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Article  |   September 2013
Subjectively homogeneous noise over written text as a tool to investigate the perceptual mechanisms involved in reading
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Journal of Vision September 2013, Vol.13, 14. doi:10.1167/13.11.14
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      Frédéric J. A. M. Poirier, Frédéric Gosselin, Martin Arguin; Subjectively homogeneous noise over written text as a tool to investigate the perceptual mechanisms involved in reading. Journal of Vision 2013;13(11):14. doi: 10.1167/13.11.14.

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Abstract
Abstract
Abstract:

Abstract  In an effort to understand the factors influencing text legibility in natural reading, we adapted the visual spread method (Poirier, Gosselin, & Arguin, 2008) to natural text. Stimuli were sentences conforming to MNREAD standards (Legge, Ross, Luebker, & LaMay 1989) mixed with dynamic probabilistic noise—i.e., each pixel in the image is associated with a probability that its polarity is inverted on a given refresh cycle of the display screen. Noise level varied continuously over the image as initially determined by Gaussian-filtered noise. Participants adjusted noise levels in the text using the mouse until the text appeared homogenously noisy. We assume that participants increased (or decreased) noise at locations where stimulus features were easy (or difficult) to encode and thus that local noise settings correlate with legibility. Data from 11 participants and 30 sentences revealed interesting effects, demonstrating the validity of the method for assessing the impact of various factors on noise resistance in natural text. For example, participants increased noise over (a) spaces and adjacent letters, (b) the second half of words, (c) words with more orthographic neighbors but fewer phonological neighbors, (d) less useful word types, (e) less complex letters, and (f) diagnostic letters (a novel metric). Our observations also offer significant insights on constraints acting upon letter identification as well as on higher-level processes that are involved in reading.

Introduction
Reading performance is dependent on many factors, including word frequency (for review, see Ferrand, 2001; Monsell, 1991), letter similarity or confusability (Appleman & Mayzner, 1982; Bouma, 1971; Fiset, Dupuis-Roy, Arguin, & Gosselin, unpublished observations; Rumelhart & Siple, 1974), orthographic and phonemic neighbors (Andrews, 1997; Coltheart, Davelaar, Jonasson, & Besner, 1977; Ferrand, 2001; Grainger & Jacobs, 1996), and letter position in the word (Nazir, Jacobs, & O'Regan, 1998; O'Regan, 1990, 1992; O'Regan & Jacobs, 1992; O'Regan & Levy-Schoen, 1987; O'Regan, Levy-Schoen, Pynte, & Brugaillère, 1984; Vitu, O'Regan, & Mittau, 1990). 
Reading has also been studied via eye tracking (e.g., O'Regan, 1990; Rayner, 1998; Rayner & Pollatsek, 1989; Rayner & Sereno, 1994). Such studies found more fixations on names, verbs, and adjectives (about 85% of them), less on prepositions, conjunctions, articles, and pronouns (about 35%), as well as more fixations on longer words than shorter words. 
The purpose of the present study is to assess the merits of a novel approach, the visual spread method (Poirier, Gosselin, & Arguin, 2008; see below), for the investigation of reading. For brevity, we will review the literature where appropriate in the Discussion section. 
The visual spread method
We developed the visual spread method to investigate saliency (Poirier et al., 2008; see also Nothdurft, 1993, 2000) where participants adjusted luminance to match the saliency produced by other attributes (e.g., color, orientation) across all locations in that image. This increased data collection efficiency compared to two alternatives forced-choice (2AFC) tasks: (a) participants produced more responses per hour of testing, and (b) each response revealed both the location and intensity of perceived saliency. 
In the present study, we adapted the visual spread task to evaluate which parts of the written sentence were more noise resistant. Our measure of noise resistance was subjective, in that participants adjusted noise levels until they perceived noise to be homogeneous over the sentence. Actually, the adjustments made by participants systematically contained more noise on some parts of the sentences than others. We assumed that participants spread the noise to equalize signal-to-noise ratios across the stimulus. If that assumption was correct, then the analysis performed on noise distribution would recover the factors contributing to the signal. 
Advantages of the visual spread method applied to reading include: (a) the data recovered covers scales ranging from single letters to entire words, (b) any factor that varies within the stimulus sentences can be correlated with the data to estimate its contribution, and (c) regression analyses can determine if factors are redundant or unique (see also Appendix D). 
We used regression analysis to determine which factors were correlated with noise resistance, including a vast array of factors related to letters, words, and spaces. Our results are congruent with the literature regarding the factors affecting reading performance despite methodological differences. The ecological validity of our method is also discussed (see Appendix D). 
Methods
Ethics statement
The research protocol was reviewed and approved by the University of Montréal Health Research Ethics Committee. Written informed consent was obtained from participants prior to their participation. 
Participants
Eleven participants volunteered (four males and seven females), including the first author, as well as university undergraduate and graduate students. Their vision was normal or corrected-to-normal. Participants were French native speakers and fluent French readers. 
Apparatus
Testing and data collection were conducted on a PC computer (P4 3 GHz; 800 × 600 pixels; 75 Hz refresh rate). Responses were recorded via mouse button presses. Viewing distance was 68.5 cm, where 16 pixels equaled 1° visual angle. The entire stimulus subtended 8° × 16°. Stimulus generation and data collection were controlled by MATLAB with Psychophysics Toolbox extensions (Brainard, 1997; Pelli, 1997). 
Procedure
Visual spread task
In the current visual spread task, participants equated noise levels over sentences. Nothdurft (1993, 2000) introduced a “saliency match” task where participants had to indicate which of two stimulus patches was more salient (i.e., which patch grabbed attention). This allowed him to equate saliency across attributes (e.g., luminance, color, orientation). In the study of Poirier et al. (2008), participants distributed luminance over an image made of randomly colored and oriented lines. Adding (or removing) luminance at an image location increased (or reduced) the visibility of features at that location. Participants' luminance matches were significantly correlated with properties known to modulate saliency. 
In the current study, on each trial, participants were shown a display containing a sentence written over three lines in black and white (Figure 1B, C). Each pixel of the stimulus was white or black and was associated with a probability of polarity inversion, which constitutes the noise level at that location. Participants were required to equate apparent noise levels over the image by left-clicking (or right-clicking) on points where noise levels were perceived as higher (or lower) than elsewhere, which decreased (or increased) the noise level within a small window around that location. The position and duration of button presses was used to dynamically adjust noise levels. 
Figure 1
 
A sample stimulus is shown without noise (A) and after adjustment by participants (B; average). Panel B is also shown with noise differences amplified (C), or with noise levels represented as gray levels (D; surround gray = 12.5% noise; lighter = less noise). The noise levels in Panel B appear roughly homogeneous over the image, despite systematic variation in noise levels as highlighted in panels C, D.
Figure 1
 
A sample stimulus is shown without noise (A) and after adjustment by participants (B; average). Panel B is also shown with noise differences amplified (C), or with noise levels represented as gray levels (D; surround gray = 12.5% noise; lighter = less noise). The noise levels in Panel B appear roughly homogeneous over the image, despite systematic variation in noise levels as highlighted in panels C, D.
Stimuli
Stimuli consisted of two parts: a sentence and probabilistic noise. Sentences were taken from a bank of French sentences (Senécal, 2001; Senécal, Gresset, & Overbury, 2002) constructed to conform to MNREAD standards (a standard reading speed test; Legge, Ross, Luebker, & LaMay, 1989): (a) 60 characters long, including spaces between words, (b) about 10 words long, (c) divided in three lines, each about equal in physical length and centered on the screen, and (d) using simple sentence structures and high-frequency words easily understood by eight-year-old children. The height of the letter “x” was 7 pixels (0.44°), and letters could extend 3 pixels (0.19°) above and/or below that. The font used was Courier. Only lowercase nonaccented letters were used in the analyses, with capital letters, accented letters, and apostrophes classified as “miscellaneous characters.” 
The noise was dynamic and probabilistic. Every pixel was associated with a probability of being displayed at opposite polarity on any frame (13.3 Hz). This probabilistic noise was defined using (detailed below): (a) initial noise levels set using filtered random noise, (b) filtered noise that was normalized, (c) and then transformed into probabilistic noise, and (d) as participants changed noise levels, values were renormalized. 
The filtered binary noise (N) was created using binary noise filtered using a Gaussian filter, defined as:  where σ = 0.5°, and (i, j) are coordinates. N was linearly scaled to a range of 0 to 1, normalized to a mean of 0.5, and values outside the 0 to 1 range were clipped. Each time N was updated by user responses, it was renormalized and reclipped (if necessary). The resulting scaled filtered noise was transformed into probability noise (P) using the following transformation:  where pixels varied from: (a) showing the sentence at all times, i.e., never inverting, N = 0, P = 0%, (b) showing random noise at all times, i.e., N = 1, P = 50%, and (c) showing sentence and noise in various amounts, average N = 0.5, average P = 12.5%. The squaring exponent made noise levels vary smoothly over time when adjusting noise levels because small changes are noticeable at low-noise levels. Dynamic noise was used rather than static noise because (a) noise density is easier to evaluate in dynamic noise due to averaging over time, and (b) participants saw real-time effects of adjusting noise. 
Participants adjusted noise levels by pressing either mouse button at a location (N varied by 0.5/s; the right/left button increased/decreased noise respectively in a Gaussian window with σ = 0.5°). Each adjustment was followed by renormalization and reclipping as described above. Normalization was done to prevent participants from setting noise at ceiling or floor values, as well as to keep average noise levels constant across participants and sentences. At 12.5% noise level, words near and far from fixation remained visible. Higher levels of noise would mask the text context, thus potentially bias results towards local properties. 
Noise could only be adjusted by participants within an “area of interest” (AOI) on and near text. Outside the AOI, pixels were kept at 12.5% noise. The AOI was defined as the areas containing letters extended two character spaces on each side and two character heights above and below, Gaussian-blurred (σ = 0.5°) to smooth the transition between inside and outside of the AOI. This encouraged participants to concentrate responses on or near text. “Surrounding space” is space contained within the AOI but located either between or outside sentences. 
Following the logic that some sentence parts are perceived more clearly than others, the point of subjective noise equality would be negatively correlated with text clarity. We henceforth use the term “noise resistance” to denote local noise density, in units of percent noise. 
Temporal sequence
The 30 sentences were divided in three test sessions. Each sentence was shown about equally often (details below). Each session was 30 min long, for a total of 90 min of testing per participant. 
Each trial lasted 20 s, during which participants could make as many adjustments as they wanted. Noise levels were adjusted in real-time. Trials were separated by a blank screen for 500 ms. On 50% of trials, the sentence was selected randomly. On other trials, the least-presented sentence was selected, to ensure that every sentence was presented about equally often. Each sentence was presented nine times on average, with repeated presentations using the noise as set in the prior trial to encourage participants to search carefully for uneven noise. 
Analysis
Analyses were performed in two steps as recommended by Lorch and Myers (1990). (1) Regression analyses were performed to extract factor weights per participant. Regression weights represent noise change per unit of change in a given factor. The standard error of the means (SEM) of those weights represents the accuracy of that mean, despite potential individual differences in strategy. (2) Those weights were analyzed using repeated measures ANOVAs (to compare weights together) and t tests (to assess whether individual weights were significantly different from zero). Due to individual variability, t tests on individual weights were less powerful than ANOVAs. For orthogonal factors, this is equivalent to measuring mean noise relative to baseline noise and performing standard analyses. However, the method generalizes to nonorthogonal factors. Note that since individual differences in strategies contribute to the error terms of these analyses, effects that are statistically significant are effects that show consistency across participants. 
For example, the analysis of space-based factors shown in Figure 2A included two steps: (1) A regression analysis extracted mean noise for surrounding space, spaces, letters near spaces, and miscellaneous characters for each participant, and (2) t tests determined independently which of these four factors influenced noise resistance. 
Table 1
 
Some sample factors and their values for each character position in a sequence of two words. Notes: “les chiens” in English: “the dogs”.
Table 1
 
Some sample factors and their values for each character position in a sequence of two words. Notes: “les chiens” in English: “the dogs”.
l e s c h i e n s
Word length 3 3 3 0 6 6 6 6 6 6
Distance from beginning 1 2 3 0 1 2 3 4 5 6
Distance from end −3 −2 −1 0 −6 −5 −4 −3 −2 −1
Distance left-right −1 0 1 0 −2.5 −1.5 −0.5 0.5 1.5 2.5
Noun 1 1 1 1 1 1
Figure 2
 
Weights (-y-axis) associated with space-based and positional-based factors. A positive (or negative) weight indicates that noise was higher (or lower) in the areas indicated by the factor. Participants increased noise on spaces surrounding and between words (A), on external letters (A), one-letter words (B), on letters further towards the right (C, D, F), and on the last letter. They decreased noise on miscellaneous characters (A). Error bars and dotted lines represent SEM.
Figure 2
 
Weights (-y-axis) associated with space-based and positional-based factors. A positive (or negative) weight indicates that noise was higher (or lower) in the areas indicated by the factor. Participants increased noise on spaces surrounding and between words (A), on external letters (A), one-letter words (B), on letters further towards the right (C, D, F), and on the last letter. They decreased noise on miscellaneous characters (A). Error bars and dotted lines represent SEM.
Some factors were decomposed into separate predictor variables to clarify trends in two steps: (1) A regression analysis extracted mean noise at each level of the variable, for each participant, and (2) an ANOVA determined if noise varied as a function of that variable. For example, the analysis of the word length effect shown in Figure 2B included two steps: (1) A regression analysis extracted mean noise for each word length and participant, and (2) an ANOVA determined if mean noise varied with word length. Note that these factors were also analyzed not decomposed (e.g., Table 2). 
Table 2
 
Summary of analyses. Notes: All analyses include the factors “spaces,” “miscellaneous characters,” “surrounding space,” and a constant. Weights are shown for independent, blocked, and full regressions. Intervals are SEM across participants. Factors marked by “—” were included in the analysis as controls. Empty lines represent factors not included in the given regressions. R2 for the full analysis was 29.5% ± 4.2%.
Table 2
 
Summary of analyses. Notes: All analyses include the factors “spaces,” “miscellaneous characters,” “surrounding space,” and a constant. Weights are shown for independent, blocked, and full regressions. Intervals are SEM across participants. Factors marked by “—” were included in the analysis as controls. Empty lines represent factors not included in the given regressions. R2 for the full analysis was 29.5% ± 4.2%.
Category Factor Independent Blocked Full Figure reference R2
Spaces & misc. Surrounding space 1.448 ± 0.211 0.659 ± 0.175 1.615 ± 0.396 2A 21.7% ± 4.1%
Spaces 1.861 ± 0.163 1.939 ± 0.169 0.754 ± 0.259
Near spaces 0.506 ± 0.063 0.506 ± 0.063 0.182 ± 0.119
Miscellanous characters −0.402 ± 0.090 −0.454 ± 0.089 −0.092 ± 0.111
Positional Word length −0.018 ± 0.011 2B–F 20.8% ± 3.9%
Left-right 0.107 ± 0.022
From end 0.084 ± 0.016
From beginning 0.060 ± 0.016
Letters Width −0.397 ± 0.268 1.181 ± 0.323 3 27.7% ± 4.3%
Confusability in noise 0.795 ± 0.120 1.339 ± 0.328
Confusability low contrast 0.581 ± 0.102 −0.880 ± 0.257
Complexity −1.092 ± 0.150 −1.446 ± 0.186
Log letter frequency 0.272 ± 0.046 0.074 ± 0.062
Diagnosticity 0.363 ± 0.132 0.099 ± 0.137
Sublexical Grapheme length 0.000 ± 0.052 −0.003 ± 0.053 0.019 ± 0.052 4A, B 20.3% ± 3.7%
Syllable length −0.017 ± 0.019 0.006 ± 0.018 −0.021 ± 0.011
Token syllable frequency 0.019 ± 0.025 −0.128 ± 0.040 −0.101 ± 0.032
Type syllable frequency 0.145 ± 0.034 0.258 ± 0.046 0.154 ± 0.050
Frequencies Log frequency 0.014 ± 0.008 −0.017 ± 0.013 0.022 ± 0.028 4C, D 20.6% ± 3.7%
Log cumulative Frequency 0.015 ± 0.009 0.024 ± 0.014 −0.021 ± 0.029
N homographs 0.021 ± 0.015 −0.011 ± 0.013 0.013 ± 0.019
N homophones 0.001 ± 0.006 0.001 ± 0.007 −0.007 ± 0.007
Log orthographic neighbors 0.052 ± 0.023 0.097 ± 0.022 0.056 ± 0.027
Log phonetic neighbors 0.000 ± 0.019 −0.056 ± 0.020 −0.037 ± 0.020
Word type Auxiliary verb 0.445 ± 0.090 0.302 ± 0.129 0.484 ± 0.253 4E, F 20.6% ± 3.8%
Conjunction 0.331 ± 0.188 0.191 ± 0.219 0.528 ± 0.255
Article 0.159 ± 0.077 0.014 ± 0.117 0.369 ± 0.222
Pronoun 0.142 ± 0.114 −0.001 ± 0.146 0.393 ± 0.187
Verb 0.017 ± 0.029 −0.121 ± 0.098 0.425 ± 0.213
Preposition −0.004 ± 0.066 −0.138 ± 0.109 0.286 ± 0.161
Noun −0.038 ± 0.073 −0.159 ± 0.080 0.339 ± 0.168
Determiner −0.093 ± 0.113 −0.223 ± 0.158 0.320 ± 0.259
Adverb −0.108 ± 0.064 −0.233 ± 0.105 0.199 ± 0.185
Adjective −0.146 ± 0.064 −0.264 ± 0.119 0.264 ± 0.210
Regression analysis combined factors in three ways: (a) “independent,” meaning that factors are entered alone, (b) “blocked,” meaning that all factors from that block were included, and (c) “full,” meaning that all factors were included. Analyses including more factors were performed to evaluate the relative importance of factors by allowing them to compete for explained variance, as well as controlling for lower-level factors. In all cases, all variables were entered simultaneously; therefore, no preference was given in ability to compete for accounted variance. All regressions include controls for spaces, surrounding spaces, and miscellaneous characters, including “independent” regressions. 
Factors
Most factors are described in the Results sections where they are analyzed. Factors requiring a lengthy explanation are described in Appendices A and B, which also include some factor statistics. 
We used a battery of factors that could potentially influence noise resistance using multiple regression analysis. Table 1 shows some sample factors for two sample words, along with the numerical value assigned to each letter position on those factors. Note that all letter positions received the same value if a factor characterizes the entire word. Note also that categorical variables were assigned a numerical code of nominal value. 
Factors were selected if they met the following criteria: (a) they had to be easily quantifiable based on physical characteristics or previously collected data, and (b) they had to vary naturally within the selected sentences, rather than requiring specific manipulations. Note that the analysis could have included further factors, and data could be re-analyzed as further factors are added. However, we believe this set of factors constitutes a fairly comprehensive list of factors present in normal reading situations. The main factors are listed in Table 2, and Table 1 shows some examples of factors used. Factors are described in Appendices A and B. Diagnosticity was a novel factor to estimate how important single letters were to word recognition. Confusability measured how likely a letter was to be confused as another letter. 
Results
Participants systematically set noise levels higher in certain locations than others, resulting in systematic noise modulations over the image, which we quantified as “noise resistance” (in units of percent noise). 
Factors underlying noise resistance were analyzed in four blocks: (a) space-based, (b) positional, (c) letter-based, and (d) text-based factors. The main results are summarized in Table 2. As new factors are added, some weights on previous factors changed (e.g., reverse direction, drop to zero). Such weight changes occur when other factors compete to explain the same variance. Such changes are thus informative and discussed below. 
Space-based factors
This block included: (a) “surrounding space” indicating the empty space directly surrounding the text, but not including spaces between words, (b) “spaces,” (c) “near spaces” indicating letters adjacent to one or two spaces, and (d) “misc. letters” including apostrophes, accented letters, and uppercase letters (Figure 2A). For these factors, a weight of zero indicated that noise was as high as noise over regular letters. 
Participants had a higher resistance to noise for surrounding space, spaces, and the external letters of words than for internal letters, ts(10) ≥ 6.9, ps < 0.0001. Participants put less noise on miscellaneous characters than on letters, t(10) = −4.5, p = 0.001. 
Positional factors
Positional factors refer to the position of a letter in a word (in number of letters; see Table 1): (a) word length (M = 5.54, SD = 2.26), (b) “left-right” distance from the word's center keeping directional information (positive was towards the right), and (c–d) distance from the beginning/end of words. The factors were analyzed separately for odd- and even-length words as well as combined into a single analysis, with similar results. 
Positional factors were decomposed into independent levels to analyze trends (see “Procedure: Analysis” section). For example, the factor “distance from beginning” is decomposed into the sub-categories “first letter,” “second letter,” etc., each of which indicates if a letter belongs to the subcategory (1 = yes, 0 = no). 
Participants increased noise on (Figure 2B through F): (a) one-letter words, F(10, 100) = 7.55, p < 0.001; LSD ps < 0.02; Figure 2B, (b) letters further towards the right of a word, linear Fs(1, 10) > 14.0, ps ≤ 0.004; Figure 2C, D, and F, (c) letters further from the center of a word, quadratic Fs(1, 10) > 13.6, ps < 0.004; Figure 2C, D, and (d) the last letter (last letter different from any previous letter; F[10, 100] = 12.06, p < 0.001; LSD ps < 0.015; Figure 2E). Taken together, these factors indicate that participants increased noise levels on letters away from the center and towards the right of words. 
Letter-based factors
This block included six factors (Appendices A and B, “Factors” section in the Methods, and Table 3): (a) letter complexity, (b) letter width, (c–d) confusability in noise or in low contrast, (e) log letter frequency, and (f) diagnosticity. The variables complexity, letter width, and diagnosticity were normalized to a maximum value of 1 for the regression analysis. 
Table 3
 
Correlations between several measures based on the same font. Notes: If the factor complexity is multiplied by −1, all correlations become positive here.
Table 3
 
Correlations between several measures based on the same font. Notes: If the factor complexity is multiplied by −1, all correlations become positive here.
Factor Noise resistance Diagnosticity Log letter frequency Complexity Confusability in low contrast
Confusability in noise 0.646 0.410 0.566 −0.756 0.953
Confusability in low contrast 0.676 0.487 0.644 −0.713
Complexity −0.561 −0.239 −0.457
Log frequency 0.428 0.810
Diagnosticity 0.442
Noise-resistant letters were frequent, easily confusable, diagnostic, and less complex (Table 3; Figure 3). Letter width had no effect on its own, t(10) = −1.5, p = 0.17, but if entered with other factors, wider letters received more noise, ts(10) ≥ 3.7, p ≤ 0.0045. That is, the letter width effect was too small to be observed on its own. 
Figure 3
 
Weights (y-axis) associated with letter-based factors, when entered independently (A) or “blocked” together (B). A weight of “0” indicates that the factor is not associated with noise increase or decrease. (C) Correlation between averaged noise and predicted noise per letter. “Low c.” is an abbreviation for “low contrast.”
Figure 3
 
Weights (y-axis) associated with letter-based factors, when entered independently (A) or “blocked” together (B). A weight of “0” indicates that the factor is not associated with noise increase or decrease. (C) Correlation between averaged noise and predicted noise per letter. “Low c.” is an abbreviation for “low contrast.”
Both confusability factors were positively correlated with noise resistance (independent: ts[10] ≥ 5.7, ps < .0003). Contrary to intuition, letters of high confusability received more noise. When entered with other factors, “confusability in noise” remained, ts(10) ≥ 3.8, ps < 0.0035, whereas “confusability in contrast” became negatively associated with noise resistance, ts(10) ≤ −3.2, ps < 0.01. In other words, participants increased noise on letters with low confusability in low contrast, and greater confusability in noise
Complex letters were less resistant to noise in all analyses, ts(10) ≤ −6.9, ps < 0.0001. 
Frequent letters received more noise, t(10) = 5.9, p = 0.0002, but this effect disappeared when other factors were included in the analysis, ts(10) ≤ 1.2, ps ≥ 0.26, suggesting that letter frequency did not contribute uniquely to explained variance. 
Higher diagnosticity was associated with an increase in noise resistance, t(10) = 2.8, p = 0.020. The effect disappeared when other factors were included, ts(10) ≤ 0.54, ps ≥ 0.60, suggesting that diagnostic letters are noise resistant due to other features. 
Taken together, letter-based factors offer a solid account of noise resistance for individual letters of the alphabet (Figure 3C). The correlation between predicted noise using letter-based factors (y-axis), and data averaged over multiple instances of a letter (-x-axis) was high (r = 0.808). Error bars indicate SEM based on individual variability, with error bars for the model based on individual variability of regression fits. 
Text-based factors
The last block of factors includes 24 factors, classified into: (a) sub-lexical statistics, (b) frequencies, and (c) word type. 
Of the sublexical factors (Figure 4C, D), only syllable frequency by type was independently correlated with noise resistance, t(10) = 4.3, p = 0.0016; all others: |ts|(10) < 0.75, ps > 0.39. In the blocked analysis, noise resistance increased with type frequency, t(10) = 5.7, p = 0.0002, and decreased with token frequency, t(10) = −3.23, p = 0.009. The syllable frequency factors (type and token) remained significant (or at least near-significant) in the full analysis, |ts(10)| > 3.09, ps < 0.012; except for token syllable frequency in the full analysis: t(10) = −2.0, p = 0.076. Grapheme and syllable length were not significant in any analysis, |ts|(10) < 1.82, ps > 0.099. This suggests that the two syllable frequency factors are unique contributors to explained variance, where words are more noise resistant if they have high type frequencies yet low token frequencies. 
Figure 4
 
Weights (y-axis) associated with text-based factors, when entered together (blocked; right) or independently (left). Factors are arranged in panels according to the blocks they were entered in. A weight of “0” indicates that the factor is not associated with noise increase or decrease. (A, B) Of the four subword statistics, only the syllabic frequencies were significantly correlated with noise levels, where participants increased noise on high syllable type frequency and low syllable token frequency. (C, D) Participants increased noise on words with more orthographic neighbors and fewer phonological neighbours. (E, F) Word type also influenced noise levels.
Figure 4
 
Weights (y-axis) associated with text-based factors, when entered together (blocked; right) or independently (left). Factors are arranged in panels according to the blocks they were entered in. A weight of “0” indicates that the factor is not associated with noise increase or decrease. (A, B) Of the four subword statistics, only the syllabic frequencies were significantly correlated with noise levels, where participants increased noise on high syllable type frequency and low syllable token frequency. (C, D) Participants increased noise on words with more orthographic neighbors and fewer phonological neighbours. (E, F) Word type also influenced noise levels.
Of the frequency factors (Figure 4E, F), log orthographic neighbor frequency was associated with an increase in noise, ts(10) ≥ 2.2, ps ≤ 0.049; near-significant in the full analysis: t(10) = 2.07, p = 0.065, and log phonological neighbor frequency was only significant in the blocked analysis, t(10) = −2.8, p = 0.019; independently: t(10) = 0.0, p = 0.99; full: t(10) = −1.84, p = 0.095. None of the other frequency-based factors was significant in any of the analyses (log lexical frequency, log cumulative frequency, number of homographs, number of homophones; |t|s ≤ 1.8, ps ≥ 0.10. Thus participants increased noise on words that were graphically similar to other words, and had a more unique pronunciation. The phonological effect was more dependent on which factors were included in the analysis. 
There was an effect of word type, F(9, 90) = 4.1, p = 0.0 (Figure 4E, F), with words associated with sentence understanding generally receiving less noise. We observed the following ranking of word type from lowest to highest noise resistance (all ps < 0.05): (a) adjectives, (b) verbs, (c) articles, and (d) auxiliary verbs. Other word categories were too variable across participants to establish a statistically reliable ordering. The word-type effect was not significant in the full analysis, F(9, 90) = 1.7, p = 0.098, suggesting that the word-type effect could be due to other factors. 
Discussion
Summary of results
Within 90 min of data collection per participant, the novel and intuitive method of visual spread produced reliable data on perceived text clarity or noise resistance throughout a set of sentences. 
Noise resistance, as measured using the visual spread task, was significantly correlated with many factors consistent with the reading literature, including (a) position of spaces, (b) letter position within words, (c) letter complexity, (d) letter confusability, and (e) lexical characteristics. We also document an effect of the novel factor of letter diagnosticity. Thus, although participants were not explicitly asked to read the sentences, their responses nevertheless correlated with some factors known to influence readability. 
Although many factors were consistent across analyses, some factors were not. This suggests either non-additive effects or smaller effects that can be masked by larger effects. Examples of nonadditivity include: (a) the log number of phonetic neighbors was significant depending on which other factors were included, (b) the “confusability in low contrast” factor reversed sign when the “confusability in noise” factor was included, (c) token syllable frequency was only significant when type syllable frequency was included in the analysis, and (d) many effect sizes were reduced with controls for letters and position. These interaction effects are discussed below where appropriate, along with what they tell us about reading. 
Overall, noise resistance seems to increase around spaces and external letters, towards the right of words, on easily confusable letters, on less complex letters, and on word with more orthographic neighbors. Other effects were found but were less consistent across analyses (see below). 
Implications for optimal viewing position
The optimal viewing position for word recognition is at the center of the word, or slightly left of center, and performance is better for ocular fixations on the first half than on the second half of the word (Nazir et al., 1998; O'Regan, 1990, 1992; O'Regan & Jacobs, 1992; O'Regan & Levy-Schoen, 1987; Vitu et al., 1990). Fixations away from the optimal position bring performance costs of about 10–20 ms per letter (Nazir et al., 1998; O'Regan, 1992; O'Regan & Levy-Schoen, 1987; O'Regan et al., 1984; Vitu et al., 1990). One reason suggested for an advantage for external letters is that they are less exposed to crowding (Bouma, 1970; Pelli, Palomares, & Majaj, 2004), i.e., letters inside words are masked by flanking letters. 
In our study, participants increased noise on and around spaces more than on the letters themselves. Noise resistance was lowest at about two letters left of word center, i.e., around the optimal viewing position. Participants increased noise on word endings (especially on the last letter), which, in French, are usually less informative (Blais et al., 2009; Clark & O'Regan, 1999). This suggests a noise placement strategy to move noise away from meaningful and crowded areas of words. 
The size of the Gaussian spread of noise adjustment used in this study could explain in part why participants increased noise on external letters. Adding noise on spaces also adds some noise over external letters. This possible artefact does not explain many effects however, e.g., lower noise on the first half of words or the letter-based effects. Nevertheless, a replication of this study could be performed with noise density set per letter instead of spread using a Gaussian. 
Implications for letter processing
Noise resistance was best predicted by the block of variables linked to letter characteristics. This suggests that modifying alphabet characteristics could substantially influence reading performance. Indeed, font choice does impact reading speed, comprehension, perceived attractiveness, and legibility (Bernard, Lida, Riley, Hackler, & Janzen, 2002; Mansfield, Legge, & Ban, 1996). This is convenient, because it is easier to change fonts (or even an alphabet) than word frequencies or statistics of word types. Our results include measures of variability within the alphabet chosen. Thus we can examine the relationships among letters that are often overlooked when reading performance is measured across sentences or paragraphs. The pattern of correlations between letter-based variables (Table 3) suggests that the alphabet is more optimal for writing than for reading (see Appendix C for details). Frequent letters are simple, making them easier to write. However, frequent and diagnostic letters are easily confusable with other letters, making them less-than-optimal for reading. 
Implications for letter degradation methods
Our study compares three methods of degrading letter visibility: probabilistic noise (here) and confusability in both noise and low contrast (Fiset et al., unpublished observations). Not surprisingly, they were all correlated. Results suggest that participants increased the visibility of letters that are already easier to identify. However, the “confusability in low contrast” weight changed sign when the “confusability in noise” weight was included in the same analysis. This suggests that these two measures have a shared component (they both degrade letter recognition) as well as a unique component (the specific way letter recognition is degraded). 
The three degradation techniques differ in how much they affect letter shape and contrast: (a) “confusability in noise” used additive noise, which influenced both letter shape and contrast, (b) “confusability in low contrast” used contrast reduction, which mainly influenced contrast, and (c) “probabilistic noise” (as used here), which influenced letter shape mainly. Thus, a fair approximation of shape degradation (probabilistic noise) would be the “shape + contrast” degradation (confusability in noise) minus the “contrast” degradation (confusability in contrast). Thus a regression approach as used here shows that different methods to degrade letters are not fully equivalent, with letters being differentially sensitive to different degradation methods. 
Implications for sublexical effects
A grapheme is defined as the written representation of a phoneme. Studies have shown that words controlled for length take longer to read or identify if they have longer graphemes or syllables (Coltheart, Curtis, Atkins, & Haller, 1993; Coltheart, Rastle, Perry, Langdon, & Ziegler, 2001; Grainger & Jacobs, 1996; Plaut, McClelland, Seidenberg, & Patterson, 1996; Rastle & Coltheart, 1998; Rey, Jacobs, Schmidt-Weigand, & Ziegler, 1998; Rey, Ziegler, & Jacobs, 2000), suggesting longer processing time for longer graphemes. Our results show that neither grapheme length nor syllable length played a role in noise resistance. Our experiment did not include time pressure, and it is possible that performance costs associated with longer graphemes mainly occur under time pressure. 
Figure 5
 
Hypothesized relationships between the variables related to letters. All correlations were positive between the variables shown. Diagnostic letters are frequently used (left). Efficiency was measured using noise resistance and simplicity (the opposite of complexity). Letter confusability was measured in low contrast and in noise (right). The results are consistent with an alphabet that promotes faster writing, but not necessarily faster or easier reading. Dotted lines indicate correlations that should be inverted when designing an alphabet to promote reading performance (without necessarily making writing performance worse), by changing the relationship between confusability and all other variables, while retaining all other relationships.
Figure 5
 
Hypothesized relationships between the variables related to letters. All correlations were positive between the variables shown. Diagnostic letters are frequently used (left). Efficiency was measured using noise resistance and simplicity (the opposite of complexity). Letter confusability was measured in low contrast and in noise (right). The results are consistent with an alphabet that promotes faster writing, but not necessarily faster or easier reading. Dotted lines indicate correlations that should be inverted when designing an alphabet to promote reading performance (without necessarily making writing performance worse), by changing the relationship between confusability and all other variables, while retaining all other relationships.
Conrad, Carreiras, and Jacobs (2008) studied the effects of syllable frequency on lexical decision: quantifying syllable frequency both by type (number of syllabic neighbors) and by token (summed word frequencies across syllabic neighbors). They found facilitation for type frequency, and inhibition for token frequency. Our study replicated their results: noise resistance increased with type frequency and decreased with token frequency. However, our findings differ from Conrad et al.'s on the sensitivity of the two effects to methodological changes or the inclusion of control variables. Conrad et al. (2008) report that the token frequency effect was reliably found across the literature and their own study, whereas the type frequency effect was dependent on methodological demands and/or statistical controls. In contrast, in our study, the type frequency effect was reliably found across analyses whereas the token frequency effect was dependent on which other variables were included in the analysis. One possibility is that the two effects are differently sensitive to methodological demands (e.g., speeded responses). Further studies could investigate the temporal properties of these effects to confirm. 
Implications for lexical frequency
Frequently occurring words are easier to recognize than less frequent words (for review, see Ferrand, 2001; Monsell, 1991) including in French (Ferrand, 2000; Grainger, Spinelli, & Ferrand, 2000; O'Regan & Jacobs, 1992). This effect is seen across word types (Gordon & Caramazza, 1985; Segui, Frauenfelder, Lainé, & Mehler, 1987). Shorter words are frequent (Zipf, 1935). Word frequency and word length seem to have independent effects on performance (O'Regan & Jacobs, 1992; Vitu et al., 1990). Reading speed is also improved for words with a higher cumulative frequency (word frequencies summed across same-family words; Beauvillain, 1996; Bradley, 1979; Burani & Caramazza, 1987; Burani, Salmaso, & Caramazza, 1984; Colé, Beauvillain, & Segui, 1989; Holmes & O'Regan, 1992; Taft, 1979). 
In our study, neither lexical frequency nor cumulative lexical frequency played a significant role, although both showed trends in the right direction, consistent with a facilitory effect. Controlling for other factors did not help these two factors reach statistical significance. It is possible that these effects may require time constraints or reading performance measurement. 
Implications for orthography
Orthographic neighborhood was measured as (a) frequency of the most frequent neighbor, and (b) the number of orthographic neighbors (Andrews, 1997; Ferrand, 2001; Grainger & Jacobs, 1996). Words with several orthographic neighbors are facilitated (Andrews, 1989, 1992; Forster & Shen, 1996; Sears, Hino, & Lupker, 1995; but see Carreiras, Perea, & Grainger, 1997; Coltheart et al., 1977), but high-frequency orthographic neighbors inhibit performance (Carreiras et al., 1997; Grainger, 1990; Grainger & Jacobs, 1996; Grainger, O'Regan, Jacobs, & Segui, 1989, 1992; Grainger & Segui, 1990; Perea & Pollatsek, 1998). These effects are dependent on various factors (Andrews, 1997; Grainger & Jacobs, 1996), including interactions with task and language. 
Here, orthographic neighbors had a facilitation effect, consistent with the literature. The orthographic-neighbor effect resisted the introduction of controls, suggesting this effect was a true higher-level effect. 
Implications for phonology
Overall, homophones impair performance: (a) less frequent words in homophonic pairs get inhibited (Davelaar, Coltheart, Besner, & Jonasson, 1978; Rubenstein, Lewis, & Rubenstein, 1971; but see Clark, 1973; Coltheart et al., 1977), (b) pseudo-homophones are harder to reject than other non-words (Coltheart et al., 1977; Rubenstein et al., 1971), and (c) higher misclassification rates for words into the category of its homophone (e.g., “rows” misclassified as a flower; Daneman & Reingold, 1993; Daneman, Reingold, & Davidson, 1995; Jared, Levy, & Rayner, 1999; Peter & Turvey, 1994; Van Orden, 1987; Van Orden, Johnston, & Hale, 1988; Van Orden et al., 1992; Ziegler & Jacobs, 1995; Ziegler, Van Orden, & Jacobs, 1997). Some of these effects are small, observable mainly with pseudo-words, present mostly in low-frequency words, and/or possibly dependent on strategy (Clark, 1973; Coltheart et al., 1977; Coltheart, Patterson, & Leahy, 1994; Davelaar et al., 1978; Jared & Seidenberg, 1991; McCusker, Hillinger, & Bias, 1981; Seidenberg, 1985a, 1985b). 
Our results show inhibition on words with more phonological neighbors, but only when the effect of orthographic neighbors is controlled for. The direction and fragility of these effects is consistent with the literature. This suggests that extra processing is required to discriminate between phonologically close words. 
Implications for word type and word length
Eye movements recorded during reading (O'Regan, 1990; Rayner, 1998; Rayner & Pollatsek, 1989; Rayner & Sereno, 1994) show that participants make more fixations on longer words (100% for eight or more letters vs. 25% for two to three letters), names, verbs, and adjectives (85%), and fewer on prepositions, conjunctions, articles, and pronouns (35%). 
Our results are consistent with a strategy of moving noise away from words that are important for understanding sentences (i.e., noise increased on auxiliary verbs & articles, and decreased on verbs & adjectives). Our analyses suggest that the word-type effect is partly or mainly due to lower-level statistics. For example, word types may be statistically different in complexity or frequency, and those differences may underlie the word type effect. 
We also found a word-length effect in the form of greater noise for single-letter words relative to longer words. This suggests that longer words may be fixated more because they extend beyond the visual span (Legge, Cheung, Yu, Cheung, Lee, & Owens, 2007; Pelli et al., 2007) or are more likely to be important, and not because they are somehow more masked or noisy. 
Conclusion
Our study is consistent with the literature on (a) optimal viewing position, (b) letter complexity, (c) syllable frequency, and (d) orthographic and phonological neighbors. We did not replicate effects of lexical frequency or word length, and it is unclear if this was due to lack of statistical power, or differences in methodology. There are three novel conclusions from our study: (a) the word type effect may reflect different word statistics across word types (e.g., length, letters), (b) letter degradation techniques have similar but not fully equivalent effects, and (c) the alphabet may have been more optimized for writing rather than for reading, given that frequent and diagnostic letters were also easily confusable. 
The efficiency of the method for data collection is noteworthy. This efficiency is gained by combining the advantages of adjustment methods to the ability to make adjustments at any location over a sentence. Essentially, participants were free to concentrate their responses at locations that deviated most from subjectively homogeneous noise, thus quickly reducing apparent noise variations throughout the stimulus. This method quickly converged on responses that were similar across participants that, once analyzed, showed effects similar to those reported in the literature. 
Our novel results can be used to generate predictions that can be tested in future work. Specifically, we predict that (a) making diagnostic letters more dissimilar from each other may help improve reading performance, (b) masking easily confusable letters will impair performance more than masking easily recognizable letters in a normal reading task, and (c) some higher-level effects in reading may be at least partially accounted for by low-level word characteristics like letter complexity, diagnosticity, and confusability. 
Further studies could extend our method to other factors related to reading. For example, the study could be extended to letter features either by decreasing the spatial scale of the noise spread in a subsequent study, or by using de-blurring techniques on the current data. Moreover, identification of noise resistance (and legibility in general) at a letter- or word-sized spatial scale would be useful in the design of text enhancement systems. 
Acknowledgments
This research was supported by a CIHR grant awarded to Martin Arguin, Frédéric Gosselin, and Dan Bub. Portions of this paper were presented at VSS 2008 (Sarasota, Florida), and Cernec 2008 (Montréal, Canada). We thank anonymous reviewers for comments. 
Commercial relationships: none. 
Corresponding author: Frédéric J. A. M. Poirier. 
Email: jamfpo@yahoo.com; frederic.poirier@umontreal.ca. 
Address: Centre de Recherche en Neuropsychologie et Cognition, Université de Montréal, Montréal, Québec, Canada. 
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Appendix A
Details of factors
All frequency data was taken from Lexique 3.55 (New, Pallier, Brysbaert, & Ferrand, 2004; New, Pallier, Ferrand, & Matos, 2001). 
Frequencies
Frequency factors are often log-transformed before analyses, for the purpose of reducing the weight of high-frequency items. Here, frequency factors were only log-transformed when doing so increased stability of results across analyses (i.e., showed fewer changes when entering or removing other factors) and/or decreased individual variability. 
Word frequency statistics included several factors: (a) lexical frequency (M = 1,243 per million; SD = 3,788; min. < 1; max. = 38,929; power law: R2 = 90.5%; exponent = −2.34), (b) cumulative word frequency, i.e., lexical frequency summed across words with the same lemma (M = 1,833 per million; SD = 4,370; min. < 1, max. = 38,929; power law: R2 = 86.7%; exponent = −2.30), (c) number of homographs, i.e., other words with same spelling as target (M = 1,688; SD = 0,827; max. = 5), (d) number of homophones, i.e., other words with same pronunciation as the target (M = 5,038; SD = 3,628; max. = 24), (e) orthographic neighbor frequency, i.e., summed frequency of other words with the same number of letters as the target that differ by a single letter (M = 4,974; SD = 5,254; max. = 25), and (f) phonological neighbor frequency, i.e., summed frequency of other words with the same number of graphemes as the target that differ by a single grapheme (M = 25,052; SD = 32,458; max = 127). 
Complexity
The factor complexity (or perimetric complexity) was defined as contour length squared divided by ink area (Attneave & Arnoult, 1956; Pelli, Burns, Farell, & Moore-Page, 2006), with contour length simplified to only include intensity changes due to horizontal and vertical edges, because line thickness was one pixel. 
Letter width
Letter width was the horizontal extent of letters, in pixels, plus one pixel for interletter spacing. 
Confusability
Confusability measures (i.e., in noise or low contrast) were taken from a study conducted in our lab (Fiset et al., unpublished observations), which used the same font as used here, although they used a finer spatial sampling. Confusability corresponds to the proportion of trials on which a particular letter, briefly exposed (16.67 ms), was reported incorrectly. Average accuracy was maintained at 50% across letters by either adding noise or lowering contrast. 
Letter frequency
Letter frequency was taken from a published dataset for written text in French (Lexique 3.55; New et al., 2001; New et al., 2004). 
Letters that appeared fewer than 10 times in the 30 sentences (i.e., “k” and “w” to “z”) were not included in correlations with noise resistance. Those letters are included in all other correlations, and correlations with or without them were similar. 
Diagnosticity
Diagnosticity was a measure of word confusability increase when a given letter cannot be recognized. Diagnosticity was calculated using the Lexique 3.55 database and an algorithm that: (1) selected a target letter and a replacement letter, (2) changed every instance of the target letter in the word list by the replacement letter, simulating letter confusion, (3) counted the number of identical words in the modified list, simulating word confusion due to letter confusion, (4) repeated Steps 1 through 3 for every target and replacement combination possible, and stored the results into a matrix, (5) subtracted from the matrix the number of words that are identical if no letter was changed, thus isolating word confusion due to letter confusion, (6) summed the matrix for a target letter across replacement letters to give the diagnosticity of that letter, i.e. the extra confusability due to the target letter being misread, and (7) normalized to the 0 to 1 range for the regression analysis. Diagnosticity calculated by factoring in word frequencies or letter frequencies produced similar results, thus only the unweighted diagnosticity is discussed here. 
Sublexical factors
Sub-lexical statistics included the following factors (statistics in our samples shown in parentheses): (1–2) letters per grapheme (“grapheme length”; M = 1.44; M = 0.36; min. = 1; max. = 3) or syllable (“syllable length”; M = 3.6; SD = 1.2; words had an average of 1.638 syllables, SD = 0.758; min. = 1; max. = 4), and (3–4) syllable frequency by type, i.e., the number of syllabic neighbors, and by token, i.e., the sum of the lexical frequencies of all syllabic neighbors (M = 1,096 and 4,646 per million; SD = 1,524 and 7,478; max. = 8,160 and 49,857 for token and type, respectively). 
Word type
Word type included the following categories, using sentence context to determine category (frequency of occurrence in our stimuli indicated in parentheses): (a) auxiliary verbs (1.7%); (b) conjunctions (0.9%); (c) articles (2.6%); (d) pronouns (5.5%); (e) verbs (19.2%); (f) prepositions (4.1%); (g) nouns (42.6%); (h) determiners (3.2%), including quantifiers, demonstrative adjectives, and possessive adjectives; (i) adverbs (5.0%); and (j) adjectives (15.2%). These categories were mutually exclusive. 
Appendix B
Letter statistics.
 
Notes: Letter statistics used in the regression model, as well as mean noise resistance for lowercase letters that appeared at least 10 times in the experiment.
Letter statistics.
 
Notes: Letter statistics used in the regression model, as well as mean noise resistance for lowercase letters that appeared at least 10 times in the experiment.
Confusability in
Noise (%) Contrast (%) Complexity Log letter frequency Noise resistance Diagnosticity
a 67.0 71.8 128.8 8.73 11.15 14,293
b 45.3 33.0 134.6 1.77 10.78 7,482
c 44.5 44.5 117.6 3.70 11.11 9,699
d 42.8 45.5 134.6 2.39 10.61 7,345
e 65.5 85.3 130.7 10.56 10.87 25,110
f 69.0 58.8 101.9 1.30 11.24 6,450
g 36.3 21.0 165.1 1.97 10.43 6,179
h 41.3 39.5 121.5 1.94 10.43 2,552
i 84.8 93.3 73.1 8.49 11.14 12,310
j 68.8 73.3 100.0 0.25 10.91 1,526
k 23.8 31.3 134.6 0.53 651
l 85.0 90.8 72.3 4.72 11.28 10,935
m 18.0 12.8 145.2 2.92 10.67 9,602
n 40.0 47.3 109.7 7.07 11.13 12,556
o 67.8 64.5 115.2 6.26 10.99 6,259
p 28.8 20.0 142.4 2.48 10.39 9,305
q 47.5 45.0 142.4 0.55 10.98 489
r 60.8 66.3 98.0 7.78 11.42 20,186
s 48.8 58.8 149.3 7.23 11.31 34,204
t 86.8 85.8 94.1 6.69 11.48 19,596
u 43.5 42.3 101.9 4.17 11.05 5,520
v 51.5 56.0 135.5 1.20 11.31 6,921
w 12.5 13.5 167.5 0.22 115
x 46.8 55.0 171.4 0.35 845
y 13.3 14.0 171.4 0.73 1,731
z 27.5 27.8 128.8 0.46 4,819
Appendix C
Implications for letter processing
The pattern of correlations between letter-based variables (Table 3) suggests that the alphabet is more optimal for writing than for reading. This argument is presented below in three parts: (a) the results are reviewed from the perspective of reading constraints, (b) the results are reviewed from the perspective of writing constraints, and (c) the results are contrasted to those of Changizi, Zhang, Ye, and Shimojo (2006) who argue, based on topology distributions, that alphabets are developed based on visual constraints rather than motor constraints. 
An alphabet designed to be easy to read would focus on making diagnostic letters (especially frequent ones) easier to read, i.e., more efficient and less confusable. Supporting this, we found that frequent and diagnostic letters were more efficiently perceived as measured by noise resistance (see also Pelli et al., 2006). However, in French at least, frequent and diagnostic letters are unfortunately easily confused with other letters (Table 3), making the alphabet suboptimal for reading. We propose that efficiently perceived simple letters are more easily confused together because they lack distinctive features (see below; Attneave & Arnoult, 1956; Pelli et al., 2006). 
An alphabet designed to be easy to write would focus on making frequent letters simple, so that writing speed would be improved. Supporting this, frequent letters were less complex. Although not directly relevant to writing performance, frequent letters tend to be more diagnostic and easily confusable (e.g., “i,” “l,” compared to “m,” “w,” “y”). That is, by meeting writing constraints, reading constraints were not optimized. Thus in designing an alphabet that is both easy to write and to read, the emphasis should be on making diagnostic and frequent letters both easy to encode (e.g., high noise resistance, low complexity) and easy to discriminate from each other (e.g., low confusability). 
The only study that looked empirically at whether alphabets were designed based on reading or writing constraints is a study comparing the topology distribution of alphabets, shorthand, trademarks, and natural scenes (Changizi et al., 2006). They measured the relative frequency of different topologies within a stimulus set (e.g., alphabets, trademarks, natural scenes), and compared topology distributions across stimulus sets. Their conclusions can be summarized as follow: (a) alphabets have topology distributions similar to trademarks and natural scenes, suggesting that they are influenced by visual constraints, (b) alphabets have a topology distribution that is dissimilar to that of shorthand, suggesting that motor constraints play a much lesser role in alphabet design, and (c) alphabets have a topology distribution that differs from scribbles or random lines, suggesting that alphabets are not random. Their conclusion conflicts with ours. However, we reconcile the diverging views below. 
Changizi et al. (2006) did their analysis over a collection of alphabets, thus they lack single-letter data to compare with. This issue is critical because the assignment of letter shapes to sounds may itself be consistent with motor constraints, consistent with our results. Early alphabet designers likely associated simple symbols to frequent sounds first, and then created symbols of increasing complexity for increasingly infrequent sounds. Although they made symbols generally easy to produce and discriminate from each other, they likely assigned simpler symbols to frequent sounds. Thus, although Changizi's account may be accurate at the alphabet level, ours may be an adequate description at the letter level. 
To further this argument, Changizi et al.'s (2006) study did not account or control for the frequency of occurrence of letters. As shown above, simple letters are frequent. Correcting their data for this bias would increase frequencies at low-complexities. This could make their results consistent with alphabets being influenced by motor constraints. 
Appendix D
Ecological validity
Every method to study reading has its strengths and weaknesses, and none is perfect (Haberlandt, 1994; Perfetti, 1985). The visual spread method used here is an efficient way of measuring noise resistance at a relatively fine spatial scale. An hour and a half of testing per participant was sufficient to extract all the effects discussed above, including effects related to single-letters, letter position, word type, and syllable frequencies. This technique also required no specialized equipment such as an eye tracker or a voice key. However, caution is advised when generalizing from our task to other reading tasks, for several reasons. 
Firstly, we did not ask participants to read sentences, and we did not measure reading comprehension. Reading effects are generally robust across methods, including passive-viewing tasks (e.g., fMRI experiments). Nevertheless, participants may sometimes adjust noise using visual factors, which may be unrelated or indirectly related to reading. For example, our results are consistent with complexity and diagnosticity, but could be more consistent with confusability if reading performance had been measured. In the presence of conflicting factors influencing noise, participants may not always spread noise to improve readability. 
Secondly, participants had ample opportunity to extract the full content of a sentence over the duration of the study (average of 3 min spent per sentence). Mechanisms that are time-sensitive may require speeded-response tasks to produce measurable effects. Moreover, our method may not capture well effects that are dependent on surprise or uncertainty (e.g., when participants are asked to search for specific information or spelling errors). 
Thirdly, the stimuli were degraded. Polarity was reversed in 12.5% of pixels, effectively changing letter shape. However, our noise levels were intermediate between studies using no noise and those using high levels of noise, such that reading sentences remained easy. 
Overall, our results are consistent with the literature. However, both the similarities and differences of results across different methodologies can be informative. Similar results inform of effects that are robust across task demands and stimuli. Different results inform of effects that are sensitive to task demands and stimulus characteristics. By integrating results across methodologies and task demands, we can gain a better understanding of the underlying mechanisms involved. 
In particular, our method differs from many other methods in the way the sentences were generated. A common research method is to generate word lists that exaggerate natural differences on few experimental factors while minimizing differences on control factors. These lists can nevertheless include sampling biases, especially with regards to other factors not considered in the selection criteria. The approach taken here respects natural frequencies and word statistics, and uses a statistical control instead. Our word sampling method is representative of normal texts, but it undersamples infrequent word types, word lengths, letters, etc. It is thus possible that some factors above would be significant with a larger sample of low-frequency words. This is not a weakness specific our study, but rather a general concern in research when attempting to generalize across studies using natural or controlled samples. 
Statistical techniques do offer advantages, namely: (a) ability to control for many factors, (b) ability to easily include low-level factors such as letter complexity or syllabic length, and (c) higher statistical sensitivity to effects that are normally masked by other factors also influencing performance. Our study raises the possibility that certain effects commonly attributed to word type could in fact be due low-level factors. A follow-up study could confirm whether word type, even controlled for low-level factors, would still impact reading performance. 
Figure 1
 
A sample stimulus is shown without noise (A) and after adjustment by participants (B; average). Panel B is also shown with noise differences amplified (C), or with noise levels represented as gray levels (D; surround gray = 12.5% noise; lighter = less noise). The noise levels in Panel B appear roughly homogeneous over the image, despite systematic variation in noise levels as highlighted in panels C, D.
Figure 1
 
A sample stimulus is shown without noise (A) and after adjustment by participants (B; average). Panel B is also shown with noise differences amplified (C), or with noise levels represented as gray levels (D; surround gray = 12.5% noise; lighter = less noise). The noise levels in Panel B appear roughly homogeneous over the image, despite systematic variation in noise levels as highlighted in panels C, D.
Figure 2
 
Weights (-y-axis) associated with space-based and positional-based factors. A positive (or negative) weight indicates that noise was higher (or lower) in the areas indicated by the factor. Participants increased noise on spaces surrounding and between words (A), on external letters (A), one-letter words (B), on letters further towards the right (C, D, F), and on the last letter. They decreased noise on miscellaneous characters (A). Error bars and dotted lines represent SEM.
Figure 2
 
Weights (-y-axis) associated with space-based and positional-based factors. A positive (or negative) weight indicates that noise was higher (or lower) in the areas indicated by the factor. Participants increased noise on spaces surrounding and between words (A), on external letters (A), one-letter words (B), on letters further towards the right (C, D, F), and on the last letter. They decreased noise on miscellaneous characters (A). Error bars and dotted lines represent SEM.
Figure 3
 
Weights (y-axis) associated with letter-based factors, when entered independently (A) or “blocked” together (B). A weight of “0” indicates that the factor is not associated with noise increase or decrease. (C) Correlation between averaged noise and predicted noise per letter. “Low c.” is an abbreviation for “low contrast.”
Figure 3
 
Weights (y-axis) associated with letter-based factors, when entered independently (A) or “blocked” together (B). A weight of “0” indicates that the factor is not associated with noise increase or decrease. (C) Correlation between averaged noise and predicted noise per letter. “Low c.” is an abbreviation for “low contrast.”
Figure 4
 
Weights (y-axis) associated with text-based factors, when entered together (blocked; right) or independently (left). Factors are arranged in panels according to the blocks they were entered in. A weight of “0” indicates that the factor is not associated with noise increase or decrease. (A, B) Of the four subword statistics, only the syllabic frequencies were significantly correlated with noise levels, where participants increased noise on high syllable type frequency and low syllable token frequency. (C, D) Participants increased noise on words with more orthographic neighbors and fewer phonological neighbours. (E, F) Word type also influenced noise levels.
Figure 4
 
Weights (y-axis) associated with text-based factors, when entered together (blocked; right) or independently (left). Factors are arranged in panels according to the blocks they were entered in. A weight of “0” indicates that the factor is not associated with noise increase or decrease. (A, B) Of the four subword statistics, only the syllabic frequencies were significantly correlated with noise levels, where participants increased noise on high syllable type frequency and low syllable token frequency. (C, D) Participants increased noise on words with more orthographic neighbors and fewer phonological neighbours. (E, F) Word type also influenced noise levels.
Figure 5
 
Hypothesized relationships between the variables related to letters. All correlations were positive between the variables shown. Diagnostic letters are frequently used (left). Efficiency was measured using noise resistance and simplicity (the opposite of complexity). Letter confusability was measured in low contrast and in noise (right). The results are consistent with an alphabet that promotes faster writing, but not necessarily faster or easier reading. Dotted lines indicate correlations that should be inverted when designing an alphabet to promote reading performance (without necessarily making writing performance worse), by changing the relationship between confusability and all other variables, while retaining all other relationships.
Figure 5
 
Hypothesized relationships between the variables related to letters. All correlations were positive between the variables shown. Diagnostic letters are frequently used (left). Efficiency was measured using noise resistance and simplicity (the opposite of complexity). Letter confusability was measured in low contrast and in noise (right). The results are consistent with an alphabet that promotes faster writing, but not necessarily faster or easier reading. Dotted lines indicate correlations that should be inverted when designing an alphabet to promote reading performance (without necessarily making writing performance worse), by changing the relationship between confusability and all other variables, while retaining all other relationships.
Table 1
 
Some sample factors and their values for each character position in a sequence of two words. Notes: “les chiens” in English: “the dogs”.
Table 1
 
Some sample factors and their values for each character position in a sequence of two words. Notes: “les chiens” in English: “the dogs”.
l e s c h i e n s
Word length 3 3 3 0 6 6 6 6 6 6
Distance from beginning 1 2 3 0 1 2 3 4 5 6
Distance from end −3 −2 −1 0 −6 −5 −4 −3 −2 −1
Distance left-right −1 0 1 0 −2.5 −1.5 −0.5 0.5 1.5 2.5
Noun 1 1 1 1 1 1
Table 2
 
Summary of analyses. Notes: All analyses include the factors “spaces,” “miscellaneous characters,” “surrounding space,” and a constant. Weights are shown for independent, blocked, and full regressions. Intervals are SEM across participants. Factors marked by “—” were included in the analysis as controls. Empty lines represent factors not included in the given regressions. R2 for the full analysis was 29.5% ± 4.2%.
Table 2
 
Summary of analyses. Notes: All analyses include the factors “spaces,” “miscellaneous characters,” “surrounding space,” and a constant. Weights are shown for independent, blocked, and full regressions. Intervals are SEM across participants. Factors marked by “—” were included in the analysis as controls. Empty lines represent factors not included in the given regressions. R2 for the full analysis was 29.5% ± 4.2%.
Category Factor Independent Blocked Full Figure reference R2
Spaces & misc. Surrounding space 1.448 ± 0.211 0.659 ± 0.175 1.615 ± 0.396 2A 21.7% ± 4.1%
Spaces 1.861 ± 0.163 1.939 ± 0.169 0.754 ± 0.259
Near spaces 0.506 ± 0.063 0.506 ± 0.063 0.182 ± 0.119
Miscellanous characters −0.402 ± 0.090 −0.454 ± 0.089 −0.092 ± 0.111
Positional Word length −0.018 ± 0.011 2B–F 20.8% ± 3.9%
Left-right 0.107 ± 0.022
From end 0.084 ± 0.016
From beginning 0.060 ± 0.016
Letters Width −0.397 ± 0.268 1.181 ± 0.323 3 27.7% ± 4.3%
Confusability in noise 0.795 ± 0.120 1.339 ± 0.328
Confusability low contrast 0.581 ± 0.102 −0.880 ± 0.257
Complexity −1.092 ± 0.150 −1.446 ± 0.186
Log letter frequency 0.272 ± 0.046 0.074 ± 0.062
Diagnosticity 0.363 ± 0.132 0.099 ± 0.137
Sublexical Grapheme length 0.000 ± 0.052 −0.003 ± 0.053 0.019 ± 0.052 4A, B 20.3% ± 3.7%
Syllable length −0.017 ± 0.019 0.006 ± 0.018 −0.021 ± 0.011
Token syllable frequency 0.019 ± 0.025 −0.128 ± 0.040 −0.101 ± 0.032
Type syllable frequency 0.145 ± 0.034 0.258 ± 0.046 0.154 ± 0.050
Frequencies Log frequency 0.014 ± 0.008 −0.017 ± 0.013 0.022 ± 0.028 4C, D 20.6% ± 3.7%
Log cumulative Frequency 0.015 ± 0.009 0.024 ± 0.014 −0.021 ± 0.029
N homographs 0.021 ± 0.015 −0.011 ± 0.013 0.013 ± 0.019
N homophones 0.001 ± 0.006 0.001 ± 0.007 −0.007 ± 0.007
Log orthographic neighbors 0.052 ± 0.023 0.097 ± 0.022 0.056 ± 0.027
Log phonetic neighbors 0.000 ± 0.019 −0.056 ± 0.020 −0.037 ± 0.020
Word type Auxiliary verb 0.445 ± 0.090 0.302 ± 0.129 0.484 ± 0.253 4E, F 20.6% ± 3.8%
Conjunction 0.331 ± 0.188 0.191 ± 0.219 0.528 ± 0.255
Article 0.159 ± 0.077 0.014 ± 0.117 0.369 ± 0.222
Pronoun 0.142 ± 0.114 −0.001 ± 0.146 0.393 ± 0.187
Verb 0.017 ± 0.029 −0.121 ± 0.098 0.425 ± 0.213
Preposition −0.004 ± 0.066 −0.138 ± 0.109 0.286 ± 0.161
Noun −0.038 ± 0.073 −0.159 ± 0.080 0.339 ± 0.168
Determiner −0.093 ± 0.113 −0.223 ± 0.158 0.320 ± 0.259
Adverb −0.108 ± 0.064 −0.233 ± 0.105 0.199 ± 0.185
Adjective −0.146 ± 0.064 −0.264 ± 0.119 0.264 ± 0.210
Table 3
 
Correlations between several measures based on the same font. Notes: If the factor complexity is multiplied by −1, all correlations become positive here.
Table 3
 
Correlations between several measures based on the same font. Notes: If the factor complexity is multiplied by −1, all correlations become positive here.
Factor Noise resistance Diagnosticity Log letter frequency Complexity Confusability in low contrast
Confusability in noise 0.646 0.410 0.566 −0.756 0.953
Confusability in low contrast 0.676 0.487 0.644 −0.713
Complexity −0.561 −0.239 −0.457
Log frequency 0.428 0.810
Diagnosticity 0.442
Letter statistics.
 
Notes: Letter statistics used in the regression model, as well as mean noise resistance for lowercase letters that appeared at least 10 times in the experiment.
Letter statistics.
 
Notes: Letter statistics used in the regression model, as well as mean noise resistance for lowercase letters that appeared at least 10 times in the experiment.
Confusability in
Noise (%) Contrast (%) Complexity Log letter frequency Noise resistance Diagnosticity
a 67.0 71.8 128.8 8.73 11.15 14,293
b 45.3 33.0 134.6 1.77 10.78 7,482
c 44.5 44.5 117.6 3.70 11.11 9,699
d 42.8 45.5 134.6 2.39 10.61 7,345
e 65.5 85.3 130.7 10.56 10.87 25,110
f 69.0 58.8 101.9 1.30 11.24 6,450
g 36.3 21.0 165.1 1.97 10.43 6,179
h 41.3 39.5 121.5 1.94 10.43 2,552
i 84.8 93.3 73.1 8.49 11.14 12,310
j 68.8 73.3 100.0 0.25 10.91 1,526
k 23.8 31.3 134.6 0.53 651
l 85.0 90.8 72.3 4.72 11.28 10,935
m 18.0 12.8 145.2 2.92 10.67 9,602
n 40.0 47.3 109.7 7.07 11.13 12,556
o 67.8 64.5 115.2 6.26 10.99 6,259
p 28.8 20.0 142.4 2.48 10.39 9,305
q 47.5 45.0 142.4 0.55 10.98 489
r 60.8 66.3 98.0 7.78 11.42 20,186
s 48.8 58.8 149.3 7.23 11.31 34,204
t 86.8 85.8 94.1 6.69 11.48 19,596
u 43.5 42.3 101.9 4.17 11.05 5,520
v 51.5 56.0 135.5 1.20 11.31 6,921
w 12.5 13.5 167.5 0.22 115
x 46.8 55.0 171.4 0.35 845
y 13.3 14.0 171.4 0.73 1,731
z 27.5 27.8 128.8 0.46 4,819
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