Word Frequency - University of Massachusetts Amherst

14 Pages·2010·0.98 MB·English

JournalofExperimentalPsychology: ©2010AmericanPsychologicalAssociation
HumanPerceptionandPerformance 0096-1523/10/$12.00 DOI:10.1037/a0016896
2010,Vol.36,No.5,1280–1293
Distributional Effects of Word Frequency on Eye Fixation Durations
Adrian Staub Sarah J. White
UniversityofMassachusettsAmherst UniversityofLeicester
Denis Drieghe Elizabeth C. Hollway
GhentUniversity UniversityofLeicester
Keith Rayner
UniversityofCalifornia,SanDiego
Recentresearchusingwordrecognitionparadigms,suchaslexicaldecisionandspeededpronunciation,
hasinvestigatedhowarangeofvariablesaffectthelocationandshapeofresponsetimedistributions,
usingbothparametricandnon-parametrictechniques.Inthisarticle,weexplorethedistributionaleffects
ofawordfrequencymanipulationonfixationdurationsinnormalreading,makinguseofdatafromtwo
recenteyemovementexperiments(Drieghe,Rayner,&Pollatsek,2008;White,2008).Theex-Gaussian
distributionprovidedagoodfittotheshapeofindividualsubjects’distributionsinbothexperiments.The
frequencymanipulationaffectedboththeshiftandskewofthedistributions,inbothexperiments,andthis
conclusion was supported by the nonparametric vincentizing technique. Finally, a new experiment
demonstratedthatWhite’s(2008)frequencymanipulationalsoaffectsbothshiftandskewinresponse-
time distributions in the lexical decision task. These results argue against models of eye movement
controlinreadingthatproposethatwordfrequencyinfluencesonlyasubsetoffixationsandsupport
modelsinwhichthereisatightconnectionbetweeneyemovementcontrolandtheprogressoflexical
processing.
Keywords:eyemovementsinreading,wordfrequency,ex-Gaussiandistribution
It is well known that the time the eyes spend on a word in Theseempiricalfindingsareamongthebenchmarkphenomena
readingisafunctionofarangeoflinguisticfactors(seeStaub& that models of eye movement control in reading, such as E-Z
Rayner,2007;Rayner,1998,inpress,forreviews).Forexample, Reader (Pollatsek, Reichle, & Rayner, 2006; Reichle, Pollatsek,
a word’s printed frequency (Inhoff & Rayner, 1986; Rayner & Fisher,&Rayner,1998;Reichle,Rayner,&Pollatsek,2003)and
Duffy, 1986) and its predictability in context (Ehrlich & Rayner, SWIFT(Engbert,Nuthmann,Richter,&Kliegl,2005),attemptto
1981; Rayner, Ashby, Pollatsek, & Reichle, 2004) each have account for. In E-Z Reader, for example, it is the progress of
substantialeffectsonmeasuressuchasthedurationofthereader’s lexicalprocessingthatdetermineswhenasaccadeprogramwillbe
first eye fixation on the word (first fixation duration) and the initiated. Specifically, the model proposes that a saccade is initi-
summed duration of all fixations before the eyes leave the word ated when the word processing system has completed an initial
(gazeduration);asfrequencyandpredictabilityeachdecrease,the stage of processing, referred to as L1 (originally termed a famil-
meandurationsincrease. iarity check), on the fixated word, and that word frequency and
predictability additively influence how long this stage takes to
complete(Rayneretal.,2004).
AdrianStaub,DepartmentofPsychology,UniversityofMassachusetts
Thereremains,however,afamilyoftheoriesofeyemovement
Amherst;SarahJ.WhiteandElizabethC.Hollway,SchoolofPsychology,
controlinreadingthat,whilenotdenyingtheexistenceoflinguis-
UniversityofLeicester;DenisDrieghe,DepartmentofPsychology,Ghent
ticinfluencesoneyefixations,proposethattheyaretheexception
University; and Keith Rayner, Department of Psychology, University of
California,SanDiego. ratherthantherule.YangandMcConkie(2001,2004;McConkie
PortionsofthisresearchweresupportedbyNationalInstituteofHealth &Yang,2003;Yang,2006;seealsoFeng,2006;O’Regan,1990)
GrantHD26765andbyBiotechnologyandBiologicalSciencesResearch havearguedthatthedurationsofmostfixationsareunaffectedby
Council Grant 12/S19168. Denis Drieghe is a postdoctoral fellow of the ongoingcognitiveprocessingofthetextateitherthelexicallevel
Fund for Scientific Research (Flanders, Belgium). We thank Andrew or at higher (e.g., syntactic) levels, but rather are a function of
Cohen for helpful discussion, and Chuck Clifton and Caren Rotello for
low-level perceptual processing and fixed oculomotor routines.
insightful comments on drafts of this paper. We thank Derek Besner,
Yang and McConkie used an experimental paradigm in which
Albrecht Inhoff, and an anonymous reviewer for their comments on an
normaltextwasreplacedduringaneyemovementwithstringsof
earlierversionofthepaper.
nonsense letters or Xs; they examined how and which fixations
CorrespondenceconcerningthisarticleshouldbeaddressedtoAdrian
Staub,DepartmentofPsychology,UniversityofMassachusetts,430Tobin durationswereaffectedbythedisplaychange.Onthebasisoftheir
Hall,Amherst,MA01003.E-mail:[email protected] results, they proposed that the distribution of fixation durations
1280
DISTRIBUTIONALEFFECTSOFFREQUENCY 1281
arisesfromamixtureofthreequalitativelydistincttypesoffixa- thesedistributionalobservationsarebasedonvisualinspectionof
tions: (1) very short fixations, the durations of which cannot be group distributions, from which inferences to individual subject
affectedbycognitiveprocessing;(2)“normal”fixations,whichare distributions should be made only with caution (e.g., Ratcliff,
vulnerable to being affected by cognitive processing due to sac- 1979; it should be noted that Yang and McConkie’s conclusions
cadecancellation;and(3)longfixations,whichreflectinstancesin are also based on analysis of group distribution functions). The
whichthesaccadethatwouldhaveterminatedanormalfixationis lack of attempts in the literature to describe individual subjects
cancelled due to higher-level processing difficulty, and a new distributionsoffixationdurationscanbeattributedtothefactthat
saccademustthenbeprogrammed.YangandMcConkieproposed inmosteyemovementexperimentsthenumberofobservationsin
that cognitive or linguistic processing influences mean fixation eachexperimentalcondition,foreachsubject,fallsfarshortofthe
duration by changing how frequently saccades that would have number required to perform such analyses (Heathcote, Brown, &
terminated “normal” fixations are canceled and replaced by later Mewhort, 2002; Speckman & Rouder, 2004); it is common to
saccades. Thus, they suggested that a variable such as word fre- includeasfewaseightortentrialspercondition.
quencydoesnothaveageneralandgradedeffectonthetimethat In the present work, we fit the ex-Gaussian distribution to
the eyes spend on a word; instead, a low frequency word simply individualsubjectdatafromtworecentlypublishedeyemovement
increasestheprobabilityofanerrorsignalthatcausescancellation experiments(Drieghe,Rayner,&Pollatsek,2008;White,2008)in
oftheinitialsaccadeplan.YangandMcConkie(2004)notedthat whicharelativelylargenumberofobservationswerecollectedin
“this implies a discrete basis for control of the durations of indi- high-andlow-frequencyconditions.Wealsoanalyzedtheshapes
vidual fixations, where, in most cases, either the normal saccade offixationtimedistributionsnon-parametricallybyexaminingthe
occurs or it is canceled and another saccade is generated later, characteristicshapesofindividualsubjectdistributionsintheform
ratherthanafine-grainedadjustmentoffixationtimebasedonthe ofvincentileplots(e.g.,Andrews&Heathcote,2001;Balotaetal.,
currentlanguageprocessingneeds”(p.419). 2008; Yap & Balota, 2007). To anticipate the results, it appears
The goal of the present work was to assess these competing thattheshapeofdistributionsoffixationdurationsisfitextremely
perspectivesonhowlinguisticprocessinginfluencesfixationtime wellbytheex-Gaussiandistribution,andthatinbothexperiments,
byinvestigatingdistributionsoffixationdurationsinnormalread- thesedistributionswerebothshiftedtotherightandincreasedin
ing,andspecifically,theeffectofwordfrequencyonthesedistri- skew in the low-frequency condition compared to the high-
butions. A sizable literature using single-word recognition para- frequency condition. To enable a direct comparison between the
digms,suchaslexicaldecision,speededpronunciation(sometimes distributionalpatternsevidentinfixationdurationsduringsentence
referredtoas“naming”),andsemanticcategorization(Andrews& readingandinsingle-wordRT,wethencarriedoutanewlexical
Heathcote,2001;Balota&Speiler,1999;Balota,Yap,Cortese,& decision experiment using the critical words employed by White
Watson,2008;Plourde&Besner,1997;Yap&Balota,2007;Yap, (2008).
Balota, Cortese, & Watson, 2006; Yap, Balota, Tse, & Besner, It should be noted that there are clear limitations on the infer-
2008), has demonstrated that individual subjects’ response time ences that can be drawn from ex-Gaussian fitting. First, it is not
(RT) distributions in these tasks are single-peaked and right- obviousthattheex-GaussianprovidesabetterfittoempiricalRT
skewed. Thus, these distributions can be well fit by the ex- datathandootherparametricestimatorsofdistributionshapesuch
Gaussiandistribution(Ratcliff,1979),whichistheconvolutionof as the Wald or the gamma distributions (Van Zandt, 2000). Sec-
a normal distribution and an exponential distribution, with two ond, it should not be assumed that data that are well fit by the
parameterscorrespondingtothenormalcomponent((cid:1),themean, ex-Gaussiandistributionareliterallygeneratedbytwounderlying
and(cid:2),thestandarddeviation),andasingleexponentialparameter processes occurring in succession, one with normally-distributed
((cid:3)). Fitting of the ex-Gaussian distribution to individual subject finishing times, and the other with exponentially-distributed fin-
datahasallowedresearcherstoassesstheproportionofanexper- ishing times. Relatedly, while there have been several interesting
imentaleffectonmeanRTthatisduetoachangeinthelocation attempts to give concrete psychological interpretations to the (cid:1)
ofthenormalcomponent(i.e.,aneffecton(cid:1)),andtheproportion and(cid:3)componentsofRTdistributions(seeLuce,1986,fordiscus-
thatisduetoachangeinthedegreeofskew(i.e.,aneffecton(cid:3)). sion), there is also reason to be skeptical of any straightforward
Several research groups (Andrews & Heathcote, 2001; Balota & mappingofthesecomponentstopsychologicalprocesses(Matzke
Speiler,1999;Plourde&Besner,1997;Yap&Balota,2007)have &Wagenmakers,2008;Yap,Balota,Tse,&Besner,2008).
demonstratedthatinfactafrequencymanipulationhasbothkinds Thus, our use of the ex-Gaussian distribution is motivated by
ofeffects:thedistributionsforlow-frequencywordsareshiftedto three straightforward considerations. First, it is of interest to de-
the right compared to distributions for high-frequency words and termine whether empirical distributions of fixation durations are
arealsoincreasedinskew.Thedistributionalshiftingsuggeststhat wellfitbytheex-Gaussian,asaredistributionsofRTsinsingle-
in single-word paradigms a word frequency manipulation affects word paradigms. Second, partitioning the frequency effect on
thedurationofsomeprocessingstageorcomponentthatisoper- fixation durations into effects on distinct ex-Gaussian parameters
ative on all (or at least most) trials, while the change in skew enablesdirectcomparisonwiththeexistingsingle-wordliterature,
indicatesthatasubsetofRTsareslowedmoredramatically. in which it is clear that a frequency manipulation affects both (cid:1)
It has previously been observed that distributions of fixation and (cid:3). Finally, changes in the (cid:1) parameter across experimental
durations in normal reading are roughly normal, but with some conditions can indeed be interpreted, in a descriptive, relatively
degreeofrightskew,andthatafrequencymanipulationappearsto theory-neutralmanner,asreflectinganeffectthatoccursonall,or
shiftthelocationofthedistributionoffixationdurations(Rayner, atleastmost,experimentaltrials,anoutcomethatisnotpredicted
1995; Rayner, Liversedge, White, & Vergilino-Perez, 2003; by either the specific saccade-cancellation account of Yang and
White, 2008), as would be predicted by E-Z Reader. However, McConkie (2001, 2004), or more generally by any account that
1282 STAUBETAL.
restrictstheinfluenceofthefixatedword’sfrequencytoasubset Inconditionsbandd,theincorrectpreviewwasreplacedbythe
offixations. correct word during an eye movement (Rayner, 1975) when the
Thisarticleproceedsasfollows.Study1consistsofadistribu- reader’s eyes crossed the space between the two critical words.
tionalanalysisoftheeyemovementdatacollectedbyDriegheet Subjectsareusuallyunawareofthepresenceofthenonwordand
al. (2008) in an experiment originally designed to investigate an thedisplaychange.
unrelated issue, namely, so-called “parafoveal-on-foveal” effects The mean frequency counts for the high-frequency and low-
(e.g.,Kennedy&Pynte,2005).Ina2(cid:4)2design,thisexperiment frequencynouns,basedontheFrancisandKucˇera(1982)norms,
manipulated both the frequency of a critical noun (word n) and were 163 per million and 8 per million, respectively. All critical
whetherthenextword(wordn(cid:5)1)wasfullyvisibletothereader nounswerefivelettersinlength,andthesentenceswerenormed
priortodirectfixationorwasreplacedbyanonworduntiltheeyes to ensure that the critical nouns were not predictable from the
fixated word n (cid:5) 1 directly (a preview manipulation; Rayner, precedingcontext.
1975).Therewere25observationspersubjectineachofthefour
conditions,buttherewasnohintofaninteractionbetweenthetwo
Results and Discussion
manipulationsonwordn(andindeed,nosignificantinteractionon
wordn(cid:5)1),soitispossibletocombineacrossthelevelsofthe
The full pattern of results is reported in Drieghe et al. (2008).
preview manipulation for the purpose of investigating the effects
We focus on the first fixation duration measure, which is most
of frequency on distributions of fixation durations on word n. In
central for the questions of interest. We also examine gaze dura-
Study2,weassessedthereliabilityofthefindingsfromStudy1by
tion,thoughwenotethatfromthepointofviewofdistributional
conducting similar distributional analyses of data collected by
analyses this is a “hybrid” measure, with most observations rep-
White(2008)inacompletelyunrelatedexperimentwithdifferent
resenting only one fixation, but some observations representing
materials and different subjects. In White’s (2008) experiment,
two fixations. (On the single fixation duration measure, which is
eachsubjectread39sentencescontainingacriticalhigh-frequency
the duration of eye fixations on those trials on which the reader
wordandanother39containingalow-frequencyword.(Theyalso
madeexactlyonefixationonthecriticalwordbeforemovingon,
read 39 sentences in a third experimental condition, discussed
allresultswereessentiallyidenticaltofirstfixationduration,both
below.) Finally, in Study 3 we presented the critical words from
intermsofthemeanandintermsofthedistributionalanalyses.)
White’s(2008)studyinaseparatelexicaldecisionexperimentin
On the critical noun there were highly significant effects of fre-
order to assess the degree of correspondence between the distri- quency on both first fixation duration (285 ms vs. 260 ms; p (cid:6)
butional effects of frequency on eye movements and on single- .001)andgazeduration(294msvs.267ms;p(cid:6).001).Therewere
word RT when the same words are employed in the two para-
no effects on the noun of the preview manipulation of the next
digms. word (Fs (cid:6) 1), and there were no interaction effects (Fs (cid:6) 1).
Readersonlyrarelymademultiplefirstpassfixationsonthisword,
doingsoon3.9%oftrialsinthehigh-frequencyconditions,andon
Study 1
4.7%oftrialsinthelow-frequencyconditions.
As noted above, the data were collapsed across the preview
Method conditionsforthepurposeofdistributionalanalysisinthelow-and
high-frequencyconditions,allowingforamaximumof50obser-
CompletemethodologicaldetailsareprovidedbyDriegheetal.
vationsforeachofthetwolevelsofwordfrequency.However,a
(2008);ashortersummarywillbeprovidedhere.Theeyemove-
substantial number of trials were excluded from analyses, either
mentsof28membersoftheUniversityofMassachusettscommu-
becausethedisplaychangedidnotoccuratpreciselytherighttime
nityweremonitoredbyaDualPurkinjeImageeyetrackerasthese
(i.e., it was either initiated or completed during a fixation, rather
subjects read individual sentences displayed on a monitor. The
thanduringthecriticalsaccade)orbecausethereaderdidnotmake
subjects’taskwastoreadnormallyandtoansweryes/nocompre-
a first-pass fixation on the critical word. (Note that incorrect
hension questions by means of a button press. One hundred sen-
displaychangecouldbegroundsforexclusioneveninconditions
tenceswerepresentedinarandomordertoeachsubject,following
a and c, in which technically there was also a change as the
10 practice sentences. Each subject read 25 sentences in each of
experimental software replaced the target word with itself.) As a
four conditions, exemplified by (1a-d) below, with the critical
result,therewasanaverageof29.7usableobservationspersubject
wordsinitalics.
inthehigh-frequencycondition(witharangefrom14to43,outof
amaximumpossibleof50)andanaverageof27.6usableobser-
1.a) Theoperawasveryproudtopresenttheyoungchild
vations per subject in the low-frequency condition (with a range
performingonTuesday.(HFnoun,correctpreview)
from9to47).Becausethenumberofobservationsfrequentlyfell
below the number that has been regarded as safely delivering
b) Theoperawasveryproudtopresenttheyoungchild
reliable ex-Gaussian parameter estimates (i.e., approximately 40;
pxvformingonTuesday.(HFnoun,incorrectpreview)
Heathcoteetal.,2002;SpeckmanandRouder,2004),weconsid-
c) Theoperawasveryproudtopresenttheyoungtenor ereditespeciallyimportanttoconfirmthepatternofresultsusing
performingonTuesday.(LFnoun,correctpreview) anon-parametricmethod,asdescribedbelow,andtoconfirmthe
patternacrossmultipleexperiments.
d) Theoperawasveryproudtopresenttheyoungtenor The ex-Gaussian distribution was fit to the data from each
pxvformingonTuesday.(LFnoun,incorrectpreview) subjectineachconditionusingtheQMPEsoftwaredevelopedby
DISTRIBUTIONALEFFECTSOFFREQUENCY 1283
Heathcote et al. (2002; Cousineau, Brown, & Heathcote, 2004).1 As an additional nonparametric means of assessing the distri-
Thefittingproceduredividestheempiricaldistributionintoquan- butionaleffectsofthefrequencymanipulation,andasameansof
tiles(i.e.,binswithanequalnumberofobservationsineach),then assessing the fit of the extracted ex-Gaussian parameters to the
uses maximum likelihood estimation to determine the distribu- typical distribution shape, we constructed vincentile plots (Rat-
tionalparametersthatcomeclosesttoproducingthecorrectquan- cliff, 1979; Vincent, 1912) of the data in each condition, as is
tileboundaries,allowingallthreeparameterstovaryfreely.Heath- commoninthesingle-wordliterature(see,e.g.,Andrews&Heath-
cote et al. (2002; see also Rouder, Lu, Speckman, Sun, & Jiang, cote,2001;Balotaetal.,2008;Yap&Balota,2007).Theseplots
2005) found that the best fits are delivered when the maximum are constructed as follows. The individual observations for each
numberofpossiblequantilesisused,i.e.,witheachdatapointin subject, in each condition, are divided into the shortest 10%
a separate bin; this method was used in the present research. All (vincentile1),nextshortest10%(vincentile2),etc.2Themeanof
distributions were successfully fit, as assessed by an algorithm theobservationsineachvincentileisthencomputed.Finally,the
internal to the QMPE software; below, we discuss the quality of mean of all individual subject values is computed, for each vin-
fit. Once the best fitting parameters for each distribution are centile, and these values (and standard errors) are displayed as
extracted, statistical analyses in which these parameter values connected points on a plot with vincentile on the x-axis and
functionasdependentvariablesmaybeusedtoaddresstheques- fixation time in ms on the y-axis. Thus, the plots illustrate how
tionofwhethertheexperimentalmanipulationsinducechangesin fixation time changes across the typical individual subject distri-
(cid:1),(cid:2),(cid:3),orsomecombinationoftheseparameters. bution (as opposed to the group distribution, which may be very
Themeanvaluesofeachoftheex-Gaussianparameters,ineach different in shape). The steepness of a curve’s slope, at the right
condition, are shown in Table 1. Recall that the (cid:1) parameter side of the graph, indicates the degree of right skew present. If a
represents the mean of the normal component, the (cid:2) parameter differencebetweentwoconditionmeansisduetoarightwardshift,
representsthestandarddeviationassociatedwiththenormalcom- withnochangeinthedegreeofskew,thenthecurvescorrespond-
ponent, and (cid:3) represents the contribution of an exponentially- ing to the two conditions will be parallel, with the curve repre-
distributedvariable,whichismanifestedintermsofthedegreeof sentingtheslowerconditionappearingabovethecurverepresent-
rightward skew. On the first fixation measure, the 16-ms differ- ing the faster condition across the full range of vincentiles. If a
enceinthe(cid:1)parameterwashighlysignificant,t(27)(cid:7)4.40,p(cid:6) difference between two condition means is due entirely to in-
.001,whilethe8-msdifferencein(cid:2)wasmarginal,t(27)(cid:7)1.89, creasedskewinonecondition,thentheverticaldistancebetween
p(cid:7).07,andthe10-msdifferencein(cid:3)wasalsomarginal,t(27)(cid:7) the corresponding curves will be small or nonexistent for the
1.97,p(cid:7).06.Onthegazedurationmeasure,the8-msdifference vincentilesontheleftsideofthegraph,butlargerontheright(i.e.,
inthe(cid:1)parameterwasnotsignificant,t(27)(cid:7)1.38,p(cid:7).18,and for the slowest part of the distributions). A difference that is due
neither was the 4-ms difference in (cid:2), t(27) (cid:7) .75, p (cid:7) .46. bothtoachangeinthelocationofthedistributionandtoachange
However,the20-msdifferencein(cid:3)wassignificant,t(27)(cid:7)2.67, in skewness will be manifested in a vertical separation that is
p(cid:6).02.Thusitappears,basedonthemeanex-Gaussianparam- presentalongthefullrangeofvincentiles,butwhichislargeron
eters, that the frequency effect on first fixation duration was due therightthanontheleft.
primarilytodistributionalshiftinginthelow-frequencycondition, ThefirsttwopanelsofFigure2arevincentileplotsforthefirst
though there is also a strong hint of increased skewing in this fixationandgazedurationdata,respectively.Oneachplot,thereis
condition;thefrequencyeffectongazedurationwasdueprimarily a separation between the high frequency and low frequency con-
to an increase in skew in the low-frequency condition. Figure 1 ditionsallalongthedistribution,withslightlygreaterseparationon
illustratesdensityfunctionsassociatedwiththemeanex-Gaussian therightsideofthegraph.Superimposedontheplotsaretriangles
parametersforthehigh-andlow-frequencyconditionsonthefirst representing predicted vincentile values obtained from the simu-
fixationdurationandgazedurationmeasures.Thesearebasedon latedex-GaussiandistributionsshowninFigure1.Theproximity
20000randomsamplesfromeachdistribution,whereeachsample of these predicted values to the actual vincentile values indicates
isgeneratedbysummingasamplefromanormaldistributionwith that the mean ex-Gaussian parameters do capture the typical dis-
mean(cid:1)andstandarddeviation(cid:2)andasamplefromanexponen- tributionshapes;seeAndrewsandHeathcote(2001)andYapetal.
tialdistributionwithrateparameter(cid:7)1/(cid:3). (2008) for discussion of this visual method for assessing ex-
Gaussian fit. Note that if an empirical distribution is not actually
well described as ex-Gaussian (e.g., it is a bimodal distribution
Table1
Study1MeanReadingTimeonFirstFixationandGaze
DurationMeasures,inMilliseconds,andMeanEx-Gaussian
1Itiscustomaryintheex-Gaussianliteraturetocarryoutdistributional
Parameters,byCondition
analysesonlyforsubjects,notforitems.
Variable M (cid:1) (cid:2) (cid:3) 2Fortheonesubjectwhohadonlynineobservationsinonecondition,
thevincentizingprocedureresultedinamissingvalueforthefirstvincen-
Firstfixationduration tile.Ingeneral,thevincentizingprocedurefirstmultipliedthetotalnumber
Highfrequency 260 206 40 55 ofobservationsby.1,.2,etc.,resulting,inmostcases,indecimalvalues;
Lowfrequency 285 222 48 65 these values were then rounded down, and the corresponding data point
Frequencyeffect 25 16 8 10 (with the data points ordered from fastest to slowest) was treated as the
Gazeduration upperboundofthecorrespondingvincentile.Forexample,iftherewere35
Highfrequency 267 211 41 59 observationsforagivensubjectinagivencondition,vincentile1would
Lowfrequency 294 219 45 79
consistofthethefastestthreefixations;vincentile2wouldconsistofthe
Frequencyeffect 27 8 4 20
nextfour;vincentile3wouldconsistofthenextthree,andsoon.
1284 STAUBETAL.
Figure1. Densityfunctionsgeneratedfrombest-fittingex-GaussianparametersinStudy1forhigh-frequency
(HF)andlow-frequency(LF)conditions:firstfixationduration(upperpanel)andgazeduration(lowerpanel).
with truly distinct peaks), this visual test will indeed fail as the effect in the gaze duration data. These plots also make clear that
predictedvincentilevalueswilltendtofalloutsidetherangeofthe the mean ex-Gaussian parameters capture the typical distribution
standard error bars around the observed values; see Andrews & shape extremely well, despite the relatively small number of ob-
Heathcote (2001) Figure 1, for an example of a moderate misfit. servationsavailablefromsomesubjects.ThegoalofStudy2was
The final panel of Figure 2 illustrates the size of the frequency to determine whether similar patterns would be observed in data
effect across the range of vincentiles, i.e., the mean difference fromanunrelatedstudy.
betweenthelow-frequencyandhigh-frequencyvalue,forbothfirst
fixation and gaze duration, as well as the standard error of this
Study 2
difference.
In sum, the vincentile plot for the first fixation duration data White(2008)comparedreadingtimesonhigh-frequencywords
confirms that the frequency effect appears across the distribution to reading times on two sets of low frequency words. These two
and is somewhat larger at the right edge of the distribution. The latter sets were matched on frequency but were distinguished
plot for gaze duration suggests an essentially similar pattern, based on the token frequency of the individual letters and multi-
though the ex-Gaussian analysis did not find a significant shift letterstringswithintheword;thislattervariablewasreferredtoas
DISTRIBUTIONALEFFECTSOFFREQUENCY 1285
Figure2. Topandmiddlepanels:vincentilesforhigh-frequency(HF)andlow-frequency(LF)conditionsin
Study1forfirstfixationduration(toppanel)andgazeduration(middlepanel).Errorbarsrepresentstandard
errorofthemean.Predictedvincentilesbasedonmeanex-Gaussianparametersarerepresentedbytriangles.
Bottompanel:Meandifferencebetweenconditionsateachvincentilewithstandarderrors.
1286 STAUBETAL.
orthographicfamiliarity.Foroneset,referredtoastheinfrequent (2008)datathanintheDriegheetal.(2008)data,probablydueto
orthographically familiar words, orthographic familarity was thefactthatmultiplefixationsonthetargetwordwerequiterare
comparabletothehigh-frequencywords;fortheotherset,referred intheDriegheetal.study.
to as the infrequent orthographically unfamiliar words, ortho- Because there was no display-change manipulation in this ex-
graphicfamiliaritywassubstantiallylower.Whiteobtainedasiz- periment,trialswereexcludedfromdistributionalanalysisonlyon
able word frequency effect in the comparison of the high- and the basis of word skipping, blinks, or track loss on the critical
low-frequencywordsthatwerematchedonorthographicfamiliar- words. There was an average of 28.9 usable observations per
ity, with longer reading times on the infrequent orthographically subjectinthehigh-frequencycondition(witharangefrom15to39
familiar words than on the frequent words on several eye move- out of a maximum possible of 39) and an average of 30 usable
mentmeasures.Asmallerorthographicfamiliarityeffectwasalso observations per subject in the low-frequency condition (with a
evident,withlongerreadingtimesontheinfrequentorthographi- rangefrom17to39).Ex-Gaussiananalysiswascarriedoutusing
cally unfamiliar words than on the infrequent orthographically the same method as for Study 1; again, all fits were successful
familiar words. For present purposes, we focus entirely on the based on the criteria applied by the QMPE software. The mean
formercomparison,andforbrevity(bothforStudy2andStudy3), valuesoftherecoveredparametersareshowninTable2.Onthe
we refer to the orthographically familiar words simply as high firstfixationmeasure,the13-msdifferenceinthe(cid:1)parameterwas
frequencyorlowfrequency.3 significant,t(29)(cid:7)2.34,p(cid:6).05,aswasthe15-msdifferencein
(cid:3),t(29)(cid:7)2.28,p(cid:6).05.Onthegazedurationmeasure,the17-ms
difference in the (cid:1) parameter was significant, t(29) (cid:7) 2.96, p (cid:6)
Method
.01,aswasthe28-msdifferencein(cid:3),t(29)(cid:7)3.69,p(cid:6).001.The
CompletemethodologicaldetailsareprovidedinWhite(2008); effectsonthe(cid:2)parameterdidnotapproachsignificanceforeither
a shorter summary will be provided here. Thirty students at the measure(ts(cid:6)1).Figure3illustratessimulateddensityfunctions
UniversityofDurham,UnitedKingdom,hadtheireyemovements basedonthemeanex-Gaussianparametersforfirstfixationdura-
monitoredbyaDualPurkinjeImageeyetrackerastheyread.Their tion and gaze duration (generated by simulating 20000 observa-
task was to read normally and to answer yes/no comprehension tionsfromeachdistribution).
questions.Alistof117experimentalsentenceswaspresentedina ThefirsttwopanelsofFigure4arevincentileplotsforthefirst
fixedpseudorandomizedordertoeachsubject,followingsixprac- fixationandgazedurationdata,respectively.AsinStudy1,there
tice sentences. In each of the experimental sentences, a critical isseparationbetweenthehigh-frequencyandlow-frequencycon-
wordappeared;therewere39sentenceswitheachofthreetypesof ditions all along the distribution, with greater separation on the
criticalword.Thecriticalwordtypeswerethefollowing:frequent rightsideofthegraph.Again,itappearsthatthesimulateddistri-
orthographicallyfamiliar(e.g.,door);infrequentorthographically butionsgeneratedfromthemeanex-Gaussianparametersproduce
familiar (e.g., gong); and infrequent orthographically unfamiliar vincentiles that are extremely close to the vincentiles in the ob-
(e.g., tusk). The words were grouped into triplets in which the serveddata.ThefinalpanelofFigure4illustratesthesizeofthe
criticalwordswerematchedonlengthandwerepresentedwiththe frequencyeffectacrosstherangeofvincentiles.Again,itisclear
same preceding sentence frame. The randomization procedure thatthefrequencyeffectispresentalongthefulldistributionbutis
ensuredthatthematchinginitialsentenceframesweredistributed largerontheright;especiallyinthegazedurationdata,itappears
widely through the experiment. All sentences were normed to that there is a strong frequency effect on the right tail of the
ensurethatthecriticalwordwasnotpredictable(seeWhite,2008, distribution. This strong skewing effect can be explained by the
fordetails). factthatinthisexperiment,theprobabilityofasecondfixationon
Criticallexicalcharacteristicsofthetwosetsofwordsofpresent the critical word was almost twice as high in the low-frequency
interestwereasfollows.BasedontheCELEXdatabase(Baayen, conditionasinthehigh-frequencycondition,addingasubstantial
Piepenbrock, & Gulikers, 1995), the mean frequencies of the numberoflonggazedurationsinthelow-frequencycondition.
words,incountspermillion,were297forthefrequentorthograph- Considering the analyses of both experiments, it is clear, first,
ically familiar words and 1.7 for the infrequent orthographically that the typical shape of fixation duration distributions is fit ex-
familiar words. As noted above, these two sets of words did not tremelywellbytheex-Gaussiandistribution.Thisfindingdoesnot
differ on the orthographic familiarity measure. They also did not indicatethatthesedistributionscouldnotbegeneratedbyamix-
differ in the number of orthographic neighbors. All words were ture model, such as the model proposed by Yang and McConkie
fourorfivecharacterslong(andasnotedabove,matchedonlength (2001, 2004) in which there are distinct subpopulations of fixa-
withineachset)withameanof4.5characters. tions;indeed,itisverylikelythatamixturemodel,withsuitably
chosenparameters,couldbemadetomimicthisshape.However,
Results and Discussion
Thefrequencymanipulationhadsignificanteffectsonbothfirst 3Inadditiontoitslackofdirectrelevancetotheissuethatisthefocus
fixationduration(280msvs.253ms;p(cid:6).001)andgazeduration ofthisarticle,theorthographicfamiliaritymanipulationisadmittedlynot
(309 ms vs. 265 ms; p (cid:6) .001). As in Drieghe et al. (2008), the well understood: Letter frequency, bigram frequency, and trigram fre-
quency all make contributions to this measure and are highly correlated
patternforsinglefixationdurationmirroredfirstfixationduration
(White,2008),andtherearealsounavoidabledifferencesbetweenthetwo
very closely. Readers made more than one fixation on the target
classesofwordsinneighborhoodsizeandinspelling-soundconsistency.
word6%ofthetimeinthehigh-frequencyconditionand11%of Asdiscussedbelow,wedidincludetheorthographicallyunfamiliarwords
the time in the low-frequency condition. The gaze duration mea- inthenewlexicaldecisionexperiment(Study3),primarilyforconsistency
sure shows a considerably larger frequency effect in the White withtheeyemovementexperiment.
DISTRIBUTIONALEFFECTSOFFREQUENCY 1287
Table2 of the underlying word recognition processes that must be com-
Study2MeanReadingTimeonFirstFixationandGaze pletedbeforeasaccadeisprogrammed.IntermsoftheE-ZReader
DurationMeasures,inMilliseconds,andMeanEx-Gaussian model,forexample,itmightbeproposedthattheskewnessofthe
Parameters,byCondition distribution of L1 (or “familiarity check”) finishing times, which
mustbecompletebeforeasaccadeprogramisinitiated,isaffected
Variable M (cid:1) (cid:2) (cid:3) byafrequencymanipulation.
Totestthisidea,weexplored,inStudy3,whetherthespecific
Firstfixationduration
Highfrequency 253 208 43 42 frequency manipulation employed by White (2008) would have
Lowfrequency 280 221 47 57 similar distributional affects in a word-recognition task in which
Frequencyeffect 27 13 4 15 saccadicprogrammingplaysnorole,namelylexicaldecision.As
Gazeduration
noted above, previous single-word experiments have generally
Highfrequency 265 204 41 57
found both (cid:1) and (cid:3) effects of a frequency manipulation, and we
Lowfrequency 309 221 46 85
Frequencyeffect 44 17 5 28 expectedthesamepatternhere.
Study 3
thereisclearlynodirectsupportforamixturemodelinthedata.
YangandMcConkie(2001,2004)doreportmulti-modaldistribu- Method
tions of fixation durations, but as noted above, these appeared in
Subjects. Thirty students at the University of Leicester par-
group distributions, and moreover, in experiments involving al-
ticipated in the experiment voluntarily or for course credit; none
teredtextratherthannormalreading.
hadparticipatedintheexperimentbyWhite(2008).Thesubjects
Second, it is clear that the effect of word frequency on the
were native English speakers, had normal or corrected-to-normal
durationofreaders’firstfixationonawordisduebothtoashifting
vision, and were na¨ıve regarding the purpose of the experiment.
of the distribution of fixation durations to the right and to an
One subject was excluded and replaced due to an exceptionally
increase in the degree of skewing. These conclusions emerged
higherrorrateforthecriticalwords(18%).
from both the ex-Gaussian analysis, which revealed significant
Materials. The same 117 stimulus words used in White
effectsoffrequencyon(cid:1)andsignificantormarginaleffectson(cid:3) (2008) were intermixed with 115 nonwords.4 As there were no
in both experiments, and from the vincentizing procedure, which
sentence frames presented in common for members of the three
revealedadistributionalshiftingforlow-frequencywords,withthe
sets of words, the word-type manipulation is best regarded as a
mostpronouncedfrequencyeffectemerginginthehighestvincen-
within-subjects but between-items manipulation in this experi-
tiles.Thegazedurationconclusionsaregenerallysimilar,though
ment.Thelengthsofthenonwordswerematchedtothelengthsof
the effect of frequency on (cid:1) was significant in the White (2008)
thewords.Inordertoencouragelexicaldecisionstobemadeon
experiment,butnotintheDriegheetal.(2008)experiment.
thebasisoflexicalaccessratherthanorthographicfamiliarity,the
The specific type of mixture model proposed by Yang and
nonwordswereconstructedsoastobeorthographicallysimilarto
McConkie(2001,2004)wouldappeartohavedifficultyaccount-
thewords;76ofthenonwordswerematchedontheorthographic
ing for the finding of a distributional shift, affecting even the
familiaritymeasuretotheorthographicallyfamiliarwords,and39
leading edge of the distribution, based on a frequency manipula-
nonwords were matched on this measure to the orthographically
tion.YangandMcConkie(2001)reportedthatalteringnormaltext
unfamiliarwords.Notethatasaresultofthiscontrol,manyofthe
during a saccade by replacing the spaces between words with
nonwordsweresimilartorealwords,forexamplecreatorfrowe.
nonlettersymbols,orevenbyreplacingallwordswithnonwords
Theitemswerepresentedinarandomordertoeachsubject.
orwithstringsofXs,hadnoeffectwhatsoeveronthedurationof
Procedure. The experiment was run using E-Prime software
fixationsshorterthanabout175–200ms,andarguedonthisbasis
(Schneider,Eschmann,&Zuccolotto,2002)onaPCwitha17-in
that there is a population of relatively short fixations that is
LCD monitor with a refresh rate of 60 Hz. Subjects responded
unaffectedbycognitiveorlinguisticprocessingofthetext.Butthe
using a Psychology Software Tools Serial Response Box. The
present data suggest that word frequency affects the duration of
stimuli were presented in 18-pt Courier font in black on a white
mostofareader’sencounterswithaninputword,andprovideno
background. Subjects undertook the experiment individually in a
evidence of a qualitative distinction between the effect on short
quiet room, and the viewing distance was approximately 60 cm.
fixationsandtheeffectonlongerfixations.
Having read the instructions, they completed one block of six
Still, it is clear that some fixation durations are affected more
practice trials followed by five blocks of experimental trials be-
dramatically than others, as evidenced by the more pronounced
tweenwhichsubjectscouldtakeashortbreakiftheywished.On
effectontherighttailofthedistribution,andthisfindingmightbe
eachtrial,thetargetstimulusappearedinthecenterofthescreen
regarded as consistent with a somewhat modified saccade-
untilthesubjectspressedaresponsekey.Subjectsrespondedwith
cancellationaccount.Suchanaccountwouldallowthatfrequency
theleft-handkeyiftheythoughtthetargetwasanonwordandwith
does affect the duration of “normal” fixations, but would also
theright-handkeyiftheythoughtthetargetwasaword.Theentire
claim that saccade cancellation plays an important role, as pro-
sessionlastedapproximately15min.
cessingdifficultyonalow-frequencywordsometimesdoesleadto
cancellation of an initially-programmed saccade. But alternately,
the especially large effect of frequency on the right tail of the 4Twoadditionalstimuliwerealsoincludedasnonwordsbut,duetoan
distribution may simply reflect the distribution of finishing times errorinthedevelopmentofmaterials,wereactuallyveryinfrequentwords.
1288 STAUBETAL.
Figure3. Densityfunctionsgeneratedfrombest-fittingex-GaussianparametersinStudy2forhigh-frequency
(HF)andlow-frequency(LF)conditions:firstfixationduration(upperpanel)andgazeduration(lowerpanel).
Results and Discussion fixed criterion was used, as is common in the eye movement
literature. (Fixations shorter than 80 ms or longer than 1200 ms
We focus on the two conditions of present interest, i.e., the
were excluded; see White, 2008, for details.) Moreover, it is
frequentorthographicallyfamiliarwordsandtheinfrequentortho-
arguably the case that routines for excluding outliers should be
graphicallyfamiliarwords,referredtoheresimplyasloworhigh
especiallyconservativewhentherighttailofthedistributionisof
frequency,asinStudy2.Table3providesthemeanaccuracyand
particularinterest,andwhenthedegreeofskewishypothesizedto
correct RT for each of these word types, as well as for the
varyacrossconditions,asinthepresentcase(see,e.g.,Heathcote,
orthographically unfamiliar words and for the orthographically
Popiel,&Mewhort,1991;Ratcliff,1993).Inaddition,inorderto
familiarandunfamiliarnonwords.
Accuracywashigherforthehigh-frequencywordsthanforthe maintain strict comparability to the eye movement analyses, we
low-frequencywords,t (29)(cid:7)9.36,p(cid:6).001,t (76)(cid:7)3.97,p(cid:6) also conducted analyses in which error responses were not ex-
1 2
.001. For the analysis of RT, errors were excluded, as were cluded,asthereareno“errors”intheeyemovementdata.There
responses shorter than 250 ms or longer than 3000 ms (0.2% of were no notable differences between the patterns of results for
trials). We did not exclude additional observations based on cut- theseanalysesandfortheanalysesinwhicherrorswereexcluded
offsforeachsubject,inordertomaintainmaximumcomparability (all statistical tests, for both mean RT and for the ex-Gaussian
totheanalysesoftheWhite(2008)experiment,forwhichasingle parameters, delivered the same verdict), so we report only the
DISTRIBUTIONALEFFECTSOFFREQUENCY 1289
Figure4. Topandmiddlepanels:vincentilesforhigh-frequency(HF)andlow-frequency(LF)conditionsin
Study2forfirstfixationduration(toppanel)andgazeduration(middlepanel).Errorbarsrepresentstandard
errorofthemean.Predictedvincentilesbasedonmeanex-Gaussianparametersarerepresentedbytriangles.
Bottompanel:Meandifferencebetweenconditionsateachvincentilewithstandarderrors.