references, anchors) based on previous trials, and consequently, dyslexics' difficulties could be attributed to either poor explicit within-trial retention or to inefficient integration of priors (or both). In the current study, we used the sequential spatial frequency discrimination task with a richer protocol with which both gratings were randomly drawn from a wide range. Thus, in addition to the groups' average performance, this protocol served to assess the magnitude of the contraction bias, which reflects the efficiency of using priors based on previous trials. 
Materials and methods
Participants
Seventy-three students participated in the study; 33 with a diagnosis of dyslexia and 40 control participants. Only native Hebrew speakers with no other learning disabilities were included in the study. Participants were recruited through advertisements at the Hebrew University and through the university's support center for learning-disabled students. The two groups of participants were matched for age and gender. All were students attending institutes of higher education (either the Hebrew University or Jerusalem's Academy of Arts). All participants signed a written consent form describing the aims and the behavioral tasks in the study. Participants were reimbursed for their time according to standard hourly student rates. The study was approved by the Hebrew University Ethics Committee for Research Involving Human Subjects. 
The same group of subjects participated in an auditory discrimination study administered in a separate session (Oganian & Ahissar, 2012). 
Inclusion criteria
All participants' general cognitive scores, as assessed by the Block Design subset of the Wechsler Adult Intelligence Scale (WAIS-III; Wechsler, 1997) were within or above the normal range of the general population (scaled score of 7 or above, i.e., no less than 2 SD below the general population average). 
All dyslexic participants had been diagnosed with a specific reading disability. In addition, they had difficulties in phonological decoding or verbal working memory (i.e., they performed at least 2 SD below the norms of age-matched control students in either single-word reading or Digit Span or both) when tested in the lab. 
Cognitive assessments
General cognitive abilities were assessed on two subtests from the Hebrew version of the WAIS-III: Block Design for visuospatial reasoning abilities and Digit Span for verbal working memory (Wechsler, 1997). 
Phonological decoding—single pseudoword and real-word reading—was assessed using two standard Hebrew lists designed by Deutsch and Bentin (1996). One list contains 24 punctuated Hebrew words, and the other contains 24 punctuated pseudowords, i.e., words with Hebrew morphology but no meaning. Both accuracy and rate were scored. 
Apparatus and stimuli
Visual stimuli were presented on a 17-in. Trinitron Multiscan II Monitor with a frame rate of 100 Hz, using a VSG graphics card (VSG software version 5.02, Cambridge Research Systems). We wrote our experiments in Matlab, using the Psychophysics Toolbox extensions (Kleiner, Brainard, & Pelli, 2007). Mean luminance was 16 cd/m2; intensity ranged between 11 and 22.9 cd/m2. The task was administered in a dark room and began after 2 min of dark adaptation. 
Experimental procedure
Two horizontal sinusoidal gratings were presented sequentially, one in the first and the other in the second interval. Each grating stimulus subtended the whole screen (34 by 48 cm) and was presented for 250 ms, with a 500-ms ISI, as schematically illustrated in Figure 1A. Participants were instructed to look at the middle of the screen (there was no fixation point) and to indicate which grating was denser by pressing the appropriate button. For each response, an appropriate sound (indicating correct/incorrect) was given as feedback. To ensure that the participants understood the concept of density before testing began, they were asked to indicate which grating was denser on a painted illustration of the task. The frequency of the first grating stimulus was randomly chosen to be in the range of 0.125 to 2.0 c/°, and the other grating was chosen based on an adaptive procedure. In the first trial, the gratings differed by 75% (i.e., the ratio between the higher and the lower spatial frequencies was 1.75), and the difference was modified adaptively across trials in a two down/one up staircase manner, which converged to 71% correct (Levitt, 1971). The initial step size was 10% and was halved every three reversals (to a minimum of 1%). The assessment consisted of 80 trials. 
Calculating the contraction bias
Figure 1B illustrates schematically the distribution of stimuli in the frequency space (f1 on the x-axis and f2 on the y-axis). Its center is the mean spatial frequency of the experiment. It shows the four different ranges of stimuli used to calculate the magnitude of the contraction bias, i.e., the difference in percentage correct in the two ranges of Bias+ and the two ranges of Bias−. As illustrated in the schematic trial plots around the main graph, in both Bias+ ranges contraction increased the perceived difference between the two stimuli whereas in the Bias− ranges it decreased this difference. 
Results
General cognitive skills
As shown in Table 1, dyslexic participants did not differ from controls in their general reasoning skills as assessed by the spatial visual reasoning task (Block Design). As expected, dyslexics had difficulties in reading accuracy and rate and in verbal memory span (Digit Span). 
Table 1
 
Participants' general cognitive and phonological skills. Notes: °n.s. * p < 0.0001.
Table 1
 
Participants' general cognitive and phonological skills. Notes: °n.s. * p < 0.0001.
Contraction bias in spatial frequency discrimination
We administered a two-interval spatial frequency discrimination task. Both stimuli were drawn from a wide range of frequencies, which enabled an assessment of the subjects' statistical accumulation of the mean spatial frequency. In each trial, participants had to indicate which of the two sequentially presented grating stimuli was denser (i.e., had a higher spatial frequency; illustrated in Figure 1A). 
We administered an adaptive procedure, which enabled us to dissociate noise level and contraction bias because the stimuli were adapted so that all the participants had a similar success rate (same percentage correct). Accordingly, the average percentage correct at the end of the adaptive procedure (i.e., not including the first 20 easy trials) was similar in both groups. Mean accuracy ± SEM in percentage was 70.5 ± 1 and 72.1 ± 1.1 among dyslexics and controls, respectively (z = 1.1, p = 0.3, Mann-Whitney U test). The two groups did not differ significantly in their just noticeable differences (JNDs; defined as the average ratio between the spatial frequencies in the last 20 trials), which were 16.2 ± 1.5 and 24.2 ± 5.0 for controls and dyslexics, respectively (mean JND ± SEM in percentage; z = 1.6, p = 0.1, Mann-Whitney U test). Thus, overall performance was similar in the two groups. 
We compared individual performance in trials that gained from using the previous stimulus distribution (Bias+) to performance in trials in which success rate deteriorated by integrating priors (Bias−). Both populations exhibited a contraction bias, i.e., better performance on trials when the first grating was closer to the mean frequency than the second grating as shown in Figure 2A. However, among dyslexics, the difference in performance between Bias+ and Bias− trials was significantly smaller than among controls (Figure 1B; z = 2.2, p = 0.026, Mann-Whitney U test of Group × Condition interaction). As shown in Figure 2B, the average difference was consistent at the level of single participants: 82.5% of the control participants compared to only 57.5% of the dyslexic participants performed better on the Bias+ trials than on the Bias− trials. 
Figure 2
 
Dyslexics' contraction bias is smaller than controls'. (A) Contraction bias averaged across participants. Ordinate shows the percentage of correct responses for the two subdivisions of trials (abscissa): Bias+ trials (left), in which the grating in the first interval is closer to the mean frequency of all previous trials, and Bias− trials (right), in which it is reversed. We omitted trials in which the spatial frequencies of the two gratings were on opposite sides of the mean frequency (mean of 12% of the trials). Controls are denoted in blue and dyslexics in red. Both populations performed better on Bias+ than on Bias− trials. However, the difference, i.e., the contraction bias, was larger among the controls. Error bars denote SEM. (B) Individuals' performance (percentage accuracy) in Bias− versus Bias+ trials. The diagonal indicates equal performance (no bias). Control participants (blue symbols) are distributed mainly below the diagonal whereas many dyslexic participants (red symbols) are above the diagonal.
Figure 2
 
Dyslexics' contraction bias is smaller than controls'. (A) Contraction bias averaged across participants. Ordinate shows the percentage of correct responses for the two subdivisions of trials (abscissa): Bias+ trials (left), in which the grating in the first interval is closer to the mean frequency of all previous trials, and Bias− trials (right), in which it is reversed. We omitted trials in which the spatial frequencies of the two gratings were on opposite sides of the mean frequency (mean of 12% of the trials). Controls are denoted in blue and dyslexics in red. Both populations performed better on Bias+ than on Bias− trials. However, the difference, i.e., the contraction bias, was larger among the controls. Error bars denote SEM. (B) Individuals' performance (percentage accuracy) in Bias− versus Bias+ trials. The diagonal indicates equal performance (no bias). Control participants (blue symbols) are distributed mainly below the diagonal whereas many dyslexic participants (red symbols) are above the diagonal.
Discussion
We investigated the magnitude of the contraction bias, i.e., overestimating the first stimulus in a trial when it is small and underestimating it when it is large with respect to the mean frequency. We found that this effect was larger in control participants than among dyslexics even though their average level of performance was similar. This suggests that the responses made by dyslexics were less affected by previous statistics. These results are consistent with previous findings (Jaffe-Dax et al., 2015) on auditory frequency discrimination tasks in which dyslexics' contraction bias was significantly smaller than that of the controls. 
Are dyslexics' deficits domain-general or modality-specific?
This study extends previous findings to the visual domain and is consistent with the hypothesis that dyslexia could be attributed to a deficit in utilizing prior stimuli. This type of deficit is expected to lead to less stable representations of online observations because priors are not efficiently used to maximize the probability of the posterior given the observed stimuli, i.e., to provide the more probable perceptual interpretation of noisy samples of the environment. When priors are not effectively used, performance is expected to be slower because more online “evidence” is needed before a reliable perceptual interpretation is formed. Additionally, the load on working memory processes increases because this “evidence” needs to be retained to enable reliable subsequent comparisons. 
Sequential effects in simple perceptual tasks were observed in many previous studies (for detailed review, see Wilder, Jones, & Mozer, 2009). Such contextual effects had an overwhelmingly large impact on the estimated limens that were reported in many psychophysical measurements (for a detailed analysis of these various effects, see Fründ, Haenel, & Wichmann, 2011). Specifically, the magnitude of the contraction bias is large in both the visual and auditory modalities (e.g., Lages & Treisman, 1998; Treisman & Williams, 1984). However, studies of perception have typically ignored the incorporation of prior knowledge and attributed perceptual performance and its limitations to noisy observation (variance of the likelihood function; see for example the discussion in Yeshurun, Carrasco, & Maloney, 2008). This may be partially attributed to the more prevailing usage of protocols that include a repeated reference stimulus. In these protocols, the range of stimuli is typically smaller, and the magnitude of the bias is often difficult to evaluate. Nevertheless, the same model is claimed to account for performance even in these protocols (Raviv et al., 2014). Importantly, the benefit introduced by the usage of a reference stimulus relies on the simple implementation of the statistics of previous trials, i.e., the reference stimulus. In the auditory modality, it has been shown that these protocols lead to greater improvement among controls than among dyslexic participants (termed “the anchoring deficit in dyslexia,” e.g., Ahissar et al., 2006; Oganian & Ahissar, 2012). 
Our observation that similar deficits in utilizing experimental statistics for serial comparisons characterize both visual and auditory tasks raises the question of the source of these shared difficulties. One hypothesis, which is consistent with the results of the current study, is that these deficits stem from some type of abnormality in the dorsal stream, whose impairment had been previously suggested for dyslexia (Boros et al., 2016; Gori, Seitz, Ronconi, Franceschini, & Facoetti, 2015; Paulesu, Danelli, & Berlingeri, 2014). According to this interpretation, the dorsal stream is involved in serial perception as well as in motor plans. In fact, recent imaging studies that have tried to dissociate the role of the dorsal and ventral streams in the context of speech perception suggest that the dorsal stream involves the frontoparietal articulatory network, which is also related to working memory (Hickok & Poeppel, 2015). The left frontoparietal network is activated both in auditory two-tone frequency discrimination tasks (Daikhin & Ahissar, 2015) and in serial spatial frequency discrimination (Reinvang, Magnussen, & Greenlee, 2002; although here in both the right and left hemispheres). One of the main bundles connecting posterior and frontal parts of the dorsal stream is the arcuate fasciculus (Dick & Tremblay, 2012), whose abnormality in dyslexia has been suggested by previous studies (e.g., Boets et al., 2013; Klingberg et al., 2000). 
The relationship between explicit and implicit working memory
Dyslexics' explicit verbal working memory is known to be impaired (Beneventi, Tønnessen, Ersland, & Hugdahl, 2010a, 2010b; Helland & Asbjørnsen, 2010; Snowling, 2000). Banai and Ahissar (2004) extended this observation to simple tones, and Ben-Yehudah and Ahissar (2004) showed that this observation also applies to the visual modality. Subsequent studies have raised the issue of the mechanisms underlying this observation. These studies found that dyslexics' difficulties in explicit auditory retention can be attributed to automatic processes of implicit memory that integrate environmental statistics into perception. For auditory discrimination tasks, it was shown that dyslexics' relative difficulties are not maximal when explicit memory load is maximal but rather when the task can be made easier using experimental statistics as in the case of a repeated reference. Based on these observations, Ahissar et al. (2006; Ahissar, 2007) proposed “the anchoring deficit hypothesis of dyslexia.” In a following study, this behavior was analyzed computationally at the level of single trials that either benefit (Bias+) or lose (Bias−) from these statistics. Dyslexics benefit less than do controls (Jaffe-Dax et al., 2015). Our current findings indicate that dyslexics' usage of implicit memory is impaired across modalities. 
Conclusion
Our lab studied dyslexics' visual performance in a series of studies. We found no deficits in strictly visual tasks (e.g., crowding, Doron, Manassi, Herzog, & Ahissar, 2015; Shovman & Ahissar, 2006). However, we consistently found that dyslexics' performance in serial comparison tasks that can benefit from experimental statistics is impaired compared to matched controls (e.g., Ben-Yehudah & Ahissar, 2004; Ben-Yehudah et al., 2001). 
Nevertheless, different dyslexic individuals may have different underlying difficulties. In particular, our cumulative observation of difficulties in explicit and implicit short-term memory applies to more than half of our dyslexic participants but not to all. We recruited our participants mainly by ads posted in academic institutes. Perhaps different recruitment procedures sample individuals with somewhat different perceptual difficulties. 
Acknowledgments
This study was supported by the Israel Science Foundation (ISF grant no. 616/11 and Canada-Israel grant no. 2425/15), the Gatsby Charitable Foundation, EPFL-HUJI collaboration, The German-Israeli Foundation for Scientific Research and Development (grant no. I-1303-105.4/2015), Canadian Institutes of Health Research (CIHR), The International Development Research Center (IDRC) and the Azrieli Foundation. 
Commercial relationships: none. 
Corresponding author: Merav Ahissar. 
Email: msmerava@gmail.com. 
Address: Edmond and Lily Safra Center for Brain Sciences, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Jerusalem, Israel. 
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Figure 1
 
Schematic illustrations of the sequential spatial frequency discrimination task and contraction toward the mean. (A) The temporal structure of a single trial. The first grating was presented for 250 ms, followed by an ISI of 500 ms. The second grating was presented for 250 ms. The observer was requested to indicate which of the two gratings had the higher spatial frequency (density). (B) The contraction bias division to trial types. The middle plot illustrates the distribution of single trials in the frequency plane (the frequencies of the first and second grating in each trial, respectively) for a typical subject. Each green dot denotes the pair of stimuli in a single trial. This plane illustrates the ranges of the different trial types. In Bias+ trials, the frequency of the first grating stimulus was closer to the mean frequency; thus, contraction of its representation toward the mean increased the perceived difference between the two gratings and consequently improved performance. In Bias− trials, the first grating was farther from the mean; thus, contraction of its representation toward the mean frequency decreased the perceived difference between the gratings and hampered performance.
Figure 1
 
Schematic illustrations of the sequential spatial frequency discrimination task and contraction toward the mean. (A) The temporal structure of a single trial. The first grating was presented for 250 ms, followed by an ISI of 500 ms. The second grating was presented for 250 ms. The observer was requested to indicate which of the two gratings had the higher spatial frequency (density). (B) The contraction bias division to trial types. The middle plot illustrates the distribution of single trials in the frequency plane (the frequencies of the first and second grating in each trial, respectively) for a typical subject. Each green dot denotes the pair of stimuli in a single trial. This plane illustrates the ranges of the different trial types. In Bias+ trials, the frequency of the first grating stimulus was closer to the mean frequency; thus, contraction of its representation toward the mean increased the perceived difference between the two gratings and consequently improved performance. In Bias− trials, the first grating was farther from the mean; thus, contraction of its representation toward the mean frequency decreased the perceived difference between the gratings and hampered performance.
Figure 2
 
Dyslexics' contraction bias is smaller than controls'. (A) Contraction bias averaged across participants. Ordinate shows the percentage of correct responses for the two subdivisions of trials (abscissa): Bias+ trials (left), in which the grating in the first interval is closer to the mean frequency of all previous trials, and Bias− trials (right), in which it is reversed. We omitted trials in which the spatial frequencies of the two gratings were on opposite sides of the mean frequency (mean of 12% of the trials). Controls are denoted in blue and dyslexics in red. Both populations performed better on Bias+ than on Bias− trials. However, the difference, i.e., the contraction bias, was larger among the controls. Error bars denote SEM. (B) Individuals' performance (percentage accuracy) in Bias− versus Bias+ trials. The diagonal indicates equal performance (no bias). Control participants (blue symbols) are distributed mainly below the diagonal whereas many dyslexic participants (red symbols) are above the diagonal.
Figure 2
 
Dyslexics' contraction bias is smaller than controls'. (A) Contraction bias averaged across participants. Ordinate shows the percentage of correct responses for the two subdivisions of trials (abscissa): Bias+ trials (left), in which the grating in the first interval is closer to the mean frequency of all previous trials, and Bias− trials (right), in which it is reversed. We omitted trials in which the spatial frequencies of the two gratings were on opposite sides of the mean frequency (mean of 12% of the trials). Controls are denoted in blue and dyslexics in red. Both populations performed better on Bias+ than on Bias− trials. However, the difference, i.e., the contraction bias, was larger among the controls. Error bars denote SEM. (B) Individuals' performance (percentage accuracy) in Bias− versus Bias+ trials. The diagonal indicates equal performance (no bias). Control participants (blue symbols) are distributed mainly below the diagonal whereas many dyslexic participants (red symbols) are above the diagonal.
Table 1
 
Participants' general cognitive and phonological skills. Notes: °n.s. * p < 0.0001.
Table 1
 
Participants' general cognitive and phonological skills. Notes: °n.s. * p < 0.0001.
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