Entropy measures and predictive recognition as mirrored in gating and lexical decision over multimorphemic Hungarian noun forms

Our paper is an attempt to indicate the relevance of information theoretical accounts to understand word recognition and morphological processing in Hungarian, along with other studies using more traditional predictors like linear position and morphological composition. The first two experiments were gating studies. The effect of the decision points was only evident in frequent words. The correct recognition means for the recognition points differ from the means for one-before-recognition points, indicating that the recognition point follows a sudden drop of the entropy value. This shows how entropy measures can be used to predict word recognition in actual language performance. The next two experiments examined the word reconstruction effect. A clear bathtub effect (Aitchison, 1987) was obtained: reconstruction was highest in the cases where both the beginning and the end were correct. The last, lexical decision based study used four basic morphological types of markers (plural, second and first possessive) and three types of case (-nak,-ban-,-ra ‘DAT, INSIDE, ONTO). The main effect of the frequency and the error type was significant. Frequent words were judged faster but less accurately, suggesting a trade-off. The later the mistake is, the faster and easier its rejection was.


THE PAST AND PRESENT OF INFORMATION THEORETICAL APPROACHES TO LANGUAGE
Information theory had a strong appeal for the nascent psycholinguistics in the early 1950s.George Miller (1951) in his textbook and in some empirical studies took up the approach represented by the Shannon-Weaver (1948, 1949) model of communication.In particular, he was trying to show that information value can be used as a possible predictor of word recognition difficulties (in fact, these efforts came up with negative results: our channels are limited not by information value, but rather by the number of chunks we are able to handle, as he himself (Miller, 1956) emphasized later.In another attempt he was trying to show that statistical approximations to English have a predictive value for sentence recognition.This was shown by using in fact rough subjective estimates of conditional probability.In the preparation of their materials subjects were given the first n words (e.g. 2 words) of a beginning sentence and were asked to put them in a sentence.In the next step with a different group of subjects the n + 1 words (the first 3 in the example) were provided as triggers for continuation.The strings prepared this way were used as stimulus materials (Miller & Selfridge, 1950).This statistical model of language, however, was very soon criticized on a theoretical basis by Chomsky (1957) who showed that information theoretical models are unable to deal with the inherent creativity of language.Soon, Miller andChomsky (1963, Chomsky &Miller, 1963) also started to claim that information theory based approaches are not only unable to deal with grammatical competence but they are also unable to account for language performance.Models of language use have to entail a grammar as well (in particular, of course, at the given time, a transformational generative grammar).Since then, one of the crucial issues for a large portion of modern psycholinguistics has been the experimental study of how the rules of this grammar are implemented in models of language use.
As for our specific issue of morphological processing, László Antal (1962Antal ( , 1964) ) in the 1960s made an interesting proposal.He started from the problems of segmentation in agglutinative languages and proposed that over words, the usual tendency is decreasing entropy.By this he basically meant the number of possible continuations at any given point that correspond to lexical density and grammatical structure.To take an English example, the string boo can continue as boot, book, boor, boom etc., having high uncertainty, while prog can only continue as progr, having no uncertainty at that point.Thus since Antal was lacking a frequency dictionary, he was using the entropy notion developed by Shannon-Weaver (1948) for equal probability outcomes where entropy is a function of the number of possible outcomes.Morphological boundaries break this monotonous decrease, and intuitively correspond to increasing entropy values.
If you take a word form like (1), the entropy value gradually decreases over the stem, and when the entropy value suddenly increases again you have a morpheme boundary.As the example below shows, there is indeed a gradual decrease of entropy over the word, now computed with not merely the options, but their frequencies also taken into account.Morpheme boundaries, however, correspond to plateaus rather than to increases.
Entropy is measured here with taking frequency into account.The entropy of the observed corpus W conditioned on the prefix x is , where is the probability of observing the word w in the corpus.At the end of twentieth century the seemingly outdated information theoretical approaches became suddenly relevant and central again.One may suggest several reasons for this revival.One crucial factor, certainly, is the ease of computation, combined with the creation of large large lexical databases, often based on web sources (Baayen, 2005), and the remarkable development of statistical models of language processing.(For an overview with an eye on the psychology of language processing see Jurafsky & Martin, 2009).Information theory-based and Markov chain models were easy to criticize on a theoretical basis half a century ago, when neither the defenders nor the critics were able to execute actual computations over large corpora.Machine produced and machine analyzed texts -be them written or oral -provide an easy target to compute entropy values, transitional probabilities and the like.In this way, it became easy to compare the predictive power of grammar based and statistical predictions for language performance.Not surprisingly both in child language research (Saffran, Aslin, & Newport, 1996), and in language processing (Kostić, 1995, Moscoso del Prado Martín, Kostić, & Baayen, 2004) information theory related concepts reappear.There are even comparative entropy studies of printed text in different languages.Borgwaldt, Hellwig, and De Groot (2005) showed that the word initial letter to sound correspondences i.e., pronunciation entropy are different in different languages, with Hungarian being the most transparent one, using an orthography that is traditionally treated as having a high letter-to-sound correspondence.This corresponds to a letter-to-sound entropy value of 0.15 in Hungarian, while the English entropy is 0.65 and the French is 0.58.
Our paper is an attempt to indicate the relevance of these notions for word recognition and morphological processing in Hungarian.Hungarian is an interesting example to study the relevance of information theoretical notions over word processing due to its extremely rich morphological paradigms.As Kornai (1992Kornai ( , 1994) ) pointed out, even if we take relatively frequent words such as asztal 'table' or szék 'chair' out of the several hundred possible word forms starting with these stems only a couple of dozens show up in the frequency dictionary (37 and 23 in the given cases).Thus to come through even once with all the forms of even a frequent word a much bigger corpus is needed than what we would experience in our entire life span.Kornai uses this example to argue for morphemic or analytic representation in a reasoning arguing for rules.We would like to show that in actual language performance, that is also an argument for the use of information values for segmentation purposes.
Results of 5 experiments shall be presented that were all done over nouns to reveal how the informational structure of the nouns shows up in word recognition and morphemic segmentation.

STRUCTURE OF HUNGARIAN NOMINAL FORMS: A FEW INTRODUCTORY REMARKS
Hungarian nouns can take many suffixed forms.Derivational suffixes, an inflectional marker of possession, plural suffixes, and case markers plus plural markers combined with the root stem in a rather systematic way illustrated in (2), (3), and (4).The overall structure is: STEM -DERIVATION -POSSESSION -POSSPLU-POSSPERS -POSSESSED -PLURAL -CASE.(See for the details in Papp, 1982;Kornai, 1994;Kiefer, 2000) There are many interesting subregularities that we shall not go into.The basic morphotactic principle is that case marking is always the last one, the morpheme sequence goes from the most lexical to the most syntactic, with some obligatory constraints.The examples below show in an intuitive way how this is related to the sequential unfolding of the word forms of nouns.
( There are several psycholinguistic issues related to any morphological system and in particular to Hungarian, which in this regard is a rich system.By richness we mean that each noun stem has several hundred possible word forms, even not counting derivational forms. 1. Segmentation: Allows for lexical access.Segmentation is also relevant for the second task, for the decisions about which units to integrate.Agglutinative languages may support these efforts by their structural features.In Hungarian the fixed first syllable stress and the word final position of case markers gives a cue concerning access of the given stem and a 'backward sign' for compilation.At the same time, whatever precedes the stress counts as one word (Kornai, 1992(Kornai, , 1994)).

Lexical access:
What is the left-to-right procedure to access stems?Are there any linear asymmetries related to this?What parts of the word token form are most transparent during processing?
3. Formal combinatorics and decomposition: Do we always analyze complex word forms into their morphemes or is holistic access also possible?The hybrid models proposed in the literature and interpreted for Hungarian are assuming a standard rule-based solution with holistic access related to derivation-inflection differences, to relative frequency, and they are as well suggesting that derived words would be processed as holistic units (for a review see Clark, 1991) especially in the case of non-transparent derivations (Marslen-Wilson et al., 1994), while inflection as a rule would be treated in an analytic manner.There are alternative views that start from considering individual schemata as starting points, and treat rule based processing as more secondary (see for a review Bybee, 2007, and for an implemented version of memory based learning Daelemans and van den Bosch, 2005).

Semantic integration:
Along with integration of forms one also needs to integrate the meaning of multimorphemic words.

Stem allomorphy:
Several Hungarian noun paradigms are characterized by multiple allomorphs.Are allomorphs always mapped onto the same citation form during access or are there different access files depending on frequency and phonetic motivation?
The studies presented here are not directly addressing these issues separately.We merely mention them to keep in mind that the results of the individual experiments using different methodologies on the final run map onto these basic issues of lexical access and morphological processing.In the present outline the studies are not directly testing individual hypotheses.Rather, they are presented as pointing towards possible processing procedures.
Gating studies that are relevant to lexical access were performed to look for the value of information values in processing word stems.For the analysis of morphological decomposition, scrambling studies and lexical decision studies were performed.

A WEB-based gating and lexical access study in Hungarian
Gating is a traditional method to look for the temporal structure of word recognition.Since it was introduced by Grosjean (1980) a generation ago, it was used to show effects of frequency, word length, stress pattern, competing words (try, cry, shy), lexical uniqueness, morphological structure and sentential contexts (for a review see Grosjean, 1996).
Two studies of gating were performed with carefully selected rare and frequent Hungarian disyllabic nouns, in the first study ever of gating in Hungarian.The present study was administered over the Internet.

Method
Materials.Sixty words were used of the type vizsga 'exam', japán 'japanese' böllér 'butcher' and the like.All items were disyllabic nouns.Thirty of them were frequent, 30 rare, and within each group 15 were used with an early uniqueness point like japán, and 15 with a late uniqueness point like cinke.Selection was based on a manual look up of the MOKK ( 2006) corpus.The actual words are listed in the Appendix together with their frequency parameters and the entropy measures.
Subjects.A group of 51 healthy students with ages ranging from 18 to 25 years (31 female (20.41 year; SD=0.98; 20 male (21.11 year; SD=1.4)) of the BME (Budapest University of Technology and Economics, Budapest, Hungary) participated in this experiment as volunteers.Every subject had normal hearing.They were recruited through campus based email networks, gave informed consent before the actual experiment and they were tested individually at their own computer site, and received partial course credit for participating.None of the subjects had any prior experience with the experimental task.
Procedure.In this experiment a within subject design was used.Every participant heard all of the word fragments with consecutively longer gates (audio segments of 90, 120, 210, 300, 390 ms) but the order of the words was randomized.After every sound segment participants had to find out what the word was and then type the total word on the computer keyboard.After typing, at every guessing they needed to assign the certainty of the answer (1 -absolutely unsure, 2 -rather unsure, 3 -rather sure, 4 -absolutely sure).If the answer was correctirrespective of the gate time and the confidence judgment -the program presented the first fragment of the next word.
Statistical analysis.The accuracy and the decision certainty were submitted to a three-way repeated-measures ANOVA with Frequency (2; rare, frequent), Uniqueness (2; early, late) and Gate length (5; 90 ms, 120ms, 210ms, 300ms, 390ms) as within-subject factors.All analyses involved Greenhouse-Geisser adjusted degrees of freedom for correction for non-sphericity.Post-hoc statistics were performed with Bonferroni tests.

Results
The basic results of the impact of frequency and uniqueness point are shown in Figure 2. Notice that in this off-line arrangement correct recognition is rather low across the board.Accuracy for frequent words was much higher when compared to rare words, F(1,50)=84.917, p<0.00001, η 2 =0.6294.The main effect of Uniqueness shows that words with early uniqueness point were recognized with higher accuracy, F(1,50)=35.708, p<0.00001, η 2 =0.4166.With the increase in presentation time (Gate length), the proportion of the correct responses increases as well, however, only between the 2nd, 3th and 4th gates (post-hoc p<0.001),F(2.6169,130.8469)=280.066,p<0.00001, η 2 =0.8485.While the accuracy for words with early and late uniqueness point was identical (post-hoc p=0.056), the Frequency × Uniqueness interaction showed much higher accuracy for frequent words with early uniqueness point, F(1,50)=97.264, p<0.00001, η 2 =0.6605).The Frequency × Gate length interaction has shown that the accuracy was higher for frequent words at 90ms, 120ms and 200ms, but lower at 390ms, F(2.6929,134.6483)=77.488,p<0.00001, η 2 =0.6078.
The Frequency × Uniqueness × Gate length interaction has shown that the accuracy, after reached the maximum at the 3nd gate, decreased more for words with late uniqueness point, F(2.3283,116.4176)=3.826,p=0.005093, η 2 =0.071.
As shown by the Uniqueness × Gate length interaction, the decision certainty differed in different gates, F(2.893,147.5431)=31.2839,p<0.00001, η 2 =0.3802.It was higher for words with late uniqueness point, at 300ms and 390ms.The Frequency × Gate length significant interaction revealed that the decision certainty after 2nd gate increased more for frequent words (post-hoc p<0.001) than for rare ones F (2.193,111.8793)=33.241, p<0.00001, η 2 =0.3946.The significant Frequency × Uniqueness interaction has shown that the decision certainty for frequent words is higher when the uniqueness point is late F(1,50)=5.8563,p=0.0191, η 2 =0.103.Finally, the significant Frequency × Uniqueness × Gate length interaction revealed that the certainty of decision for rare words depends much less on the uniqueness point (a significant difference was found only at 390ms) and that it is much higher for words with late uniqueness point and for shorter gate durations, F(3.11,158.6402)=8.84,p<0.00001, η 2 =0.1477.

Gating and grammatical constraints
In the second gating experiment, laboratory based individual measurements were used.

Method
Materials and design.The entire design was very similar to the Experiment I with only a few differences.In Experiment II a mixed design was applied, with one between subjects factor.The between subjects factor was grammatical priming instructions.One group of participants was given the following information: "You will hear only two syllabic nouns without suffixes", another group of the participants was not given this information.The grammatical constraint was introduced to look for possible top-down effect on recognition.Every participant heard all the word fragments shown in the Appendix with consecutively longer gates.In Experiment II, however, rather than using a stepwise increase over the same sequence, the sequence of words was randomized.Each subject heard all five length versions of each stimulus, but in a cross-stem randomized order.
Procedure.After every sound segment participants had to find out what the word was, and say out loudly the total word into a microphone that measured the reaction time of the answer.And thereafter at every guessing they needed to assign the certainty of the answer (1 -absolutely unsure, 2 -rather unsure, 3 -rather sure, 4 -absolutely sure).If the answer was correctirrespective of the gate time and the confidence judgment-, the program presented the next item.
Subjects.Fourteen adults with ages ranging from 18 to 60 years (7 female (28.0 years, SD=13.14;7 male (28.16 years, SD=14.05)participated in this experiment.Every subject had normal hearing.They were tested individually and they all gave informed consent before the experiment.None of the subjects had any prior experience with the experimental task.
Statistical analysis.The accuracy and the decision certainty were submitted separately to a three-way repeated-measures ANOVA with Frequency (2; rare, frequent), Uniqueness (2; early, late) and Gate length (5; 90ms, 120ms, 210ms, 300ms, 390ms) as within-subject factors.The grammatical constraint was used as between-subject factor.All analyses involved Greenhouse-Geisser adjusted degrees of freedom for correction for non-sphericity.

Reanalysis of the gating result using entropy measures
With the entropy measurements we wanted to give a more robust generalization of the intuitive notion of uniqueness point.In a way, an exploratory study was run along the lines initiated by Moscoso del Prado Martín, Kostić, and Baayen (2004) and by Wurm, Ernestus, Shreuder, and Baayen (2006) who had shown that using an information gain predictor which is combining the entropy of the stem with the conditional entropy of the bound morphemes, better prediction can be obtained for word recognition data then merely using frequencies as predictors.
To obtain corpus based interpretations of uniqueness points we worked with the MOKK corpus and frequency dictionary of Hungarian (http://mokk.bme.hu/resources/webcorpus/index_html).For a description of the corpus see Kornai et al. (2006).We used the stratum of the corpus that has a 96% correspondence to regular Hungarian orthography.That is roughly equivalent to everyday written Hungarian.This means 589 million word tokens and 7.2 million word types.For the gating experiments, we worked with the non-inflected nouns of the corpus.The corpus is part of speech tagged, and is passed through an automatized morphological disambiguator.
Each of the audio segments the subjects had to work with was manually transcribed.These transcripts are called 'prefixes' in the following.Thus prefixes are not grammatical prefixes, but the strings preceding a given point.

Information metrics used
Several metrics were defined over prefixes.They all measure how a word beginning constrains the set of possible continuations.Beginning types occurrences log: This metric is simply the number of word forms thus tokens in the corpus starting with the given beginning.This is much skewed variable, so its base 2 logarithm is used as a normalized variable.Beginning frequency log: This is the number of TOKENS in our corpus starting with the given beginning.One can consider this the weighted version of the former, weighted by word frequencies.Here again, the logarithm is used.Entropy: Entropy of the corpus, conditioned on the given beginning.Informally, this means the expected number of questions we need in a "20 Questions" game, if we must guess a randomly chosen word (by the frequency distribution in the corpus) with the given beginning.More formally, the entropy of the observed corpus W conditioned on the beginning x is , where is the probability of observing the word w in the corpus, conditioned on the fact that w starts with the beginning x.Typically, although not necessarily, the entropy monotonically decreases when calculated for longer and longer beginnings of a given word.Entropy change: The decrease in entropy when compared to the previous gate.This is defined as where is the beginning at the current gate, and is the beginning at the previous gate.The value is not defined for the first gate.Also, the entropy change is measured over a fix 90 ms time interval, except for the first two gates.

Entropy values of the word items
As an item based post hoc test of the relevance of frequency and uniqueness, a two way analysis of variance was performed over the entropy values for the fourth letter position shown in the Appendix, with frequency and uniqueness point as the two factors.Both factors were significant.For frequency F(1,56)=19.213, p<0.001, rare items had a much lower entropy at the fourth letter than frequent ones (0.844 vs 1.782), which indicates that there is less variability with the decrease of frequency.At the same time, the selection variable of late versus early decision point also had a significant effect (F(1,56)=27.478,p<0.001).The early uniqueness point items had much lower entropy (0.752) at the fourth letter than late decision point items (1.874).This can be taken as a post hoc support of our classification.Comparison of the eta squares as an estimate of variance explained shows that decision point had a stronger effect (0.329) than frequency (0.255).While there was a significant interaction, its impact is very weak in explained variance (0.09). Figure 5 shows the overall differences.These estimates have to be carefully interpreted.They certainly give a post hoc support for our selection of items, but one has to bear in mind that the items were manually selected.

Recognition and entropy
Based on the data matrix in Experiment II, for each event of successful recognition, the beginning at the recognition point was paired with the beginning at the immediately preceding gate (we call this one-beforerecognition point).Figure 6 shows the means on the different measurements of the beginning metrics, for both the recognition points (dashed) and onebefore-recognition points (solid).The data for each gate were aggregated (the x axis of the graphs).In Experiment II, by applying the Mann-Whitney-Wilcoxon test, we verified that the means for the recognition points differ from the means for one-beforerecognition points at a high significance level.This is true for each of the metrics we analyzed here.We note that this result is the least obvious for the entropy change measure, as it is a highly non-monotonous function of beginning-length.Intuitively, this means that the recognition point follows a sudden drop of the entropy value, which is the hypothesis we started from.On the other hand, the confidence of the subjects in their prediction (standardized on a subject level) has no statistically significant correlation with the entropy change of the gate.
Going further, we used linear regression to rank the above metrics according to their capacity to predict our observations.Table 1 shows the Akaike Information Criterion values (Akaike, 1974).Smaller values mean better fitting models.As we can see, the entropy measure proved to be the best linear predictor of recognition points.This result is in line with the model of Moscoso del Prado Martín, Kostić, and Baayen (2004).Namely, what is treated traditionally as a uniqueness point in gating research is actually a decrease in entropy.Entropy based measures proved to be better here than merely frequency, similar to the more complex model of Moscoso del Prado Martín et al. (2004).

Scrambling words and reconstruction
In the last decade a lot has been written on the transposed letter effect.Essentially, people are able to reconstruct letter transpositions while reading, and the beginnings and ends are especially crucial in this process as already shown by Bruner and O'Dowd (1958) with tachistoscopic presentations (e.g., Chambers, 1979, Perea, Duñabeitia, & Carreiras, 2008), such as reading porblem as problem.The essential issue of the different models is how to account for the broken coalition between letters and their positions in given words.
In looking for different possible informational factors in morphological processing, rather than merely stem words, two experiments were done in Hungarian to look for the reconstruction effects depending on the position of the misplaced letters, thus arguing for a positional effect in word access in an agglutinative language.

Method
Subjects and procedure.Volunteer university students (n=40) in an off-line experiment administered over the Internet.They were asked to reconstruct misspelled words in writing.
Materials.Stem words and suffixed words were both used.In the list of 33 forms in one subgroup of items the beginning and the end of the word were correct, but the middle was misspelled (szitimkus for szimpatikus).In another group of forms only the beginning was correct (sötbténe for sötétben 'in the darkness'), and in the third group only the ending was correct (mléény for mellény 'vest').One third of the letters were reordered in every word in a way such that no letter stayed in its original place.Each group contained 11 words.The word length was between 5 and 15 letters.

Results
As Figure 7 shows, reconstruction was highest in the case when both the beginning and the end were correct, in line with the English classical data of Bruner and O'Dowd (1958) and Chambers (1979).Thus, in compensating for letter misplacement the beginnings that are crucial for lexical access, as well as the ends that are crucial for sentential role assignment are most attended to (both contrasts were significant t(39)=6.95 and t(39)=7.50,respectively, both p<0.001).

A systematic study of letter misplacement (Várhelyi, 2010)
In a further study, more carefully selected stimulus materials were used, and the changes only involved two letters.

Method
Materials.Hungarian words of 7 and 8 letters with frequencies between 1000 and 100,000 in the MOKK corpus were used with no vowels in the critical to be exchanged positions.
Let us see the examples with the target word probléma 'problem'.1. mispositioning at the beginning messing up the first two letters RPOBLÉMA 2. mispositioning at the beginning messing but involving the second and third letters PORBLÉMA 3. mispositioning in the middle PROLBÉMA 4. mispositioning at the end but keeping the last letter intact PROBLMÉA 5. mispositioning at the end involving the last and the penultimate letter PROBLÉAM In the actual lists the experimental material was interspersed with 120 pseudowords, also manipulated with scrambling.The use of pseudowords made the lexical decision task a relevant decision.
Procedure.A priming method was used, rather than active reconstruction.In each pair the prime was the misspelled word, and the target the correct one.Thus in the given example RPOBLÉMA as a prime was followed by PROBLÉMA as the target.Subjects had to decide if the target was a word.A 100 ms prime was followed by the target, with a 100 ms exposure time.
Subjects.Twenty volunteer university students took part in the exp eriment.
Figure 8 shows the basic position effects on reaction times.Smaller reaction times indicate more priming.A clear bathtub effect (Aitchison, 1987) was obtained: the distortions in the middle had the least effects on priming towards the target word.Indirectly this indicates that if the beginning and the end is correct in the prime, there is more facilitation towards the access of the target word.The morphological structure and the linear composition of words has a clear effect on the recognition of complex words.Earlier studies in Hungarian used lexical decision times to look for the relative importance of different linear and grammatical parts of the word in lexical access and morphological analysis.Pléh and Juhász (1995) employed examples like (4) in a visual lexical decision study to look for the relevance of grammatical prefixes, stems, derivational and inflectional suffixes.Figure 9 shows the reaction times for the different locations of errors.A clear bathtub effect (Aitchison, 1987) was observed here as well.Errors in the middle were recognized much more slowly.This was interpreted as implying that in reading Hungarian people pay attention to the beginning for lexical access and to the end for grammatical role assignment.
Figure 9.A clear bathtub effect in lexical decisions over multimorphemic Hungarian nouns (Pléh and Juhász, 1995) Prefi x Stem Derivation Case EXPERIMENT 5 A systematic study of morphemic structure and linear position in lexical decisions In this study an effort was made to obtain a more systematic analysis of the overall effects found by Pléh and Juhász (1995).In particular, we wanted to use the same stems as used in the gating studies, but in morphologically more complex word forms, and with a clearer control for possible frequency effects.Our further hope is to use more sophisticated entropy based predictions to reanalyze the results later.

Method
Materials and design.In the basic arrangement of the experimental material -prepared by Judit Fazekas -four basic morphological types were used: -stem böllér 'sticker' -plural böllér-ek 'stickers' -case böllér-nek 'stickerDAT' -Plur + case böllér-ek-nek 'stickersDAT' Three types of markers (plural, second and first possessive) and three types of case (-nak,ban-,-ra 'Dat, INSIDE, ONTO).Suffixes were used that all take the citation allomorph, since we did not want to complicate matters with issues of fusion and other morphological phenomena.
An entirely within subject design was used, where each subject saw each combination but the items were randomized between subjects.The general outline was: frequency (2 levels) x morphological structure (3 levels) in placing the errors (stem, marker, case).Within the suffix errors there were two subtypes: vowel harmony errors, and non-existing stems.Each subject had to decide about 360 words half of which were correct, and half of which were wrong.In the entire study 4700 items were tested.
Subjects.A group of 72 healthy students with ages ranging from 18 to 34 years (44 female (21.41 year;SD=2.44;28 male (21.75 year;SD=1.86)) of the BME (Budapest University of Technology and Economics, Budapest, Hungary) participated in this experiment as volunteers.Every subject had normal or corrected-to-normal vision.They were tested individually and they all gave informed consent before the experiment and received partial credit for participating.None of the subjects had any prior experience with the experimental task.
Procedure.The task was a simple word/nonword decision task.The subjects watched the screen and had to decide about pop up words (that appeared on the center of the screen) that was a correct Hungarian word (press button 'I') or not (press button 'R').Before the word/ nonword appearance there was a fixation mark (duration was random between 600-1400 ms) on the centre of the screen.
In paired comparisons the correct forms were slower to be accepted.Within the errors, non-existing stems were slower to be rejected than non-existing markers (i.e.word middle errors) or case markers.There was no clear bathtub effect in the reaction times.If anything, word end case marker errors were recognized slower.
The two vowel harmony errors were not different between each other.As expected, however, vowel harmony errors were slower to be rejected than nonexisting phonemes at the given position.This is similar to the general observation introduced by the famous prefix-stripping effect: if you have to make decisions about an existing but misplaced morpheme, rejection takes longer, since it involves two steps (Taft, 1979).
Separate analyses were also made of frequent and rare stem items.Basically for correct performance the significant effects are obtained for both sets of errors.However, in frequent stems the word middle distortion towards a nonexisting form (non-existing marker) leads to surprisingly low performance as shown on Figure 12.That also resulted in being no significant paired difference here between stem errors and word middle errors.At the same time, reaction times with these items were rather fast in both groups as Figure 13 shows.Thus, there might be a trade-off here.

GENERAL DISCUSSION
The series of experiments have provided some relevant data on lexical access and morphological processing in a strongly agglutinative language, Hungarian.Out of the five issues outlined in the introduction, the data have implications regarding three of them.
Regarding segmentation and lexical access both the results of the gating experiments (Experiment I and II) and those of the scrambling studies (Experiments IV and V) are relevant.In accord with data supporting the cohort theory of Marslen-Wilson (1975, 1984) the onset of words is very crucial in lexical access and processing of root morphemes.According to the gating results a syllable length segment can lead to 50 % of correct recognition.This is related to the uniqueness point issue as well, i.e., competing words have a top down inhibitory effect on recognition.The more rivals are there to a word, the later the recognition point.Therefore, early uniqueness words are recognized earlier.This effect, however, disappears in rare words.Rare words seem to be recognized in a more strictly bottom up manner.A more specific effect found was the effect of grammatical constraints, which, given the instructions, can be seen as a specific top down effect.The scrambling studies indicate a strong word onset primacy in Hungarian as well, similar to effects found over many other languages.
The entropy effects are by far not trivial.The low entropy connected to early uniqueness points shows that the uniqueness points used so many times in fact are related to a more objective measure, the entropy at the given point.Thus, we suggest entropy to be used in further studies instead of the uniqueness point.The uniqueness point is only sensitive to the absolute values, while entropy and its change is sensitive to a frequency distribution.In a nutshell, entropy change is important in explaining neighbourhood effects.
The relationships between entropy measures and recognition performance should be seen with a careful epistemological attitude.The entropy values are derived from a large impersonal data set.It is far from trivial that these objective, external characterizations have a determining power over individual recognition performance.In the details of this, determining power entropy values had more explanatory power than mere frequency.Thus, the studies that still have to be continued strongly support the original insights of Kostić (1995) regarding the use of information metrics in studying the underlying mechanisms both of lexical access and morphological decomposition.

Appendix
The nouns with their parameters from the lexical database together with the entropy measures.The absolute frequencies are orom a corpus of 589 million word tokens.Source: the MOKK corpus (http://szotar.mokk.bme.hu/szoszablya/searchq.php)

Figure 1 .
Figure 1.Entropy value changes over a multiple suffixed Hungarian noun.Entropy data based on the MOKK corpus (see below).

Figure 2 .
Figure 2. Proportion of correct responses by different gates.The error bars show the standard error of mean.

Figure 3 .
Figure 3. Effects of constraints, frequency, and uniqueness points on gating recognition.The error bars show the standard error of mean

Figure 4 .
Figure 4.The effect of decisions points is only present in frequent words.The error bars show the standard error of mean.

Figure 5 .
Figure 5.The entropy values at point four of the different items

Figure 6 .
Figure 6.Different entropy measures and recognition in the gating study

Figure 7 .
Figure 7. Words are better reconstructed if the beginning and end are both correctly spelled

Figure 10 .
Figure 10.Correctness of acceptance-rejection as a function of word structure.The error bars show the standard error of mean.

Figure 11 .
shows the overall results for reaction times.

Figure 11 .
Figure 11.Reaction time data in the lexical decision task.The error bars show the standard error of mean.

Figure 12 .
Figure 12.In frequent items word middle distortions lower performance.The error bars show the standard error of mean.

Figure 13 .
Figure 13.Reaction times in both frequent and rare items are fast in word middle non-existing form errors.The error bars show the standard error of mean.

Table 1 .
Information criterion values for the different predictors

Table 1 .
Rare words