Interdependency in lateralization of written word and face processing in right-handed individuals

It has been suggested that the right hemisphere lateralization typically observed for face processing may depend on lateralization of written word processing to the left hemisphere; a pattern referred to as the causal complementary principle of lateralization. According to a strong version of this principle, a correlation should be found between the degree of left and right hemisphere lateralization for word and face processing respectively. This has been observed in two studies, but only for left-handed individuals. The present study tested whether a similar lateralization pattern could be found in a relatively large sample of right-handed individuals ( N ¼ 210) using behavioral measures (divided visual ﬁeld paradigms). It was also tested whether the degree of right hemisphere lateralization for face and global shape processing would correlate positively, as predicted by a strong version of the input asymmetry principle of lateralization. This was tested in a subsample ( n ¼ 189). Bayesian analyses found no evidence for lateralization interdependency as the observed data were 4 e 17 times more likely under the null hypothesis. Unfortunately, the reliabilities of the lateralization measures were found to be poor. While this dampens the ﬁrmness of the conclusions that can be drawn, it is argued that at present there is no positive evidence for strong interdependency between written word and face processing in right-handed individuals. © 2023


Introduction
There is overwhelming evidence supporting Broca's notion from 1865 that language functioning in right-handed individuals is lateralized to the left hemisphere.There is also a lot of evidence suggesting that face processing e or at least face recognition e is lateralized to the right hemisphere (Rossion & Lochy, 2021).Furthermore, it has been suggested that the pattern of lateralization for language and face processing is interdependent.Ellis (1983), for example, proposed that the right hemispheres' dominance in processing of visuospatial information, including faces, might have come as a consequence of (phylogenetical) development of language function in the left hemisphere.This notion of interdependence is the essence of what has been termed the causal complementary principle of lateralization (Badzakova-Trajkov, Corballis, & H€ aberling, 2016;Bryden, H ecaen, & DeAgostini, 1983).
More recently, and somewhat more specifically, it has been proposed that it is the ontogenetic acquisition of reading skills that induces the rightward shift in face processing (Dehaene & Cohen, 2011;Dehaene et al., 2010).On this account, efficient written word and face processing is assumed to require access to the same resources, for example cortical patches mediating high-resolution foveal vision, but also to differ in that reading requires connections to other language functions whereas face recognition does not.It is this combination of competition and pressure for efficient interhemispheric connectivity that is assumed to cause the interdependent lateralization of written word and face processing (Behrmann & Plaut, 2020).In the following this specific hypothesis will be referred to as the Reading-induced Lateralization Hypothesis (RLH).
The RLH is intriguing, and elegant in its simplicity, but it has not found a lot of support.As an example, the RLH predicts that individuals with developmental dyslexia should not show the typical right lateralization for face processing because the initial trigger for lateralization of face processing e the acquisition of written word recognition e is impaired (Collins, Dundas, Gabay, Plaut, & Behrmann, 2017).Contrary to this prediction we found that individuals with developmental dyslexia did show the expected right hemisphere advantage for face processing and that the magnitude of this advantage was similar to that observed for neurotypicals (Gerlach et al., 2022).More critically, in a recent systematic review by Rossion and Lochy (2021) e which drew on evidence from infants, children, literate/illiterate adults, and also covered different methodologies including divided visual field studies, lesion studies and neuroimaging e it was concluded that there was little evidence supporting the RLH.The strongest evidence in favor of the RLH has come from a few studies reporting correlations between degree of left and right lateralization for word and face processing respectively.In a sample of left-handers (N ¼ 27), Gerrits, Van der Haegen, Brysbaert, and Vingerhoets (2019) reported a significant negative correlation in the middle fusiform gyrus in activation-based laterality indexes based on word production (fluency) and face recognition, and also a similar tendency for a negative correlation between written word and face recognition lateralization indexes (r ¼ À.36, p ¼ .065).In a larger and mixed sample of left-and right-handed participants (N ¼ 121), Brederoo et al. (2020) reported a similar behavioral correlation between laterality indexes based on lexical decision and face similarity matching: The stronger the lateralization was for written words to the left hemisphere the stronger was the lateralization for faces to the right hemisphere (r corrected ¼ À.29, BF 10 ¼ 6.12).However, post hoc analyses of their data suggests that there is only (anecdotal) evidence for such a relationship for the left-handed participants (n ¼ 53, r ¼ À.32, BF 01 ¼ .58)whereas there is in fact strong evidence for the nullhypothesis (of no effect) in the right-handed participants (n ¼ 68, r ¼ À.02, BF 01 ¼ 10.4).This could suggest that causal complementarity may be restricted to left-handers, as has been found previously for the lateralization of language production and spatial attention (Cai, Van der Haegen, & Brysbaert, 2013;Zago et al., 2016).If this is the case, it indicates that left-handed individuals may differ systematically from right-handed individuals in the lateralization pattern for written word/face processing, and there is evidence suggesting that left-handed individuals do exhibit less lateralized or even slightly left-lateralized activation of the fusiform face area compared with right-handed individuals (Badzakova-Trajkov, H€ aberling, Roberts, & Corballis, 2010;Bukowski, Dricot, Hanseeuw, & Rossion, 2013;Fr€ assle, Krach, Paulus, & Jansen, 2016;Willems, Peelen, & Hagoort, 2010).Also, a similar behavioral effect was found by Brederoo et al. (2020) where both the left-and the right-handers showed right hemisphere lateralization for face processing and left lateralization for word processing but where these effects were larger for the right-than for the left-handed individuals.It is not clear, however, how a less lateralized face processing system in left-handers should cause this group to show signs of causality when right-handers e with a presumably more lateralized face processing system e apparently do not (Brederoo et al., 2020).Also, the left-handers with left hemisphere language dominance in the Gerrits et al. (2019) sample matched previous reports of right-handed individuals in terms of face recognition lateralization (Rossion, Hanseeuw, & Dricot, 2012).
Another possible explanation for the inconsistency between right-and left-handers takes as its starting point that lateralization effects are often small and highly variable across individuals (Badzakova-Trajkov et al., 2010;Cai, Lavidor, Brysbaert, Paulignan, & Nazir, 2008;Gerlach & Poirel, 2020).From an individual difference approach variability is of course desirable (Hedge, Powell, & Sumner, 2018), but in combination with small sample sizes, which characterizes many of the studies reported in this area (Rossion & Lochy, 2021), this can create a concern for type 1 errors/ limited reproducibility (Button et al., 2013).This concern should be considered in the context of the suggestion that stable estimates of correlations (based on Pearson's r) may require sample sizes of N ¼ 250 (Sch€ onbrodt & Perugini, 2013).Consequently, another explanation for the inconsistency across studies is sampling error.Even though it is not possible to establish whether previous findings reflect sampling error, one can minimize sampling error by testing the RHL in larger samples than has been done so far.This is the main objective of the present study which examined the potential correlation between the degrees of lateralization effects for written word and face processing in a relatively large sample of right-handed individuals (N ¼ 210) who performed a divided visual field task with delayed matching of written words and faces.If evidence of a correlation is found, where the degree of left lateralization for word processing predicts the degree of right lateralization for face processing, this will support the RLH and thus also the causal complementary principle.If more evidence is found for the null hypothesis, this will support the notion that the sources that influence the lateralization of given functions are independent of one another; the so-called "statistical" complementary principle (Badzakova-Trajkov et al., 2016;Bryden et al., 1983).
The causal complementary principle is concerned with lateralization patterns across the hemispheres.But what about processes that are lateralized to the same hemisphere; are they independent, as the statistical complementary principle holds, or are they related?According to one notion e which have been termed the input asymmetry principle (Andresen & Marsolek, 2005) e we should expect positive correlations in the lateralization of processes that are related.Two processes that are typically found to be right lateralized are face processing (see above) and processing of global shape information, as for example processing at the global shape level in Navon's (1977) paradigm with compound stimuli (see e.g., Martin, 1979;Yovel, Levy, & Yovel, 2001).This colateralization could be incidental, but it could also reflect some degree of contingency.In support of the latter possibility there is evidence from both neurotypicals (Gerlach & Starrfelt, 2018), acquired prosopagnosics (Rossion, 2015), and developmental prosopagnosics (Avidan, Hasson, Malach, & Behrmann, 2005;Gerlach, Klargaard, Petersen, & Starrfelt, 2017) that global shape information is important for face processing, and perhaps more important for faces than for other classes of stimuli such as written words (Gerlach & Starrfelt, 2021, 2022).More direct support for a contingency, and for the input asymmetry principle, was provided in the study by Brederoo et al. (2020) who also found a positive correlation between lateralization of face processing and global shape processing with compound stimuli (r corrected ¼ .39,BF 10 ¼ 11.2).There are, however, two limitations associated with Brederoo et al.'s finding.(i) As was the case for the correlation between face and word processing (see above) post hoc analyses performed on their data indicate that the effect is only present in the left-handed group (r ¼ .34,95% credible interval [.09, .56],BF 01 ¼ .41),whereas data in the right-handed group is five times more likely under the null hypothesis (r ¼ .15,95% credible interval [À.08..37],BF 01 ¼ 5.1).(ii) Brederoo et al. (2020) based their comparisons on incongruent stimuli, that is, compound stimuli where the identity of the local level elements differ from the identity of the global level shape (Brederoo, Nieuwenstein, Lorist, & Cornelissen, 2017).This only taps interference effects but not the global precedence effect proper (with faster reaction time to global congruent compared with local congruent stimuli) (Gerlach & Poirel, 2020).The present study provided an opportunity to examine the relationship between lateralization effects for face and global shape processing in a larger sample than the one tested by Brederoo et al. (2020) because 189 out of the 210 (90%) participants who completed the delayed matching task with faces and written words also provided data with compound stimuli that could be used to examine lateralization effects in global/local processing.If the lateralization effects for face and global shape processing obey the input asymmetry principle, one would expect to see positive correlations between lateralization effects for face processing and: (i) global-to-local interference effects (as found by Brederoo et al. (2020)), and (ii) global precedence effects.
In summary, the present study examined whether the following three hypotheses could be confirmed in a relatively large sample of right-handed individuals: (i) there is a negative correlation between lateralization effects for written word and face processing (confirming the RLH/causal complimentary principle) (N ¼ 210): the more written word processing is lateralized to the left hemisphere the more face processing will be lateralized to the right hemisphere, (ii) there is a positive correlation between lateralization for face processing and global-to-local interference (n ¼ 189), and (iii) between lateralization for face processing and global precedence effects (n ¼ 189).If hypothesis two and three are confirmed this will provide evidence in favor of the input asymmetry principle.If, on the contrary, there is more evidence in support of the null hypothesis this will favor the statistical (independence) principle of lateralization.It should be noted beforehand that the causal complementary principle and the statistical independence principle are not mutually exclusive.It is entirely possible that lateralization of face processing is contingent on lateralization of word processing but not on lateralization of global shape processing.No part of the study procedures/analyses was pre-registered prior to the research being conducted.
On a final note, it is important to distinguish between two versions of the causal complimentary and input asymmetry principles.In what can be considered the light versions, these principles only imply that the direction of lateralization of two functions is opposite (causal complementary) or similar (input asymmetry).In the strong versions the two functions are not only assumed to show opposite/similar directions of lateralization but also to show the same (or similar) degrees of lateralization.Hence, if one function is strongly left lateralized the other function should be strongly right lateralized (causal complementary) or they should show the same (or similar) degrees of lateralization in the same direction (input asymmetry).Given that the present work only included righthanded individuals (with assumed typical lateralization) it is the strong versions of these principles that are tested.Tests of the light versions would require inclusion of left-handed individuals who more often than right-handed individuals show an atypical lateralization pattern (cf. the above).While these versions are often not distinguished explicitly, many studies seem to implicitly operate with the strong versions.This, for example, is the case with the RLH that is tested here (Behrmann & Plaut, 2020;Dundas, Plaut, & Behrmann, 2013).

The divided visual field task with delayed matching of written words and faces
In the following I report how sample size was determined, all data exclusions, all inclusion/exclusion criteria, whether inclusion/exclusion criteria were established prior to data analysis, all manipulations, and all measures in the study.
This task was modeled over the divided visual field task developed by Dundas et al. (2013), and we have previously applied the specific setup used here to examine lateralization for written words and faces in developmental prosopagnosia and dyslexia (Gerlach et al., 2022).Hence, only the essential features of the task will be described below, and the reader is referred to Gerlach et al. (2022) for additional details.
Participants were seated in front of a laptop screen and instructed to fixate a centrally presented cross each time it appeared.Participants were instructed to decide if two succeeding stimuli were the same or different by pressing "1" to indicate "same" or "2" to indicate "different" (using the touchpad buttons that were centrally placed on the laptop).The participants were free to use either hand they pleased but were instructed to use one hand only.The experimental setup was the same for all stimulus types which comprised cars, faces, cropped faces, and words.The words were four-letter, regular Danish nouns, where the two words in each wordpair (reference/target) only differed in one of the two central letters.In the following, only data from written words and cropped faces will be presented.This is because the category 'car' is irrelevant for the hypotheses examined and because we found that 'cropped faces' e which only shows the internal features of the face (see Fig. 1) e yielded stronger lateralization effects than full faces (Gerlach et al., 2022).The stimuli used for this task and for Navon's paradigm below can be found at: https://osf.io/ngm9u/.
On each trial, the central fixation cross appeared for 2000 msec, followed by a target stimulus shown centrally for 1000 msec.Then the central fixation cross reappeared for 300 msec, followed by the second stimulus presented for 150 msec shown randomly to the left or the right side of the central fixation cross.The center of the second stimulus was presented approximately 3.3 degrees of visual angle off screen center and subtended between 3.1 and 6.1 degrees of visual angle in width and 1.9e6.3degrees of visual angle in height depending on the stimulus category.The participants had 4000 msec to respond but were instructed to respond as quickly and accurately as possible (see Fig. 1).There were eight experimental blocks of 40 trials comprising a total of 320 trials with an equal number of same (40 trials) and different trials (40 trials) for each of the four categories with half presented in each visual field.Stimuli from the different categories were mixed within blocks with small breaks between blocks and all stimuli were displayed in both visual fields.Both accuracy and reaction time (RT) were measured.In both this experiment, and the Navon experiment presented below, participants were tested in groups of approximately 40.
Participants were instructed to be quiet and also to sit still after having completed the experiment not to disturb other participants.These instructions were followed.

Navon's paradigm with compound letters
The specific setup used here to examine global/local processing of compound stimuli has been described in detail elsewhere (Gerlach & Poirel, 2020).Basically, the participants were presented with large letters, either 'H' or 'S', that could consist of either smaller 'H's or 'S's.The compound stimuli could either be congruent (same large and small letters) or incongruent (different large and small letters).In separate blocks, the participant had to indicate the identity of the letter at the global level (large letter) while ignoring letters at the local level (small letters) or the reverse (a selective attention version).A total of 320 trials were performed with stimuli presented at four locations (top, bottom, left, and right) with their center positioned 3.34 of visual angle from a fixation cross.Half the stimuli were congruent and half incongruent.
Hence, for each condition 20 stimuli were presented in each visual field (e.g., global shape judgments with incongruent stimuli presented to the left).The order of position and consistency was randomized.
A trial began with a fixation cross presented in the middle of the screen for 1 sec, which the participants were instructed to look at whenever present.They were also informed that stimuli over the course of the task would appear at each of the four locations with equal probability but in random sequence.The fixation cross was followed by stimulus onset which was replaced after 180 msec by a blank screen which remained until response.RTs were recorded by means of the touchpad (1 ¼ 'H' and 2 ¼ 'S' in all conditions).The participants were free to use either hand they pleased but were instructed to use one hand only.

Participants
246 first-year psychology students, naı ¨ve to the specific hypotheses tested, took part in the study as part of their course in cognitive psychology.The course is approved by the study board at the Department of Psychology, University of Southern Denmark, and the experiments conducted do not require formal ethical approval/registration according to Danish Law and the institutional requirements.Prior to participation, the students were informed that data collected in the experiments might be used in an anonymous form in future publications.Participants were free to opt-out if they wished, and participation in the experiments was taken as consent.Hence, the sample size was determined by the number of students who took the course in the period 2018e2019 and were present at the test dates.
Although language functions are usually lateralized to the left hemisphere, a small percentage of people e of which most are left-handed e have a right language lateralization.Furthermore, and as discussed in the introduction, left-handed individuals are often reported to show less lateralization than right-handed individuals.Thus, as is custom in studies of laterality, all analyses were limited to individuals who reported themselves right-handed.This led to the exclusion of 21 left-Fig.1 e Illustration of a trial in the delayed matching task with cropped faces.The task is to decide whether the target picture is identical to the reference picture ("same" response) or not ("different" response).In the present example the correct answer is "different".The trials with words had an identical setup.Note that the proportions of the stimuli with respect to the frame do not reflect the proportions of the actual experiment.It is for illustration only.
handed and 11 ambidextral individuals.Following Brederoo et al. (2020), participants were also removed from the dataset if they performed at chance level in each visual field in a given condition (if performance is at chance level in one but not both visual fields this could reflect lateralization effects rather than poor performance).This resulted in the removal of four additional participants (all right-handed).The final sample thus comprised 210 individuals (160 females) who performed the delayed matching task with written words and faces that was used to test hypothesis one.Additional demographic data, such as age and ethnicity, were not collected due to data protection regulations.
189 of the 210 participants (143 females) also completed Navon's paradigm with compound letters.This dataset was used to examine hypotheses two and three above regarding interdependence between lateralization for faces and global shape processing.The dataset from the word and face processing task has not been part of prior publications but part of the dataset from Navon's paradigm (n ¼ 69) was part of the sample (N ¼ 400) presented in Gerlach and Poirel (2020).

Statistical analyses
As in Gerlach et al. ( 2022) d 0 was used as the dependent measure in the analysis of data from the delayed matching task with written words and faces.d 0 is a bias-free measure of discrimination sensitivity expressed as a standardized effect size with a high score indicating better sensitivity (e.g., Wickens, 2002).Another reason for not conducting the analyses on RT is that the response-hand was not balanced across participants.Such balancing is often done in divided visual field studies to eliminate potential response-hand/visual field biases that can affect latency.Note though that responsehand/visual field bias is not an issue in the RT analyses of data from Navon's paradigm because these analyses are based on subtraction-scores (where response-hand is a constant across conditions, see below).
The first analyses performed sought to establish whether the expected laterality effects could be found with higher sensitivity for words in the right visual field/left hemisphere (RVF/LH) compared with the left visual field/right hemisphere (LVF/RH) and for faces in the LVF/RH compared with the RVF/ LH.Next, to compare the interdependency between lateralization of written words and faces two simple differencescores were computed for each participant: (i) d 0 LVF Words À d 0 RVF Words , and (ii) d 0 LVF Faces À d 0 RVF Faces .Positive values on these laterality indexes indicate a LVF/RH advantage whereas negative values indicate a RVF/LH advantage.These difference-scores were next subjected to a Bayesian correlation analysis.If the RLH is correct, one would expect this analysis to yield a credible negative correlation.It should be noted that some prefer to use lateralization indexes based on ratios rather on plain differences-scores (e.g., Brederoo et al., 2020).Just to ensure that the present finding concerning a potential correlation between the laterality indexes for words and faces is not limited to a particular way of measuring visual field/hemispheric differences, the same analysis was also performed on ratios in addition to simple difference-scores.The difference between simple difference-scores and ratios is that for the ratio-score the difference between two measures is scaled by the sum of the two measures e.g., In keeping with our earlier study of VF differences in Navon's paradigm, RT on correct trials was used as the dependent measure for this paradigm.There are two main reasons for this choice.First the indexes we have previously derived from this paradigm, and which have proven reliable, were based on RT (Gerlach & Poirel, 2018, 2020).Secondly, for most participants we have tested with this particular setup, error rates have often been very small which means that error rates are not as sensitive as RT for revealing differences (see Gerlach & Poirel, 2020).Two indexes of global shape processing were derived for the present purposes: (i) a Global Precedence index, which is based on the difference in RT to local and global identity judgments on congruent trials only.Positive values on this index reflect faster processing of global compared with local shape information, and (ii) a Global-to-Local Interference index, which is based on the difference in RT to local identity judgments on incongruent and congruent trials.Positive values on this index reflect that global shape information interferes with report of local shape identity.Both indexes were computed for each participant as a standardized mean difference (Cohen's d), that is, as the difference between the two RT means of interest divided by their pooled standard deviations.Prior to computing the Navon indexes the data for correct trials were trimmed for each participant excluding any RT that fell above or below 2½ SDs from the mean of a given participant for each of the four main conditions comprising the Navon paradigm (global consistent, global inconsistent, local consistent & local inconsistent) for each of the four VFs.This resulted in the removal of 2.5% trials on average from each participant (SD ¼ 1, range: .5e5%).
The first analyses with these measures of global/local processing aimed to examine whether our earlier finding of no VF difference for the Global Precedence index, and higher values on the Global-to-Local Interference index in the LVF/RH compared with the RVF/LH, could be reproduced (Gerlach & Poirel, 2020).Next, to compare the interdependency between lateralization of face processing and lateralization of Global Precedence effects and Global-to-Local Interference effects, two simple difference-scores were computed for each participant for Global Precedence and Global-to-Local Interference effects respectively: (i) Global Precedence LVFeRVF , and (ii) Global-to-Local Interference LVFeRVF.As with the lateralization indexes for words and faces, positive values on these indexes will indicate more efficient processing of global compared with local shape in the LVF/RH compared with the RVF/LH, and more global-to-local Interference in the LVF/RH compared with the RVF/LH.These difference-scores were next subjected to Bayesian correlation analyses.If the input asymmetry principle is correct one would expect these analyses to yield credible positive correlations (the more right lateralized global shape processing is, the more right lateralized face processing will also be).Note that these analyses were not performed on ratios also as was the analysis for lateralization of words and faces.This is because the Global Precedence and the Globalto-Local Interference indexes are already based on difference-scores.Computing ratios based on differencescores will yield instances where the numerator will have a higher value than the denominator, because some of the difference-scores are negative, giving rise to meaningless ratios.
An aspect that is important to consider in research based on individual differences is the reliability of the measures used because the magnitude of observed correlations will scale with the reliability of the measures they are based on (Spearman, 1904).This has implications for both the interpretation of the magnitude of observed correlations as well as for the sample size required to detect "true" correlations (the lower the reliability of the measures the more observations are need to detect a given effect size) (Hedge et al., 2018).To address this issue some recommend that observed correlations should be adjusted for measurement error (reliability) yielding less biased estimates (Schmidt & Hunter, 1999).This can be achieved by using the disattenuation formula by Spearman (1904), which is the observed correlation divided by the square root of the product of the two measures' reliabilities.The adjusted correlation is itself an estimate that is affected by sampling error which will also affect the estimates of the reliabilities that it rests upon (Hedge et al., 2018).Hence, r Adjusted may yield values higher than 1 when reliability is low, and the adjustment in general does lead to overestimation when reliability is low (L.L. Wang, 2010).For these and related reasons r Adjusted should be considered carefully (Winne & Belfry, 1982).
The question of reliability is of particular concern for complex measures, such as difference-scores or ratio-scores, as are used here, because complex measures will often have lower reliability that the components they are based on (Peter, Churchill, & Brown, 1993); in particular when the components are highly correlated (Edwards, 2001).There may be two reasons for this: (i) the spread of (within-participant) measurement error from the individual components to the complex (aggregate) measure, and (ii) a reduction of between-participant variance.Of these reasons the latter is often neglected although reduction of between-participant variance may in principle contribute as much to poor reliability as measurement error (Hedge et al., 2018).
To assess the reliability of the measures used here, each measure was first calculated based on odd and even trials for each participant.These odd and even measures were then subjected to analyses yielding interclass correlation coefficients (ICC) (Liljequist, Elfving, & Skavberg Roaldsen, 2019).ICCs are estimated based on the general formula: Betweenparticipant variance/(Between-participant variance þ Error variance þ Session variance), where session variance corresponds to systematic differences between sessions (here measures based on odd and even trials respectively) across participants, and error variance to non-systematic changes within participants across sessions (with some participants scoring higher on odd compared to even trials or the reverse).Given that ICC estimates are based on a ratio, it is easy to see how reliability can be affected by the magnitude of both between-participant variance and measurement error.Following the recommendations by Koo and Li (2016), the estimates of ICCs presented here are based on a mean-rating (k ¼ 2), absolute-agreement, and 2-way mixed-effects model.
It has been recommended by some (e.g., DeGutis, Wilmer, Mercado, & Cohan, 2013) that measures based on regression are to be preferred to for example difference-scores because measures based on regression are more reliable.This approach, however, is associated with other problems (Gerlach & Mogensen, 2023;Willett, 1988) and should probably only be used when it is clear which condition is the baseline condition, that is, the condition that does not tap into the construct of interest (Ross, Richler, & Gauthier, 2015).This is not the case here because it cannot be concluded a priori that a particular hemisphere does not contribute to the effect of interest.Thus, regression measures will yield different outcomes depending on which visual field is considered "baseline".This is not an issue with difference-scores because the same outcome will be obtained regardless of which condition is subtracted from the other.For these reasons, measures based on regression were not used here.

Correlations between laterality indexes
There was no credible correlation between lateralization effects for written words and faces in the delayed matching task, and this regardless of whether the indexes were based on difference-scores (r ¼ .02,95% Interference effects (r ¼ .12,95% credible interval [À.02, .26],BF 01 ¼ 4.0).See Fig. 4 for a graphical representation of the individual datapoints.

Reliability
As can be seen from Table 1, the reliability of the measures was not impressive.The reliabilities of the d 0 measures within each visual field were around or below what can be considered "moderate" (.53e.70) (Liljequist et al., 2019).The reliability of the Global Precedence index was also moderate within each visual field (.67e.68) whereas the reliability of the Global-to-Local Interference index was poor (.28e.46).The reliabilities of the measures based on difference-scores were even worse (ranging from .0 for words to .42 for the Global Precedence index), and measures based on ratios were simply not reliable at all (the 95% CI crossed zero).As can be seen from Fig. 5, which shows the absolute size of the variance components for each of the measures, the poorer reliability of the measures based on difference-scores is not caused by an overall reduction in the amount of variance associated with these measures relative to the measures they were derived from.This would also be unfortunate given that variability between participants is desirable in correlational research.In fact, the differencescores for the Global Precedence index and the Global-to-Local Interference index had a higher amount of variance than the measures they were derived from.Hence, for words and faces the poorer reliability of the difference-scores is caused both by an increase in error variance and a slight drop in between-participant variance whereas for the Global Precedence and the Global-to-Local Interferences indexes the poorer reliability is caused by the increase in error variance being larger than the increase in between-participant variance.
The consequence is that for all difference-scores, the amount of error variance increases relative to the amount of betweenparticipant variance compared to what is the case for the measures they were derived from.This can be seen in Fig. 6 which shows the relative size of the variance components for all the measures.

Discussion
Word processing was associated with a significant albeit small RVF/LH advantage (d ¼ À.18), and face processing was associated with a significant and larger LVF/RH advantage (d ¼ .36).Even though it is not of prime importance for the main aim of this study e which is to examine the interdependency between the degree of lateralization for word and face processing e it is reassuring that the paradigm was able to reproduce the expected VF pattern.The same was true of the Global Precedence index and the Global-to-Local Interference index.As we have found previously (Gerlach & Poirel, 2020), there was no effect of VF for the Global Precedence index but a significantly larger Global-to-Local interference effect in the LVF/RH than in the RVF/LH (d ¼ .24).As there was an overlap of 69 participants in the sample tested here and the sample tested in Gerlach and Poirel (2020) these analyses were also performed without the overlapping individuals.These analyses revealed similar results with no VF difference for the Global Precedence effect but significantly more Global-to-Local interference in the LVF/RH than in the RVF/LH (d ¼ .2,n ¼ 120).
Even though the two paradigms e the delayed matching task and the Navon paradigm e gave rise to the expected VF effects, there was no evidence of any systematic relationship between the VF effects revealed by the two paradigms.The observed data for interdependency of VF effects for words and faces were 17 times more likely under the null-hypothesis, and the observed data for interdependency between VF effects for faces and the Global Precedence and the Global-to-Local interference indexes were respectively 13 and 4 times more likely under the null-hypothesis.This does not mean that there is no relationship between for example Global Precedence effects and face processing.Indeed, we have previously presented evidence supporting such a relationship with larger Global Precedence effects being associated with more efficient face processing (Gerlach & Starrfelt, 2018).It just means that such effects are probably not modulated by hemispheric differences.
Table 1 e The mean score of each of the measures and its associated 95% confidence interval (in brackets).Also shown is the interclass reliability of the measures and their associated 95% confidence interval (in brackets).
c o r t e x 1 6 9 ( 2 0 2 3 ) 1 4 6 e1 6 0 One thing that needs to be considered in order to evaluate these findings is the reliability of the measures they are based on, and this aspect is somewhat disappointing.Not unprecedented in studies based on individual differences, the reliabilities of the measures were low (e.g., DeGutis et al., 2013;Hedge et al., 2018;Ross et al., 2015;Wang, Li, Fang, Tian, & Liu, 2012).There may be several reasons for this including the use of difference-scores/ratios (cf. the section on statistical analyses), the use of paradigms developed for group-based studies where between-participant variation (sensitivity) is detrimental (Hedge et al., 2018), VF effects being small because lateralization is more often than not relative rather than absolute (Bryden et al., 1983), VF effects being affected by several factors (Hellige & Sergent, 1986;Sergent & Hellige, 1986), and the use of too few trials to obtain stable measures (Brysbaert, 2019).In the following I will discuss two of these reasons (number of trials and sensitivity) in a little more detail, as it may be helpful for the design of future studies.
It is generally the case that increasing the number of trials will increase the reliability of a measure (Brysbaert, 2019), and hence power, and figures around 40e50 per condition have been suggested for simple designs (as the present) with repeated measures (Brysbaert & d'Ydewalle, 1990;Brysbaert & Stevens, 2018).In this respect it is worth noting that those conditions in the present experiment that involved the largest number of trials in each VF (words and faces in the delayed   1).This suggests that the number of trials per se is probably not the main reason for the reliabilities observed.Another, and perhaps more likely reason is sensitivity.As can be seen from Table 1, performance was quite high, and variation rather low, for the processing of words and faces in the delayed matching experiment.This can be illustrated by computing the coefficient of variation (the mean divided by the standard deviation multiplied by 100) for each condition.This coefficient of variation was low for words presented in both the LVF (¼7) and RVF (¼5), somewhat higher for faces (LVF ¼ 9, RVF ¼ 11), but much higher for the measures of Global Precedence effects (LVF ¼ 83, RVF ¼ 92) and Global-to-Local Interference effects (LVF ¼ 65, RVF ¼ 71).Hence, the word and face measures seem to do a more poorly job differentiating performance across participants than the Global Precedence and Global-to-Local Interference measures probably because these conditions were too easy (i.e., less sensitive to individual variation).Given that reliability is estimated based on correlation coefficients, such estimations are affected by restriction of range.Accordingly, reliability may also turn out low if the range of values of the measures are restricted even if the measures are stable themselves.I am not arguing that this is the only or main reason for the modest to poor reliabilities observed here, but it is probably a contributing factor.This is also a reminder that reliability is not only a product of the measurement instrument but also the sample.Had the present delayed matching experiment been conducted with a sample with a more diverse constellation of reading proficiencies (than the one characterizing university students) reliability may have turned out higher.This does not change the outcome, however.The measures still do a poor job of differentiating performance in this sample and doing it in a consistent manner.
There is no quick fix to this situation.However, one can work backwards and try to estimate what magnitude a 'true' effect should have had in order to be detected given the present circumstances (low reliability).The test of the relationship between VF effects for face processing and the Global Precedence index, which had the highest reliabilities, was based on a sample of 189 individuals.By means of a conventional power analysis this should yield sufficient sensitivity to detect an effect at r !.18(assuming an a-level of .05,onetailed, and a b-level of .2) (Faul, Erdfelder, Lang, & Buchner, 2007).This estimation, however, does not factor in the reliability of the measures which were .24and .42 for the Face LVFeRVF and the Global Precedence LVFeRVF indexes respectively.This can be achieved by rearranging Spearman's attenuation formula (Spearman, 1904): True correlation Â (√ (reliability of measure A Â reliability of measure B)) ¼ observed correlation.Thus, if the 'true' effect was indeed r ¼ .18 the observable correlation would amount to r ¼ .06given the reliabilities of the Face LVFeRVF and the Global Precedence LVFeRVF indexes.Assuming again an a-level of .05,one-tailed, and a blevel of .2 it would require a sample size of 1716 for a future study with the same reliabilities to detect it.In other words, if the measures have had perfect reliability, the present study would have had enough power to detect effects as small as r !.18.However, given that the measures had considerably lower reliabilities it would require a sample size of 1716 to detect true effect as small as r !.18.One can also ask what effect size the present study could have been expected to detect had the reliability of the present measures been known in advance.Again, Spearman's formula can be used to provide the answer: Detectable correlation with perfect reliability given N/ √ (reliability of measure A Â reliability of measure B) ¼ detectable correlation adjusted for reliability.For interdependency between the Face LVFeRVF and the Global Precedence LVFeRVF indexes this yields a detectable effect size of r !.57[.18/√ (.24 Â .42)].The same calculation for the relationship between the Face LVFeRVF and the Global-to-Local interference LVFeRVF indexes yields an effect size at r !.71[.18/√ (.24 Â .27)].Performing the same estimation for the relationship between the Word LVFeRVF and the Face LVFeRVF indexes is clearly a dubious enterprise because the Word LVFeRVF index was not reliable at all (ICC ¼ 0; 95% CI [À.3, .24]).However, for the sake of illustration one could take the optimistic view and assume an ICC ¼ .24(the highest value of the measure's associated 95% CI).This would yield a detectable effect size at r !.71[.17/√ (.24 Â .24)].Clearly, the poor reliabilities of the present measurements dampen the firmness regarding the conclusions that can be based on the present findings even though they are based on a relatively high-powered study in terms of N compared with similar studies in the field.This is not a statement of whether the null findings found here are more or less likely than the alternative hypothesis of an effect e which would be misleading (Hoenig & Heisey, 2001) e but an illustration of the fact the present study had less power than one would assume based on N alone.

General discussion
It is typically found that processing of written words is more efficient in the right visual field (RVF)/left hemisphere (LH) than in the left visual field (LVF)/right hemisphere (RH), and that the reverse is the case for processing of faces.According to the causal complementary principle of lateralization these lateralization patterns are supposed to be interdependent because the acquisition of language functions causes a rightward shift in face processing (Ellis, 1983).This idea is clearly at the heart of the Reading-induced Lateralization Hypothesis (RLH) where it is specifically the acquisition of reading skill that is assumed to drive the RH lateralization of face processing (Behrmann & Plaut, 2020;Dehaene et al., 2010), and in a linear manner: The stronger written word processing is lateralized to the left hemisphere, the stronger face processing will be lateralized to the right hemisphere (strong complementarity).The best support in favor this proposition c o r t e x 1 6 9 ( 2 0 2 3 ) 1 4 6 e1 6 0 has come from studies showing a negative correlation between the degree of left lateralization for word processing and the degree of right lateralization for face processing (Brederoo et al., 2020;Gerrits et al., 2019).However, as argued in the 'Introduction', these effects have so far only been evident for left-handed individuals that more often than right-handed individuals show an atypical lateralization pattern (Gerrits, 2022).Hence, in the present study it was examined whether similar effects could be observed in a relatively large sample of right-handed individuals (N ¼ 210).The present study also provided an opportunity to examine whether the degree of RH lateralization for face processing could be predicted based on the degree of RH lateralization for a global relative to local shape processing bias.This was possible to examine because a subsample of the individuals (n ¼ 189) also performed Navon's paradigm (Navon, 1977) from which two indexes of global shape processing could be derived.Such a relationship has been examined once previously by Brederoo et al. (2020) in a mixed group of left-and right-handed individuals.They found a positive relationship thus honoring the input asymmetry principle of lateralization according to which lower-level functions will cause ipsilateral lateralization of higher-level functions that depends upon them (Andresen & Marsolek, 2005).Again, it must be noted that this interdependency was only significant for left-handed individuals.
At the group-level the present study reproduced the expected effects with a (small) RVF/LH advantage for word processing (d ¼ À.18), a somewhat larger LVF/RH advantage for face processing (d ¼ .36),and a larger effect of global-to-local interference in the LVF/RH compared with the RVF/LH (d ¼ .24).There was no significant visual field difference for the global precedence effect proper which is also in keeping with a prior study (Gerlach & Poirel, 2020).On the individual level we found no evidence for interdependence between degree of lateralization of word and face processing.In fact, the data was 17e18 times more likely under the null hypothesis of no relationship.The same was true for the interdependence between degree of lateralization of face and global shape processing where the data were respectively 13 and 4 times more likely under the null hypothesis for the global precedence effect and the global-to-local interference effect respectively.
Taken at face value the present study e which is relatively high-powered in terms of sample size (N ¼ 210/189) compared with similar studies e provides strong evidence against both the RLH and the input asymmetry principle of lateralization for face and global shape processing in right-handed individuals.Unfortunately, the reliabilities of the lateralization measures used in the study turned out rather unsatisfactory (ICC: 0e.42).Because reliability is both a product of the measures (measurement error) and the sample (between-participant variance) this could not have been known prior to conducting the study (although the author must admit that in hindsight the use of four-letter words to differentiate reading performance in university students could strike one as rather optimistic).Nevertheless, if perfect reliability had been achieved the present study should have been sensitive enough to detect interdependency with effect sizes at r !.18(assuming an a-level of .05,one-tailed, and a b-level of .2). Factoring in the (estimated) reliabilities obtained, the estimated observable effect size increased to r !.57or r !.71depending on the laterality index in question.While there is generally little gained by using power analyses in a post hoc manner (Hoenig & Heisey, 2001;Zhang et al., 2019), the estimated drop in sensitivity due to poor reliability does dampen the claim that the present study provides strong evidence against interdependency.A more tempered conclusion is that the results of the present study are at odds with interdependency effects being very strong.Having said this, it should be taken into consideration that similar (negative findings) were found based on the data provided by Brederoo et al. (2020) when analyses were limited to right-handed individuals (see also Can ario, Jorge, & Castelo-Branco, 2020), and these data were produced with measures that seems to have had better reliability than the present (SpearmaneBrown corrected splithalf reliabilities between .49and .8).Considered together there is thus no positive evidence from right-handers to support the RLH or the notion that the degree of RH lateralization for face processing is contingent on the degree of RH advantage for global shape processing.This is most compatible with the statistical complementary principle of lateralization according to which typical lateralization patterns, even if stable at the group-level, reflect influences of divergent and independent sources at the individual level (Andresen & Marsolek, 2005).However, it could be argued that the results are compatible with light versions of the complementary and input asymmetry principles in that reading acquisition and/or global shape processing might determine the direction of laterality for face processing but that once set, these factors play no further influence on the degree of lateralization.

Credit author statement
Being the sole author this is N/A.

Fig. 3 e
Fig. 3 e Histograms showing the individual variation across the four indexes of laterality.
matching task) turned out to have similar reliabilities to the conditions with 20 trials (the measures of Global Precedence and Global-to-Local effects) (cf.Table

Fig. 5 e
Fig. 5 e The absolute size of the three variance components for each of the measures in the delayed matching task (upper panel) and the Navon paradigm (lower panel).The interclass correlation coefficient is the proportion of the total variance attributed to variance between individuals.

Fig. 6 e
Fig. 6 e The relative size of the three variance components for each of the measures in the delayed matching task (upper panel) and the Navon paradigm (lower panel).The size of each bar is normalized for the total amount of variance in the measure.