Quantifying Past Tense Accuracy 1
Quantifying the relative contributions of lexical and phonological factors to regular past tense accuracy
Amanda J. Owen Van Horne a,b
& Melanie Green c a
Dept. of Communication Sciences & Disorders b Member, DeLTA Center
University of Iowa c
Waukegan Public School District 60, Waukegan, IL
Keywords: Past tense, telicity, lexical frequency, target selection, consonant cluster, child language, SLI
Contact Information: Amanda J. Owen Van Horne, 121 A SHC, Dept. of Communication
Sciences & Disorders, 400 Hawkins Dr., University of Iowa, Iowa City, IA 52242. Phone: 319-
335-6951. Email: amanda-owen-vanhorne@uiowa.edu

Quantifying Past Tense Accuracy 2
Declaration of Interest
The authors have no real or perceived conflicts of interest.

Quantifying Past Tense Accuracy 3
Abstract
Background.
Telicity, frequency of the inflected form, and stem final phonemes have all been shown to influence past tense, but it is not known what the relative contribution of each of these factors is, which limits the ability of clinicians to select therapy targets (Weiler, 2013).
Aims.
This study aimed to quantify the influence of lexical and phonological factors on the production of past tense by school age children with SLI.
Methods & Procedures.
Archival elicited production data from children with SLI between the ages of 6 and 9 and their typically-developing age- and MLU-matched peers were reanalyzed for use of simple regular past tense -ed. Past tense accuracy was predicted using measures of telicity, frequency of the verb in its inflected form and in all of its forms, and properties of the final consonant of the verb stem.
Outcomes & Results.
All of the factors under consideration contributed to predicting use of past tense. All children were highly accurate within facilitative contexts. All children were less accurate when verbs were atelic, rarely heard in the past tense, or ended in a word final obstruent or alveolar consonant. Being diagnosed with SLI affected overall accuracy rates but did not influence how facilitative a given factor was
Conclusions & Implications.
Some factors, e.g., telicity, that have been believed to be useful only when children are first discovering past tense appear to be influential in later years.
Clinicians should consider the properties of the target words when they select stimuli for use in therapy. These data provide a means for balancing the relative influence of a variety of factors as clinicians attempt to select past tense targets.

Quantifying Past Tense Accuracy 4
Clinicians working with children with language impairments are repeatedly faced with the question of how to effectively select stimuli for use in teaching a linguistic target.
Appropriate target selection has the potential to enhance a client’s success in therapy and to improve the efficacy of intervention. However, the process of selecting targets is not clear and the primary guidance comes from expert opinion (Weiler, 2013; Crystal, 1985) rather than data.
Even a clinician who is well versed in the literature and knows that completed-ness of the event
(Leonard, Deevy, Kurtz, Krantz Chorev, Owen, Polite, Elam, & Finneran, 2007b), past tense frequency (Marchman, Wulfeck, & Ellis Weismer, 1999; Oetting & Horohov, 1997), and phonological complexity (Leonard, Davis & Deevy, 2007a; Marshall & van der Lely, 2006,
2007;) influence accuracy may still struggle to balance these factors in order to select the best verbs for use in therapy. Should she select a verb like walk because it is frequently heard in the past tense even though it ends in the consonant cluster /kt/ and may not have a clear end point?
Or a word like answer that is somewhat abstract and yet receives high telicity ratings and has an easy to produce word ending? There is limited evidence in the literature to guide a clinician who needs to balance competing influences on past tense accuracy.
This paper aims to quantify the relative contribution of factors that influence past tense accuracy to aid clinicians in selecting therapy targets. Upon evaluating these factors, we obtain a rank ordering of verbs from ‘easy’ to ‘hard’, which can be used to facilitate target selection in assessment and intervention programs. A secondary goal is to determine whether these factors are equally influential across two groups of typically-developing (TD) children and a group of children with specific language impairment (SLI). Information about how these factors interact with the individual child or with diagnostic group may further influence clinicians’ selection of verb targets.

Quantifying Past Tense Accuracy 5
Variability in Verb Morphology
Lexical factors - Frequency and Telicity
The role of frequency on the accuracy of inflection is well established across morphemes, including plural (Rice & Oetting, 1993) and past tense (Marchman, et al., 1999; Oetting &
Horohov, 1997). In these studies, children with SLI had greater difficulty inflecting low frequency words than their peers, even when the confound between frequency and regularity was removed. Frequency influences morphological production across the lifespan (Wulff, Ellis,
Roemer, Bardovi-Harlig, & LeBlanc, 2009), with some groups being more sensitive to frequency effects than others (Blom & Paradis, 2013). Frequency can be characterized in two ways – overall frequency of the lexical item and frequency of the inflected form. Although most studies have relied on frequency of the inflected form (Marchman, et al.,1999; Oetting & Horohov,
1997), overall frequency is more readily available and intuitive. It would be helpful if clinicians knew whether these two values could be used interchangeably or if they should only rely on one value.
In contrast, lexical aspect has primarily been studied in young children and appears to be a way that children discover tense marking. Aspect refers to the nature of an event in time
(Vendler, 1957), including whether it is habitual, completed, ongoing, iterative, etc. In this paper we will primarily be concerned with telic events, which are events that have a clear endpoint, and with atelic events, which are events that are ongoing in nature. Initially, TD 2-year-olds produce simple past markers with telic events (e.g., - he ate a sandwich; he died yesterday ) and past progressive markers with atelic events (e.g., - he was eating dinner; he’s been dying all week long ) (Bloom, Lifter, & Hafitz, 1980; Johnson & Fey, 2006; Shirai & Andersen, 1995). As illustrated in the preceding sentences, most verbs can be grammatically realized as either telic or

Quantifying Past Tense Accuracy 6 atelic events, but some events are more naturally realized as a completed event while others are more naturally ongoing.
In addition to influencing emergence of past tense, lexical aspect influences the likelihood that young children will choose a particular form of inflection. TD 3- to 4-year-old children were more likely to produce the simple past when the elicitation context used a prototypically telic event (e.g., drop, close ) than when it used a non-prototypically telic event
(e.g., rake, dance ; Leonard, et al., 2007b). However children with SLI were less sensitive than their TD peers to this contrast (Leonard, et al., 2007b), using past tense equally often for prototypically telic and atelic events. Unsurprisingly, verbs that are highly telic are more likely to be heard in the past tense, introducing a confound between frequency and telicity. Which factor is more important and should receive more attention from clinicians? Most of the research on the influence of telicity has been carried out with preschoolers and framed as a means of children “bootstrapping” into the paradigm. This study examines older children and we ask whether aspectual factors continue to influence production during the school years over and above the contribution of frequency.
Phonological Factors
Phonological factors that influence accurate past tense production have received especially close examination in English due to the debate over how individuals maintain the regular/irregular distinction. However, even when the question is restricted to regular past tense, phonology seems influential, with general agreement that more complex articulatory contexts are more difficult (Leonard, et al., 2007a; Marshall & van der Lely, 2006; Marchman et al., 1999;
Marshall & van der Lely, 2007; Oetting & Horohov, 1997). Oetting and Horohov (1997) found that children with SLI and their TD peers were both more accurate when a verb ended in a liquid

Quantifying Past Tense Accuracy 7 or a vowel and were equally less accurate when the word ended in a consonant. Marshall and van der Lely (2007) observed an influence only when the addition of the past tense formed a consonant cluster. Marchman et al., (1999) suggested that it is not any consonant combination that is difficult, but rather that children with SLI were more likely than their peers to omit past tense forms when the stem ended in [t] or [d]. They attribute this to problems with understanding the past tense pattern, but relate it to articulatory changes as well.
Relationship between Lexical and Phonological Factors
There is preliminary evidence that both phonological and lexical factors contribute to past tense accuracy, at least in TD children (Johnson & Morris, 2007). Johnson and Morris (2007) elicited past tense forms from TD 2-year-olds using verbs that ended in an obstruent (e.g., walk, jump) or a non-obstruent (e.g., roll, chew ). Using elicitation scenarios that either had a clear endpoint (telic – chewed up ) or were ongoing (atelic – chewed all day ), they observed that children’s overall accuracy dropped when both the phonological and aspectual cues were nonfacilitative (see Table 5b). There was no difference in performance between 2 facilitative factors or 1 facilitative and 1 non-facilitative factor. In contrast, the results from a single child with SLI suggested that combinations of facilitative and non-facilitative factors might influence performance different in children with language impairment. This child was 100% accurate for telic items with a non-obstruent coda, 33% accurate when either one of those factors was present and 0% accurate when neither factor applied. As only one child with SLI was studied, it is not clear whether the more graded influences generalize to a larger group of children with SLI.
To summarize, variable production of past tense seems to be mediated by the frequency, aspectual and phonological properties of the individual lexical item being inflected. This study aimed to quantify the relative contributions of lexical and phonological factors to the production

Quantifying Past Tense Accuracy 8 of simple regular past tense inflection. We first identified appropriate predictors for each factor of interest (frequency, telicity, phonology) and then we considered how predictions of accuracy are altered when these factors are combined. In each case we were also concerned with how each factor interacts with diagnostic group.
Methods
Data Collection
Participants
The children studied here were initially recruited for participation in a study of complex syntax production (Owen, 2010). All research reported below was completed in accordance with the ethical guidelines for human subjects research as described in the Belmont report and required by the National Institutes of Health and the Institutional Review Board at the University of Iowa. Fourteen children with SLI (5;0-8;1) and 24 TD children participated in Owen (2010), providing the data reanalyzed in this study. The TD children were divided into 2 groups: 13 of the TD children were matched within 3 months of age to a child with SLI; 11 of the TD children were 4-year-olds who were matched within 5 raw score points on the Expressive Vocabulary
Test (EVT, Williams, 1997) and within .35 words on MLU in a 100-utterance language sample to a child with SLI.
The children in the SLI group met at least two of the following four criteria: a) enrolled in intervention within the last 12 months; b) scored below the 10th percentile on the Structured
Photographic Expressive Language Test – 2 nd
edition (SPELT-II; Werner & Kresheck, 1983) ; c) scored below a standard score of 7 on the nonword repetition subtest of the NEPSY (Kemp,
Korkman, & Kirk, 1998); d) obtained a composite standard score at or below 85 on the Test of
Narrative Language (TNL, Gillam & Pearson, 2004). TD children had no history of intervention

Quantifying Past Tense Accuracy 9 and scored at or above the typical range on all of the speech and language measures described above. All children scored above 83 on the Kaufman Basic Intelligence Test-II, Matrices Subtest ,
(KBIT-II, Kaufman & Kaufman, 2004) and passed a hearing screening. Table 1 summarizes relevant information about the participants’ assessment information.
Stimuli
The data for this study are the verbs produced in 3 complex syntax elicitation tasks.
These data are particularly relevant because verbs were repeated across the different elicitation conditions, yielding multiple productions of the same verb for each child, allowing examination of the contribution of the verb to accuracy. In the original study, three different types of sentences were chosen as targets: 1) coordinated clauses (e.g., Ernie hopped and Elmo kicked the ball ), 2) a main clause and a finite complement clause (e.g., Ratty guessed that Elmo kicked the ball ), and 3) a main clause and a temporal adverbial clause (e.g., The aliens whistled when
Minnie kicked the ball).
Thirty-six (36) items were constructed for each sentence type. The protocols for eliciting the stimuli and the design of the sentences are summarized in Owen
(2010). Example scenarios are given in Appendix A.
All of the sentences consisted of a main clause made up of a subject and a verb, followed by another finite clause. The coordinate and adverbial conditions used the same regular action verbs in the first clause, while the complement condition used mental and communication verbs.
The verb figured out was the only verb + particle included in the elicitation items and it was discarded from analyses. The 36 verbs (18 regular) in the second clause of each sentence type were repeated 3 times – once in each sentence condition. Thus, 82 different verbs were elicited via 108 different sentences. Given our focus on regular verbs, it is worth pointing out that only

Quantifying Past Tense Accuracy 10
60 of these verbs were regular and 21 were irregular. Of the 60 regular verbs, one verb was elicited 6 times, 23 were elicited 3 times, and 36 were elicited twice. (See Appendix B).
Procedures
For each sentence type, children watched a short puppet show enactment and then a question prompt was posed (see Appendix A for example elicitation scenarios and Owen, 2010 for a full description of the elicitation methods). The experimenter provided the first word of the first clause and encouraged the child to complete the rest of the sentence. If a child did not respond or provided an incomplete response, the examiner asked the child to say the whole sentence. If the child still did not produce a full response, the examiner provided the first clause of the sentence and again asked the child to complete the sentence. All responses were audiorecorded and transcribed, using the on-line written record as a guide. Transcription reliability was computed for nine transcripts (three from each group) for word level accuracy (mean: 90%; range: 75-100%) and for tense marking (mean: 93% range: 81-100%). Table 2 shows percent correct use of past tense marking using the response inclusion and scoring criteria from Owen,
2010. Children in all three groups were neither at floor nor at ceiling; the target sentences were sufficiently difficult for all three groups of children.
Data Reduction
Outcome Variables
Unlike the prior study’s focus on the influence of sentence-level factors such as clausal complexity, here we focus on word-level factors. Therefore, one-clause (truncated) productions were included here to maximize the number of responses available for analysis. 8208 tokens were potentially available for analysis. Of these, 823 were 1-clause responses that were not

Quantifying Past Tense Accuracy 11 analyzed in Owen (2010). A total of 4558 responses were discarded due to being irregular verbs
(inflected or bare, N = 2175), non-target verbs (N = 920), using non-simple past inflections (e.g., past progressive, simple present tense, N=836) or being unintelligible (N = 652). Verbs that were not the target for that item, but matched another target were retained (N=413). Thus the analyses involved 3625 tokens of 60 verb types as shown in Appendix B.
Predictor Variables
Lexical frequency.
Three lexical frequency variables were calculated from the parental lexical frequency information in the CHILDES database (MacWhinney, 2000): Lemma Frequency, Past
Frequency and Stem Frequency . This database was selected because it is freely available, however this database does not differentiate between the noun and verb forms of the target item
(e.g., take a walk, we walk around ) or between participial forms ( I walked, he has walked ), which influenced the frequency counts below. One was added to all sums to eliminate zeros from the data set and all frequency variables were log transformed to normalize their distribution.
Lemma Frequency was the sum of frequency information for all forms of the word. For example, for walk , a regular verb, the frequencies of walk, walked, walks, and walking were summed. Past
Frequency only included correct productions of the simple past form (e.g., walked ). Participial forms were indistinguishable from simple past in CHILDES (e.g., the dog got walked; he has walked home; he walked ). Stem Frequency consisted of the uninflected stem forms, whether correctly produced (e.g., I walk ), a noun form ( the walk ) or bare due to omission (e.g., he walk).
Telicity.
Most previous studies have used lists of activity/achievement verbs to construct categories of prototypically telic and atelic verbs. As a study of archival data, this was not

Quantifying Past Tense Accuracy 12 possible here. Instead, we used adult ratings of the verbs situated within the elicitation scenarios.
Thus, 7 adults read the elicitation scenarios and rated them on a scale of 1-4 with regard to the clearness of the endpoint. They were instructed to read the elicitation script and determine whether the verb was ongoing (1) or completed (4). All 7 raters used the full rating scale, but means (range:2.2-3.4) and standard deviations (.92-1.38) varied across raters. To correct for differences in use of the scale, each rater’s scores were normalized and then averaged to yield a single score for each verb. As seen in appendix C, ratings were consistent with expectations at the extreme values, providing ecological validation of the adult ratings. See Appendix C.
Articulatory complexity
1
.
The articulatory difficulty of the child's production was determined by the characteristics of the final consonants. For the manner variable, words that ended in [b, d, ɡ, p, t, k, θ, f, s, ʃ, ð, v, z, ʒ, ʤ, ʧ] were coded as obstruents; words ending in other sounds were coded as non-obstruent.
Place of production was also considered. Homo-organic production of the final consonant of the stem and the past tense inflection depresses accuracy (Marchman, et al., 1999). Thus we also coded verbs as ending in alveolar/ alveo-palatal place of articulation for [d, t, s, ʃ, z, ʒ, ʤ, ʧ, j, r, l, n] or other.
1 Although we would hypothesize that the phonotactic probability of the inflected forms would be an excellent potential predictor of accuracy, this measure is not reported for two reasons. First, neither the Vitevitch and Luce (2004) nor the Storkel and Hoover (2010) databases incorporate inflected forms into their dictionaries. The results seemed misleading in terms of the weightings for the probability of those phoneme combinations or phonemes in that position. Even selecting only the last syllable or coda of the inflected word yielded unusual frequency metrics since attested – indeed frequent - combinations were not found in the database. Second, adding an inflection makes the stem longer, shifting the word to a more or less common length and influencing the way that the length corrections were carried out (see Storkel, 2004). Thus the length normalization procedure does not work properly for words that are inflected forms. Following a reviewer’s suggestion, we removed phonotactic probability entirely rather than report nonsignificant results when the metrics are in question.

Quantifying Past Tense Accuracy 13
Statistical Approach
Following Baayen, Davidson, and Bates (2008) and Jaeger (2008), we adopted a mixed model logistic regression as our statistical approach. Although this approach is less transparent than ANOVA or simple linear regression, it is the best means of answering our question about verb ranking for three reasons: it weights the reliability of a factor based on how many data points are available; it allows one to carry out by-item and by-subject analyses simultaneously; and the binomial distribution closely mirrors the underlying distribution of the data since we recorded past tense as either correct (1) or omitted (0). Given that this approach is new and can be difficult to interpret, the technical details are reported for the interested reader followed by more narrative interpretations aimed at a clinical audience in the discussion sections.
Mixed model regression includes both random and fixed effects. The inclusion of random effects mathematically adjusts the intercepts for each child and verb. For instance, the random intercept for child rightly assumes that each child has a different mean accuracy level. If we mathematically accommodate these differences, the fixed effects will act in similar ways across each child. The use of random slopes assumes that a factor (in this case, elicitation condition) may influence each child’s production in systematic but non-identical ways. We initially selected an appropriate random effects structure, then we developed models for each of our main variables of interest and confirmed that the random effect structure remained appropriate. Finally, we combined all the variables of interest into a final model that allows interpretation of the relative influence of each variable. At each point, models with random effects were compared to models without random effects and checked for goodness of fit via chi-squared analyses. Given the widely differing scales used for our variables, results are reported for centered and scaled variables to make comparison across parameter estimates more straightforward. This is

Quantifying Past Tense Accuracy 14 consistent with the goal of determining the relative contribution of each variable on past tense accuracy. Categorical variables were contrast coded and centered prior to scaling.
Results
The initial reduced model included both random and fixed factors related to the subject and the verb. In addition to the random effects for subject described above, a random slope for elicitation condition and a random intercept for verb were also supported by chi-squared tests for goodness of fit (X 2 (5) =184.40, p < 0.0001). This random effects structure assumes that the three different elicitation conditions may have influenced each child’s accuracy in slightly different ways and accounts for that variance and is consistent with the findings of Owen (2010), which found that children were more accurate in the coordinate condition and in the first clause of the utterance. Like subject, each verb also influenced the mean accuracy level in a slightly different way. The fixed factor in the reduced model was group (age, MLU, SLI) with the agematched group set as the reference variable. As expected, both the MLU-matched group (p=.055) and the SLI group (p<.0001) were more likely to omit regular past tense than the age-matched group.
We tested whether lexical frequency measures or telicity ratings accounted for past tense production by TD children and children with SLI, over and above the contributions of group. All lexical frequency variables were highly inter-correlated (see Table 3). Therefore, Past Frequency , the variable most highly related to the outcomes, was entered first into the model, significantly improving model fit over the reduced model (X
2
(3) =12.88, p = 0.0049). Then Lemma
Frequency and Stem Frequency were each regressed against Past Frequency and the residual

Quantifying Past Tense Accuracy 15 values were entered
2
. The residuals of Lemma Frequency resulted in slightly lower log likelihood values in the model, X 2 (3) =8.48, p= 0.037. Addition of Stem Frequency residuals did not further improve model fit (p>.50). We also considered whether simply entering the ratio of Past
Frequency to Lemma Frequency was as good a predictor as entering the Past Frequency and the residuals of Lemma Frequency separately, but this was not the case. Testing for interactions demonstrated that only the residuals for Lemma Frequency interacted with group (p<.002).
Figure 1 shows the influence of the Past Frequency and Lemma Frequency on the outcomes for each group set to the same scale to allow for easy comparison.
Telicity ratings were also highly correlated with the Past Frequency variable. Thus, we regressed telicity against the two frequency predictors and assessed whether the residuals contributed significantly to the outcomes. Telicity residuals were a significant predictor and did not interact with group variables (p > .50). Taken together this suggests that telicity contributes over and above frequency in predicting past tense accuracy.
Finally the articulatory factors ( obstruent/non-obnstruent and alveolar/non-alveolar ) were entered into a model with lexical factors, reassessed for fit, and checked for interactions with diagnostic group. The lexical factors improved model fit over the phonological factors alone
(X 2 (3) = 34.11, p<.0001) and vice versa (X 2 (6) = 29.94, p<.0001). The final model is reported in
Table 4. As expected, words that ended in obstruent consonants (nasals, fricatives, affricates, and stops) were less accurate than words that ended in sonorants (liquids, glides, and vowels), reflecting problems forming consonant clusters (Marshall & van der Lely, 2007). Words ending in alveolars were also difficult to a similar degree, as has been previously reported by Marchman
2 Regressing one variable (e.g., Lemma Frequency ) against another variable (e.g., Past
Frequency ) tells you about the relationship between these two variables. The residuals are a measure of the error in the model. Entering the residuals essentially provides information about how surprised you should be by the Lemma Frequency given that you know Past Frequency.

Quantifying Past Tense Accuracy 16 et al., (1999). These results are illustrated in Figure 2. The MLU-matched group was less influenced by the presence of a word final obstruent than the other two groups (p =.03), but still did not produce these at the same level of accuracy as they did words ending in sonorants.
The primary goal of this study was to compare the relative contribution of the various factors. Figure 3 provides a means of visually comparing the magnitude of the standardized coefficients, setting the age-matched group’s performance as the intercept. As the reader can see, the phonological factors and lexical frequency/telicity factors both account for similar sized changes in the child’s rate of inflection, but in opposite directions (phono: β = -0.72; freq: β =
+0.68). Although children with SLI still start at a lower rate of inflection (group: β = -1.16), the lack of interactions indicates that the facilitative effects of frequency and telicity (β = +0.77) and phonology (β = -0.63) are not significantly different than that of the age-matched group. For an
MLU-matched child the effect of phonology is less than that observed for an age-matched child, and the influence of lexical frequency and telicity variables is greater (phono: β = -0.58; freq: = β
= +0.87).
Discussion
Although prior work has independently considered the influence of word familiarity, past frequency, telicity, and stem-final phonology on past tense accuracy, we are not aware of work that has considered how these factors may together contribute to past tense accuracy. Although many of these variables are inter-related, each made unique contributions to the prediction of past tense use, suggesting that all variables must be given equal consideration in selection of target words for teaching the past tense. A key contribution of this study is that past tense frequency and telicity are not interchangeable variables and that these variables continue to influence accuracy well beyond the initial emergence of past tense markers.

Quantifying Past Tense Accuracy 17
Telicity and Past Frequency make unique contributions to accuracy
The unique contributions of telicity and Past Frequency are an important point to bear in mind. Even though adults’ intuitions about the “completed-ness” of events is highly related to the frequency with which these words are produced in past tense (r=.30; p=.02), both factors separately contribute to the likelihood that past tense will be used by children to a comparable degree. This finding is consistent with the work of Wulff and colleagues (2009). Because telicity was entered as a residual of the frequency based information, we can be confident that the contribution of telicity is over and above how often completed events are heard in the past tense.
Thus we might assume that telicity might contribute even more if we did not correct for the contribution of frequency. It is possible that our selection of predictors influenced our outcomes.
Telicity was rated after the fact by adults reading the scripts used by experimenters, not by watching enactments. More valid ratings would have entailed videotaped observations of the events as they were enacted for children. Both the Johnson and Fey (2006) and Leonard et al.,
(2007b) studies used verb events specifically designed to be clearly telic or atelic which enhances the differences in these verb types.
Prior work has suggested that telicity is primarily useful for helping children ‘crack into’ the tense system (e.g., Leonard et al., 2007b). Our results extend the contribution of event semantics into older ages and a continuum of telicity. Telicity is a persistent influence on the use of regular past tense beyond ages 2 to 3 for TD children and 4 to 6 for children with SLI
(Johnson & Fey, 2006; Johnson & Morris, 2007; Leonard, et al., 2007b). Telic events may not just be a way to bootstrap into the inflection system, only to be superseded by frequency later on.
Instead they may serve as persistent cues, enhancing the use of past tense across the lifespan
(Wulff et al., 2009). Clinicians may be able to promote accuracy by selecting highly telic events

Quantifying Past Tense Accuracy 18 for use in intervention or presenting ambiguous verbs in ways that make them appear more telic
(see Appendix C).
The frequency of the inflected form is a well-examined factor (Marchman et al., 1999;
Oetting & Horohov, 1997), thus it should not come as a surprise that Past Frequency was a significant predictor of past tense accuracy. While our results are generally in agreement with those of Marchman et al., (1999) in finding that verb frequency influenced all groups similarly, we differ from Oetting and Horohov (1997) who found that group differences were only apparent for verbs that were rarely inflected/low frequency forms. We see that frequency of the inflected form affects all groups similarly across the entire range of frequency, highlighting the variable as one worthy of attention when selecting verbs for intervention.
The residuals of lemma frequency were also a significant predictor, altering the pattern of responses for the MLU-matched group as compared to the age-matched group. As seen in Figure
1, for the MLU matched children, positive residual values are associated with increased accuracy, suggesting that greater familiarity with the word form, in any form, is associated with greater accuracy. Because the beta coefficients are scaled (see Figure 3), we can compare them directly and we see that Past Frequency contributes approximately 4 times more than Lemma Frequency to past accuracy for this group. For the age and SLI groups, lemma frequency at first appears to work in competition with the past frequency, reducing accuracy (β age
= -0.13; β sli
= -0.04). The beta coefficient suggests that words that are commonly heard in alternative forms are less likely to be inflected with the regular past tense inflection, but this effect is not reliable (p-values of .12 to .19) and should not be over-interpreted.
The fact that the ratio of Past Frequency to Lemma Frequency could not replace Past
Frequency is consistent with the findings of Nicoladis and colleagues (2007) who found that

Quantifying Past Tense Accuracy 19 both type and token frequency of the inflected forms uniquely influenced production of past tense by bilingual children. A minimum number of exposures to the target form seemed to be required in their study; greater rates of exposure led to more accurate production. Others examining second language learners have also observed that Past Frequency and Lemma
Frequency separately contribute to accuracy levels (Blom & Paradis, 2013). Second language learners may have less exposure to English and smaller verb vocabularies, like our MLUmatched group. This would suggest that clinicians should ensure minimal familiarity with target words but should still select words primarily on the basis of their frequency in the inflected form rather than their overall frequency.
Application of phonological and lexical variables to real words
For the age-matched children and for the children with SLI, the lexical and phonological coefficients were comparable in magnitude and could either enhance or reduce accuracy. From a practical standpoint, this is easiest to understand when particular words are used as examples.
Take for instance the words close and kiss, that have high telicity ratings. In these cases, the beneficial effect of telicity cancels out the potentially detrimental effect of that word ending in /s/ or /z/. Close is slightly more telic and substantially more common in the past tense form and thus is more accurate than kiss. Contrast this with play another frequently correct word . It is highly accurate primarily because it is phonologically simple, rather than because it has high telicity or past frequency ratings. Although many of the example words are action verbs, mental/ communication verbs can also lead to highly accurate responses. Verbs like answer and remember were rated as more telic, had average past tense frequency values, and were phonologically facilitative, leading to high accuracy values.
It is worth bearing in mind that the direction of influence can switch. A word, such as sail,

Quantifying Past Tense Accuracy 20 which is rarely heard in the past tense and had low telicity ratings is much less likely to be accurately inflected . Just as phonology and telicity can cancel each other out, so can frequency and telicity. Consider turn, which was rated as ongoing by the adult raters, but was commonly heard in the past tense . It ranks as mid-accuracy verb. Verbs that are never observed in the past tense, in CHILDES hum, rake, giggle , and imagine naturally get low telicity ratings. In these cases any advantages provided by the phonological form cannot overcome the negative influence of telicity and frequency. Verbs, such as exercise, and rest , which get low ratings on both telicity and frequency measures and have uniformly poor phonological characteristics, are among the least likely verbs to be inflected.
Comparison to other studies
To further clarify how logistic regression influences the interpretation of results, we compare our results to those from Johnson and Morris (2007) in Table 5. It is worth noting that our results mirror theirs fairly closely. Although our children tend to be more accurate overall, they are also 2+ years older than their participants were. If we were to have run parametric statistics, we might have observed an interaction between telicity and phonology in either study.
The reader should note that the phonological factors have very little influence when the target verb is highly telic/common in the past tense when children start at a fairly high level of accuracy (Table 5d and 5e). Differences are more readily observable based on phonology in the
SLI group (Table 5c) because they start at a lower level of accuracy. Differences between easy and complex articulatory contexts are most observable in the low frequency/atelic verbs for all groups of children, but especially in the SLI group. Thus we have extended the findings from
Johnson and Morris’ case study of a single 4-year-old child with SLI to a larger group of older children with SLI.

Quantifying Past Tense Accuracy 21
Although studies consistently find that the children with SLI do more poorly than their
TD peers in overall accuracy, whether or not this is exacerbated by a non-facilitative context was less clear (i.e., Oetting & Horohov, 1997; Marchman et al., 1999; Leonard et al., 2007a, 2007b; van der Lely & Ullman, 2001). Our models suggest that each factor is influential, but that interactions between diagnostic group and those factors are not likely. Our choice of statistical method may be influencing our outcomes. Logistical regression emphasizes movement between two extreme points and changes in the error rate. When errors are rare (as they are for the agematched group), a factor that doubles the error rate may not lead to a great change in the overall accuracy level . Likewise, for the SLI group, for whom errors are more common, the doubling of the same factor led to large changes in accuracy. Such differences may mislead researchers into believing that interaction effects are present when in fact the factors are acting in similar ways on the likelihood of producing an error across groups of children; it is actually the base rate of errors that differs.
The primary areas in which group interactions were observed were in words ending in obstruent consonants and lemma frequency, both of which influenced the MLU-matched group differently than the age-matched group. The interactions with the younger group both served to reduce the degree of difference between high and low frequency verbs and between verbs with more or less-facilitative phonological contexts. Given that these children begin at a lower level of overall accuracy, the interactions serve to reduce the differences between the different types of verbs for this group and thus boost overall accuracy.
Conclusion
This study has implemented the recommendations of Weiler (2013) who reminded us of
Crystal’s (1985) suggestion that verb selection for teaching a target morpheme should not be

Quantifying Past Tense Accuracy 22 random or arbitrary. Verbs have certain properties that make them more or less facilitative and attention to these properties may enhance therapeutic effectiveness. Selection of verbs that are telic, commonly inflected in the past tense, and end in facilitative phonological contexts is likely to lead to higher accuracy levels. Selection of verbs that are atelic, less commonly inflected in the past tense and end in obstruents or alveolars are likely to lead to lower initial accuracy but may make good generalization targets. Clinicians should ensure that clients have mastered the past tense in both types of contexts.

Quantifying Past Tense Accuracy 23
Acknowledgements
This work was supported by an internal research grant from the University of Iowa. We would like to thank the children and families who participated in this project and the support of
Augustana College (Allison Haskill) and the Scottish Rite Program (Elizabeth Merrifield) for assistance with subject recruitment. This paper benefited from discussion within the Language
Discussion Group at the University of Iowa. Susan Wagner Cook provided advice on statistical analysis. Jean Gordon read and commented on the paper and its presentation of material.
Portions of the paper were presented at BUCLD held in Boston, MA in 2009.

Quantifying Past Tense Accuracy 24
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Quantifying Past Tense Accuracy 28
What this paper adds
Section 1: What is already known.
Young children are more accurate at producing past tense when a verb is prototypically telic (completed) and when a verb ends in a vowel. Only one study, examining typically-developing 2-year-olds has examined how telicity and phonology influence production of past tense together. They found that phonology is only influential when the verb is in an atelic (ongoing) context. Less is known about how these factors are related to lexical frequency, another common measure associated with past tense production. Understanding how these words level factors interact with each other and which factors are more influential would assist clinicians in selecting target words for use in intervention and therapy.
Section 2: What this study adds. Past tense frequency, telicity, and phonological factors uniquely and approximately equally contribute to the prediction of past tense use. Manipulation of all three factors is critical for successful control of stimuli during intervention. Verbs can be ranked in order of difficulty, such that verbs that are most commonly heard in the past tense, prototypically telic, and end in a vowel or a non-alveolar consonant are most likely to be produced correctly. Although children with SLI were overall less accurate, these factors influenced children with SLI and their age-matched peers in similar ways. MLU-matched children were more sensitive to lemma frequency and less sensitive to phonological factors as compared to their peers.