Storage/composition theoretical models

A variety of theoretical proposals regarding the computation of existing inflected forms have been put forth. These can be grouped in two broad classes: single-mechanism models and dual-system models.

Single-mechanism models propose that all inflected forms are computed with the same basic mechanisms. For example, according to connectionist models, all previously-encountered inflected words are represented in a distributed associative memory [1]–[6]. Such models suggest that forms that exhibit a common and consistent inflectional pattern (regular forms, as well as some irregulars, such as sing-sang, ring-rang) rely primarily on phonological representations in this distributed memory. Rule-only models constitute another type of single-mechanism model. Here, too, all inflected forms (i.e., both regular and irregular) are handled by the same or similar mechanisms, which in this case, involve rule-based processes [7]–[10].

Dual-system models, on the other hand, hold that while some inflected forms are stored, the computation of others depends on (de)composition by rule-governed processes in a separate computational and neurocognitive system. Irregularly inflected forms (e.g., dug), which cannot be fully specified by a default rule, are claimed to depend on memorized representations. Regulars hold a different status. Some dual-system models hold that regulars are always composed (e.g., walk +ed) by a default rule [11]–[13]. Others, however, suggest that even if regulars can be assembled by rule-governed processes, they can also be stored, and indeed often are, with the likelihood of storage depending on various item-level (e.g., frequency) and subject-level (e.g., sex) factors [14]–[20]. For example, women, who appear to have superior verbal memories as compared to men [21]–[25], may also be more likely than men to store regularly inflected forms [14], [20], [25].

These models, as well as similar ones, have been proposed not only for adults, but also for children. Models claiming the dependence of all inflected forms on (an associative) memory suggest that children, like adults, rely on word storage or pattern association for both regulars and irregulars. For example, Bybee [26], [27] suggests that the child memorizes specific verb items (whether regular or irregular forms), and forms networks of associations among them, which eventually reveal common subparts (e.g., play in plays and playing) and allow for generalization of common inflection patterns by analogy. Connectionist models also emphasize the dependence of all the child's forms (regardless of regularity type) on memory [5], [28]–[30]. Rule-only models suggest that children would gradually induce multiple rules from the lexicon through ‘minimal generalization’ [7].

Dual-system models have taken a different approach to the development of the representation and computation of inflected forms. Children are thought to initially memorize both regular and irregular inflected forms (e.g., talked, dug), though by an early age, e.g. by around age 3 for English past-tense, they acquire the appropriate rule(s) – as evidenced, for example, by their fairly consistent –ed affixation not only of regulars (e.g., talk-talked), but also of nonce verbs (e.g., rick-ricked), and even irregular verbs, resulting in over-regularizations such as goed or eated [31]–[33]. Thus, at least after a very early age, children are thought to compute inflected forms in a qualitatively similar way to adults – that is, depending on both storage and composition, even though the extent to which each of these may be relied on may differ between children and adults. For example, the fact that adults hardly ever over-regularize [31], [34], is explained on a dual-system view by the tendency for children to have been exposed to fewer irregularly-inflected forms than adults; children thus have weaker memory traces for irregulars than adults, making it more likely for a child to fail at retrieving an irregular form from memory and thus less likely to resort to rule-based composition and over-regularizations [31].

Frequency effects and imageability effects as diagnostic tests of storage

In the current study we use two related techniques to investigate the storage vs. composition of existing (real) regular and irregular English past-tense forms in children. These two techniques – probing for frequency effects and for imageability effects – can help distinguish between storage and composition, and can therefore be used to test predictions made by various models with respect to this distinction.

The method of probing for “frequency effects” is based on the fact that lexical forms that are more frequently encountered are also more rapidly or more successfully accessed in memory than forms encountered with lower frequency, findings which hold for both adults and children [35]–[39]. If inflected forms are stored, they should exhibit such frequency effects. That is, such forms should show correlations between their inflected-form frequencies and measures of their accessibility (e.g., response times). In contrast, inflected forms that are composed rather than stored should not exhibit such correlations, once access to their stems is controlled for. The presence of frequency effects therefore can and has been used as a diagnostic test of the storage of inflected forms.

A second and more recent method for investigating the storage of lexical forms involves probing for “imageability effects” [20]. The logic of imageability effects is based on the well-documented finding that, in adults as well as children, lexical items for which a visual mental image is more easily formed are also more easily memorized and accessed than forms that are harder to visualize [40]–[49]. Therefore, stored forms, including stored inflected forms, may be expected to exhibit imageability effects: that is, correlations between their imageability and measures of their accessibility. For example, if irregular past tense forms are stored, those of verbs with higher imageability (e.g., dug) should be better memorized and thus accessed faster than those of verbs with lower imageability (e.g., thought), regardless of the fact that their (stored) stems should also show this effect. Such imageability effects should hold even when stem access is controlled for (e.g., by presenting the stems to subjects in a production paradigm). In contrast, inflected forms that are composed would not be expected to show imageability effects (e.g., walked vs. balked), once access to their stems is controlled for. Note that if lexical access to stems rather than past-tense forms was in fact driving imageability effects in past-tense production, we would expect to see imageability effects on all past-tense forms, including forms that are posited to be composed (e.g., regulars in males); as we will see however, this is not the case, either in the present study or for previous findings [20]. Thus imageability effects on inflected forms seem to be due to the retrieval of those forms rather than their stems (even though the imageability of stems and past-tense forms are likely to be the same or very similar). In sum, inflected forms that are stored should exhibit imageability effects in addition to or instead of frequency effects (depending on which of these factors has the greatest influence), allowing imageability effects to be used as another diagnostic of storage.

It should be noted that whereas proponents of different theoretical views largely agree that the presence of frequency effects is indicative of storage [50], there is less consensus concerning the interpretation of an absence of frequency effects (imageability effects are a new diagnostic, and have not been discussed in this respect, but one may expect a similar argument to apply). Single mechanism proponents have argued that a lack of frequency effects on certain inflected forms need not necessarily indicate that these forms are not stored. For example, given that all regulars have a similar stem-past phonological transformation, this generalized phonological pattern is thought to be learned in associative memory, leaving little or no influence for the frequencies of individual past-tense forms. In this case the contribution of neighboring (i.e., phonologically similar) regulars to a given verb's memory traces may overwhelm the contribution of each verb's individual past tense frequency, resulting in weakened past tense frequency effects for regulars [28], [29], [51].

In contrast, proponents of dual-system models claim that inflected forms that depend on composition rather than storage are not expected to exhibit frequency effects, once confounding factors, including phonological similarity to other verbs, are controlled [52], [53]. On this view, irregularly inflected forms should always show signs of storage (e.g., from frequency and/or imageability effects), whereas regulars should show storage in some circumstances but not others (e.g., for females but not for males). Importantly, this particular pattern of predictions has not been made by single-mechanism models, allowing the two types of models to be potentially distinguished.

Previous evidence from adults

Most studies of frequency effects on existing inflectional forms have focused on adults. A number of studies have reported frequency effects for irregular but not regular inflected forms. This pattern of results has been observed for English past-tense forms [6], [20], [52], [54], [55], German noun plurals [56], [57], German past participles [58], and French verb forms [59]. Consistent with this pattern, a lack of frequency effects has also been reported for regular inflected forms in Dutch [60]. However, other studies have reported frequency effects for regular inflected forms, for example in English noun plurals [61], English past tense forms [6], [62], Finnish noun plurals [63], and Dutch verb forms [53].

These discrepant findings for regular inflected forms may be explained by a range of item and subject-level factors that may influence the storage of regulars. Results from several studies support this view, and have revealed that only certain types of regulars show frequency effects, or certain subject groups show frequency effects on regulars. For example, frequency effects have been observed for higher-frequency (but not lower-frequency) regular forms in a number of studies, including in English regular past-tense forms [3], [15], [20], Dutch noun plurals [16], Swedish definite nouns [17], and Finnish (genitive, locative, and partitive) nouns [18], [19]. Of particular interest in the current study, frequency effects on regulars have been observed in women but not men for English past tense forms [20], and were found to be stronger in women than men for Danish noun, verb, and adjective forms [64].

To our knowledge, imageability effects on the processing of inflectional morphology have been examined thus far in only one study, Prado and Ullman (2009) [20], which found imageability effects for irregular but not regular past-tense forms among men. In contrast, imageability effects were not observed for women on either regulars or irregulars [20]. See Discussion below.

Previous evidence from children

In children, who represent the focus of the current investigation, only a handful of empirical studies of frequency effects on existing (i.e., not nonce) inflected forms have been carried out, and no studies have examined imageability effects. The findings with regards to frequency effects on regular forms have been somewhat mixed. One study of frequency effects on the processing of inflected forms in British English [65] examined accuracy rates in the production of regular and irregular past-tense forms in 36 typically-developing children ages 5;5 to 8;9 (as well as children with Specific Language Impairment, not discussed here). Frequency effects were observed for irregulars but not regulars. Similar results were obtained in a study on German past participles, in which reaction times were obtained from 40 children between 5 and 12 years old, all of whom listened to verb stems and were asked to produce corresponding past participle forms [58]. Again, frequency effects were found for irregulars but not for regulars. In contrast, two studies have reported frequency effects on either both [66] or neither [67] regulars and irregulars. A study of 15 Quebec French-speaking children aged 2;11 to 4;6 reported frequency effects on accuracy across both regular and irregular past tense (passé composé) forms [66]. In contrast, a study of 18 British English-speaking children, mean age 11, found no frequency effects on response times across regular and irregular past-tense forms [62]. Finally, a recent study of 307 British English-speaking 4–8 year old children investigating frequency effects in noun plurals and past tenses found inconsistent frequency effects for both regulars and irregulars across age groups though the dependent variable (percentage of responses with inflected forms) collapsed together correctly inflected and over-regularized responses, making it difficult to assess the results with respect to correctly inflected forms [67]. Note that studies of children's production of nonce or overregularized forms (or other errors) [31], [68]–[72] are beyond the scope of the present study, which focuses on the computation of correct existing forms.

Although these previous studies of frequency effects constitute important initial steps in the investigation of the storage/composition distinction of inflected forms in children, they do not take into account a number of issues, some or all of which may have contributed to inconsistencies across the results. First, no prior study on children has examined imageability effects. Given that imageability effects have been shown to be a useful diagnostic of storage in adults [20], investigating imageability effects in children may shed light on the storage versus composition of inflected forms at younger ages as well. Second, previous studies of children have not explored the role of subject-level factors such as sex. Given that sex has been found to influence frequency as well as imageability effects in adults [20], [64], this factor should also be examined in children. Analyses stratified by sex might help explain potential frequency or imageability effects on regulars, and may explain at least some of the inconsistencies across previous results. Methodologically, frequency has previously been treated as a dichotomous variable in most studies, divided into ‘high’ and ‘low’ frequency groups. This dichotomization may have led to degraded measurement and loss of power [73], [74]. Additionally, the data have generally been averaged over subjects and responses, a technique that has similar consequences [73], [74]. Statistical techniques such as those used in the current study avoid this loss of power and therefore could lead to the detection of frequency effects where they might have remained undetected in previous studies.

The Current Study

Here we investigate children's storage vs. composition of existing English past-tense forms by examining both frequency and imageability effects, as well as the possibility of sex differences with regard to these effects. Methodologically, we use approaches that avoid the loss of power entailed by using averaged data and dichotomizing continuous variables, and we control (experimentally and/or statistically) for a large number of potentially confounding factors. Finally, we provide direct comparisons with adult data in order to probe for developmental changes between boys and girls and adult men and women.

Subjects

We tested forty-five healthy right-handed monolingual North American English-speaking children (8–12 years old, mean age  = 9.67, SD = 1.35; 22 girls) from the greater Washington DC area. The age range for the children was selected a priori based on the following considerations: a) we wanted to examine children who are past what is traditionally considered the age of overregularization [31], and b) the age range was similar to the age ranges in previous work investigating frequency effects on the production of past-tense forms in children [58], [62]. The children had a mean of 4.6 years of education (SD = 1.4). Handedness was assessed based on the Edinburgh questionnaire [75]. All children had normal or corrected-to-normal hearing and vision, and none had any known history of developmental, psychiatric or neurological disorders. Ten children produced correct answers for fewer than half of the items of either verb type (regular and irregular). Since only response times to correct answers were analyzed (see below), these children were excluded to avoid insufficient data points from any child (note that including these ten children in the analyses yielded an almost identical pattern of findings). The remaining 35 children (8–12 years old; mean age  = 9.91, SD = 1.38; 16 girls) had a mean of 4.89 years of education (SD = 1.47). Children were also tested on the Reading section of the Wechsler Individual Achievement Test Second Edition (WIAT-II) [76] and scored within the normal range (two of the 35 children analyzed did not complete this test). Reading scores for girls (M = 118.2, SD = 8.81) did not differ statistically from those for boys (M = 112.1, SD = 11.36, t(31)  = 1.69, p = 0.100).

In addition, we directly compared the data from the children to data from 71 adults (18–50 years, mean age  = 24.97, SD = 7.83; mean 15.34 years of education, SD = 1.79; 35 women), whose frequency and imageability effects were previously reported in Prado and Ullman (2009) [20]. All adults met the same language, handedness, and neuropsychological criteria as the children.

Ethics statement

This study was approved by the Georgetown University Institutional Review Board. Children's parents provided written consent and children provided oral assent, which was documented by the experimenter on the consent form at the beginning of the test session.

The Past Tense Production Task

Subjects were tested on a past tense production task that has been described in detail in previous literature [20], [77]. In summary, we examined subjects' performance on the production of 29 irregular verbs (e.g., hold-held), and 29 regulars (e.g., fail-failed: these did not include inconsistent regulars, whose stems are phonologically similar to the stems of irregulars, e.g., squeeze-squeezed, whose stem is similar to freeze-froze). The test items did not include any no-change verbs (e.g., hit-hit) or any verbs for which both a regular and an irregular past-tense are acceptable (e.g., dive-dived/dove). The 29 regulars and 29 irregulars were matched group-wise on the following measures (further described below): stem (uninflected form) frequency, past-tense frequency, and imageability (paired t-tests, ps>.40).

To quantify past-tense frequency (and stem frequency), two counts were used in combination: (1) a frequency count extracted by a stochastic part-of-speech analyzer from a 44 million word corpus of unedited Associated Press news wires [52], [78] (AP); and (2) the Francis and Kucera [79] count (FK), derived from a 1 million word corpus composed of a variety of sources. All analyses were carried out on the natural logarithm of the sum of the two frequency counts, first augmented by 1 to avoid the undefined ln(0).

These frequency counts were chosen for several reasons. First, frequency counts from large corpora are highly desirable because they provide much greater signal than those from small corpora. Since it was crucial to have large corpora, it was not possible to use corpora specifically involving children in the relevant age range, which are typically much smaller in size. Second, this decision is also in line with previous studies, which have likewise used adult frequency counts in work with children in the same age range as our subjects [58], [62], [65]. Third, it has been shown that verb familiarity ratings obtained from children in this age range correlate with adult frequency counts [65]; additionally, frequency counts based on child-addressed speech as well as child speech correlate with adult frequency counts [58]. It might be argued that the potential inappropriateness of adult frequency counts for children could lead to a high likelihood of false negatives for children's frequency effects. However, in the present study children did not in fact show weaker frequency effects than adults on irregulars (which must be stored), suggesting that the adult frequency counts employed here are sufficient to detect frequency effects in the children examined in this study.

Only verbs that were likely to be known by 8-year-olds were included, as determined by the unanimous judgments of five adult native speakers of North-American English, based on the procedure described in [38]. Additionally, note that the children in our study responded accurately enough for us to detect frequency effects on irregulars, and were even more accurate on regulars (see Results).

The imageability ratings, which were taken from Prado and Ullman (2009) [20], ranged from 1 (low imageability) to 5 (high imageability). As in previous studies of imageability in children [38], [80], the present study used imageability ratings obtained from adults. Although it might be argued that the use of adult imageability ratings as a predictor for both age groups might lead to a higher likelihood of false negatives in children than adults (i.e., weaker imageability effects in children), in fact the only reliable difference between children and adults found for imageability effects (on regulars) was more reliable in children (girls) than adults (women), arguing against such a confound (see Results).

The imageability ratings were based on the uninflected form of the verb (e.g., dig, walk), which was used as a proxy for the imageability of the past tense since, as a semantic property, imageability is not expected to differ between the uninflected form and the past tense form. The details of the methodology used for obtaining these imageability ratings are described in Prado and Ullman (2009) [20]. In brief, 28 subjects completed a paper and pencil task in which they were asked to rate a set of words, including the verbs used in the present investigation, in terms of their imageability (on a scale from 1 to 5). Half of the subjects who contributed the ratings were men and half women. Mean imageability ratings were computed for each item over all subjects. The imageability ratings across all regulars and irregulars did not differ between the males and females; additionally the regulars and irregulars did not differ in their imageability ratings. The obtained imageability ratings correlated with previously published imageability ratings.

Analysis.

Frequency and imageability effects were examined on RT data. During testing, the experimenter noted items where the RTs were not triggered by the subject's response; these response times were not analyzed. RT analyses were performed only on correct first-responses (94.29% of all first responses to the 58 regular and irregular verbs). Very fast responses, that is RTs faster than 500 ms, were discarded as being likely due to computer error (3.64% of non timer-error correct responses). Extreme outliers for each subject – that is, responses whose RTs were more than 3.5 standard deviations from the given subject's mean– were also excluded (0.32% of correct responses).

The RT data were analyzed in SAS for Windows Release 9.3 (Cary, NC) using mixed-effects regression modeling. This statistical method allows each individual RT from each subject to be entered into one model, without averaging the RTs in a way that would result in a substantial loss of information. Moreover, it allows both item- and subject-level covariates that may influence the pattern of results to be included in the same model. Variables such as frequency and imageability were entered into the model as continuous factors, rather than dichotomized (e.g., as a two-level factor of ‘high’ vs. ‘low’ frequency, as in many previous studies), thereby avoiding loss of power and other problems [73], [74]. Mixed-effects regression models account for subject variability by including the baseline performance (model intercept) of each subject as a random effect. For more complete discussions of this statistical method, see References [81], [82]; for similar analyses, see Reference [68].

In our model, natural logarithm-transformed RT was the dependent variable; imageability, past-tense frequency (natural-log transformed; see above), verb-type (regular vs. irregular) and age-group (child vs. adult) were included as fixed effects. Interactions were specified between age-group, verb-type, and each of frequency and imageability separately, generating separate frequency and imageability coefficients for children and adults, separately for regular and irregular verbs. As in previous work, we included a random effect of subject on the intercept [20]. Significance of all effects was assessed using α = 0.05. All p-values are reported as two-tailed. Degrees of freedom were computed using the Satterthwaite approximation.

Fourteen potentially confounding subject- and item-level variables were included as covariates in all analyses. Explicitly including these covariates in the model allows one to directly account for variability attributable to them, which enhances prediction accuracy and decreases the size of the residual error [74]. The fourteen covariates, which are described in detail in Table 1, included two subject-level variables (education and sex), and twelve item-level variables controlling for a range of phonological, semantic and other properties of the verbs (e.g., phonological neighborhood).

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Table 1. Covariates included in the mixed-effects model.

https://doi.org/10.1371/journal.pone.0074683.t001

All fourteen covariates were entered as fixed main effects into the mixed-effects model described above. The covariates were also tested for additional inclusion as random effects in the model [20]. To evaluate whether an item-level covariate should be (additionally) included as a random effect (by subject), which would allow the model to account for differences in the effect of the covariate between subjects, each covariate was separately entered as a random effect into a model that was otherwise identical to the model with the covariates included only as fixed effects. The subject-level covariates were tested in the same way. Any covariate whose inclusion as a random effect resulted in a substantial Akaike's Information Criterion reduction (AIC, a smaller-is-better measure of model fit), as compared to the model with covariates entered only as fixed effects, was retained as a random effect (as well as a fixed effect) in the final mixed-effects model; otherwise it was included only as a fixed effect. Of the fourteen covariates, only verb order improved model fit as a random factor (from AIC = 2118.7 to AIC = 2002.1), and was therefore (additionally) included as such.

Children's regulars versus irregulars

Over all children (n = 35), examination of the effect of imageability on past tense production response times revealed significant negative coefficients (i.e., the magnitude of the coefficient was significantly greater than zero) both for irregular and for regular past tense forms, with no reliable difference between the coefficients for the two verb types (Figure 1A). That is, significant imageability effects were found for both irregular and regular past-tense forms. Examination of the effect of frequency on response time revealed a significant negative coefficient for irregular past tense forms (i.e., frequency effects were found on irregulars), whereas frequency effects were not observed for regular past tense forms; the difference between the coefficients for the two verb types was significant (Figure 1B).

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Figure 1. Children's imageability and frequency effects for regular and irregular past-tense forms.

In each scatterplot, the line represents the prediction of the mixed effects regression model with regard to the effect of imageability or frequency on the natural logarithm of response times, with the effect of all covariates removed. Points on the graph represent residuals from the model (with the effects of the covariates removed) for the 29 regular and 29 irregular verbs. B represents the unstandardized regression coefficient, indicating the slope of the regression line, t represents the t-statistic of the comparison between B and zero, and p represents the statistical significance of this comparison.

https://doi.org/10.1371/journal.pone.0074683.g001

Thus, the children exhibited imageability effects on irregulars as well as regulars. In contrast, they exhibited frequency effects on irregulars only. The children's lack of frequency effects on regulars does not appear to be explained by confounding statistical or experimental factors. First, it is not explained by ceiling effects on regulars: the RT variance did not differ (as measured by Folded F-tests) between the verb types (F(28,28)  = 1.23, p = .592). Note also that the mean RTs for regulars and irregulars did not differ (regulars: M = 7.80, SE = 0.02; irregulars: M = 7.79, SE = 0.02; t₁(34)  = 0.20, p = .841, t₂(56) = 0.21, p = .838). Second, it is also not accounted by low power due to smaller sample sizes for regulars. In fact, there were more correctly-produced past-tense forms (on which the RT analyses were carried out) for regulars than irregulars (accuracy on regulars: M = 97.92%, SE = 0.52%; irregulars: M = 78.74%, SE = 3.66%; t₁(34)  = 10.86, p<.0001, t₂(56)  = 5.19, p<.0001). Third, as noted above, the regular and irregular verbs were matched on imageability, as well as stem and past-tense frequency. Moreover, fourteen potentially explanatory variables were included as covariates in the regression model, statistically equating regulars and irregulars with regard to various properties.

Regulars versus irregulars in boys versus girls: Could the inclusion of female subjects explain imageability effects on regulars?

The previous study examining adults' frequency and imageability effects on past tense production revealed sex differences for regulars [20]. In particular, storage (i.e., frequency) effects on regulars were largely due to such effects for women but not men [20]. We therefore examined the possibility that similar sex differences may exist in children; in other words, that the storage (i.e., imageability) effects on regulars observed in the present study may be due to the data from the girls. We thus examined imageability effects on regulars and irregulars in girls versus boys. Likewise, even though no overall frequency effect was found for regulars, we also investigated whether boys and girls differed in frequency effects, as was previously found for adults. To generate separate imageability and frequency coefficients for boys and girls, we added an interaction with sex (male vs. female) to the verb-type by age group by imageability interaction and to the verb-type by age group by frequency interaction in the same model as described above.

Imageability effects in girls versus boys.

The sex by verb-type by imageability interaction was significant (Figure 2; center box). Girls showed significant imageability effects on regulars, but not irregulars, with the verb-type difference not significant (Figure 2A). In contrast, boys showed significant imageability effects on irregulars, but not regulars, with a significant verb-type difference (Figure 2B). Additionally, the coefficients for irregulars did not differ between the boys and girls, whereas the coefficients for regulars did differ significantly between the sexes (Figure 2; middle row).

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Figure 2. Children's imageability effects for regular and irregular past-tense forms, by sex.

In each scatterplot, the line represents the prediction of the mixed effects regression model with regard to the effect of imageability on the natural logarithm of response times, with the effect of all covariates removed. Points on the graph represent residuals from the model (with the effects of the covariates removed) for the 29 regular and 29 irregular verbs. B represents the unstandardized regression coefficient, indicating the slope of the regression line, t represents the t-statistic of the comparison between B and zero, and p represents the statistical significance of this comparison.

https://doi.org/10.1371/journal.pone.0074683.g002

The observed lack of imageability effects on regulars in boys does not seem to be attributable to confounding factors such as ceiling effects or low power. First, the RT variance in boys did not differ (as measured by Folded F-tests) between regulars and irregulars: F(28,28)  = 1.25, p = .557. Moreover, boys' mean RTs for regulars and irregulars did not differ (regulars: M = 7.757, SE = 0.027; irregulars: M = 7.786, SE = 0.024; t₁(18) = 0.24, p = .811, t₂(56)  = 0.80, p = .425). Second, boys produced more correct past-tense forms for regulars than irregulars (accuracy on regulars: M = 97.50%, SE = 0.7%; irregulars: M = 76.22%, SE = 0.38%; t₁(18) = 9.65, p<.0001, t₂(56)  = 5.58, p = .0001). Finally, note that the same subject- and item-level covariates described above were included in the model used in this analysis.

Frequency effects in girls versus boys.

The three-way interaction between sex, verb-type and frequency was not significant (Figure 3; center box). For the girls, there was a significant frequency effect for irregulars but not regulars, though the difference between the two verb types was not significant (Figure 3A). For the boys, a negative frequency coefficient for irregulars approached significance, and differed significantly from the coefficient for regulars (which was positive, Figure 3B). The coefficients for irregulars did not differ between the boys and girls, whereas the coefficients for regulars did differ significantly between the sexes (Figure 3; middle row). Over both verb types, frequency effects were found in girls (B = −0.017, t(5290)  = 2.89, p = .004), but not in boys (B = −0.001, t(5299)  = 0.11, p = .915), with a significant difference between them (B = −0.017, t(5195)  = 2.36, p = .018).

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Figure 3. Children's frequency effects for regular and irregular past-tense forms, by sex.

In each scatterplot, the line represents the prediction of the mixed effects regression model with regard to the effect of frequency on the natural logarithm of response times, with the effect of all covariates removed. Points on the graph represent residuals from the model (with the effects of the covariates removed) for the 29 regular and 29 irregular verbs. B represents the unstandardized regression coefficient, indicating the slope of the regression line, t represents the t-statistic of the comparison between B and zero, and p represents the statistical significance of this comparison.

https://doi.org/10.1371/journal.pone.0074683.g003

In summary, examination of potential sex differences among the children indicated that girls but not boys showed imageability effects on regulars, which may largely explain the imageability effects on regulars in the full group of children. Conversely, boys but not girls showed imageability effects on irregulars. We also examined potential sex differences in frequency effects; here, neither girls nor boys showed frequency effects for regulars (although the coefficients for girls and boys were significantly different), while both sexes showed frequency effects for irregulars (these only approached significance for boys, but did not differ from the frequency effects found in girls).

Further analyses: Comparisons between children and adults

In order to probe for potential developmental changes, we directly compared children's patterns of imageability and frequency effects on regulars and irregulars to the data from adults previously obtained in Prado and Ullman (2009) [20]. Because sex differences were observed here for children (the sex by verb-type by imageability interaction was significant, as were the sex differences in both the imageability and frequency coefficients for regulars), below we examined males and females separately in the comparisons with adults, both for imageability and for frequency effect analyses. (Note that the pattern for adults obtained here was similar to that reported in Prado and Ullman (2009) [20], though the coefficients and p-values are slightly different, since the model here included additional data (the children's data) and additional covariates).