The transposed word effect is consistent with serial word recognition and varies with reading speed

Abstract

The scientific study of reading has long been animated by questions of parallel vs. serial processing. Do readers recognize words serially, adding each one sequentially to a representation of the sentence structure? One fascinating phenomenon to emerge from this research is the transposed word effect: when asked to judge whether sentences are grammatical, readers often fail to notice grammatical errors caused by transposing two words. This effect could be evidence that readers recognize multiple words in parallel. Here we provide converging evidence that the transposed word effect is also consistent with serial processing because it occurs robustly when the words in each sentence are presented serially. We further investigated how the effect relates to individual differences in reading speed, to gaze fixation patterns, and to differences in difficulty across sentences. In a pretest, we first measured the natural English reading rate of 37 participants, which varied widely. In a subsequent grammatical decision task, we presented grammatical and ungrammatical sentences in two modes: one with all words presented simultaneously, and the other with single words presented sequentially at each participant’s natural rate. Unlike prior studies that used a fixed sequential presentation rate, we found that the magnitude of the transposed word effect was at least as strong in the sequential presentation mode as in the simultaneous mode, for both error rates and response times. Moreover, faster readers were more likely to miss transpositions of words presented sequentially. We argue that these data favor a “noisy channel” model of comprehension in which skilled readers rely on prior knowledge to rapidly infer the meaning of sentences, allowing for apparent errors in spatial or temporal order, even when the individual words are recognized one at a time.

1. INTRODUCTION

In the study of reading, there has been much controversy as to whether multiple words are processed in parallel or serially (Snell & Grainger, 2019; White, Boynton & Yeatman, 2019). Computational reading models such as SWIFT (Engbert et al. 2002), Glenmore (Reilly & Radach 2006), and OB1-reader (Snell et al. 2018) posit that attention may be distributed to support the parallel lexical processing of multiple words. Other models, such as E-Z Reader (Reichle, Pollatsek & Rayner, 2006) assume that attention is allocated sequentially to one word at a time, perhaps because of severe capacity limits in the word recognition circuitry (White, Palmer, Boynton & Yeatman, 2019; White, Palmer & Boynton, 2020).

Proponents of parallel word recognition models have cited as evidence the “transposed word effect” (inspired by the transposed letter effect (Bruner & O’Dowd, 1958; Christianson et al., 2005). Mirault, Snell, and Grainger (2018) found that when asked to rapidly judge the grammaticality of French sentences, subjects were slower to correctly judge – and more likely to misjudge – an ungrammatical sentence created by transposing two words of a grammatical sentence (e.g., The white was cat big) in comparison to “control” ungrammatical sentences that could not be made grammatical by changing word order (e.g., The white was cat slowly). The authors argued that this transposed word (TW) effect is due to parallel processing of multiple words, combined with a noisy encoding of each word’s spatiotopic position. Uncertainty in the word positions allows readers to access a representation of the grammatical base (i.e., the sentence with the corrected word order), which interferes with their ability to correctly judge the sentence as ungrammatical.

Related phenomena have been found in two other paradigms: first, a change-detection task, in which participants struggle to notice the that two sentences differ in the transposition of two words (Pegado & Grainger, 2019, 2021). Second, the “word-in-sequence” identification task requires participants to type in one post-cued word that was presented in a string of five words. Accuracy is best if all the words form a grammatical sentence (Snell & Grainger, 2017), and accuracy is also better for transposed-word sentences than control ungrammatical sentences (Wen, Mirault & Grainger, 2022).

Altogether, these studies show that when readers see a sentence containing two words in a transposed order, they sometimes process it as if it were grammatical and fail to notice the transposition. These data have supported a parallel processing framework, as made concrete by the OB1-reader model (Snell et al., 2018). Through top-down syntactic control and contextual knowledge, the parallel activation of adjacent words allows for words to be recognized out of the order in which they appear, and mismapped onto the representation of a grammatical sentence structure in short-term memory.

Such a parallel interpretation has been challenged by three studies published in the last year that demonstrate that the transposed word effect occurs, to some extent, even when the words are presented one at a time (Liu et al, 2022; Huang & Staub 2022; Mirault et al. 2022). This mode of presenting sentences (rapid serial visual presentation, RSVP) enforces serial processing of words. Nonetheless, participants still struggle to judge sentences with transposed words as ungrammatical, in three different languages (Chinese, English, and French, respectively).

Therefore, the transposed word effect is not necessarily evidence of parallel processing of words in natural reading. It is also consistent with serial models of reading, combined with a “noisy channel” account of how sentence-level constraints determine the inference of the sentence meaning (Gibson et al., 2013; Huang & Staub, 2021a). At a “post-lexical” stage when the whole sentence is being integrated, according to this idea, the reader uses prior linguistic knowledge to infer the most likely meaning of the sentence, allowing for apparent errors in word order. To account for the TW effect when all words are presented at once and a sentence is read naturally, serial models assume that before each saccade attention shifts into the parafovea to acquire “preview” information about the upcoming word, after the currently fixated word has been identified (word n+1). This rapid sequential processing of words may allow readers to mis-represent word order (Rayner et al., 2013) at a post-lexical stage.

The issue remains debated, however, because all three of the recent studies found that the transposed word effect with sequential word presentation was smaller than when all words in the sentence are presented simultaneously. Importantly, the presentation rate was fixed and equal for all participants: 250 ms per word (4 words/s) in two studies (Liu et al., 2022; Huang & Staub, 2022), and 300 ms per word (3.3 words/s) in the third (Mirault et al., 2022). The difference in error rate between transposed and control sentences was consistently smaller in the sequential (serial) presentation mode than the simultaneous (parallel) mode. It makes no difference whether the subject must wait until the end of the RSVP sequence to respond or can respond as early as they wish (Huang & Staub, 2022; Mirault et al, 2022). Moreover, the lengthening of correct response times (RTs) for transposed sentences was observed only in the simultaneous mode and not the sequential mode (Liu et al., 2022, Mirault et al., 2022). One interpretation is that there is more uncertainty, or “bottom-up noise,” about word order in the simultaneous mode because attention can be divided between multiple words at a time (Mirault et al., 2022).

One potential concern is that the fixed sequential presentation rate (250 or 300 ms/word) may have been too slow, at least for some participants. Reading rates vary widely even among skilled readers. If the words are presented more slowly than a participant naturally reads, there is more time to integrate word n into the sentence structure before word n+1 becomes available for processing. That could explain the smaller TW effect produced for serial in comparison to parallel displays. Moreover, in order for any top-down influence that would alter the representation of word order to occur, it must operate rapidly enough that it prevents any disruption in the forward progression of saccadic eye movements for the transposition to go unnoticed by the reader (Huang & Staub, 2021).

In the present study, we test several novel hypotheses regarding the transposed word effect under both simultaneous and sequential word presentations. Our primary innovation is to set the sequential presentation rate to each participant’s natural reading rate as assessed in a separate experiment. On the one hand, this may make the transposed word effect equivalent to what is observed in the simultaneous mode (normal reading). On the other hand, if the normal transposed word effect is partly due to parallel processing of multiple attended words (especially for RTs), then the effect will remain smaller in the sequential mode (Mirault et al., 2022). By examining individual differences in the effect magnitudes, we also test the following prediction: if parallel word processing is possible, it is likely to be utilized more effectively by faster readers. Those fast readers would also be expected to have a bigger transposed word effect (compared to slow readers) in the simultaneous mode, but not in the sequential mode. Alternatively, if the transposed word effect is due primarily to post-lexical inference, it should be larger when readers have to rely more on their knowledge, such as in the sequential mode when some information they normally use is removed. To better understand why sentences with transposed words are judged as grammatical, we also analyze eye movements in the simultaneous presentation mode, and differences in processing difficulty across sentences.

2. METHODS

2.1. Participants

Thirty seven participants (32 female) were recruited at Columbia University and Barnard College (New York City, NY). All participants were fluent English speakers, reported having normal or corrected-to-normal vision, and ranged in age from 18 to 30 years (M = 20.4 years, SEM = 0.35). They received monetary compensation or course credit and provided informed consent in accordance with the Declaration of Helsinki and the Barnard College Institutional Review Board. On the composite TOWRE-II Test of Word Reading Efficiency (Torgesen, Rashotte & Wagner, 1999), all scored an index value near or above the norm of 100 (M = 112, SEM = 1.6). The sample size was chosen in advance of data collection on the basis of a pilot experiment (N=15) with similar design. A power analysis suggested that in order to obtain a mean transposed word effect (comparing error rates for control vs. transposed sentences) in the sequential presentation mode, we would need at least 28 participants for 90% power. After the first 9 participants, we decided to increase the inter-line spacing of the passages presented for the initial reading rate test, in order to ease our analysis of eye movements. We then ran another 28 subjects as planned. However, we found that reading rates were not appreciably affected by the line spacing change, and that change did not apply to the main grammatical decision task, so we include all 37 participants in the analyses below.

2.2. Apparatus

We used custom MATLAB software (MathWorks, Natick, MA, USA) and the Psychophysics Toolbox (Brainard 1997; Pelli 1997) to present stimuli on a ViewPixx 3D screen (VPixx Technologies) with a 120 Hz refresh rate and 1920 x 1080-pixel resolution. The background brightness was set to the screen’s maximum (100 cd/m²). Participants were seated 60 cm from the screen. The stimuli consisted of a small green fixation dot of 0.2 degrees of visual angle (°) in diameter and black letter strings in Courier New font. The letter “x” was 0.4° tall. The movement of the subject’s right eye was recorded using an EyeLink 1000+ eye-tracker (SR Research, Toronto, ON, Canada) at 500 Hz.

2.3. Pre-test: Reading Rate Determination

2.3.1. Design and Stimuli:

The stimuli consisted of 36 two-sentence passages, ranging in length from 29 to 58 words. All stimuli are listed in the Supplementary Materials. Half the passages were logical and semantically coherent. The semantically incoherent passages were each constructed from one coherent passage by changing the second sentence to introduce a contradiction or logical flaw (see example in Supplemental Figure S1). Each participant viewed only either the semantically coherent or incoherent version of each passage, for a total of 18 trials in a single block. This structure allowed us to test each passage under both coherent conditions. The line spacing was 1.5 lines for the first 9 subjects, then we increased it to 2, in order to better detect return sweep eye movements.

2.3.2. Procedure:

Participants were instructed to read each passage at their natural pace and then report whether the passage was semantically coherent or not. Each trial began with a green fixation dot at the top left of the screen. Participants were told to initiate each trial by pressing the space bar while fixating on that dot. The trial only began if the estimated gaze position was within 1° horizontally and 1° vertically of the dot. Then the whole passage appeared. After reading through the passage at their normal speed, participants fixated their gaze on the subsequent green dot located to the right of the final word and pressed the spacebar again. Then a question appeared on the screen: “Was the passage semantically coherent or not?” Participants responded by using the index and middle fingers of their right hand to press either the left arrow for “no” or the right arrow for “yes.” Feedback was provided immediately with a high-pitched beep (correct) or low-pitched beep (incorrect) beep. Participants completed two practice trials before beginning the experimental block, finishing in roughly 20 minutes.

2.3.3. Analysis:

To determine each participant’s reading rate, we processed the raw eye traces. Saccades were defined as intervals in which the 2D gaze velocity exceeded 40 degrees/second, lasting at least 6 ms and displacing the gaze position by more than 1 letter width (0.36°). Fixations were the period between saccades, excluding periods with blinks (and the 60 ms before and after each blink when the eye trace was disturbed). The gaze position (x,y) was averaged within each fixation interval, and then assigned to the nearest word. The total number of words read, W, was defined as the number of words in the passage, plus the number of words that were fixated during regressions when the participant moved their eyes backwards in the text. For a fixation on word n to be counted as one of these re-readings, another word ahead of n had to be fixated first. The total reading time, T, was defined as the duration in seconds between the onset of first fixation on the passage and the offset of the last fixation on the passage, before the subject looked to the green dot to finish the trial. The reading rate on each trial was calculated as W/T, in words/second. To set the sequential presentation rate in the grammatical decision task (see below), we used the mean reading rate on semantically coherent trials with a correct response.

2.4. Main experiment: Grammatical decision task

2.4.1. Design and Stimuli:

We presented participants with three types of English sentences (one per trial): grammatical sentences, “control” ungrammatical sentences, and “transposed” ungrammatical sentences. They all were 5 words long, and were created in the same way as Mirault et al. 2018 (see examples Table 1, full list in the Supplementary Materials). First, we created two stimulus sets each containing 160 grammatical base sentences. We derived the ungrammatical test sentences from one set of the grammatical bases. To create the “transposed” ungrammatical test sentences, we simply reversed the order of the 3rd and 4th words of each grammatical base. To create the “control” sentences, we first created “ungrammatical base” sentences by exchanging the final words of each pair of grammatical bases. Then we transposed the 3rd and 4th words of those ungrammatical bases to create the “control” ungrammatical test sentences. Therefore, both “control” and “transposed” sentences were created by swapping words 3 and 4 of a base sentence, but only the “transposed” sentences could be made grammatical by undoing that transposition.

Table 1.

Construction of critical ungrammatical test sentences from base pair sentences.

Sentence	Example
Base
Grammatical	The black bear was hungry. The tall man read quietly.
Ungrammatical	The black bear was quietly. The tall man read hungry.
Test
Transposed Word	The black was bear hungry. The tall read man quietly.
Control	The black was bear quietly. The tall read man hungry.

Only the test sentences were used as the ungrammatical stimuli, leading to a set of 160 transposed word sentences and 160 control sentences. However, each participant saw only either the control or transposed version of the original base sentence, for a total of only 160 ungrammatical sentences per participant. This structure allowed us to test the same words in both of the test sentence conditions. The other unmodified set of 160 grammatical sentences were presented to participants intermingled with the ungrammatical sentences, for a total of 320 trials.

2.4.2. Trial sequence:

On each trial (illustrated in Figure 1A-B), participants viewed one five-word sentence and judged as quickly and accurately as possible whether or not it formed a grammatical sentence. Each trial began when the participant fixated (within 1°) on a green dot and pressed the spacebar. Then a five-word sentence appeared, with all the words presented either simultaneously or sequentially. In the simultaneous mode, the fixation dot was displayed one character space to the left of the first letter of the upcoming words, to mimic natural left-to-right reading conditions. Then all 5 words appeared simultaneously, on one line. They remained visible until the participant made a response. In the sequential mode, the fixation dot appeared at the center of the screen and then the words appeared one at a time, centered at the same location. The rate of presentation was equal to the reading rate calculated in the pretest (see above), with the duration of each word rounded to units of 8.3 ms (1 video frame). There was no blank interval between words. After the final word appeared, a blank screen appeared until the participant responded.

Figure 1:

(A) Example simultaneous presentation trial in the grammatical decision task, with a transposed stimulus. (B) Example sequential presentation trial. (C) Smoothed distributions of reading rates in words per second. The printed numbers are the means, which are also represented by the horizontal lines. The short vertical lines are 95% bootstrapped CIs. For the sequential presentation mode, these data are presentation rates set to match each individual’s reading rate from the pretest. For the simultaneous condition, reading rates are averaged across grammaticality conditions. Each trial’s rate is the total time spent reading the stimulus, divided by the number of words presented (5) plus the number of words that were fixated during regressions (glances leftwards in the text). (D) The correlation between individual participant reading rates, in the sequential mode (x-axis) vs simultaneous mode (y-axis).

The participant reported whether the sentence presented was grammatical, along with their confidence in the judgment, by pressing one of four keys (Z or X with their left hand, < or > with their right hand). ‘Z’ was for “sure ungrammatical,” ‘X’ for “guess ungrammatical,” “<“ for “guess grammatical,” and “>“ for “sure grammatical.

After instructions and ten practice trials with independent stimuli, each participant completed four experimental blocks: two with sequential presentation mode and two with simultaneous presentation mode, in alternating order. Half the participants began with a sequential block and the other half began with a sequential block. Each block consisted of 80 sentences: 40 grammatical, 20 transposed, and 20 control. The assignment of word sentences to presentation modes (sequential or simultaneous), was also counterbalanced: each subject was assigned to one of two groups. Group 1 saw a random half of the sentences in the sequential presentation; Group 2 saw those same sentences in simultaneous presentation, and vice versa.

2.4.3. Analysis:

First, we excluded trials with response times longer than 3 standard deviations above each participant’s grand mean. As a result we lost 1.5% of trials (ranging 0.3 to 2.6% across participants). For each condition we then computed the error rate (proportion of trials with incorrect responses), and the geometric mean of correct response times (relative to the onset of the first word on each trial).

To characterize the effects of sentence type and presentation mode, and their interaction, we took two complementary approaches: the first was to average across trials within each participant, and then fit linear mixed effects models (LMEs) with fixed effects of sentence type and presentation mode, and the interaction between those two, with participant as a random effect with random slopes and intercepts. Those give results similar to an ANOVA, which we followed up with pairwise t-tests, bootstrapped 95% confidence intervals, and Bayes Factors (BFs). The BF is the ratio of the probability of the data under the alternate hypothesis (that two conditions differ), relative to the probability of the data under the null hypothesis (Rouder et al., 2009). For example, a BF of 10 indicates that the data are ten times more likely under the alternate hypothesis than the null hypothesis. We computed BFs using the bayesFactor toolbox in MATLAB (https://github.com/klabhub/bayesFactor: DOI: 10.5281/zenodo.4394422).

The second approach was to fit generalized linear mixed effects models (GLMEs) to the raw data, predicting individual trial response time (log₁₀ transformed) or accuracy. These models had the same predictors as the subject-level models, but with an additional random effect for the particular sentence presented on each trial. Single-trial accuracy was fit with a binomial distribution and a logit linking function. The grammatical sentences were excluded from the LME and GLME analyses, to focus on the transposed word effect (compared to control sentences).

We also analyzed eye movements in the simultaneous presentation condition, similarly to how we analyzed the passage reading data in the pretest. Each fixation between the sentence onset and the participant’s keypress was assigned to a word. We then calculated the total reading rate, and the proportion of trials when each word was skipped. We also characterized each saccade as either being forward right one word, re-fixating the current word, skipping ahead, or a regression leftwards.

3. RESULTS

3.1. Natural reading rates vary widely across participants

In the reading rate pretest, participants made correct semantic coherence judgements on 88.6% of trials (SEM = 1.6%). The reading rate on correctly judged coherent passages, calculated as the mean number of ms spent processing each word (including words re-read after having moved ahead), was 4.92 words/s (SEM = 0.16). There was a wide range of individual differences: 3.0 to 7.3 words/s. These differences were highly reliable: split-half correlation coefficient = 0.90. Moreover, it is not the case that the faster readers were less careful readers: reading rate correlated positively with accuracy in the semantic coherence judgment (r=0.42, p=0.009).

In the subsequent grammatical decision task, we set the word presentation rate for the sequential mode to match each individual’s reading rate from the pre-test. The reason we calculated reading rates in this way, including words re-read during regressions in the numerator, was to match the rate at which words enter the visual system in both simultaneous and sequential rates. If two readers spent the same total time processing a passage, but one makes regressions to re-read some words, then our estimated rate will be higher for that person because they were effectively reading more words per minute. However, making regressions usually also increases the total reading time, balancing out this effect. Some regressions were common, so our estimated reading rates were slightly higher than if we did not include re-read words in the numerator (by 0.61 words/s on average, t(36)=10.7, p<10⁻¹²).

Figure 1C plots the distribution of reading rates in the grammatical decision task, estimated as the average number of words per second, for both presentation modes. The presentation rates for the sequential mode (red distribution) were determined from the passage reading pretest. The rates for the simultaneous mode (pink distribution) were calculated for each subject in the same way as in the pretest. These two reading rates within the grammatical decision task (simultaneous mode rate, and sequential presentation rate) did not differ: t(36) = 0.62, p = 0.54; BF = 0.21. In fact, they were well correlated across individuals, as shown in Figure 1D. Therefore, the reading rate assessed in the pretest captured a reliable trait that varied across individuals, which we accounted for in the sequential mode.

3.2. The transposed word effect occurs in both simultaneous and sequential presentations

Figure 2 plots the mean error rates and correct RTs in each presentation mode, for each grammaticality condition. For grammatical sentences, error rates were on average 2.0% higher in the sequential mode than the simultaneous mode (SEM = 0.70%, t(36)=2.86, p=0.007; BF=5.5), and correct RTs (calculated from the start of the sentence presentation) were on average 101 ms slower (SEM = 27 ms; t(36)=3.64, p=0.0008; BF=36.2). We also computed signal detection estimates of sensitivity (d′) and bias (β, the likelihood ratio of sensory evidence given target presence to absence at the decision criterion). In this analysis we treated any ungrammatical sentence as a “target”, and grammatical sentences as the non-targets, d′ was lower in the sequential mode by 0.44 on average (SEM = 0.14; t(36) = 3.03, p = 0.005; BF = 8.4). There was also an inconsistent trend for participants to be more liberal (lower β) in the sequential mode (mean difference = 1.26, SEM=0.62, t(36) = 2.01, p = 0.052; BF = 1.07).

Figure 2:

Performance in the grammatical decision task. (A) Mean error rates and (B) correct RTs in each condition. Error bars are +/− 1 SEM. Asterisks indicate significant differences between the transposed and control conditions: *p<0.05; **p<0.01, **p<0.001. (C) Smoothed distributions of individual subject transposed word effects (TW effects) on error rates: transposed - control. The horizontal lines and printed numbers represent the mean effects, with 95% CIs as vertical bars. (D) Smoothed distributions of TW effects on correct RTs, format as in (C). (E) Scatter plot of individual TW effects on error rates, showing the correlation between TW effects in the simultaneous vs. sequential modes. The solid diagonal line is a linear regression. The dashed diagonal line has a slope of 1 and is where all the points would fall if the TW effect was equally large in the two presentation modes. The dots that fall above this diagonal line are participants who had a greater TW effect in the sequential mode. (F) Data as in panel (E), but for correct RTs.

For both measures of performance, there were significant transposed-word effects (TW effects): lower accuracy and slower response times for reporting that the transposed sentences were ungrammatical compared to reporting that the control sentences were ungrammatical. Figure 2C and 2D also plot the across-subject distributions of those TW effects, with the means printed on top. Bootstrapped 95% confidence intervals (CIs) exclude 0 for both presentation modes, for error rates and RTs. Thus, it was consistently more difficult for participants to detect ungrammaticality caused by a simple word transposition, no matter the presentation mode.

Individual participant TW effects are plotted in Figure 2E (differences error rates) and 2F (differences in RTs). These plots also show that there was at best a modest correlation between the TW effect magnitudes in the simultaneous presentation mode (x-axes) and in the sequential model (y-axes). Figure 2E also demonstrates how many participants had larger TW effects on accuracy in the sequential mode (points that fall above the dashed diagonal identity line).

Table 2 shows the results of trial-level GLME models with maximal random effects structure fit to the response times and probability correct. They assessed the main effects of sentence type (transposed vs control) and presentation mode (sequential vs simultaneous), and the interaction. All analyses demonstrate robust effects of sentence type (worse performance for transposed than control). There were no significant interactions between presentation mode and sentence type, and the TW effect was significant in each presentation mode evaluated separately, for error rates (both p<10⁻¹⁷) and RTs (both p≤0.01). However, in an analysis of each subject’s proportion correct (rather than an analysis of single trial data as described above), we found that the TW effect was stronger for sequentially than simultaneously presented words. Specifically, the difference in TW effect magnitude between the two presentation modes was 8.3% (SEM=2.8%, 95% bootstrapped CI = [2.7 14.4], t(36) =2.89, p = 0.007; BF = 6.1). In the Supplementary Materials, Table S1 contains the results of subject-level LMEs that also show an interaction between sentence type and presentation mode for accuracy (but not response time).

Table 2:

Results of generalized linear mixed effect models fit to the single-trial data to estimate the effects of presentation mode (“mode”, sequential vs. simultaneous), ungrammatical sentence type (“type”, transposed vs. control), and their interaction. The “y” in the equation stands in for response accuracy or response time. The grammatical sentences were excluded from this analysis.

y ~ 1 + mode*type + (1 ∣ sentence num) + (1 + mode*type ∣ subject)
Factor	Mean estimate	t	DF	P
	Probability correct (binomial distribution, logit function)
(Intercept)	2.50	21.16	5799	8x10−96
mode	0.148	1.51	5799	0.132
type	0.880	11.08	5799	2.9x10−28
mode:type	−0.06	−0.96	5799	0.336
	Correct log10(RT)
(Intercept)	0.214	16.8	5095	6.5x10−62
mode	0.006	1.30	5095	0.195
type	−0.006	−3.33	5095	8.7x10−4
mode:type	−0.002	−1.14	5095	0.253

Therefore, the evidence is somewhat mixed as to whether the TW effect is reliably larger with sequentially than simultaneously presented words. We are confident, however, that the TW effect is at least as strong in the sequential presentation mode, when parallel recognition of words is impossible, as in the simultaneous presentation mode

In addition to categorizing each sentence as grammatical or ungrammatical, participants also reported (in the same keypress) their confidence in the decision (“guess” or “sure”). On average, participants reported high confidence on 98.8% of trials (range=78% – 100%). This percentage was only slightly lower on error trials: 96% (effect of accuracy: t(5801)=6.13, p=10⁻⁹), which limits our ability to analyze these data. Nonetheless, we investigated whether confidence differs between the two presentation modes on trials when participants miscategorize transposed sentences as grammatical. Indeed, the percentage of errors with high confidence was greater by 5 in the simultaneous mode (t(34) = 2.41, p = 0.021; BF = 2.25). Therefore, despite matching presentation rates to reading rates, the simultaneous mode was somewhat easier, both objectively (lower error rates) and subjectively (higher confidence on errors).

3.3. Faster readers are more likely to miss transpositions in the sequential mode

We next examined whether individual differences in reading rate predicted performance in the task. Figure 3A shows that reading rates in the simultaneous mode did not well predict individual accuracy for categorizing ungrammatical sentences. (Note that one prior study found this correlation to be modest but significant; Huang & Staub, 2021). However, Figure 3B shows that the presentation rate did correlate with errors for transposed sentences in the sequential mode. Faster readers (as assessed in the pretest, which determined their presentation rate) miscategorized more of the transposed stimuli as being grammatical, but only when the words were presented sequentially. This is remarkable given that sequential presentation rates were correlated with individual reading rates in the simultaneous mode (Fig. 1D). These correlations do not seem to be explained by differences in decision criteria (bias to report “grammatical”) across participants. A signal detection measure of decision bias, β, did not significantly correlate with reading rate in either mode (r=−0.13, p=0.45, r=0.17, p=0.3, respectively). Sensitivity in units of d′ (corrected for bias) did correlate with reading rate, only for sequentially presented transposed sentences (r=−0.56, p=0.001), consistent with the basic error rates allotted in Figure 3.

Figure 3.

The transposed word effect varies across slow and fast readers. (A) For the simultaneous presentation mode: individual participant error rates for transposed (green) and control sentences (blue) as a function of their reading rate. Correlation coefficients are printed for each sentence type, and the solid lines are linear regressions. (B) Similar format, but for the simultaneous mode. The x-axis is the participant's presentation rate (which was well matched to their simultaneous mode reading rate, the x-axis in panel A). There was a strong correlation only for transposed sentences in the sequential mode. (C) This plot shows how the transposed word effect (TW effect; transposed – control) differs between slow and fast readers, for each presentation mode (light vs dark bars). Participants were assigned to the slow or fast group by a median split of reading speeds in the pretest. Error bars are +/− 1 SEM. ** p=0.002.

We also found that for accuracy, fast readers have a larger transposed word effect in the sequential mode than in the simultaneous mode (Figure 3C). We split our subjects into two groups based on their reading speed in the pretest: slow readers (below the median of 295 words/s) and fast readers (at or above the median). Within each group, for each presentation mode, we computed the mean transposed word effect (TW effect: performance difference on control–transposed sentences). The TW effect on error rates was affected by an interaction between reading group and presentation mode (F(1,70) =7.07, p=0.01). For slow readers, there was no difference between modes (t(17)=0.15, p=0.88; BF=0.25). But for fast readers, the TW effect was larger in the sequential mode (t(18)=3.61, p=0.002; BF=20.3). For RTs there was no interaction between group and mode (F<1, p=0.45), and the TW effect did not differ across modes for either group of readers. For fast readers, the mean TW effect on RTs was numerically larger in the simultaneous mode, but not consistently across participants (t(18)=1.40, p=0.18; BF=0.55).

One possible explanation for these results is that in the simultaneous presentation mode, fast readers detect transpositions by slowing down: making more fixations, including regressions to re-read some suspicious words. But in the sequential mode, they cannot do that, so they are more likely to misjudge the sentences with transpositions. This hypothesis was not supported by an analysis of transposed sentences that were judged correctly: first, faster readers were not more likely to re-read more words than slow readers (r=−0.02, p=0.90). Second, the average number of re-read words in the simultaneous mode did not predict the error rate for transposed trials in the sequential mode (r=0.23, p=0.18).

To push this idea further, we also fit an LME to predict error rates for sequentially presented transposed sentences as a function of two factors calculated from correctly judged transposed trials in the simultaneous mode: the mean first fixation duration per word, and the mean number of fixations per trial (excluding immediate refixations on the same word). The first fixation duration had a significant linear effect (−0.23 percent error per ms, t(34)=2.80, p=0.008), but the number of fixations did not (3.6 percent error per fixation; t(34)=1.28, p=0.21). Therefore, the reason that fast readers are especially bad at detecting transpositions in the sequential mode is due to how quickly they can process words (as reflected in individual fixation durations). It is probably not because they are prevented from making the regressions they ‘normally’ do in the simultaneous mode (as would be reflected in the total number of fixations).

Another possibility is that fast readers have more robust prior knowledge of typical sentence structures and are better at shifting attention ahead to upcoming words (using “parafoveal preview”). Doing so would help readers skip words, and indeed, in the pretest, faster readers skipped more words (r=−0.67, p<0.001). The proportion of words each participant skipped also correlated with their error rates for sequentially presented transposed sentences (r=0.39, p=0.017). However, reading speed also correlated with those same error rates, as shown in Figure 3B (green points). To test whether word skipping explains any additional variance in task accuracy, we regressed out the effect of reading speed from the proportion of words skipped. The resulting “residuals” did not correlate with error rates for sequential transposed sentences (r = −0.04, p=0.8). Moreover, in a combined LME model, reading speed predicted those error rates (p=3x10⁻⁴) but the proportion of words skipped did not (p=0.73). Therefore, word skipping did not independently predict accuracy for transposed sentences in the sequential mode, but it was well correlated with reading speed, which did.

Nonetheless, we speculate that in the simultaneous mode, the best readers use parafoveal vision to rapidly glean information from the text to confirm or reject predictions about the sentence structure. In the sequential presentation mode, they cannot do that, so they rely even more on their strong priors. As a result, they are more likely to incorrectly accept sequences of words that appear out of order as grammatical. Slower readers, in contrast, may have weaker priors and expectations, and in both presentation modes process each word more carefully.

3.4. Across-trial variations in reading speed and fixation patterns help explain missed transpositions

Having analyzed differences in performance across participants, we next analyzed variations across trials within each participant. To begin, we analyzed how eye movement traces relate to accuracy on individual trials in the simultaneous presentation mode. The fundamental question is whether each participant is less accurate on trials when they read less carefully: more quickly, skipping more words, and not making regressions. As shown in Figure 4, that is generally true, especially for the transposed condition. For three different eye movement metrics, we sorted trials of each sentence type into two bins and compared accuracy across them. We also fit generalized linear mixed effects models (GLMEs) to predict single-trial accuracy as a function of these eye movement factors.

Figure 4:

The influence of eye movement patterns on error rates in the simultaneous presentation mode. Error bars are +/− 1 SEM. Asterisks: * p<0.05; **p<0.01. The numbers printed on the bars indicate the proportion of trials with that sentence type that fall into the second bin (e.g., 58% of grammatical trials were in the “fast” reading bin). (A) For each subject we first calculated their median reading rate across all trials, then split the trials of each condition into two bins: “slow” (rate <= median) and “fast” (rate > median). Each trial’s reading rate was, as before, calculated as the number of words read (five plus the number re-read) divided by total reading time. (B) Trials are sorted depending on whether both words 3 and 4 in the sentence were fixated in the first pass through the sentence, or at least one of them was skipped. (C) Trials are sorted depending on whether the subject made at least one regressive eye movement. Collapsing across sentence types, there is a significant difference in accuracy between trials with and without a regression (see text).

First, reading speed on each trial covaried with response accuracy, but in opposite directions for grammatical vs. ungrammatical sentences (Figure 4A). The GLME detected a significant interaction between sentence type and single-trial reading speed (F(2, 5790)=9.70, p<10⁻⁴). On grammatical trials, slower reading was associated with slightly but not significantly higher error rates (t(35)=1.63, p=0.11; BF=0.6). The reverse was true on transposed trials: when subjects read faster, they were more likely to miss the grammatical error (t(35)=4.38, p=10⁻⁴; BF=241). That effect was not significant on control trials (t(35)= 1.76, p=0.09; BF=0.73).

Second, accuracy was influenced by whether or not participants skipped the 3rd or 4th words in the sentence in the first pass of their eyes through the text (Figure 3B). On average, participants did that on 36.6% of trials (SEM=2.1%, range = [12.7 78.0]). The main effect of skipping on accuracy, across sentence types, was not significant (F(1, 5791)=1.27, p=0.26), nor was the interaction (F(2, 5791)=1.47, p=0.23). However, we had prior reason to predict that the effect would only occur on transposed trials, where these particular words (3 and 4) were key. Indeed, participants were more likely to miss the grammatical error if they skipped either of those transposed words (t(36) = 2.52, p = 0.016; BF = 2.77). This result is consistent with an analysis by Huang & Staub (2022).

Third, participants were overall more accurate when they made at least one regression: a backwards saccade to re-read some of the text (Figure 3C; F(1, 5791)=6.19, p=0.013). That effect did not vary significantly across sentence types (F(2, 5791)=1.83, p=0.16). On average, participants made 1.24 regressions per trial (SEM=0.09, range = [0.05 2.46]).

Altogether, these results demonstrate that participants are less likely to notice a word transposition when they read more quickly, skipping at least one transposed word or not re-reading part of the sentence. A related question is: does a transposition in the sentence disrupt eye movements, even if the reader ultimately reports that the sentence was grammatical? To address this, we compared correctly judged grammatical trials and incorrectly judged transposed trials. Between those trials there were no significant differences in reading speeds, the probability skipping the 3^rd or 4^th word, or the mean number of regressions (all p>0.1, BF<0.6). Thus, on trials when readers that report transposed sentences as grammatical, they scan the text much like they do when reading truly grammatical sentences (consistent with Huang & Staub, 2021).

3.5. The speed-accuracy tradeoff is flipped in the sequential presentation mode

In Figure 5 we adopt an approach used by Mirault et al. (2022), plotting “conditional accuracy functions,” to examine how response speed and accuracy co-vary in each condition. For each condition, for each subject, we sorted the trials by response time (calculated from the onset of the first word or whole sentence) and then segregated them into 4 bins of equal size. Figure 5A and 5B plot mean accuracy (proportion correct) in those four bins, as a function of the mean RT in each bin. For ungrammatical sentences in the simultaneous mode, accuracy is worst for the fastest responses, rises as processing time increases, then levels off (Figure 5A). That is a classic speed-accuracy tradeoff. For all other conditions, including transposed sentences in the sequential mode (Figure 5B), accuracy is best for the fastest responses and then monotonically drops off.

Figure 5:

Associations between response time and accuracy. The left column is for the simultaneous presentation mode, and the right column for the sequential mode. Panels (A) and (B) plot across-subject mean accuracy in four bins of trials sorted according to response time. Error bars are +/− 1 SEM. In panels (C) and (D), each dot is an individual sentence. The x-axis is the across-subject mean of z-scored RTs for each sentence. The y-axis is the proportion of subjects that judged each sentence correctly. The solid lines are best-fitting linear regressions. The text in the lower right corners reports the correlation coefficients for each sentence type (G=grammatical; C=control, T=transposed). * p<0.05; **p<0.01.

Confirming this pattern for transposed sentences, we found an interaction between the effects of presentation mode and z-scored response time in a GLME of single-trial probability correct (F(1, 2883)=13.8, p=2x10⁻⁴). That is all consistent with Mirault et al. (2022), although their results differed in that they found the sequential mode TW effect was absent in the first RT bin and then gradually grew. We did not find that, perhaps because we adjusted the presentation rate for each participant. In the prior study (Mirault et al., 2022), the presentation rate may have been too slow for many participants, so many trials were simply too easy, leading to fast RTs with no TW effect on accuracy.

These conditional accuracy functions highlight a key difference between the two presentation modes: in the simultaneous mode, participants are free to attend to any words in any order, and to stop processing the stimuli at any time. Therefore, many missed transpositions are due to reading too quickly, with less careful eye movements (as shown in Figure 4). Thus, the conditional accuracy function in Figure 5A has a positive slope (a speed-accuracy tradeoff). In the sequential mode, the rate and order of the perceptual input is constant and controlled by the experimenter. Differences across trials in response time and accuracy are driven by late-stage processes related to how well the participant comprehends each sentence: “better” performance means that the participant reaches correct decisions quickly, so there are both faster RTs and higher accuracy. Therefore, the lines in Figure 5B (sequential mode) have a negative slope. (Note that two prior studies found that it makes little difference if participants are allowed to respond before the sequence of words is over; Huang & Staub, 2022; Mirault et al., 2022).

There are at least two possible sources of this variance in behavior across trials: fluctuations in the participant’s mental state, and differences in the sentences themselves. In the final, exploratory analysis we found some evidence for the second source. To do so, we first z-scored each participant’s response times from all conditions. Then for each unique sentence presented in the experiment, we calculated the across-participant mean z-scored RT, and the proportion of participants who judged that sentence correctly. Figures 5C and 5D plot the correlations between those two measures of sentence difficulty, for each presentation mode. Each point is a single sentence. In all conditions but one, there was a negative correlation, meaning that the sentences that were judged more slowly (i.e., higher RTs) were judged correctly by fewer participants. This suggests that some sentences are inherently more difficult, such that the participants ponder them for longer and yet come to the correct decision less often.

The one exception to this trend is for transposed sentences in the simultaneous mode (green data in Figure 5C). In this case, the correlation was significantly positive: sentences that tended to be read more slowly were more likely to be judged correctly. Conversely, some sentences were associated with fast but more inaccurate responses, perhaps because they more immediately appear to be grammatical. This pattern in Figure 5C-D mostly matches the slopes of lines in Figure 5A-B. In both analyses we are confronted with different patterns for transposed sentences in the two presentation modes. As discussed below, we propose that these different patterns are caused by the perception of multiple words during each gaze fixation in the simultaneous presentation mode (using “parafoveal preview,” which is not possible in the sequential mode). This explanation does not entail that multiple words are fully recognized and integrated simultaneously. Another possibility is that the reader rapidly shifts attention from word to word during each fixation (Reichle, Pollatsek & Rayner, 2006), gleaning just as much information as they need to perform the task.

4. DISCUSSION

4.1. Summary

The primary finding of this study is that the transposed word (TW) effect is robust when words in each sentence are presented sequentially. In fact, the effect is at least as strong as when the words are all presented simultaneously, provided that the rate of sequential presentation is set to each participant’s natural reading rate. In our data, natural reading rates vary reliably by over a factor of 2 across individuals. The recent studies that used a fixed presentation rate (3.3 or 4 words/s) found a weaker transposed word effect than in the simultaneous mode (Liu et al, 2022; Huang & Staub, 2022; Mirault et al, 2022). For many participants in those studies, the fixed rate may have just been too slow, and therefore too easy. (As shown in Figure 1D, most of our participants were reading faster than 4 words/s).

On the basis of these data, we argue that a reader’s poor ability to notice transpositions does not necessarily indicate that they recognize multiple words in parallel when reading normal text (as also argued by Liu et al., 2022; Hung & Staub, 2022). The strong TW effect in the sequential mode demonstrates that it is also consistent with models of reading that assume that words are encoded serially at the lexical level (e.g., Reichle, Pollatsek & Rayner, 2006). It is also consistent with a TW effect that arises when participants perform a similar task on spoken, rather than written, sentences (Dufour, Mirault & Grainger, 2022).

4.2. Theoretical implications

These data leave us with an important theoretical question: which model of language comprehension explains the failure to notice transposed words, if the words are read (or heard) sequentially in the order they are written (or spoken)? One general framework is the “noisy channel” or “rational inference” model: the reader infers the most likely intended message, given the perceived message (Gibson et al., 2013). To do so, they use prior knowledge about the world, about the rules of language, and about how linguistic messages may be corrupted by errors in production, transmission, or perception (Ryskin et al., 2018). In the case of reading sentences with transposed words, this model implies that there is an initial stage of ‘perceiving’ the sentence with the transposition as it is written, followed by a Bayesian inference stage when the perceived sentence is ‘corrected’ to the most likely sentence intended by the writer. In broad strokes, this model can explain data from both simultaneous and sequential presentation modes. But some key questions must be answered: Does the rational inference happen after all the words in a sentence are read, or does it happen continuously as each word is recognized and integrated into the sentence structure? Moreover, if the ungrammatical sentence is indeed first “perceived” as it is written, why do participants so often incorrectly report that is grammatical?

These questions are not so difficult to answer if we assume that readers recognize multiple words in parallel. In that case, rational inference could be immediately applied to all the words that are recognized at once. The reader knows that words are sometimes written or perceived in the wrong order (the latter being quite plausible if multiple words are recognized simultaneously; Snell & Grainger, 2019). Using that knowledge, the reader could quickly and unconsciously reassign the words to a grammatical order.

But the data from the sequential word presentation mode demonstrates that we must also account for TW effect with serial models of reading. One may assume that each word, once recognized, is immediately integrated into a representation of sentence structure (as in the EZ reader model; see Staub & Huang, 2021). To account for the TW effect, any rational inference would have to happen once enough of the sentence is read to make a guess at the intended message, which could be several words later. But in that case, it should be rather easy for the reader to notice transpositions. Their eye movements would also likely be disrupted by the transposition, regardless of their final decision about grammaticality. But that doesn’t seem to occur (in our data, or in Huang & Staub, 2021).

One explanation that fits the rational inference with a serial model of reading is as follows (here we closely follow Staub & Huang, 2021). Words are recognized serially, but multiple words may be held in a memory buffer until rational inference is applied and those words are integrated to the sentence structure. That process may wait until reaching the plausible end of a phrase, clause, or sentence. At that point, rational inference corrects apparent word order errors. The reader is not consciously aware of the order of words initially stored before ‘correction’ (or perhaps they rapidly forget it while moving on to the end of the sentence).

Our data provide additional insight: fast readers more often judge transposed sentences as grammatical, especially in the sequential mode (Fig. 3). That could be because fast readers (who are presented with words very quickly in the sequential mode) know that increased speed risks errors, so their ‘priors’ favor the grammatical intended message (Staub & Huang, 2021). However, in our data it is not generally true that the faster readers made more errors: in the pre-test, they were more accurate than slow readers, and in the control and grammatical conditions of the grammatical decision task, there correlations between reading speed and accuracy were weak at best. An alternate explanation is that when words are read or presented more quickly, the process of rational inference – applied to multiple words held in a memory trace – can occur sooner, with less opportunity for conscious awareness of the error. Thus, more transposed sentences are judged as grammatical by the fast readers.

This explanation of the TW effect, which assumes that individual words are recognized serially, can apply to both the sequential presentation mode and the more ‘natural’ simultaneous mode. In contrast, a model of parallel word encoding cannot explain the TW effect in the sequential presentation mode. That alone does not mean that parallel models of natural reading (e.g., Snell et al. 2018) are incorrect, however. Just as the TW effect in the simultaneous presentation mode cannot be taken as evidence against a serial model of word encoding, the same effect in the sequential mode cannot be taken as evidence against the parallel model of natural reading.

Indeed, some authors who found the TW effect to be larger in the simultaneous mode than sequential mode argue that parallel processing contributes to that larger effect by adding noise to the representation of word positions (and therefore word order; Mirault et al., 2022). However, that interpretation is challenged by two findings we reported above: (1) the effect in sequential presentation can be made at least as strong as in the simultaneous mode by adjusting the presentation rate (Figure 2); (2) faster readers are worse than slower readers at detecting transpositions in the sequential mode, but not in the simultaneous mode (Figure 3). If we assume that (a) faster readers are better at processing multiple words in parallel and (b) that parallel processing contributes to the failure to notice transpositions, then we predict that faster readers should have a larger effect in the simultaneous presentation mode than in the sequential mode. That is not what we found. One potential explanation for our data is the reverse of Mirault et al.’s hypothesis: the perception of multiple words during each gaze fixation is, when deployed carefully, what allows skilled readers to notice transpositions. Removing that capability by presenting one word at a time causes the best readers to make errors, perhaps because when they are deprived of parafoveal preview they rely more on their prior knowledge of sentence structure.

4.3. Differences between presentation modes

Despite finding a robust TW effect in both presentation modes, we do not claim that the modes are equivalent to each other. The distinct correlations with reading speed (Figure 3) were just one of the differences we found between the two modes. Another difference concerns the relation between speed and accuracy (Figure 5). In the simultaneous mode, faster responses to ungrammatical responses are less likely to be correct, while the reverse is true in the sequential mode. Part of that variance is explained by differences in the sentences themselves (as opposed to differences in each participant’s cognitive state across trials, which are also important).

We propose that the differences between modes are due to the ability that skilled readers have, in the simultaneous mode, to perceive multiple words during each gaze fixation and check predictions based on their prior expectations about sentence structure. This ability does not necessarily require parallel processing of multiple words but could involve sequential shifts of attention within each fixation (Schotter, Angele & Rayner, 2012). In any case, some transposed word sequences may be deceptive when viewed parafoveally – perhaps even the low-level visual shape conforms to a prediction based on expected grammatical structure. That contributes to rapid, incorrect judgments of the sentence as grammatical. Others give just enough early evidence of a grammatical error that the reader can slow down and then come to the correct decision. The sequential presentation mode removes those differences across sentences, and also puts the naturally faster readers at a disadvantage for detecting transpositions.

4.4. Conclusion

In sum, the transposed word effect is a fascinating phenomenon that deserves an explanation. However, it is not diagnostic in regards to the debate over the extent of parallel word recognition during natural reading. Even if it is true that readers sometimes divide attention and recognize multiple words in parallel (e.g., Snell et al. 2018), that parallel processing may not be what causes the transposed word effect. Alternatively, the effect may have entirely different causes when words are presented sequentially. That is a less parsimonious explanation for the entire data set, however, than an explanation with a single cause. In line with several recent papers (Huang & Staub, 2022; Liu et al., 2022) we argue that the transposed word effect is primarily caused by post-lexical “rational inference” based on visual input that the reader knows is noisy, combined with prior knowledge of sentence structure. In line with this, transpositions are more likely to be missed when they occur within a syntactic phrase (Wen, Mirault & Grainger, 2021). Future research may benefit from further examining the particular types of word combinations that are most likely to be missed, in terms of visual, orthographic, syntactic and semantic features.

DATA AVAILABILITY:

Data and analysis code will be shared upon publication of this manuscript.