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Effects of Word Frequency and Length in Discrete and Serial Word Reading

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Title: Effects of Word Frequency and Length in Discrete and Serial Word Reading
Language: English
Authors: Sandra Romero (ORCID 0009-0008-2959-1779), George K. Georgiou (ORCID 0000-0002-9081-992X), Angeliki Altani (ORCID 0000-0002-0145-4931), Athanassios Protopapas (ORCID 0000-0002-7285-8845)
Source: Reading and Writing: An Interdisciplinary Journal. 2025 38(10):2897-2928.
Availability: Springer. Available from: Springer Nature. One New York Plaza, Suite 4600, New York, NY 10004. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-460-1700; e-mail: customerservice@springernature.com; Web site: https://link.springer.com/
Peer Reviewed: Y
Page Count: 32
Publication Date: 2025
Document Type: Journal Articles
Reports - Research
Education Level: Elementary Education
Grade 5
Intermediate Grades
Middle Schools
Early Childhood Education
Grade 2
Primary Education
Descriptors: Word Frequency, Reading, Naming, Vocabulary, Spanish Speaking, Elementary School Students, Grade 5, Grade 2, Syllables, Serial Ordering
DOI: 10.1007/s11145-024-10620-w
ISSN: 0922-4777
1573-0905
Abstract: When encountering sequences of familiar words ("serial reading"), skilled readers are thought to take advantage of the presentation format by processing multiple words simultaneously in a "cascaded" manner. This is possible when individual words are read "by sight," similar to naming letters or digits. Accordingly, previous studies have shown that as readers become more experienced, fluent reading increasingly parallels serial naming of familiar symbols, while reading individual words ("discrete reading") parallels discrete naming. However, most studies have focused on high-frequency, short words, which are more amenable to cascaded processing; different performance patterns across presentation formats (serial vs. discrete) would be expected for longer, less frequent words. Therefore, in this study, we examined how word frequency and length influence the effect of word presentation format and the relation of word reading with serial and discrete digit naming. We tested 201 Spanish-speaking children in Grades 2 and 5 on serial and discrete digit naming and serial and discrete word reading of eight sets of words varying in length (two vs. four syllables) and frequency (high vs. low). Results showed that the serial word presentation format benefitted reading rates across word sets, particularly for short, high-frequency words and more strongly among fifth graders. Furthermore, the difference between serial and discrete reading and its interaction with word length and frequency were more closely associated with serial naming than discrete naming. The pattern of findings supports the hypothesis that readers employ cascaded processing to the extent individual words in the serial reading task are automatized.
Abstractor: As Provided
Entry Date: 2026
Accession Number: EJ1499625
Database: ERIC
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  Value: <anid>AN0190299323;2ap01dec.25;2025Dec19.04:18;v2.2.500</anid> <title id="AN0190299323-1">Effects of word frequency and length in discrete and serial word reading </title> <p>When encountering sequences of familiar words ("serial reading"), skilled readers are thought to take advantage of the presentation format by processing multiple words simultaneously in a "cascaded" manner. This is possible when individual words are read "by sight," similar to naming letters or digits. Accordingly, previous studies have shown that as readers become more experienced, fluent reading increasingly parallels serial naming of familiar symbols, while reading individual words ("discrete reading") parallels discrete naming. However, most studies have focused on high-frequency, short words, which are more amenable to cascaded processing; different performance patterns across presentation formats (serial vs. discrete) would be expected for longer, less frequent words. Therefore, in this study, we examined how word frequency and length influence the effect of word presentation format and the relation of word reading with serial and discrete digit naming. We tested 201 Spanish-speaking children in Grades 2 and 5 on serial and discrete digit naming and serial and discrete word reading of eight sets of words varying in length (two vs. four syllables) and frequency (high vs. low). Results showed that the serial word presentation format benefitted reading rates across word sets, particularly for short, high-frequency words and more strongly among fifth graders. Furthermore, the difference between serial and discrete reading and its interaction with word length and frequency were more closely associated with serial naming than discrete naming. The pattern of findings supports the hypothesis that readers employ cascaded processing to the extent individual words in the serial reading task are automatized.</p> <p>Keywords: Cascaded processing; Serial naming; Word frequency; Word length; Spanish; Psychology and Cognitive Sciences Psychology Cognitive Sciences</p> <p>Supplementary Information The online version contains supplementary material available at https://doi.org/10.1007/s11145-024-10620-w.</p> <p>Word reading fluency, and the effortless and automatic word recognition that underlies it (e.g., Hudson et al., [<reflink idref="bib30" id="ref1">30</reflink>]; Kuhn & Stahl, [<reflink idref="bib37" id="ref2">37</reflink>]), requires transitioning from sounding out to recognizing words as whole units or sight words (Ehri, [<reflink idref="bib22" id="ref3">22</reflink>]). Word characteristics such as length and frequency are thought to influence this transition. Length effects are often considered to be indicative of a piecemeal and at least partially sequential phonological recoding strategy (Spinelli et al., [<reflink idref="bib55" id="ref4">55</reflink>]): The reader must recognize more graphemes and convert them to phonemes, so longer words take longer to process. In contrast, word frequency effects are indicative of orthographic learning (Brysbaert et al., [<reflink idref="bib11" id="ref5">11</reflink>]): High-frequency words are more familiar to the reader and, because of frequent exposure, are processed with a higher degree of automaticity. With increased automaticity, sequential recoding gives way to sight word reading. Accordingly, length effects diminish for high-frequency words, leading to the observed interaction between word frequency and length (e.g., Zoccolotti et al., [<reflink idref="bib64" id="ref6">64</reflink>]). Despite occasional inconsistencies in the literature, such effects have long been established, both with words presented in isolation and in sentences (e.g., Ballot & Zesiger, [<reflink idref="bib6" id="ref7">6</reflink>]; Tiffin-Richards & Schroeder, [<reflink idref="bib56" id="ref8">56</reflink>]).</p> <p>An additional crucial factor in the development of reading fluency concerns the serial nature of fluent reading, which involves processing of multiple words (in word lists or sentences) in a temporally overlapping manner termed "cascading" (Protopapas et al., [<reflink idref="bib43" id="ref9">43</reflink>], [<reflink idref="bib44" id="ref10">44</reflink>]). It has been suggested that efficient cascading is only possible when individual words have been automatized. Therefore, the extent to which a word reading task is processed via cascading should depend on the length and frequency of the words it includes. This study brings together cascaded processing with effects of word frequency and length to examine their joint implications on reading words presented both in isolation and in lists among Grade 2 and 5 Spanish-speaking children.</p> <hd id="AN0190299323-2">Effects of word length and frequency across reading development</hd> <p>The influence of word length and frequency on word recognition has long been established (see Barton et al., [<reflink idref="bib7" id="ref11">7</reflink>] and Brysbaert et al., [<reflink idref="bib11" id="ref12">11</reflink>], for reviews). Different tasks have been used to study the effects of word length and frequency, often involving time-based measures to understand the level of automaticity in word processing. These measures include vocal reaction times in word naming tasks, motor response times in lexical decision tasks, as well as eye movement measures, such as gaze duration, when reading target words embedded in sentences. The rationale for employing these methods is that longer (typically 7–8 letters or more) or less familiar words require more cognitive effort to be processed. Consequently, readers may need more time to produce a response or require longer gaze duration.</p> <p>To study frequency effects, researchers have typically categorized high- and low-frequency words based on standardized measures such as frequency per million words (fpm). Words with 100 or more fpm are often classified as high-frequency (e.g., Davies et al., [<reflink idref="bib18" id="ref13">18</reflink>]; Joseph et al., [<reflink idref="bib32" id="ref14">32</reflink>]) and with 20 or fewer fpm as low-frequency (e.g., Ballot & Zesiger, [<reflink idref="bib6" id="ref15">6</reflink>]; Cuetos & Suárez-Coalla, [<reflink idref="bib17" id="ref16">17</reflink>]).[<reflink idref="bib1" id="ref17">1</reflink>] Significant differences between processing high- and low-frequency words appear as early as Grade 1 (e.g., Zoccolotti et al., [<reflink idref="bib65" id="ref18">65</reflink>]) and Grade 2 (e.g., Hasenäcker & Schroeder, [<reflink idref="bib29" id="ref19">29</reflink>]; Rau et al., [<reflink idref="bib47" id="ref20">47</reflink>]) and persist across the lifespan (Davies et al., [<reflink idref="bib19" id="ref21">19</reflink>]). Frequency effects are steeper from Grades 3‒4 onward, across languages (e.g., German: Schröter & Schroeder, [<reflink idref="bib50" id="ref22">50</reflink>]; Italian: Zoccolotti et al., [<reflink idref="bib65" id="ref23">65</reflink>]; Spanish: Cuetos & Suárez-Coalla, [<reflink idref="bib17" id="ref24">17</reflink>]). However, the interaction between frequency and age group is somewhat inconsistent. Some studies have found a decreasing effect of word frequency with age (e.g., Davies et al., [<reflink idref="bib19" id="ref25">19</reflink>]), whereas others have found no interaction with, for example, grade level (e.g., Burani et al., [<reflink idref="bib12" id="ref26">12</reflink>]).</p> <p>Length effects, like frequency effects, are observed across development but change with reading experience (e.g., Schröter & Schroeder, [<reflink idref="bib50" id="ref27">50</reflink>], for Grades 1 to 6; Zoccolotti et al., [<reflink idref="bib65" id="ref28">65</reflink>], for Grades 1 to 8). Across languages, studies have shown that the difference between shorter and longer words is more pronounced among beginning readers from Grades 1 and 2 (e.g., Dutch: Martens & de Jong, [<reflink idref="bib39" id="ref29">39</reflink>]; German: Rau et al., [<reflink idref="bib47" id="ref30">47</reflink>]; French: Ballot & Zesiger, [<reflink idref="bib6" id="ref31">6</reflink>]; Italian: Zoccolotti et al., [<reflink idref="bib64" id="ref32">64</reflink>]; Spanish: Cuetos & Suárez-Coalla, [<reflink idref="bib17" id="ref33">17</reflink>]). These studies show that response times of young readers are affected by every additional unit (e.g., letter or syllable); however, length effects are reduced as a function of age and stabilize around Grade 3 (e.g., Cuetos & Suárez-Coalla, [<reflink idref="bib17" id="ref34">17</reflink>]; Rau et al., [<reflink idref="bib47" id="ref35">47</reflink>]; Schröter & Schroeder, [<reflink idref="bib50" id="ref36">50</reflink>]; Zoccolotti et al., [<reflink idref="bib65" id="ref37">65</reflink>]), eventually disappearing among older children (Martens & de Jong, [<reflink idref="bib39" id="ref38">39</reflink>]) or adults (e.g., Bijeljac-Babic et al., [<reflink idref="bib10" id="ref39">10</reflink>]). However, a possible reason some studies with more experienced readers did not find length effects in upper grades or adults might be the use of words with a limited length range, such as 3 to 6 letters. Therefore, to accurately assess length effects over time, studies should include words with eight or more letters (see New et al., [<reflink idref="bib41" id="ref40">41</reflink>], for a review) or multisyllabic words.</p> <p>In addition, research with children (e.g., Davies et al., [<reflink idref="bib18" id="ref41">18</reflink>]; Monster et al., [<reflink idref="bib40" id="ref42">40</reflink>]) and adults (e.g., Ferrand, [<reflink idref="bib24" id="ref43">24</reflink>]; Weekes, [<reflink idref="bib60" id="ref44">60</reflink>]) has shown that the effect of word length diminishes as word frequency increases and increases as word frequency decreases, with this interaction effect also depending on reading experience. For example, among Grade 2 children, the effect of length appears to be similar for both high and low-frequency words (e.g., Hasenäcker & Schroeder, [<reflink idref="bib29" id="ref45">29</reflink>]; Rau et al., [<reflink idref="bib47" id="ref46">47</reflink>]); however, it becomes gradually less pronounced for high-frequency words from Grade 3 onwards (e.g., Rau et al., [<reflink idref="bib47" id="ref47">47</reflink>]; Zoccolotti et al., [<reflink idref="bib65" id="ref48">65</reflink>]). Among adults, length effects are only noticeable with words that are both long and low-frequency (e.g., Ferrand, [<reflink idref="bib24" id="ref49">24</reflink>]). However, not all studies examining children at different stages of learning to read have reported this interaction effect (e.g., Ballot & Zesiger, [<reflink idref="bib6" id="ref50">6</reflink>]).</p> <p>Based on these findings, the independent effects of length and frequency, as well as their interaction, can be interpreted as reflecting different phases in word processing. Among novice readers, the presence of length effects in short words, regardless of word frequency, indicates a piecewise decoding approach used to read all types of words. Among more experienced readers, the decreasing effect of length, particularly for high-frequency words, suggests increasingly parallel processing of the letter string and sight-word recognition. However, even expert readers with extensive sight-word vocabularies may still rely on a sequential, piecewise word-processing strategy for the most complex, less familiar words.</p> <hd id="AN0190299323-3">Discrete versus serial word reading</hd> <p>A common characteristic of the tasks often used to investigate frequency and length effects is that they present words in isolation in single-word displays (i.e., one by one on a computer screen). This mode of presentation has been termed "single-item" (e.g., Ziaka & Protopapas, [<reflink idref="bib61" id="ref51">61</reflink>]) or "discrete" word reading (Protopapas et al., [<reflink idref="bib44" id="ref52">44</reflink>]; Zoccolotti et al., [<reflink idref="bib67" id="ref53">67</reflink>]). It can be contrasted with multiple-word display (or simply "multiple display"; Conforti et al., [<reflink idref="bib15" id="ref54">15</reflink>]; or "multi-item"; Ziaka & Protopapas, [<reflink idref="bib61" id="ref55">61</reflink>]), also termed "serial" word reading (Protopapas et al., [<reflink idref="bib44" id="ref56">44</reflink>]). In keeping with the cascading literature, in the present study we will be using the terms "discrete" and "serial" word reading to refer to single-word and multiple-word displays, respectively.</p> <p>A few studies have explored the effects of frequency and length in serial word reading by analyzing total reading time (e.g., Davies et al., [<reflink idref="bib18" id="ref57">18</reflink>]; Zoccolotti et al., [<reflink idref="bib65" id="ref58">65</reflink>]), which includes both the time taken to pronounce the words and the silent intervals between words. The results have been similar to studies of discrete word reading; namely, total reading times decreased with reading experience, yet word length effects persisted for low-frequency words (see Zoccolotti et al., [<reflink idref="bib65" id="ref59">65</reflink>], for an analysis spanning Grades 1 to 8). However, these studies are limited in that they did not directly compare the effects of length and frequency between the discrete and serial formats.</p> <p>In subsequent studies, Zoccolotti and collaborators (e.g., Conforti et al., [<reflink idref="bib15" id="ref60">15</reflink>]; Zoccolotti et al., [<reflink idref="bib66" id="ref61">66</reflink>]) compared discrete and serial word reading among Italian Grade 6 children with and without dyslexia. They also manipulated word length (five vs. seven letters) across the two presentation formats. To obtain a directly comparable metric between serial and discrete word reading, they measured total reading time for the discrete responses as well (i.e., including both response onset latency and articulation duration). Zoccolotti et al. ([<reflink idref="bib66" id="ref62">66</reflink>]) found a three-way interaction between group (typical vs. dyslexic), length (short vs. long), and format (discrete vs. serial). The interaction reflected the finding that, for children without dyslexia, the serial format facilitated reading, with a similar effect on short and long words; whereas for children with dyslexia, serial reading hindered reading of longer words. Following up, Conforti et al. ([<reflink idref="bib15" id="ref63">15</reflink>]) found that the effects of lexicality (words vs. pseudowords) and length were greater in serial than in discrete word reading, especially for children with dyslexia. The difference in the effects of lexicality and length between groups of children at different levels of reading skill highlights the importance of the serial reading format and its differential implications across reading development for different types of words.</p> <hd id="AN0190299323-4">The cascading hypothesis</hd> <p>It has long been known that the format words are presented in (i.e., serial or discrete) influences reading performance; for example, words in context are read faster than words in isolation (Jones et al., [<reflink idref="bib31" id="ref64">31</reflink>]). The difference between discrete and serial word reading rate, termed "serial advantage" (Altani et al., [<reflink idref="bib1" id="ref65">1</reflink>], [<reflink idref="bib4" id="ref66">4</reflink>]), has been found to greatly increase with reading skill across orthographies (Grades 1–5, Greek and English; Altani et al., [<reflink idref="bib3" id="ref67">3</reflink>]). This suggests that more advanced readers benefit more from the serial format by temporally overlapping processing of multiple successive words, that is, cascading.</p> <p>Serial word reading has also been examined through its association with serial naming (Rapid Automatized Naming, or simply RAN) tasks. RAN involves naming of overlearned items such as digits or letters simultaneously presented in an array formation. RAN is a robust concurrent and longitudinal predictor of reading fluency (see Araújo et al., [<reflink idref="bib5" id="ref68">5</reflink>]; Song et al., [<reflink idref="bib54" id="ref69">54</reflink>], for meta-analyses). Even though the reason why RAN is such a good predictor of reading fluency remains a subject of debate, researchers concur that the serial format of RAN tasks, which resembles serial word reading, is crucial for the RAN-reading relation (e.g., Georgiou et al., [<reflink idref="bib27" id="ref70">27</reflink>]; Georgiou & Parrila, [<reflink idref="bib26" id="ref71">26</reflink>]; Protopapas et al., [<reflink idref="bib45" id="ref72">45</reflink>]). A line of evidence supporting this conclusion comes from several studies across more and less consistent orthographies, which have documented a developmental shift in the association between discrete and serial word reading and RAN: Increasing reading skill is associated with a strengthening of the relation between serial reading and RAN, offset by a weakening of the relation between discrete and serial reading (Altani et al., [<reflink idref="bib2" id="ref73">2</reflink>], [<reflink idref="bib3" id="ref74">3</reflink>]; de Jong, [<reflink idref="bib20" id="ref75">20</reflink>]; Protopapas et al., [<reflink idref="bib43" id="ref76">43</reflink>], [<reflink idref="bib44" id="ref77">44</reflink>]; Romero et al., [<reflink idref="bib49" id="ref78">49</reflink>]).</p> <p>Accordingly, researchers have proposed that becoming a fluent reader, from slow word-by-word reading to effortless and smooth reading, requires a skill to simultaneously schedule multiple adjacent words in lists or sentences into successive stages, one after the other, in a cascaded manner (Altani et al., [<reflink idref="bib3" id="ref79">3</reflink>]; Protopapas et al., [<reflink idref="bib43" id="ref80">43</reflink>], [<reflink idref="bib44" id="ref81">44</reflink>]). That is, while the orthographic-phonological representation of a word is processed, the preceding word is uttered, and the next one is viewed. Evidence suggests that cascaded processing, as indexed by serial digit naming (i.e., RAN digits), is the main predictor of growth in word reading fluency after controlling for early decoding (e.g., Diamanti et al., [<reflink idref="bib21" id="ref82">21</reflink>]; Romero et al., [<reflink idref="bib49" id="ref83">49</reflink>]).</p> <hd id="AN0190299323-5">Format-specific associations</hd> <p>The efficiency of cascading in serial naming is thought to be contingent upon the level of automaticity of the individual items to be named (Protopapas et al., [<reflink idref="bib44" id="ref84">44</reflink>], [<reflink idref="bib45" id="ref85">45</reflink>]). Serial digit naming indexes cascaded processing because naming of individual digits is highly automatized, therefore individual differences in serial digit naming are dominated by cascading efficiency. Accordingly, for cascaded processing to operate efficiently in serial word reading, and thus for serial digit naming to resemble serial reading, each word must be efficiently and automatically processed as a sight word (de Jong, [<reflink idref="bib20" id="ref86">20</reflink>]). This explains why most studies examining the relations between serial and discrete word reading with RAN have used frequent short words that are easily recognized by sight (e.g., Altani et al., [<reflink idref="bib1" id="ref87">1</reflink>], [<reflink idref="bib2" id="ref88">2</reflink>], [<reflink idref="bib3" id="ref89">3</reflink>]; de Jong, [<reflink idref="bib20" id="ref90">20</reflink>]; Georgiou et al., [<reflink idref="bib28" id="ref91">28</reflink>]). In addition to the strong association between serial naming and serial reading, these studies have consistently shown that, for intermediate and advanced readers, discrete word reading is more strongly associated with discrete naming (i.e., speeded naming of individual symbols presented in isolation), indicating that short and high-frequency words are processed with a high degree of automaticity, similar to highly automatized symbols such as digits (Ehri & Wilce, [<reflink idref="bib23" id="ref92">23</reflink>]). There are, in other words, format-specific associations between naming and reading (de Jong, [<reflink idref="bib20" id="ref93">20</reflink>]).</p> <p>Format-specific associations concern more advanced readers, who read many words by sight. What about less advanced readers, who primarily read words by employing a phonological recoding strategy? If one goes through a word piecewise, either by graphemes or by syllables (or any combination of sub-word chunks), this amounts to sequential intra-word processing, the efficiency of which might also be indexed by serial naming. Thus, de Jong ([<reflink idref="bib20" id="ref94">20</reflink>]) hypothesized that, for beginner readers, format-specific associations do not apply; rather, discrete word reading would have a stronger association to serial—rather than discrete—naming, capturing serial intra-word processing, even when reading short and high-frequency words (e.g., de Jong, [<reflink idref="bib20" id="ref95">20</reflink>]; van den Boer & de Jong, [<reflink idref="bib57" id="ref96">57</reflink>]).</p> <p>One corollary of de Jong's ([<reflink idref="bib20" id="ref97">20</reflink>]) hypothesis is that discrete reading of low-frequency or longer words should be more strongly predicted by serial than by discrete digit naming, at least for readers for whom such words are not read by sight. Two studies have empirically tested this assumption, namely, Georgiou et al. ([<reflink idref="bib28" id="ref98">28</reflink>]) and van den Boer et al. ([<reflink idref="bib58" id="ref99">58</reflink>]). In both studies, the contribution of serial naming to the discrete reading of short high-frequency words was very small to nonsignificant. However, serial naming accounted for unique variance in discrete word reading of items with higher complexity, even after controlling for discrete naming. These more complex items were low-frequency characters and high-frequency two-character words read by Chinese first graders (Georgiou et al., [<reflink idref="bib28" id="ref100">28</reflink>]), and 8-letter words and pseudowords read by fifth-grade English and Dutch children (van den Boer et al., [<reflink idref="bib58" id="ref101">58</reflink>]). Moreover, age-related differences reflecting cascaded processing were found between these studies, concerning the association between serial naming and serial word reading of words varying in complexity. Specifically, for older Dutch and English readers, serial naming was a main predictor of serial reading regardless of word length and lexical status, suggesting that, at this stage of reading development, children benefit from the serial presentation of words regardless of their characteristics. In contrast, for Chinese beginning readers, serial naming was a unique predictor of serial reading of high-frequency items but not low-frequency ones, after accounting for individual word reading skills, supporting claims that high-frequency words are more amenable to cascaded processing.</p> <hd id="AN0190299323-6">The present study</hd> <p>In the present study we consider the implications of the cascading processing framework for discrete and serial reading of words differing in frequency and length. The role of task format (serial vs. discrete) in the effects of word frequency and length has not been fully explored even though concrete expectations can be based on the cascading hypothesis. Several studies have addressed serial vs. discrete reading, and many others have examined word frequency and length effects, as noted above. However, very few studies have combined the two, and those have tended to use pseudowords, rather than low-frequency words, and groups of children with reading difficulties (dyslexia), rather than typically developing readers at different levels of reading skill. Yet the cascading framework suggests that format should strongly moderate frequency and length effects, because any enhancement of single-word processing towards higher automaticity is expected to lead to additional gains through higher cascading efficiency. Thus, the serial format can be expected to be somewhat associated with greater length effects, especially for beginner readers, and strongly associated with greater frequency effects, especially for more advanced readers. Conversely, short and more frequent words should benefit most from the serial format, with implications for the role of cascading in reading fluency and its development.</p> <p>Thus, our first research question is: <emph>How does format (serial vs. discrete) influence the effects of word frequency and length in the word reading rate of children at different stages of reading development?</emph> Given the importance of automaticity for efficient cascading, we expected that (a) format would make little difference at relatively early stages of reading development, when few individual words are automatized, but a very substantial difference in more advanced readers; and (b) length and frequency would moderate the effects of format, with frequency attaining even greater importance for more advanced readers. Conversely, format would have a larger effect on short and frequent words, which are more likely to be read by sight and thus enable efficient cascading (by more advanced readers).</p> <p>Second, we considered the extent to which the association between digit naming and word reading across the discrete and serial formats would be modulated by word characteristics such as frequency and length, at different levels of reading skill. Previous studies have probed the modulation of the association by length and/or lexicality but have not taken a comprehensive approach encompassing fully crossed factors over a wide range of reading skill. In our design, we have fully crossed word frequency (low vs. high), length (short vs. long), format (serial vs. discrete), and grade (2nd vs. 5th). The cascading processing framework suggests that individual differences in word reading efficiency should be uniquely attributable to serial (but not discrete) digit naming in accordance with format effects. That is, the association of serial (but not discrete) word reading with digit naming should be higher for shorter, more frequent words; in other words, we would expect an interaction of serial digit naming with frequency, length, and their interaction with format.</p> <p>Thus, our second research question is: <emph>To what extent do word characteristic (i.e.</emph>, <emph>format</emph>, <emph>frequency</emph>, <emph>and length) modulate the relation of serial and discrete naming with reading?</emph> We expected that the format-specific associations between digit naming and word reading would be primarily observed for short, high-frequency words, which are likely to be read by sight, especially by the more advanced readers. We also expected that frequency would modulate the associations with digit naming more strongly than length, as frequency is the more decisive factor for automaticity.</p> <p>Our study includes Spanish-speaking readers attending Grades 2 and 5. Spanish is among the most transparent alphabetic European orthographies (Seymour et al., [<reflink idref="bib52" id="ref102">52</reflink>]). This is important because length effects are larger in consistent orthographies (e.g., Kwok et al., [<reflink idref="bib38" id="ref103">38</reflink>]; Ziegler et al., [<reflink idref="bib63" id="ref104">63</reflink>]), likely because consistent spelling systems favor word decoding through smaller psycholinguistic grain sizes such as phonemes or syllables (Ziegler & Goswami, [<reflink idref="bib62" id="ref105">62</reflink>]). All Spanish words can be read correctly using phonological recoding, as even letters with multiple pronunciations follow clear and consistent orthographic rules, and lexical stress is marked when needed. Thus, our study is well placed to be compared with related previous work in Greek and Italian, which are also largely orthographically consistent.</p> <hd id="AN0190299323-7">Method</hd> <p></p> <hd id="AN0190299323-8">Participants</hd> <p>Ninety-two Grade 2 students (55% female; <emph>M</emph><subs>age</subs> = 7.9; <emph>SD</emph> = 0.4) and 109 Grade 5 students (61% female; <emph>M</emph><subs>age</subs> = 11.0; <emph>SD</emph> = 0.3) participated in this study. Students were recruited from five elementary schools located in different parts of a large metropolitan city in central-west Mexico. All Grade 2 and Grade 5 students from the participating schools were invited to participate; however, we only assessed those with parental consent. All participants spoke Spanish as their first language and had no severe learning or developmental disabilities based on school records. This study received ethics approval from the Research Board of the University of Alberta.</p> <hd id="AN0190299323-9">Materials</hd> <p></p> <hd id="AN0190299323-10">Naming tasks</hd> <p>The digits 1, 4, 5, and 7 were selected for serial and discrete naming. The digit words are pronounced in Spanish as /u.no/, /kwa.tro/, /sin.ko/, and /sje.te/, respectively. They are all two syllables long.</p> <hd id="AN0190299323-11">Reading tasks</hd> <p>Words varying in length (short vs. long) and frequency (low vs. high) were selected for the reading tasks.</p> <hd id="AN0190299323-12">Frequency</hd> <p>Words were selected based on their frequency, either low or high. Consistent with previous studies, low-frequency words were defined as those with less than 20 fmp, whereas high-frequency words had 100 or more fmp (e.g., Ballot & Zesiger, [<reflink idref="bib6" id="ref106">6</reflink>]; Cuetos & Suárez-Coalla, [<reflink idref="bib17" id="ref107">17</reflink>]; Davies et al., [<reflink idref="bib18" id="ref108">18</reflink>]; Joseph et al., [<reflink idref="bib32" id="ref109">32</reflink>]). All word frequencies were taken from the LEXESP corpus (Sebastián et al., [<reflink idref="bib51" id="ref110">51</reflink>]), which comprises around five million words, and are reported in the Zipf scale (van Heuven et al., [<reflink idref="bib59" id="ref111">59</reflink>]).</p> <hd id="AN0190299323-13">Length</hd> <p>In line with previous studies on serial and discrete naming and reading, we manipulated word length based on the number of syllables (e.g., Altani et al., [<reflink idref="bib1" id="ref112">1</reflink>], Altani et al., [<reflink idref="bib2" id="ref113">2</reflink>], [<reflink idref="bib3" id="ref114">3</reflink>]; de Jong, [<reflink idref="bib20" id="ref115">20</reflink>]; Protopapas et al., [<reflink idref="bib43" id="ref116">43</reflink>]; Romero et al., [<reflink idref="bib49" id="ref117">49</reflink>]). We selected two-syllable words[<reflink idref="bib2" id="ref118">2</reflink>] for the short condition and four-syllable words for the long condition. Short words averaged five letters and long words averaged eight letters, consistent with lengths reported in studies comparing short and long words (e.g., Davies et al., [<reflink idref="bib18" id="ref119">18</reflink>]; Hasenäcker & Schroeder, [<reflink idref="bib29" id="ref120">29</reflink>]; Khelifi et al., [<reflink idref="bib35" id="ref121">35</reflink>]; Zoccolotti et al., [<reflink idref="bib65" id="ref122">65</reflink>]).</p> <p>Words were arranged into four categories: (<reflink idref="bib1" id="ref123">1</reflink>) high-frequency and short (High-Short), (<reflink idref="bib2" id="ref124">2</reflink>) low-frequency and short (Low-Short), (<reflink idref="bib3" id="ref125">3</reflink>) high-frequency and long (High-Long), and (<reflink idref="bib4" id="ref126">4</reflink>) low-frequency and long (Low-Long). Each category included two sets of words, one for serial presentation (36 items) and one for discrete presentation (36 items). We subsequently created eight lists of 36 words each (see Supplementary Materials). In addition to length and frequency, words were matched on the number of phonemes, number of letters, and initial syllabic structure between serial and discrete sets from each category (see Table 1).</p> <p>Table 1 Descriptive statistics of linguistic measures from words used in the reading tasks</p> <p> <ephtml> <table rules="groups"><thead><tr><th align="left"><p>Reading Task</p></th><th align="left"><p>Measure</p></th><th align="left"><p><italic>M</italic></p></th><th align="left"><p><italic>SD</italic></p></th><th align="left"><p>Min</p></th><th align="left"><p>Max</p></th><th align="left" /><th align="left" colspan="9"><p>Initial Syllabic Structure</p></th></tr><tr><th align="left" /><th align="left" /><th align="left" /><th align="left" /><th align="left" /><th align="left" /><th align="left" /><th align="left"><p>V</p></th><th align="left"><p>VC</p></th><th align="left"><p>VCC</p></th><th align="left"><p>CV</p></th><th align="left"><p>CVC</p></th><th align="left"><p>CCV</p></th><th align="left"><p>CVV</p></th><th align="left"><p>CCVC</p></th><th align="left"><p>CVVC</p></th></tr></thead><tbody><tr><td align="left" rowspan="3"><p>Serial High-Short Words</p></td><td align="left"><p>Frequency</p></td><td char="." align="char"><p>5.2</p></td><td char="." align="char"><p>0.2</p></td><td char="." align="char"><p>5.0</p></td><td char="." align="char"><p>5.6</p></td><td align="left" /><td char="." align="char"><p>3</p></td><td char="." align="char"><p>3</p></td><td char="." align="char"><p>0</p></td><td char="." align="char"><p>21</p></td><td char="." align="char"><p>5</p></td><td char="." align="char"><p>3</p></td><td char="." align="char"><p>0</p></td><td char="." align="char"><p>1</p></td><td char="." align="char"><p>0</p></td></tr><tr><td align="left"><p>Phonemes</p></td><td char="." align="char"><p>4.4</p></td><td char="." align="char"><p>0.7</p></td><td char="." align="char"><p>3.0</p></td><td char="." align="char"><p>6.0</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left"><p>Letters</p></td><td char="." align="char"><p>4.5</p></td><td char="." align="char"><p>0.7</p></td><td char="." align="char"><p>4.0</p></td><td char="." align="char"><p>6.0</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" rowspan="3"><p>Discrete High-Short Words</p></td><td align="left"><p>Frequency</p></td><td char="." align="char"><p>5.2</p></td><td char="." align="char"><p>0.2</p></td><td char="." align="char"><p>5.0</p></td><td char="." align="char"><p>5.6</p></td><td align="left" /><td char="." align="char"><p>3</p></td><td char="." align="char"><p>2</p></td><td char="." align="char"><p>0</p></td><td char="." align="char"><p>21</p></td><td char="." align="char"><p>5</p></td><td char="." align="char"><p>4</p></td><td char="." align="char"><p>0</p></td><td char="." align="char"><p>1</p></td><td char="." align="char"><p>0</p></td></tr><tr><td align="left"><p>Phonemes</p></td><td char="." align="char"><p>4.5</p></td><td char="." align="char"><p>0.6</p></td><td char="." align="char"><p>4.0</p></td><td char="." align="char"><p>6.0</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left"><p>Letters</p></td><td char="." align="char"><p>4.6</p></td><td char="." align="char"><p>0.6</p></td><td char="." align="char"><p>4.0</p></td><td char="." align="char"><p>6.0</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" rowspan="3"><p>Serial Low-Short Words</p></td><td align="left"><p>Frequency</p></td><td char="." align="char"><p>3.3</p></td><td char="." align="char"><p>0.5</p></td><td char="." align="char"><p>1.0</p></td><td char="." align="char"><p>3.9</p></td><td align="left" /><td char="." align="char"><p>3</p></td><td char="." align="char"><p>3</p></td><td char="." align="char"><p>0</p></td><td char="." align="char"><p>15</p></td><td char="." align="char"><p>8</p></td><td char="." align="char"><p>5</p></td><td char="." align="char"><p>1</p></td><td char="." align="char"><p>1</p></td><td char="." align="char"><p>0</p></td></tr><tr><td align="left"><p>Phonemes</p></td><td char="." align="char"><p>4.6</p></td><td char="." align="char"><p>0.6</p></td><td char="." align="char"><p>4.0</p></td><td char="." align="char"><p>6.0</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left"><p>Letters</p></td><td char="." align="char"><p>4.7</p></td><td char="." align="char"><p>0.7</p></td><td char="." align="char"><p>4.0</p></td><td char="." align="char"><p>6.0</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" rowspan="3"><p>Discrete Low-Short Words</p></td><td align="left"><p>Frequency</p></td><td char="." align="char"><p>3.3</p></td><td char="." align="char"><p>0.5</p></td><td char="." align="char"><p>1.0</p></td><td char="." align="char"><p>4.0</p></td><td align="left" /><td char="." align="char"><p>3</p></td><td char="." align="char"><p>3</p></td><td char="." align="char"><p>0</p></td><td char="." align="char"><p>15</p></td><td char="." align="char"><p>8</p></td><td char="." align="char"><p>4</p></td><td char="." align="char"><p>1</p></td><td char="." align="char"><p>2</p></td><td char="." align="char"><p>0</p></td></tr><tr><td align="left"><p>Phonemes</p></td><td char="." align="char"><p>4.6</p></td><td char="." align="char"><p>0.7</p></td><td char="." align="char"><p>4.0</p></td><td char="." align="char"><p>6.0</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left"><p>Letters</p></td><td char="." align="char"><p>4.7</p></td><td char="." align="char"><p>0.7</p></td><td char="." align="char"><p>4.0</p></td><td char="." align="char"><p>6.0</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" rowspan="3"><p>Serial High-Long Words</p></td><td align="left"><p>Frequency</p></td><td char="." align="char"><p>5.2</p></td><td char="." align="char"><p>0.2</p></td><td char="." align="char"><p>5.0</p></td><td char="." align="char"><p>5.6</p></td><td align="left" /><td char="." align="char"><p>6</p></td><td char="." align="char"><p>6</p></td><td char="." align="char"><p>0</p></td><td char="." align="char"><p>13</p></td><td char="." align="char"><p>6</p></td><td char="." align="char"><p>3</p></td><td char="." align="char"><p>0</p></td><td char="." align="char"><p>0</p></td><td char="." align="char"><p>1</p></td></tr><tr><td align="left"><p>Phonemes</p></td><td char="." align="char"><p>9.4</p></td><td char="." align="char"><p>1.2</p></td><td char="." align="char"><p>8.0</p></td><td char="." align="char"><p>12.0</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left"><p>Letters</p></td><td char="." align="char"><p>9.5</p></td><td char="." align="char"><p>1.1</p></td><td char="." align="char"><p>8.0</p></td><td char="." align="char"><p>12.0</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" rowspan="3"><p>Discrete High-Long Words</p></td><td align="left"><p>Frequency</p></td><td char="." align="char"><p>5.3</p></td><td char="." align="char"><p>0.2</p></td><td char="." align="char"><p>5.0</p></td><td char="." align="char"><p>5.6</p></td><td align="left" /><td char="." align="char"><p>7</p></td><td char="." align="char"><p>7</p></td><td char="." align="char"><p>1</p></td><td char="." align="char"><p>12</p></td><td char="." align="char"><p>6</p></td><td char="." align="char"><p>2</p></td><td char="." align="char"><p>0</p></td><td char="." align="char"><p>0</p></td><td char="." align="char"><p>0</p></td></tr><tr><td align="left"><p>Phonemes</p></td><td char="." align="char"><p>9.1</p></td><td char="." align="char"><p>1.0</p></td><td char="." align="char"><p>7.0</p></td><td char="." align="char"><p>12.0</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left"><p>Letters</p></td><td char="." align="char"><p>9.1</p></td><td char="." align="char"><p>1.0</p></td><td char="." align="char"><p>8.0</p></td><td char="." align="char"><p>12.0</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" rowspan="3"><p>Serial Low-Long Words</p></td><td align="left"><p>Frequency</p></td><td char="." align="char"><p>3.3</p></td><td char="." align="char"><p>0.5</p></td><td char="." align="char"><p>1.5</p></td><td char="." align="char"><p>4.0</p></td><td align="left" /><td char="." align="char"><p>7</p></td><td char="." align="char"><p>6</p></td><td char="." align="char"><p>0</p></td><td char="." align="char"><p>14</p></td><td char="." align="char"><p>7</p></td><td char="." align="char"><p>1</p></td><td char="." align="char"><p>0</p></td><td char="." align="char"><p>1</p></td><td char="." align="char"><p>0</p></td></tr><tr><td align="left"><p>Phonemes</p></td><td char="." align="char"><p>8.8</p></td><td char="." align="char"><p>0.9</p></td><td char="." align="char"><p>7.0</p></td><td char="." align="char"><p>11.0</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left"><p>Letters</p></td><td char="." align="char"><p>8.9</p></td><td char="." align="char"><p>1.0</p></td><td char="." align="char"><p>7.0</p></td><td char="." align="char"><p>11.0</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" rowspan="3"><p>Discrete Low-Long Words</p></td><td align="left"><p>Frequency</p></td><td char="." align="char"><p>3.2</p></td><td char="." align="char"><p>0.6</p></td><td char="." align="char"><p>1.3</p></td><td char="." align="char"><p>4.0</p></td><td align="left" /><td char="." align="char"><p>7</p></td><td char="." align="char"><p>6</p></td><td char="." align="char"><p>1</p></td><td char="." align="char"><p>14</p></td><td char="." align="char"><p>7</p></td><td char="." align="char"><p>1</p></td><td char="." align="char"><p>0</p></td><td char="." align="char"><p>0</p></td><td char="." align="char"><p>0</p></td></tr><tr><td align="left"><p>Phonemes</p></td><td char="." align="char"><p>8.7</p></td><td char="." align="char"><p>1.0</p></td><td char="." align="char"><p>7.0</p></td><td char="." align="char"><p>11.0</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left"><p>Letters</p></td><td char="." align="char"><p>8.8</p></td><td char="." align="char"><p>1.0</p></td><td char="." align="char"><p>7.0</p></td><td char="." align="char"><p>11.0</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /></tr></tbody></table> </ephtml> </p> <p>Note. V = Vowel; C = Consonant. Word frequencies are from the LEXESP database (Sebastián et al., [<reflink idref="bib51" id="ref127">51</reflink>]) and reported in the Zipf scale (van Heuven et al., [<reflink idref="bib59" id="ref128">59</reflink>])</p> <hd id="AN0190299323-14">Procedure</hd> <p>Children were individually tested by the first author or a trained research assistant. The research assistants were senior undergraduate students in psychology with experience in psychoeducational testing of children. All testers were native Spanish speakers. Testing took place in a quiet space in the children's school during school hours. Children sat in front of a computer where the tasks were displayed in random order using the DMDX software (Forster & Forster, [<reflink idref="bib25" id="ref129">25</reflink>]). The digits and words appeared on the computer screen in a black 18-point Consolas font with a white background. The four digits were presented nine times each to match the 36 items in the word sets. Both digits and words were presented in serial and discrete format.</p> <p>In the discrete tasks, the 36 items were named/read aloud one at a time. The tester presented the next item by using the right-click on the mouse, after the participant had provided a complete verbal response or after the time for naming/reading the item ran out. In the serial tasks, the items were displayed simultaneously in a 9 × 4 matrix. One verbal response was recorded for naming/reading the entire set of digits or words in serial presentation. Before the start of each naming/reading trial, children were given four practice items and were instructed to read/name the items as fast as possible without making any mistakes. All responses were audio recorded with DMDX. The DMDX experiment script is available at Open Science Framework (OSF) online repository (https://osf.io/pm3na/?view_only=15aeb22cdf29417685da6509d43797c8).</p> <hd id="AN0190299323-15">Data processing</hd> <p>Each child produced 185 audio recordings, comprising 180 discrete responses and 5 serial responses. To extract the response times, the audio files were processed with CheckVocal 3.0.2 (Protopapas, [<reflink idref="bib42" id="ref130">42</reflink>]). For each item presented in a discrete format, the response time included onset latency and articulation time. Once we obtained the individual response times, we then calculated the average of log-transformed response times of correctly read or named items for each discrete task. For serial tasks, the raw response time included the total time to name/read the whole set of words or digits. The errors in serial digit naming were ignored. The number of errors in serial reading were recorded in a separate spreadsheet and later used to adjust the serial reading rate for correctly read items. Finally, all response times were converted to a rate of items named/read per second. The data for our study and data processing and analyses scripts are available in the OSF online repository.</p> <hd id="AN0190299323-16">Statistical analysis</hd> <p>Statistical analysis was conducted in two parts: First, for the main analysis, we fit linear mixed-effects models separately by grade to measure the effects of format (discrete vs. serial), length (short vs. long), frequency (high vs. low), and serial and discrete digit naming. The baseline model predicted word reading rate using the fixed effect of format and the random effects for participants (random intercepts and random slopes for format). We gradually expanded the model structure by adding each factor and its interactions stepwise. First, we entered the effects of either frequency or length (both fixed and random effects) and examined whether they were modulated by format. We then added both frequency and length to the model simultaneously, first additively and then interacting. After establishing the baseline effects of the word-related factors, we assessed the extent to which these factors modulated the association between word reading and digit naming, by adding either discrete or serial digit rate (fixed term only, interacting with format, frequency, and length). Next, we examined both discrete and serial digit naming together in the full model to assess the extent to which each predicts word reading rate beyond the other. Finally, we fitted a model to all the data together, including both grade levels and all fixed (and random) factors to specifically probe which effects (and their interactions) significantly interacted with grade level. The analyses were conducted in R v.4.3.1 (R Core Team, [<reflink idref="bib46" id="ref131">46</reflink>]) using the lme4 package v.1.1–33 (Bates et al., [<reflink idref="bib9" id="ref132">9</reflink>]).</p> <p>The second part of the analyses was specifically modeled after analyses commonly performed in previous studies (e.g., Altani et al., [<reflink idref="bib2" id="ref133">2</reflink>], [<reflink idref="bib3" id="ref134">3</reflink>]; Georgiou et al., [<reflink idref="bib28" id="ref135">28</reflink>], 2023; Protopapas et al., [<reflink idref="bib43" id="ref136">43</reflink>]; Romero et al., [<reflink idref="bib49" id="ref137">49</reflink>]) to examine the unique contribution of serial naming to discrete and serial word reading. This was done for comparability with the existing literature. We performed several hierarchical regression analyses (a) to examine the predictive power of serial and discrete naming in the prediction of discrete word reading after controlling for the effect of the other, and (b) to examine the additional variance accounted for by serial naming in serial word reading after controlling for discrete word reading. To best match previous studies, these regression analyses were conducted separately by grade level and word category. Thus, unlike our main analyses outlined above, the individual-regressions approach does not allow us to test whether qualitatively observed patterns of differences in proportions of variance accounted for actually correspond to statistically supported differences between grades or word groups.</p> <hd id="AN0190299323-17">Results</hd> <p></p> <hd id="AN0190299323-18">Data cleaning and preliminary analysis</hd> <p>We excluded six complete cases in Grade 2 due to technical issues with the sound quality of the recordings. To assess accuracy, words were marked as incorrect if they were decoded incorrectly, sounded out but not blended, or skipped/not read. Overall accuracy was high across tasks, ranging from 93 to 99%. However, individual task scores with accuracy below 70% were omitted from the analyses. The decision to establish a minimum accuracy threshold was based on previous studies suggesting that reading speed develops once accuracy levels approach 70% (e.g., Altani et al., [<reflink idref="bib3" id="ref138">3</reflink>]; Juul et al., [<reflink idref="bib33" id="ref139">33</reflink>]; Karageorgos et al., [<reflink idref="bib34" id="ref140">34</reflink>]). Consequently, six individual scores from the discrete data were excluded due to low accuracy (one from High-Long words, one from High-Short words, two from Low-Long words, and two from Low-Short words) and two from the serial scores (one from High-Short words and one from Low-Short words). Additionally, 15 data points were missing from the discrete data (three from digits, three from Low-Short words, two from High-Short words, four from Low-Long words, and three from High-Long words) and 26 from serial data (six from digits, four from Low-Short words, five from High-Short words, six from Low-Long words, and five from High-Long words). Almost all the missing data were from Grade 2.</p> <p>The descriptive statistics for the cleaned-up sample are displayed in Table 2. Most reading and naming variables approximated a normal distribution, as indicated by skewness and kurtosis values within or close to the acceptable ranges for normality, and by visual inspection of univariate Q-Q plots.</p> <p>Table 2 Descriptive statistics for all naming and reading variables</p> <p> <ephtml> <table rules="groups"><thead><tr><th align="left" /><th align="left" /><th align="left"><p><italic>N</italic></p></th><th align="left"><p>Mean</p></th><th align="left"><p><italic>SD</italic></p></th><th align="left"><p>Min.</p></th><th align="left"><p>Max.</p></th><th align="left"><p>Skew.</p></th><th align="left"><p>Kurtosis</p></th></tr></thead><tbody><tr><td align="left" colspan="9"><p><italic>Grade 2</italic></p></td></tr><tr><td align="left" /><td align="left"><p>d_Digits</p></td><td align="left"><p>83</p></td><td align="left"><p>0.93</p></td><td align="left"><p>0.14</p></td><td align="left"><p>0.63</p></td><td align="left"><p>1.44</p></td><td align="left"><p>0.55</p></td><td align="left"><p>1.18</p></td></tr><tr><td align="left" /><td align="left"><p>d_High-Short</p></td><td align="left"><p>83</p></td><td align="left"><p>0.69</p></td><td align="left"><p>0.20</p></td><td align="left"><p>0.21</p></td><td align="left"><p>1.08</p></td><td align="left"><p>−0.32</p></td><td align="left"><p>−0.55</p></td></tr><tr><td align="left" /><td align="left"><p>d_Low-Short</p></td><td align="left"><p>82</p></td><td align="left"><p>0.56</p></td><td align="left"><p>0.17</p></td><td align="left"><p>0.16</p></td><td align="left"><p>0.93</p></td><td align="left"><p>−0.12</p></td><td align="left"><p>−0.73</p></td></tr><tr><td align="left" /><td align="left"><p>d_High-Long</p></td><td align="left"><p>81</p></td><td align="left"><p>0.41</p></td><td align="left"><p>0.15</p></td><td align="left"><p>0.11</p></td><td align="left"><p>0.72</p></td><td align="left"><p>0.11</p></td><td align="left"><p>−0.69</p></td></tr><tr><td align="left" /><td align="left"><p>d_Low-Long</p></td><td align="left"><p>80</p></td><td align="left"><p>0.32</p></td><td align="left"><p>0.11</p></td><td align="left"><p>0.10</p></td><td align="left"><p>0.61</p></td><td align="left"><p>0.13</p></td><td align="left"><p>−0.18</p></td></tr><tr><td align="left" /><td align="left"><p>s_Digits</p></td><td align="left"><p>80</p></td><td align="left"><p>1.41</p></td><td align="left"><p>0.30</p></td><td align="left"><p>0.67</p></td><td align="left"><p>2.00</p></td><td align="left"><p>0.03</p></td><td align="left"><p>−0.47</p></td></tr><tr><td align="left" /><td align="left"><p>s_High-Short</p></td><td align="left"><p>80</p></td><td align="left"><p>0.92</p></td><td align="left"><p>0.45</p></td><td align="left"><p>0.09</p></td><td align="left"><p>1.78</p></td><td align="left"><p>0.13</p></td><td align="left"><p>−1.02</p></td></tr><tr><td align="left" /><td align="left"><p>s_Low-Short</p></td><td align="left"><p>81</p></td><td align="left"><p>0.58</p></td><td align="left"><p>0.24</p></td><td align="left"><p>0.12</p></td><td align="left"><p>1.08</p></td><td align="left"><p>0.14</p></td><td align="left"><p>−0.95</p></td></tr><tr><td align="left" /><td align="left"><p>s_High-Long</p></td><td align="left"><p>81</p></td><td align="left"><p>0.46</p></td><td align="left"><p>0.25</p></td><td align="left"><p>0.06</p></td><td align="left"><p>1.07</p></td><td align="left"><p>0.63</p></td><td align="left"><p>−0.45</p></td></tr><tr><td align="left" /><td align="left"><p>s_Low-Long</p></td><td align="left"><p>81</p></td><td align="left"><p>0.32</p></td><td align="left"><p>0.14</p></td><td align="left"><p>0.08</p></td><td align="left"><p>0.73</p></td><td align="left"><p>0.49</p></td><td align="left"><p>−0.19</p></td></tr><tr><td align="left" colspan="9"><p><italic>Grade 5</italic></p></td></tr><tr><td align="left" /><td align="left"><p>d_Digits</p></td><td align="left"><p>109</p></td><td align="left"><p>1.13</p></td><td align="left"><p>0.17</p></td><td align="left"><p>0.68</p></td><td align="left"><p>1.51</p></td><td align="left"><p>−0.15</p></td><td align="left"><p>−0.21</p></td></tr><tr><td align="left" /><td align="left"><p>d_High-Short</p></td><td align="left"><p>109</p></td><td align="left"><p>1.03</p></td><td align="left"><p>0.16</p></td><td align="left"><p>0.57</p></td><td align="left"><p>1.42</p></td><td align="left"><p>0.05</p></td><td align="left"><p>−0.06</p></td></tr><tr><td align="left" /><td align="left"><p>d_Low-Short</p></td><td align="left"><p>109</p></td><td align="left"><p>0.88</p></td><td align="left"><p>0.16</p></td><td align="left"><p>0.53</p></td><td align="left"><p>1.27</p></td><td align="left"><p>−0.13</p></td><td align="left"><p>−0.50</p></td></tr><tr><td align="left" /><td align="left"><p>d_High-Long</p></td><td align="left"><p>109</p></td><td align="left"><p>0.74</p></td><td align="left"><p>0.15</p></td><td align="left"><p>0.41</p></td><td align="left"><p>1.07</p></td><td align="left"><p>−0.17</p></td><td align="left"><p>−0.41</p></td></tr><tr><td align="left" /><td align="left"><p>d_Low-Long</p></td><td align="left"><p>109</p></td><td align="left"><p>0.58</p></td><td align="left"><p>0.14</p></td><td align="left"><p>0.27</p></td><td align="left"><p>0.88</p></td><td align="left"><p>−0.17</p></td><td align="left"><p>−0.72</p></td></tr><tr><td align="left" /><td align="left"><p>s_Digits</p></td><td align="left"><p>109</p></td><td align="left"><p>1.98</p></td><td align="left"><p>0.39</p></td><td align="left"><p>0.81</p></td><td align="left"><p>2.79</p></td><td align="left"><p>−0.44</p></td><td align="left"><p>0.39</p></td></tr><tr><td align="left" /><td align="left"><p>s_High-Short</p></td><td align="left"><p>109</p></td><td align="left"><p>1.69</p></td><td align="left"><p>0.45</p></td><td align="left"><p>0.78</p></td><td align="left"><p>2.68</p></td><td align="left"><p>−0.06</p></td><td align="left"><p>−0.78</p></td></tr><tr><td align="left" /><td align="left"><p>s_Low-Short</p></td><td align="left"><p>109</p></td><td align="left"><p>1.07</p></td><td align="left"><p>0.34</p></td><td align="left"><p>0.37</p></td><td align="left"><p>1.85</p></td><td align="left"><p>0.20</p></td><td align="left"><p>−0.63</p></td></tr><tr><td align="left" /><td align="left"><p>s_High-Long</p></td><td align="left"><p>109</p></td><td align="left"><p>1.12</p></td><td align="left"><p>0.37</p></td><td align="left"><p>0.35</p></td><td align="left"><p>1.96</p></td><td align="left"><p>0.10</p></td><td align="left"><p>−0.64</p></td></tr><tr><td align="left" /><td align="left"><p>s_Low-Long</p></td><td align="left"><p>108</p></td><td align="left"><p>0.69</p></td><td align="left"><p>0.24</p></td><td align="left"><p>0.20</p></td><td align="left"><p>1.42</p></td><td align="left"><p>0.44</p></td><td align="left"><p>0.09</p></td></tr></tbody></table> </ephtml> </p> <p>Note. d = discrete; s = serial</p> <p>Post-hoc pairwise comparisons within a mixed-effects model of response rate by grade, task content, and task format (with Bonferroni adjustment) showed that Grade 5 students outperformed Grade 2 students (all <emph>p</emph> s < 0.001) in all the discrete (digits, <emph>β</emph> = 0.198, <emph>SE</emph> = 0.03; High-Short, <emph>β =</emph> 0.344, <emph>SE</emph> = 0.04; Low-Short, <emph>β =</emph> 0.328, <emph>SE =</emph> 0.03; High-Long, <emph>β =</emph> 0.334, <emph>SE</emph> = 0.03; Low-Long, <emph>β</emph> = 0.260, <emph>SE</emph> = 0.02) and serial (digits, <emph>β =</emph> 0.573, <emph>SE</emph> = 0.04; High-Short, <emph>β =</emph> 0.777, <emph>SE</emph> = 0.06; Low-Short, <emph>β =</emph> 0.489, <emph>SE =</emph> 0.05; High-Long, <emph>β =</emph> 0.658, <emph>SE</emph> = 0.05; Low-Long, <emph>β =</emph> 0.376, <emph>SE</emph> = 0.04) measures.</p> <p>Serial versus discrete comparisons within grade levels showed significantly higher (all <emph>p</emph> s < 0.001) naming/reading rates in the serial version of all tasks in Grade 5 (digits, <emph>β =</emph> 0.855, <emph>SE</emph> = 0.02; High-Short, <emph>β =</emph> 0.662, <emph>SE =</emph> 0.02; Low-Short, <emph>β =</emph> 0.184, <emph>SE</emph> = 0.02; High-Long, <emph>β =</emph> 0.373, <emph>SE</emph> = 0.02; Low-Long, <emph>β =</emph> 0.113, <emph>SE</emph> = 0.02). However, in Grade 2, significant differences (all <emph>p</emph> s < 0.001) between serial and discrete tasks were found only for digits (<emph>β =</emph> 0.480, <emph>SE</emph> = 0.03) and High-Short words (<emph>β =</emph> 0.230, <emph>SE</emph> = 0.03).</p> <hd id="AN0190299323-19">Correlations between all variables across grades</hd> <p>Table 3 displays the correlation coefficients among all variables, separately for each grade level. All reading tasks were strongly correlated with one another, irrespective of presentation format, in both Grade 2 (<emph>r</emph>s > 0.78–0.93) and Grade 5 (<emph>r</emph>s = 0.63–0.90). Additionally, serial and discrete digit naming showed a moderate correlation across grade levels (Grade 2: <emph>r</emph> =.44; Grade 5: <emph>r</emph> =.47). When examining the relation of discrete naming with reading in Grade 2, the results showed a weak to moderate association between discrete digit naming and discrete reading of High-Short, Low-Short, and High-Long words (<emph>r</emph>s = 0.29–0.38). However, the correlation coefficient between discrete digit naming and discrete reading of Low-Long words and serial reading of all word categories was not significant in this grade. In contrast, the correlation between discrete naming and reading was significant across all types of words and presentation formats in Grade 5 (<emph>r</emph>s = 0.28–0.76). Finally, concerning the relation between serial naming and reading, serial digit naming was moderately correlated with all discrete and serial reading variables in both Grade 2 (<emph>r</emph>s = 0.33–0.46) and Grade 5 (<emph>r</emph>s = 0.41–0.74).</p> <p>Table 3 Correlation coefficients (Pearson´s <emph>r</emph>) across naming and reading tasks for each grade level</p> <p> <ephtml> <table rules="groups"><thead><tr><th align="left" /><th align="left"><p>1.</p></th><th align="left"><p>2.</p></th><th align="left"><p>3.</p></th><th align="left"><p>4.</p></th><th align="left"><p>5.</p></th><th align="left"><p>6.</p></th><th align="left"><p>7.</p></th><th align="left"><p>8.</p></th><th align="left"><p>9.</p></th><th align="left"><p>10.</p></th></tr></thead><tbody><tr><td align="left"><p>1. d_Digits</p></td><td align="left"><p>–</p></td><td align="left"><p>0.61***</p></td><td align="left"><p>0.76***</p></td><td align="left"><p>0.42***</p></td><td align="left"><p>0.62***</p></td><td align="left"><p>0.47***</p></td><td align="left"><p>0.37***</p></td><td align="left"><p>0.48***</p></td><td align="left"><p>0.28**</p></td><td align="left"><p>0.44***</p></td></tr><tr><td align="left"><p>2. d_Low-Short</p></td><td align="left"><p>0.29**</p></td><td align="left"><p>–</p></td><td align="left"><p>0.82***</p></td><td align="left"><p>0.88***</p></td><td align="left"><p>0.90***</p></td><td align="left"><p>0.50***</p></td><td align="left"><p>0.77***</p></td><td align="left"><p>0.75***</p></td><td align="left"><p>0.75***</p></td><td align="left"><p>0.76**</p></td></tr><tr><td align="left"><p>3. d_High-Short</p></td><td align="left"><p>0.38***</p></td><td align="left"><p>0.88***</p></td><td align="left"><p>–</p></td><td align="left"><p>0.69***</p></td><td align="left"><p>0.85**</p></td><td align="left"><p>0.49***</p></td><td align="left"><p>0.63***</p></td><td align="left"><p>0.68***</p></td><td align="left"><p>0.58***</p></td><td align="left"><p>0.70***</p></td></tr><tr><td align="left"><p>4. d_Low-Long</p></td><td align="left"><p>0.22</p></td><td align="left"><p>0.90***</p></td><td align="left"><p>0.84***</p></td><td align="left"><p>–</p></td><td align="left"><p>0.86***</p></td><td align="left"><p>0.41***</p></td><td align="left"><p>0.80***</p></td><td align="left"><p>0.69***</p></td><td align="left"><p>0.83***</p></td><td align="left"><p>0.77***</p></td></tr><tr><td align="left"><p>5. d_High-Long</p></td><td align="left"><p>0.29*</p></td><td align="left"><p>0.91***</p></td><td align="left"><p>0.92***</p></td><td align="left"><p>0.92***</p></td><td align="left"><p>–</p></td><td align="left"><p>0.46***</p></td><td align="left"><p>0.73***</p></td><td align="left"><p>0.70***</p></td><td align="left"><p>0.70***</p></td><td align="left"><p>0.77***</p></td></tr><tr><td align="left"><p>6. s_Digits</p></td><td align="left"><p>0.44***</p></td><td align="left"><p>0.33**</p></td><td align="left"><p>0.46***</p></td><td align="left"><p>0.35**</p></td><td align="left"><p>0.41***</p></td><td align="left"><p>–</p></td><td align="left"><p>0.55***</p></td><td align="left"><p>0.74***</p></td><td align="left"><p>0.49***</p></td><td align="left"><p>0.61***</p></td></tr><tr><td align="left"><p>7. s_Low-Short</p></td><td align="left"><p>0.22</p></td><td align="left"><p>0.85***</p></td><td align="left"><p>0.85***</p></td><td align="left"><p>0.87***</p></td><td align="left"><p>0.87***</p></td><td align="left"><p>0.45***</p></td><td align="left"><p>–</p></td><td align="left"><p>0.84***</p></td><td align="left"><p>0.87***</p></td><td align="left"><p>0.85***</p></td></tr><tr><td align="left"><p>8. s_High-Short</p></td><td align="left"><p>0.20</p></td><td align="left"><p>0.84***</p></td><td align="left"><p>0.90***</p></td><td align="left"><p>0.85***</p></td><td align="left"><p>0.92***</p></td><td align="left"><p>0.46***</p></td><td align="left"><p>0.90***</p></td><td align="left"><p>–</p></td><td align="left"><p>0.76***</p></td><td align="left"><p>0.85***</p></td></tr><tr><td align="left"><p>9. s_Low-Long</p></td><td align="left"><p>0.17</p></td><td align="left"><p>0.85***</p></td><td align="left"><p>0.78***</p></td><td align="left"><p>0.93***</p></td><td align="left"><p>0.89***</p></td><td align="left"><p>0.43***</p></td><td align="left"><p>0.87***</p></td><td align="left"><p>0.84***</p></td><td align="left"><p>–</p></td><td align="left"><p>0.85***</p></td></tr><tr><td align="left"><p>10. s_High-Long</p></td><td align="left"><p>0.20</p></td><td align="left"><p>0.82***</p></td><td align="left"><p>0.84***</p></td><td align="left"><p>0.87***</p></td><td align="left"><p>0.90***</p></td><td align="left"><p>0.42***</p></td><td align="left"><p>0.89***</p></td><td align="left"><p>0.89***</p></td><td align="left"><p>0.90***</p></td><td align="left"><p>–</p></td></tr></tbody></table> </ephtml> </p> <p>Note. Correlation coefficients above the diagonal correspond to Grade 5 participants. s = serial; d = discrete *<emph>p</emph> <.05, **<emph>p</emph> <.01, ***<emph>p</emph> <.001</p> <hd id="AN0190299323-20">Factors affecting reading rate</hd> <p>As noted above, to examine factors affecting reading rate and their interactions, individual variables, as well their combinations and interactions, were entered in successive linear mixed-effects models, starting with format, followed by frequency or length, then both and their interaction, followed by serial and discrete digit naming individually and finally together. Two-level factors (grade, format, length, and frequency) were difference-coded (− 0.5, + 0.5); grade-specific variables for discrete and serial digit naming were centered.</p> <p>All successive additions to the model were statistically significant (<emph>p</emph>s < 0.01). Proportions of variance accounted for were based on the marginal coefficient of determination for generalized mixed-effects models calculated using function r.squaredGLMM in library MuMIn v.1.47.5 (Bartón, [<reflink idref="bib8" id="ref141">8</reflink>]). Model statistics, fit indices, and the total and additional proportional variance accounted for by each model are displayed in Table 4.</p> <p>Table 4 Results of linear mixed effects models for word reading rate by format, frequency, length, and serial and discrete digit naming</p> <p> <ephtml> <table rules="groups"><thead><tr><th align="left" /><th align="left" /><th align="left" colspan="5"><p>Grade 2</p></th><th align="left" colspan="4"><p>Grade 5</p></th></tr><tr><th align="left" /><th align="left" /><th align="left" colspan="3"><p>Fixed</p></th><th align="left" colspan="2"><p>Random</p></th><th align="left" colspan="2"><p>Fixed</p></th><th align="left" colspan="2"><p>Random</p></th></tr><tr><th align="left"><p>Model</p></th><th align="left" /><th align="left" colspan="2"><p>Estimate</p></th><th align="left"><p><italic>SE</italic></p></th><th align="left"><p>Var.</p></th><th align="left"><p><italic>SD</italic></p></th><th align="left"><p>Estimate</p></th><th align="left"><p><italic>SE</italic></p></th><th align="left"><p>Var.</p></th><th align="left"><p><italic>SD</italic></p></th></tr></thead><tbody><tr><td align="left" /><td align="left"><p>(Intercept)</p></td><td align="left" colspan="2"><p>0.54***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.03</p></td><td align="left"><p>0.19</p></td><td align="left"><p>0.98***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.04</p></td><td align="left"><p>0.20</p></td></tr><tr><td align="left" /><td align="left"><p>Format</p></td><td align="left" colspan="2"><p>0.08***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.10</p></td><td align="left"><p>0.33***</p></td><td align="left"><p>0.03</p></td><td align="left"><p>0.03</p></td><td align="left"><p>0.18</p></td></tr><tr><td align="left" /><td align="left"><p>Marginal <italic>R</italic>²</p></td><td align="left" colspan="2"><p>0.016</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>0.155</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>AIC</p></td><td align="left" colspan="2"><p>95.1</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>688.8</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>BIC</p></td><td align="left" colspan="2"><p>122.3</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>717.4</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Log-likelihood</p></td><td align="left" colspan="2"><p>−41.8</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>−338.4</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" colspan="11"><p>2a</p></td></tr><tr><td align="left" /><td align="left"><p>(Intercept)</p></td><td align="left" colspan="2"><p>0.54***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.04</p></td><td align="left"><p>0.19</p></td><td align="left"><p>0.98***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.04</p></td><td align="left"><p>0.21</p></td></tr><tr><td align="left" /><td align="left"><p>Format</p></td><td align="left" colspan="2"><p>0.08***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.11</p></td><td align="left"><p>0.33***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.04</p></td><td align="left"><p>0.19</p></td></tr><tr><td align="left" /><td align="left"><p>Frequency</p></td><td align="left" colspan="2"><p>0.17***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.09</p></td><td align="left"><p>0.34***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.00</p></td><td align="left"><p>0.05</p></td></tr><tr><td align="left" /><td align="left"><p>Format × Frequency</p></td><td align="left" colspan="2"><p>0.13***</p></td><td align="left"><p>0.03</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.11</p></td><td align="left"><p>0.37***</p></td><td align="left"><p>0.04</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.12</p></td></tr><tr><td align="left" /><td align="left"><p>Marginal <italic>R</italic>²</p></td><td align="left" colspan="2"><p>0.112</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>0.360</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Δ<italic>R</italic>²</p></td><td align="left" colspan="2"><p>0.096</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>0.206</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>AIC</p></td><td align="left" colspan="2"><p>−44.4</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>290.8</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>BIC</p></td><td align="left" colspan="2"><p>22.3</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>362.3</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Log-likelihood</p></td><td align="left" colspan="2"><p>37.2</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>−130.4</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" colspan="11"><p>2b</p></td></tr><tr><td align="left" /><td align="left"><p>(Intercept)</p></td><td align="left" colspan="2"><p>0.53***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.04</p></td><td align="left"><p>0.19</p></td><td align="left"><p>0.98***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.04</p></td><td align="left"><p>0.21</p></td></tr><tr><td align="left" /><td align="left"><p>Format</p></td><td align="left" colspan="2"><p>0.08***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.11</p></td><td align="left"><p>0.33***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.04</p></td><td align="left"><p>0.19</p></td></tr><tr><td align="left" /><td align="left" colspan="2"><p>Length</p></td><td align="left"><p>−0.31***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.10</p></td><td align="left"><p>–0.38***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.00</p></td><td align="left"><p>0.05</p></td></tr><tr><td align="left" /><td align="left" colspan="2"><p>Format × Length</p></td><td align="left"><p>−0.10***</p></td><td align="left"><p>0.03</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.10</p></td><td align="left"><p>–0.18***</p></td><td align="left"><p>0.03</p></td><td align="left"><p>0.00</p></td><td align="left"><p>0.07</p></td></tr><tr><td align="left" /><td align="left"><p>Marginal <italic>R</italic>²</p></td><td align="left" colspan="2"><p>0.284</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>0.370</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Δ<italic>R</italic>²</p></td><td align="left" colspan="2"><p>0.267</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>0.216</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>AIC</p></td><td align="left" colspan="2"><p>−378.8</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>276.2</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>BIC</p></td><td align="left" colspan="2"><p>−312.0</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>347.8</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Log-likelihood</p></td><td align="left" colspan="2"><p>204.4</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>−–123.1</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" colspan="11"><p>3a</p></td></tr><tr><td align="left" /><td align="left"><p>(Intercept)</p></td><td align="left" colspan="2"><p>0.53***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.04</p></td><td align="left"><p>0.20</p></td><td align="left"><p>0.98***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.05</p></td><td align="left"><p>0.22</p></td></tr><tr><td align="left" /><td align="left"><p>Format</p></td><td align="left" colspan="2"><p>0.08***</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.12</p></td><td align="left"><p>0.33***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.05</p></td><td align="left"><p>0.21</p></td></tr><tr><td align="left" /><td align="left"><p>Length</p></td><td align="left" colspan="2"><p>−0.31***</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.11</p></td><td align="left"><p>–0.39***</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.08</p></td></tr><tr><td align="left" /><td align="left"><p>Frequency</p></td><td align="left" colspan="2"><p>0.18***</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.10</p></td><td align="left"><p>0.34***</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.10</p></td></tr><tr><td align="left" /><td align="left"><p>Format × Length</p></td><td align="left" colspan="2"><p>−0.10***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.11</p></td><td align="left"><p>–0.18***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.12</p></td></tr><tr><td align="left" /><td align="left"><p>Format × Frequency</p></td><td align="left" colspan="2"><p>0.13***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.12</p></td><td align="left"><p>0.37***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.03</p></td><td align="left"><p>0.16</p></td></tr><tr><td align="left" /><td align="left"><p>Marginal <italic>R</italic>²</p></td><td align="left" colspan="2"><p>0.382</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>0.578</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Δ<italic>R</italic>² (Length)</p></td><td align="left" colspan="2"><p>0.270</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>0.217</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Δ<italic>R</italic>² (Freq.)</p></td><td align="left" colspan="2"><p>0.099</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>0.207</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>AIC</p></td><td align="left" colspan="2"><p>−939.5</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>‒852.8</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>BIC</p></td><td align="left" colspan="2"><p>−815.0</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>‒719.3</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Log-likelihood</p></td><td align="left" colspan="2"><p>497.8</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>454.4</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" colspan="11"><p>3b</p></td></tr><tr><td align="left" /><td align="left"><p>(Intercept)</p></td><td align="left" colspan="2"><p>0.53***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.04</p></td><td align="left"><p>0.20</p></td><td align="left"><p>0.98***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.05</p></td><td align="left"><p>0.22</p></td></tr><tr><td align="left" /><td align="left"><p>Format</p></td><td align="left" colspan="2"><p>0.08***</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.12</p></td><td align="left"><p>0.33***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.05</p></td><td align="left"><p>0.22</p></td></tr><tr><td align="left" /><td align="left"><p>Length</p></td><td align="left" colspan="2"><p>−0.31***</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.11</p></td><td align="left"><p>–0.39***</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.09</p></td></tr><tr><td align="left" /><td align="left"><p>Frequency</p></td><td align="left" colspan="2"><p>0.18***</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.11</p></td><td align="left"><p>0.34***</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.10</p></td></tr><tr><td align="left" /><td align="left"><p>Format × Length</p></td><td align="left" colspan="2"><p>−0.11***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.12</p></td><td align="left"><p>–0.18***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.13</p></td></tr><tr><td align="left" /><td align="left"><p>Format × Frequency</p></td><td align="left" colspan="2"><p>0.13***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.13</p></td><td align="left"><p>0.37***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.03</p></td><td align="left"><p>0.16</p></td></tr><tr><td align="left" /><td align="left"><p>Length × Frequency</p></td><td align="left" colspan="2"><p>−0.12***</p></td><td align="left"><p>0.01</p></td><td align="left" /><td align="left" /><td align="left"><p>‒0.10***</p></td><td align="left"><p>0.01</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Format × Length× Freq.</p></td><td align="left" colspan="2"><p>−0.16***</p></td><td align="left"><p>0.02</p></td><td align="left" /><td align="left" /><td align="left"><p>‒0.22***</p></td><td align="left"><p>0.02</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Marginal <italic>R</italic>²</p></td><td align="left" colspan="2"><p>0.397</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>0.585</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Δ<italic>R</italic>²</p></td><td align="left" colspan="2"><p>0.015</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>0.072</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>AIC</p></td><td align="left" colspan="2"><p>−1104.2</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>‒1008.8</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>BIC</p></td><td align="left" colspan="2"><p>−970.8</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>‒865.7</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Log-likelihood</p></td><td align="left" colspan="2"><p>582.1</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>534.4</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" colspan="11"><p>4a</p></td></tr><tr><td align="left" /><td align="left"><p>(Intercept)</p></td><td align="left" colspan="2"><p>0.54***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.04</p></td><td align="left"><p>0.20</p></td><td align="left"><p>0.98***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.04</p></td><td align="left"><p>0.19</p></td></tr><tr><td align="left" /><td align="left"><p>Format</p></td><td align="left" colspan="2"><p>0.08***</p></td><td align="left"><p>0.14</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.12</p></td><td align="left"><p>0.33***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.04</p></td><td align="left"><p>0.21</p></td></tr><tr><td align="left" /><td align="left"><p>d_Digits</p></td><td align="left" colspan="2"><p>0.05*</p></td><td align="left"><p>0.02</p></td><td align="left" /><td align="left" /><td align="left"><p>0.12***</p></td><td align="left"><p>0.02</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Length</p></td><td align="left" colspan="2"><p>−0.31***</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.10</p></td><td align="left"><p>–0.39***</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.07</p></td></tr><tr><td align="left" /><td align="left"><p>Frequency</p></td><td align="left" colspan="2"><p>0.18***</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.10</p></td><td align="left"><p>0.34***</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.08</p></td></tr><tr><td align="left" /><td align="left"><p>Format × d_Digits</p></td><td align="left" colspan="2"><p>0.01</p></td><td align="left"><p>0.01</p></td><td align="left" /><td align="left" /><td align="left"><p>0.05*</p></td><td align="left"><p>0.02</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Format × Length</p></td><td align="left" colspan="2"><p>−0.11***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.12</p></td><td align="left"><p>–0.18***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.13</p></td></tr><tr><td align="left" /><td align="left"><p>d_Digits × Length</p></td><td align="left" colspan="2"><p>−0.03**</p></td><td align="left"><p>0.01</p></td><td align="left" /><td align="left" /><td align="left"><p>‒0.05***</p></td><td align="left"><p>0.01</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Format × Frequency</p></td><td align="left" colspan="2"><p>0.13***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.13</p></td><td align="left"><p>0.37***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.15</p></td></tr><tr><td align="left" /><td align="left"><p>d_Digits × Frequency</p></td><td align="left" colspan="2"><p>0.03*</p></td><td align="left"><p>0.01</p></td><td align="left" /><td align="left" /><td align="left"><p>0.06***</p></td><td align="left"><p>0.01</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Length × Frequency</p></td><td align="left" colspan="2"><p>−0.12***</p></td><td align="left"><p>0.01</p></td><td align="left" /><td align="left" /><td align="left"><p>‒0.10***</p></td><td align="left"><p>0.01</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Format × d_Digits × Length</p></td><td align="left" colspan="2"><p>−0.01</p></td><td align="left"><p>0.02</p></td><td align="left" /><td align="left" /><td align="left"><p>‒0.02</p></td><td align="left"><p>0.02</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Format × d_Digits × Freq.</p></td><td align="left" colspan="2"><p>0.00</p></td><td align="left"><p>0.02</p></td><td align="left" /><td align="left" /><td align="left"><p>0.06***</p></td><td align="left"><p>0.02</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Format × Length × Freq.</p></td><td align="left" colspan="2"><p>−0.15***</p></td><td align="left"><p>0.02</p></td><td align="left" /><td align="left" /><td align="left"><p>‒0.22***</p></td><td align="left"><p>0.02</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>d_Digits × Length× Freq.</p></td><td align="left" colspan="2"><p>−0.01</p></td><td align="left"><p>0.01</p></td><td align="left" /><td align="left" /><td align="left"><p>‒0.01</p></td><td align="left"><p>0.01</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Format × d_Digits × Length× Freq.</p></td><td align="left" colspan="2"><p>−0.01</p></td><td align="left"><p>0.02</p></td><td align="left" /><td align="left" /><td align="left"><p>0.00</p></td><td align="left"><p>0.02</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Marginal <italic>R</italic>²</p></td><td align="left" colspan="2"><p>0.431</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>0.674</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Δ<italic>R</italic>²</p></td><td align="left" colspan="2"><p>0.034</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>0.090</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>AIC</p></td><td align="left" colspan="2"><p>−1112.3</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>‒1099.4</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>BIC</p></td><td align="left" colspan="2"><p>−943.3</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>‒918.2</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Log-likelihood</p></td><td align="left" colspan="2"><p>594.1</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>587.7</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" colspan="11"><p>4b</p></td></tr><tr><td align="left" /><td align="left"><p>(Intercept)</p></td><td align="left" colspan="2"><p>0.53***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.03</p></td><td align="left"><p>0.18</p></td><td align="left"><p>0.98***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.03</p></td><td align="left"><p>0.17</p></td></tr><tr><td align="left" /><td align="left"><p>Format</p></td><td align="left" colspan="2"><p>0.08***</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.11</p></td><td align="left"><p>0.33***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.03</p></td><td align="left"><p>0.16</p></td></tr><tr><td align="left" /><td align="left"><p>s_Digits</p></td><td align="left" colspan="2"><p>0.09***</p></td><td align="left"><p>0.02</p></td><td align="left" /><td align="left" /><td align="left"><p>0.14***</p></td><td align="left"><p>0.02</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Length</p></td><td align="left" colspan="2"><p>−0.31***</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.10</p></td><td align="left"><p>–0.39***</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.00</p></td><td align="left"><p>0.07</p></td></tr><tr><td align="left" /><td align="left"><p>Freq.</p></td><td align="left" colspan="2"><p>0.18***</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.10</p></td><td align="left"><p>0.34***</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.08</p></td></tr><tr><td align="left" /><td align="left"><p>Format × s_Digits</p></td><td align="left" colspan="2"><p>0.06***</p></td><td align="left"><p>0.01</p></td><td align="left" /><td align="left" /><td align="left"><p>0.14***</p></td><td align="left"><p>0.02</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Format × Length</p></td><td align="left" colspan="2"><p>−0.11***</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.11</p></td><td align="left"><p>–0.18***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.11</p></td></tr><tr><td align="left" /><td align="left"><p>s_Digits× Length</p></td><td align="left" colspan="2"><p>−0.05***</p></td><td align="left"><p>0.01</p></td><td align="left" /><td align="left" /><td align="left"><p>‒0.05***</p></td><td align="left"><p>0.01</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Format× Freq.</p></td><td align="left" colspan="2"><p>0.13***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.12</p></td><td align="left"><p>0.37***</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.11</p></td></tr><tr><td align="left" /><td align="left"><p>s_Digits× Freq.</p></td><td align="left" colspan="2"><p>0.05***</p></td><td align="left"><p>0.01</p></td><td align="left" /><td align="left" /><td align="left"><p>0.06***</p></td><td align="left"><p>0.01</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Length × Freq</p></td><td align="left" colspan="2"><p>−0.12***</p></td><td align="left"><p>0.01</p></td><td align="left" /><td align="left" /><td align="left"><p>‒0.10***</p></td><td align="left"><p>0.01</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Format × s_Digits× Length</p></td><td align="left" colspan="2"><p>−0.05**</p></td><td align="left"><p>0.02</p></td><td align="left" /><td align="left" /><td align="left"><p>‒0.07***</p></td><td align="left"><p>0.02</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Format× s_Digits × Freq.</p></td><td align="left" colspan="2"><p>0.04*</p></td><td align="left"><p>0.02</p></td><td align="left" /><td align="left" /><td align="left"><p>0.12***</p></td><td align="left"><p>0.0</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Format × Length × Freq.</p></td><td align="left" colspan="2"><p>−0.15***</p></td><td align="left"><p>0.02</p></td><td align="left" /><td align="left" /><td align="left"><p>‒0.22***</p></td><td align="left"><p>0.02</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>s_Digits × Length × Freq.</p></td><td align="left" colspan="2"><p>−0.04***</p></td><td align="left"><p>0.01</p></td><td align="left" /><td align="left" /><td align="left"><p>‒0.01</p></td><td align="left"><p>0.01</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Format × d_Digits × Length× Freq.</p></td><td align="left" colspan="2"><p>−0.05*</p></td><td align="left"><p>0.02</p></td><td align="left" /><td align="left" /><td align="left"><p>0.05*</p></td><td align="left"><p>0.02</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Marginal <italic>R</italic>²</p></td><td align="left" colspan="2"><p>0.514</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>0.743</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Δ<italic>R</italic>²</p></td><td align="left" colspan="2"><p>0.117</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>0.158</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>AIC</p></td><td align="left" colspan="2"><p>−1132.9</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>‒1091.6</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>BIC</p></td><td align="left" colspan="2"><p>−963.9</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>‒910.3</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Log-likelihood</p></td><td align="left" colspan="2"><p>604.5</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>583.8</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" colspan="11"><p>5</p></td></tr><tr><td align="left" /><td align="left"><p>(Intercept)</p></td><td align="left" colspan="2"><p>0.53***</p></td><td align="left" /><td align="left"><p>0.03</p></td><td align="left"><p>0.18</p></td><td align="left"><p>0.98***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.03</p></td><td align="left"><p>0.16</p></td></tr><tr><td align="left" /><td align="left"><p>Format</p></td><td align="left" colspan="2"><p>0.08***</p></td><td align="left" /><td align="left"><p>0.01</p></td><td align="left"><p>0.11</p></td><td align="left"><p>0.33***</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.03</p></td><td align="left"><p>0.16</p></td></tr><tr><td align="left" /><td align="left"><p>d_Digits</p></td><td align="left" colspan="2"><p>0.01</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>0.07***</p></td><td align="left"><p>0.02</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>s_Digits</p></td><td align="left" colspan="2"><p>0.08***</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>0.11***</p></td><td align="left"><p>0.02</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Length</p></td><td align="left" colspan="2"><p>−0.31***</p></td><td align="left" /><td align="left"><p>0.01</p></td><td align="left"><p>0.10</p></td><td align="left"><p>−0.39***</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.00</p></td><td align="left"><p>0.06</p></td></tr><tr><td align="left" /><td align="left"><p>Freq.</p></td><td align="left" colspan="2"><p>0.18***</p></td><td align="left" /><td align="left"><p>0.01</p></td><td align="left"><p>0.10</p></td><td align="left"><p>0.34***</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.00</p></td><td align="left"><p>0.07</p></td></tr><tr><td align="left" /><td align="left"><p>Format × d_Digits</p></td><td align="left" colspan="2"><p>−0.02</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>−0.02</p></td><td align="left"><p>0.02</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Format × s_Digits</p></td><td align="left" colspan="2"><p>0.07***</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>0.15***</p></td><td align="left"><p>0.02</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Format × Length</p></td><td align="left" colspan="2"><p>−0.10***</p></td><td align="left" /><td align="left"><p>0.01</p></td><td align="left"><p>0.11</p></td><td align="left"><p>−0.18***</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.11</p></td></tr><tr><td align="left" /><td align="left"><p>d_Digits× Length</p></td><td align="left" colspan="2"><p>−0.01</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>−0.03**</p></td><td align="left"><p>0.01</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>s_Digits × Length</p></td><td align="left" colspan="2"><p>−0.04**</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>−0.04***</p></td><td align="left"><p>0.01</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Format × Frequency</p></td><td align="left" colspan="2"><p>0.13***</p></td><td align="left" /><td align="left"><p>0.01</p></td><td align="left"><p>0.12</p></td><td align="left"><p>0.37***</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.11</p></td></tr><tr><td align="left" /><td align="left"><p>d_Digits× Frequency</p></td><td align="left" colspan="2"><p>0.01</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>0.04***</p></td><td align="left"><p>0.01</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>s_Digits × Frequency</p></td><td align="left" colspan="2"><p>0.05***</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>0.05***</p></td><td align="left"><p>0.01</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Length × Frequency</p></td><td align="left" colspan="2"><p>−0.12**</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>−0.10***</p></td><td align="left"><p>0.01</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Format × d_Digits × Length</p></td><td align="left" colspan="2"><p>0.02</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>0.02</p></td><td align="left"><p>0.02</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Format× s_Digits × Length</p></td><td align="left" colspan="2"><p>−0.06***</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>−0.08***</p></td><td align="left"><p>0.02</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Format × d_Digits× Freq.</p></td><td align="left" colspan="2"><p>−0.02</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>0.01</p></td><td align="left"><p>0.02</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Format × s_Digits× Freq.</p></td><td align="left" colspan="2"><p>0.05**</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>0.11**</p></td><td align="left"><p>0.02</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Format× Length× Freq.</p></td><td align="left" colspan="2"><p>−0.16***</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>−0.22</p></td><td align="left"><p>0.02</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>d_Digits × Length× Freq.</p></td><td align="left" colspan="2"><p>0.01</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>0.02</p></td><td align="left"><p>0.01</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>s_Digits × Length × Freq.</p></td><td align="left" colspan="2"><p>−0.04***</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>−0.02</p></td><td align="left"><p>0.01</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Format× d_Digits × Length × Freq.</p></td><td align="left" colspan="2"><p>−0.01</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>0.03</p></td><td align="left"><p>0.02</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Format× s_Digits × Length × Freq.</p></td><td align="left" colspan="2"><p>−0.05*</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>−0.07**</p></td><td align="left"><p>0.02</p></td><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Marginal <italic>R</italic>²</p></td><td align="left" colspan="2"><p>0.518</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>0.765</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Δ<italic>R</italic>² (s_digits)</p></td><td align="left" colspan="2"><p>0.087</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>0.090</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Δ<italic>R</italic>² (d_digits)</p></td><td align="left" colspan="2"><p>0.004</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>0.022</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>AIC</p></td><td align="left" colspan="2"><p>−1137.9</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>−1165.6</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>BIC</p></td><td align="left" colspan="2"><p>−933.4</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>−946.2</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left" /><td align="left"><p>Log-likelihood</p></td><td align="left" colspan="2"><p>615.0</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>628.8</p></td><td align="left" /><td align="left" /><td align="left" /></tr></tbody></table> </ephtml> </p> <p>Note. Unstandardized coefficients are presented separately by grade level. The total marginal <emph>R</emph>² for each model and the additional variance (Δ<emph>R</emph>²) accounted for by individual steps are included. d = discrete; s = serial. *<emph>p</emph> <.05, **<emph>p</emph> <.01, ***<emph>p</emph> <.001</p> <hd id="AN0190299323-21">Serial versus discrete presentation format (model 1)</hd> <p>Word presentation format (serial vs. discrete) had a highly significant effect in both Grade 2 and Grade 5. The magnitude of the effect was vastly different across grades: Format accounted for 1.6% of word reading rate variance among second graders and 15% among fifth graders.</p> <hd id="AN0190299323-22">Frequency (Model 2a) and length (model 2b)</hd> <p>In both grades, frequency and length (entered separately) had large and significant effects on word reading rate and significantly interacted with format. In Grade 2, length (including its interaction with format) accounted for a much larger proportion of variance than frequency (including its interaction with format) (28% vs. 11%). In Grade 5, length and frequency accounted for similar proportions of variance (36% vs. 37%).</p> <hd id="AN0190299323-23">Frequency and length (together, model 3a and 3b)</hd> <p>We added frequency and length to the model simultaneously, first additively (Model 3a) and then interacting (Model 3b). We also examined whether the interaction between frequency and length was moderated by format. All effects and interactions were highly significant, indicating that the effects of frequency and length, as well as their interaction, were moderated by presentation format (see Fig. 1). Specifically, the difference between serial and discrete word reading was more pronounced for High-Short words in both grade levels. In Grade 2, model comparison revealed that length accounted for an additional 27% of the variance in reading rate beyond frequency, while frequency accounted for an additional 10% beyond length. Their interaction accounted for a further 1.5% of the variance beyond their additive effects. In Grade 5, length accounted for an additional 21% of the variance in reading rate beyond frequency, whereas frequency accounted for an additional 20% beyond length. Their interaction accounted for only 0.7% of the variance beyond their additive effects.</p> <p>Graph: Fig. 1 Reading rate modulated by grade, format, length, and frequency. Note. All panels are set to a common scale corresponding to model-estimated reading rates (words per second) in the observed ranges. HF = High-Frequency; LF = Low-Frequency</p> <hd id="AN0190299323-24">Discrete digit naming (model 4a)</hd> <p>In Grade 2, discrete digit naming had a significant effect and accounted for an additional 3% of the variance in word reading rate beyond the effects of format, frequency, and length. The relation between discrete digit naming and word reading rate was significantly modulated by frequency and length but not by format. Figure 2 illustrates the association between discrete digit naming and word reading rate, with the highest slopes for High-Short words and the lowest for Low-Long words across discrete and serial word reading. In Grade 5, discrete digit naming was also significantly associated with word reading rate and accounted for an additional 9% of the variance. Discrete digit naming showed significant interactions with frequency and length. In contrast to Grade 2, in Grade 5, discrete digit naming interacted with format and with the interaction of format with frequency, but not with length. This indicated that the association between discrete digit naming and word reading in Grade 5 differed between the serial and discrete word reading formats, with variations between low- and high-frequency words but not between short and long words. Figure 2 (bottom left) illustrates these differences. Overall, the slopes of the lines for discrete word reading (blue lines) were greater than for serial word reading (red lines), consistent with format-specific associations. The slope differences were greater for low-frequency words than for high-frequency words. The slopes were smallest for Low-Long words and largest for High-Short words, consistent with discrete digit naming being associated with single-word reading efficiency.</p> <p>Graph: Fig. 2 Modeled associations between serial/discrete word reading and serial and discrete digit naming, modulated by length and frequency. Note. All panels are set to a common scale for both axes, corresponding to model-estimated reading/naming rates (words/digits per second) in the observed ranges. HF = High-Frequency; LF = Low-Frequency</p> <hd id="AN0190299323-25">Serial digit naming (model 4b)</hd> <p>In both Grade 2 and Grade 5, serial digit naming had a significant effect and, unlike discrete digit naming, almost all interactions with serial digit naming were significant, including the four-way interaction with format, frequency, and length. This indicates that the association between serial digit naming and word reading, and its modulation by word frequency and length, varied significantly between the serial and discrete word reading formats. As displayed in Fig. 2, serial digit naming was most strongly associated with the reading rate of High-Short words and least associated with reading Low-Long words. Additionally, these associations were stronger for serial word reading than for discrete word reading (evidenced by the greater slopes of the red than the blue lines). Adding serial digit naming to the model accounted for an additional 12% of the variance in word reading rate in Grade 2 and 16% in Grade 5.</p> <hd id="AN0190299323-26">Serial and discrete digits together (model 5)</hd> <p>We examined both discrete and serial digit naming together in the full model to assess the extent to which each predicts word reading rate beyond the other. In Grade 2, none of the contrasts involving discrete digit naming—whether simple effects or interactions—were significant, whereas serial digit naming and all its interactions remained significant. Model comparison indicated that adding discrete digit naming to the model that already included serial digit naming contributed a very small proportion of additional variance (0.3%) in word reading rate. In contrast, adding serial digit naming after discrete digit naming accounted for an additional 9%.</p> <p>In Grade 5, there was a significant effect of discrete digit naming and its interactions with frequency and length. Serial digit naming and almost all its interactions were highly significant. The addition of discrete digit naming to the model contributed a significant additional 2% of variance in reading rate beyond the effects of serial digit naming, format, frequency, and length. In comparison, adding serial digit naming after discrete digit naming accounted for a significant additional 9% of variance in word reading rate.</p> <hd id="AN0190299323-27">Model including all data (grades 2 and 5 together)</hd> <p>So far, we have qualitatively commented on differences between Grades 2 and 5 based on different patterns of findings in the grade-specific models. To find out which differences between grades are statistically supported, we fit a series of models with data from both grades toward a final model with all the data and all predictors and their interactions. There were significant interactions between grade and format (<emph>β</emph> = 0.26, <emph>SE</emph> = 0.04, <emph>p</emph> <.001), frequency (<emph>β</emph> = 0.16, <emph>SE</emph> = 0.02, <emph>p</emph> <.001), and length (<emph>β</emph> = −0.08, <emph>SE</emph> = 0.02, <emph>p</emph> <.001). Although the three-way interaction between grade, frequency, and length did not reach significance (<emph>β</emph> = 0.03, <emph>SE</emph> = 0.02, <emph>p</emph> =.091), the four-way interaction, including format, was statistically significant (<emph>β</emph> = −0.06, <emph>SE</emph> = 0.03, <emph>p</emph> =.032). As shown in Fig. 1 the interaction between frequency and length was substantial only for serial words, and greater in Grade 5. The complete model output can be found in Sect. 2.6 of the R Markdown file, available at the OSF repository: https://osf.io/pm3na/?view_only=15aeb22cdf29417685da6509d43797c8.</p> <p>In the final model including digit naming, there were no significant interactions involving discrete digits and grade, indicating that the association with discrete digits was not differentially modulated by format, frequency, or length between the two grades. However, there was a significant three-way interaction between grade, format, and serial digit naming (<emph>β =</emph> 0.17, <emph>SE</emph> = 0.08, <emph>p</emph> =.025). This confirms that the differential association of serial digit naming with word reading in the two formats varies across grades. Specifically, serial digit naming is more predictive of serial than discrete word reading, and this differential association is greater in Grade 5 than in Grade 2.</p> <hd id="AN0190299323-28">Discrete and serial digit naming as predictors of discrete word reading</hd> <p>We conducted hierarchical regression analyses using discrete word reading of each word type as the outcome variable, with serial and discrete digit naming as the predictor variables. Table 5 illustrates the proportion of variance accounted for by serial and discrete naming when entered at either Step 1 or Step 2 of the analysis.</p> <p>Table 5 R² changes in discrete and serial digits entered at step 1 or step 2 to predict discrete word reading</p> <p> <ephtml> <table rules="groups"><thead><tr><th align="left" rowspan="2"><p>Predictors</p></th><th align="left" colspan="2"><p>High-Short</p></th><th align="left" colspan="2"><p>Low-Short</p></th><th align="left" colspan="2"><p>High-Long</p></th><th align="left" colspan="2"><p>Low-Long</p></th></tr><tr><th align="left"><p>Grade 2</p></th><th align="left"><p>Grade 5</p></th><th align="left"><p>Grade 2</p></th><th align="left"><p>Grade 5</p></th><th align="left"><p>Grade 2</p></th><th align="left"><p>Grade 5</p></th><th align="left"><p>Grade 2</p></th><th align="left"><p>Grade 5</p></th></tr></thead><tbody><tr><td align="left"><p>1. Discrete digits</p></td><td align="left"><p>0.15***</p></td><td align="left"><p><bold>0.58***</bold></p></td><td align="left"><p>0.09*</p></td><td align="left"><p><bold>0.37***</bold></p></td><td align="left"><p>0.08*</p></td><td align="left"><p><bold>0.39***</bold></p></td><td align="left"><p>0.05</p></td><td align="left"><p>.<bold>18</bold>***</p></td></tr><tr><td align="left"><p>2. Serial digits</p></td><td align="left"><p>0.11**</p></td><td align="left"><p>0.02*</p></td><td align="left"><p>0.05*</p></td><td align="left"><p>0.06***</p></td><td align="left"><p>0.10***</p></td><td align="left"><p>0.04*</p></td><td align="left"><p>0.08*</p></td><td align="left"><p>0.06**</p></td></tr><tr><td align="left"><p>1. Serial digits</p></td><td align="left"><p><bold>0.21***</bold></p></td><td align="left"><p>0.24***</p></td><td align="left"><p><bold>0.11***</bold></p></td><td align="left"><p>0.25***</p></td><td align="left"><p><bold>0.16***</bold></p></td><td align="left"><p>0.21***</p></td><td align="left"><p><bold>0.12***</bold></p></td><td align="left"><p>0.17 <bold>***</bold></p></td></tr><tr><td align="left"><p>2. Discrete digits</p></td><td align="left"><p>0.04***</p></td><td align="left"><p>0.36*</p></td><td align="left"><p>0.03*</p></td><td align="left"><p>0.18**</p></td><td align="left"><p>0.02***</p></td><td align="left"><p>0.21*</p></td><td align="left"><p>0.01*</p></td><td align="left"><p>0.07**</p></td></tr><tr><td align="left"><p>Total <italic>R</italic>²</p></td><td align="left"><p>0.26</p></td><td align="left"><p>0.60</p></td><td align="left"><p>0.14</p></td><td align="left"><p>0.43</p></td><td align="left"><p>0.18</p></td><td align="left"><p>0.42</p></td><td align="left"><p>0.13</p></td><td align="left"><p>0.24</p></td></tr></tbody></table> </ephtml> </p> <p>Note. The <emph>R²</emph> changes in bold are a visual aid to emphasize the strongest predictor for each word type in Grades 2 and 5 *<emph>p</emph> <.05, **<emph>p</emph> <. 01, ***<emph>p</emph> <.001</p> <p>The results for Grade 2 indicated that serial digit naming was a significant predictor of discrete word reading for all word types when entered at either Step 1 (11–21% of the variance) or Step 2 (5–11% of the variance) of the regression equation. In Grade 5, discrete digit naming remained a significant predictor of all discrete reading variables even when entered at Step 2 of the regression equation. When entered at Step 1, discrete digit naming accounted for 58% of the variance in the discrete reading of High-Short words, 37% in Low-Short words, 39% in High-Long words, and 18% in Low-Long words. Serial naming also accounted for unique variance in discrete reading for all word types when entered at Step 2 (2–6% of the variance); although apparently less in Grade 5 than in Grade 2.</p> <hd id="AN0190299323-29">Discrete word reading and serial digit naming as predictors of serial word reading</hd> <p>Next, we conducted multiple hierarchical regression analyses to examine the unique contribution of serial digit naming (presumed to index cascaded processing) to serial reading rate. Discrete word reading of the corresponding type of words was entered in the regression equation first (e.g., discrete reading of High-Short words predicting serial reading of High-Short words). This approach allowed us to attribute any additional amount of variance explained by serial digit naming to inter-word serial processing rather than individual word reading abilities, by controlling for discrete reading of the same type of words each time.</p> <p>As shown in Table 6, the inclusion of discrete word reading and serial digit naming in the regression model accounted for a substantial amount of variance in the serial reading rate across all word types, (ranging from 47 to 70% in Grade 5 and from 72 to 86% in Grade 2). However, in Grade 2, serial digit naming did not significantly account for additional proportional variance beyond discrete word reading, except for Short-Low words. In contrast, in Grade 5, serial digit naming predicted additional variance in the serial reading of all word types. More specifically, it accounted for 22% of unique variance in serial reading of High-Short words, 8% in High-Long words, 4% in Low-Short words, and 3% in Low-Long words.</p> <p>Table 6 R² changes in the prediction of serial reading</p> <p> <ephtml> <table rules="groups"><thead><tr><th align="left" /><th align="left" colspan="2"><p>High-Short</p></th><th align="left" colspan="2"><p>Low-Short</p></th><th align="left" colspan="2"><p>High-Long</p></th><th align="left" colspan="2"><p>Low-Long</p></th></tr><tr><th align="left" /><th align="left"><p>Grade 2</p></th><th align="left"><p>Grade 5</p></th><th align="left"><p>Grade 2</p></th><th align="left"><p>Grade 5</p></th><th align="left"><p>Grade 2</p></th><th align="left"><p>Grade 5</p></th><th align="left"><p>Grade 2</p></th><th align="left"><p>Grade 5</p></th></tr></thead><tbody><tr><td align="left"><p>1. Discrete Reading</p></td><td align="left"><p>0.81***</p></td><td align="left"><p>0.47***</p></td><td align="left"><p>0.72***</p></td><td align="left"><p>0.59***</p></td><td align="left"><p>0.81***</p></td><td align="left"><p>0.59***</p></td><td align="left"><p>0.86***</p></td><td align="left"><p>0.70***</p></td></tr><tr><td align="left"><p>2. Serial Digit Naming</p></td><td align="left"><p>0.00</p></td><td align="left"><p>0.22***</p></td><td align="left"><p>0.03***</p></td><td align="left"><p>0.04***</p></td><td align="left"><p>0.00</p></td><td align="left"><p>0.08***</p></td><td align="left"><p>0.01*</p></td><td align="left"><p>0.03***</p></td></tr><tr><td align="left"><p>Total <italic>R²</italic></p></td><td align="left"><p>0.81</p></td><td align="left"><p>0.69</p></td><td align="left"><p>0.75</p></td><td align="left"><p>0.62</p></td><td align="left"><p>0.81</p></td><td align="left"><p>0.67</p></td><td align="left"><p>0.87</p></td><td align="left"><p>0.72</p></td></tr></tbody></table> </ephtml> </p> <p>Note. *<emph>p</emph> <.05, **<emph>p</emph> <.01, ***<emph>p</emph> <.001</p> <hd id="AN0190299323-30">Discussion</hd> <p>We aimed to examine whether and to what extent the presentation format of words—either discrete or serial—influenced the effects of frequency (i.e., the difference between high- and low-frequency words) and length (i.e., the difference between short and long words) in Spanish-speaking children at different stages of reading development (i.e., Grades 2 and 5). Our findings revealed a significant effect of format and its interactions with both word length and frequency. Specifically, children in both grade levels read words faster in a serial format than in a discrete format; the difference was greatest for short, high-frequency words, especially in Grade 5. Moreover, the difference between discrete and serial word reading (i.e., the format effect) interacted with the effect of serial digit naming (but not discrete digit naming): As seen in Fig. 2 (the slope differences between red and blue lines), serial digit naming was more strongly associated with serial than with discrete word reading almost exclusively for High-Short words in Grade 2; whereas for Grade 5 the differential association was more widespread, but still strongest for High-Short and weakest for Low-Long words. These results are consistent with expectations based on the cascading hypothesis (Protopapas et al., [<reflink idref="bib43" id="ref142">43</reflink>], [<reflink idref="bib44" id="ref143">44</reflink>]), suggesting that effortless and fluent word reading requires (a) efficient (i.e., automatized) recognition of individual words—more likely for frequent and shorter words; and (b) a cognitive skill to efficiently and simultaneously schedule multiple words presented in lists or sentences—a skill captured by serial naming.</p> <hd id="AN0190299323-31">Reading words in serial format amplifies frequency and length effects</hd> <p>Several studies have shown that serial presentation formats facilitate the processing of various stimuli (e.g., digits, letters, words) in both children (Altani et al., [<reflink idref="bib4" id="ref144">4</reflink>]) and adults (Jones et al., [<reflink idref="bib31" id="ref145">31</reflink>]). In accordance with this expectation, our results showed a significant effect of format, that is, a serial advantage: Serial reading led to faster reading rates in both grade levels. However, the effect was much larger and more extensive in Grade 5, where it applied across word groups, whereas in Grade 2 it was primarily evident in short, high-frequency words (see Fig. 1). Moreover, in both grades the serial advantage was more pronounced with shorter and more familiar words; thus, beyond the independent effect of format, in the following section, we will discuss the implications of serial reading of more complex words, specifically in terms of length and frequency.</p> <p>Our results revealed a substantial effect of word length, indicating—unsurprisingly—that two-syllable words were processed faster than four-syllable words. Most importantly, we observed a significant interaction between word length and format, suggesting that the difference between short and long words was more pronounced in the serial format. These findings with Grade 2 and Grade 5 Spanish-speaking children are similar to those observed with typically developing Grade 6 Italian children (Conforti et al., [<reflink idref="bib15" id="ref146">15</reflink>]; Zoccolotti et al., [<reflink idref="bib66" id="ref147">66</reflink>]). We also found an interaction between word length and grade level. However, this was not exactly similar to previous reports of larger length effects among younger readers (e.g., Ballot & Zesiger, [<reflink idref="bib6" id="ref148">6</reflink>]; Zoccolotti et al., [<reflink idref="bib64" id="ref149">64</reflink>]) and a smaller or negligible effect among older children (e.g., Martens & de Jong, [<reflink idref="bib39" id="ref150">39</reflink>]). Although slightly more variance was attributable to word length in Grade 2 than in Grade 5, indicating a more consistent effect of length, in our data the magnitude of the reading rate difference between short and long words was actually greater in Grade 5, suggesting that fifth graders took advantage of short words to a higher degree, especially if they were frequent (see Fig. 1). One possible explanation for the discrepancy is our use of a broad binary length categorization (two vs. four syllables), which may have limited our ability to capture finer differences between grades across a continuum of length. Another possibility may have to do with the length of our "long" words, which was quite substantial (7–12 letters), indeed longer than the words used in the aforementioned studies.</p> <p>As for word frequency, our results showed that high-frequency words were—again, unsurprisingly—read faster than low-frequency words. Crucially, the frequency effect was significantly larger in serial than in discrete reading. Similar to length effects, grade-level differences emerged. Consistent with other cross-sectional studies (e.g., Schröter & Schroeder, [<reflink idref="bib50" id="ref151">50</reflink>]; Zoccolotti et al., [<reflink idref="bib65" id="ref152">65</reflink>]), the word frequency effect was significantly larger in older children, indicating a higher level of automatization for familiar words among more experienced readers. Moreover, whereas serial reading of both low- and high-frequency words was faster than discrete reading among Grade 5 children, the serial advantage was most clearly evident only for high-frequency words among Grade 2 children. These developmental differences were expected because more experienced readers recognize more words by sight, whereas younger children rely mostly on phonological recoding to read unfamiliar words.</p> <p>Finally, the three-way interaction between length, frequency, and format indicated that high-frequency, short words benefited the most from the serial format; and the four-way interaction with grade indicates that this benefit was greater in Grade 5.</p> <p>In sum, our findings support Conforti et al.'s ([<reflink idref="bib15" id="ref153">15</reflink>]) conclusion that serial reading amplifies the effects of word manipulations (in our case, frequency and length, and their nonadditive combination). The significant effect of format across word categories and grade levels provides support for the cascading hypothesis (Protopapas et al., [<reflink idref="bib43" id="ref154">43</reflink>], [<reflink idref="bib44" id="ref155">44</reflink>]), in which readers overlap the processing of multiple words. The observation that high-frequency, short words benefited most from the serial format aligns with previous studies showing that these words elicit larger offset eye-voice spans in experienced readers during serial reading, thus increasing reading speed (e.g., Silva et al., [<reflink idref="bib53" id="ref156">53</reflink>]).</p> <p>Moreover, our study supports previous findings indicating that the amount of very high-frequency, short words included in texts is a crucial factor in reading fluency performance (e.g., Compton et al., [<reflink idref="bib14" id="ref157">14</reflink>]). Considered within the cascaded processing framework, our results highlight the importance of highly familiar words for fluent reading as well as the relevance of the finding that the majority of tokens in passages are high-frequency words (Korochkina et al., [<reflink idref="bib36" id="ref158">36</reflink>]). On the other hand, given that most of these high-frequency tokens are function words, as noted by Korochkina et al., our findings can also be taken to support the notion that successful transitioning from beginner level to functional literacy requires familiarization with a wider range of words to support fluent reading with concomitant comprehension.</p> <hd id="AN0190299323-32">Serial digit naming as a measure of cascaded processing</hd> <p>The importance of the serial format in word reading fluency is further supported by its relation to serial naming. Our results showed that adding serial digit naming to a model that already included discrete digit naming resulted in a significant additional contribution, whereas the reverse did not. Most importantly, across grade levels, the difference between serial and discrete reading was associated with serial naming but not with discrete naming. Additionally, all interactions involving the interaction between serial digit naming and format were significant, whereas those involving discrete digit naming were not.</p> <p>In addition, our study found developmental differences in the relation of serial naming with reading. Specifically, among second graders, serial naming accounted for little to no additional variance in serial reading beyond discrete word reading. Since efficient cascading processing depends on words being recognized by sight and as fast as single digits, our findings suggest that, at this stage of reading development, sight-word recognition in Spanish-speaking second graders is not consolidated (this will be discussed further in the next section). However, among fifth graders, the contribution of discrete word reading to serial reading decreased, whereas the contribution of serial naming increased. This pattern of results aligns with previous cross-sectional studies in Greek (Altani et al., [<reflink idref="bib2" id="ref159">2</reflink>], [<reflink idref="bib3" id="ref160">3</reflink>]), English (Altani et al., [<reflink idref="bib3" id="ref161">3</reflink>]), Korean and Chinese (Georgiou et al., [<reflink idref="bib28" id="ref162">28</reflink>]), suggesting that as sight-word recognition consolidates, cascaded processing becomes more crucial in transitioning from word-by-word reading to fluent, effortless reading.</p> <p>Although the aforementioned studies showed that serial naming predicted serial reading over and above the effects of discrete word reading, our results suggested that discrete word reading continued to predominate in the prediction of serial reading, except for high-frequency short words in Grade 5. Altani et al. ([<reflink idref="bib1" id="ref163">1</reflink>]) suggested that reading fluency might be more strongly influenced by discrete word reading in transparent orthographies due to a prevalent sequential decoding strategy, which could support the implementation of intra-word cascaded processing across formats. However, this hypothesis requires further examination. In this context it may be relevant to point out that our "short" words were two-syllables (4–6 letters) long, thus perhaps closer to "long" words in some studies in languages such as English or Dutch, in which monosyllabic content words are common.</p> <hd id="AN0190299323-33">Word recognition: a serial and discrete naming perspective</hd> <p>The relation between discrete word reading and serial and discrete digit naming could provide an alternative perspective on the study of word recognition and the effects of length and frequency. As de Jong ([<reflink idref="bib20" id="ref164">20</reflink>]) hypothesized, if a word is read by sight, the discrete reading of highly familiar words will more closely resemble the discrete naming of highly familiar symbols such as digits. However, if words are not recognized by sight, readers will use a sequential recoding approach, integrating multiple sub-word units in a serial manner. This would result in a stronger relation between serial naming and discrete word reading.</p> <p>As expected, among Grade 2 children, serial naming remained the main predictor of discrete word reading, even after controlling for the effects of discrete naming. This result was replicated across word sets, consistent with a serial intra-word processing approach to word reading among beginning readers. The opposite pattern was found among Grade 5 readers, as discrete naming was the stronger predictor of discrete reading in all cases. Interestingly, serial naming remained a significant predictor of discrete word reading, even for short high-frequency words. The persistent contribution of serial naming to word reading among advanced readers may appear to stand in contrast to previous studies in other languages in which the role of serial naming in word reading was negligible after controlling for discrete naming (e.g., English: Altani et al., [<reflink idref="bib2" id="ref165">2</reflink>]; Chinese: Georgiou et al., [<reflink idref="bib28" id="ref166">28</reflink>]; Dutch: van den Boer & de Jong, [<reflink idref="bib57" id="ref167">57</reflink>]). However, as noted above, all those studies used monosyllables whereas our short words were two syllables long. Our results with Grade 5 children are more similar to those of Grade 3 Greek readers in Altani et al. ([<reflink idref="bib1" id="ref168">1</reflink>]), in which serial naming was a significant predictor of two-syllable, high-frequency words. Altani et al. also used two-syllable digits and words to control naming requirements across tasks, as we did. Therefore, both our findings and those of Altani et al. could be attributed to a serial process at the intra-word level.</p> <p>Moreover, the strength of the relation of discrete naming with discrete reading, varying across word categories and grade levels, suggests a spectrum of automaticity in word recognition. For example, in both grade levels, the strongest association with discrete naming was found for short, high-frequency words; however, this was very strong in Grade 5 but only moderate in Grade 2. Conversely, the weakest correlation was found for long, low-frequency words in both grade levels, with a moderate association among fifth graders and non-significant among second graders.</p> <p>Taken together, our findings suggests that, whereas sight word reading may gradually emerge, advanced Spanish readers still resort to some kind of phonological recoding for some types of words (Cuetos & Suárez-Coalla, [<reflink idref="bib17" id="ref169">17</reflink>]). The latter is also evidenced by persistent length effects observed in the vocal reaction times of adult Spanish readers (e.g., Cuetos & Barbón, [<reflink idref="bib16" id="ref170">16</reflink>]) and a stable relation between RAN and discrete nonword reading across grade levels (e.g., Rodríguez et al., [<reflink idref="bib48" id="ref171">48</reflink>]). In line with these findings, Ziegler et al. ([<reflink idref="bib63" id="ref172">63</reflink>]) suggested that experienced readers, particularly from transparent orthographies, demonstrate flexibility in using and switching between different psycholinguistic grain sizes. Moreover, variations in the interrelations between serial and discrete naming with reading across different word sets suggest that an absolute binary categorization of sequential versus whole word processing may be inadequate (Altani et al., [<reflink idref="bib1" id="ref173">1</reflink>], [<reflink idref="bib2" id="ref174">2</reflink>]; van den Boer & de Jong, [<reflink idref="bib57" id="ref175">57</reflink>]). Instead, our findings align more closely with van den Boer et al.'s ([<reflink idref="bib58" id="ref176">58</reflink>]) suggestion that parallel processing may operate for sub-word units (e.g., syllables, morphemes), while other parts of the word may be processed serially during word recognition. We believed this is particularly relevant for multisyllabic words and reading in a transparent orthography like Spanish.</p> <hd id="AN0190299323-34">Limitations</hd> <p>Some limitations of the present study are worth noting. First, our study is correlational and any significant associations between discrete/serial naming and reading do not imply causation. Second, research in transparent orthographies has shown that the morphological composition of words impacts efficient word recognition (e.g., Burani et al., [<reflink idref="bib12" id="ref177">12</reflink>]). Unfortunately, in this study we did not account for the morphological complexity inherent in longer words compared to shorter ones. Another limitation concerns syllabic frequency, which is known to influence word reading fluency in Spanish (Carreiras & Perea, [<reflink idref="bib13" id="ref178">13</reflink>]). We only balanced the initial syllabic structure for serial and discrete presentation within each word category, but not across. Finally, our findings primarily apply to average readers. Although the proportion of excluded data due to inaccurate or missing responses was below 7% for all tasks, we likely excluded dysfluent readers, particularly from Grade 2, from our sample. Future research should explore the implications specifically for less skilled readers.</p> <hd id="AN0190299323-35">General conclusion</hd> <p>In conclusion, our study showed that words presented in a serial format rather than a discrete format yielded faster reading rates across length and frequency groups. Moreover, the effects of word length, frequency, and their interaction were more pronounced during serial reading. Our findings confirm that the words more likely to be recognized by sight—highly frequent and short—benefited the most from serial presentation. This implies that readers efficiently apply cascaded processing during reading fluency tasks to the extent that individual words are automatized. This process is captured by the increasing association between serial naming and serial reading. Finally, our findings align with traditional paradigms for studying frequency and length effects in words read in isolation (e.g., vocal response times), supporting previous arguments that serial and discrete naming also capture the degree of automaticity with which individual words are processed.</p> <hd id="AN0190299323-36">Funding</hd> <p>This study was supported by a grant from the Social Sciences and Humanities Research Council of Canada (RES0029061) to Dr. George Georgiou. The work of Athanassios Protopapas is partially funded by The Research Council of Norway, Centres of Excellence, Grant 331640. The work of Sandra Romero is partially funded by the National Council of Humanities, Science and Technology of Mexico (CONAHCYT, 2020-000017-02 EXTF-00165).</p> <hd id="AN0190299323-37">Declarations</hd> <p></p> <hd id="AN0190299323-38">Conflict of interest</hd> <p>The authors have no conflict of interest to disclose.</p> <hd id="AN0190299323-39">Electronic supplementary material</hd> <p>Below is the link to the electronic supplementary material.</p> <p>Graph: Supplementary Material 1</p> <hd id="AN0190299323-40">Publisher's note</hd> <p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p> <ref id="AN0190299323-41"> <title> References </title> <blist> <bibl id="bib1" idref="ref17" type="bt">1</bibl> <bibtext> Altani A, Georgiou GK, Deng C, Cho JR, Katopodi K, Wei W, Protopapas A. Is processing of symbols and words influenced by writing system? Evidence from Chinese, Korean, English, and Greek. Journal of Experimental Child Psychology. 2017; 164: 117-135. 10.1016/j.jecp.2017.07.006</bibtext> </blist> <blist> <bibl id="bib2" idref="ref73" type="bt">2</bibl> <bibtext> Altani A, Protopapas A, Georgiou GK. Using serial and discrete digit naming to unravel word reading processes. Frontiers in Psychology. 2018; 9: 524. 10.3389/fpsyg.2018.00524</bibtext> </blist> <blist> <bibl id="bib3" idref="ref67" type="bt">3</bibl> <bibtext> Altani A, Protopapas A, Katopodi K, Georgiou GK. From individual word recognition to word list and text reading fluency. Journal of Educational Psychology. 2020; 112; 1: 22-39. 10.1037/edu0000359</bibtext> </blist> <blist> <bibl id="bib4" idref="ref66" type="bt">4</bibl> <bibtext> Altani A, Protopapas A, Katopodi K, Georgiou GK. Tracking the serial advantage in the naming rate of multiple over isolated stimulus displays. Reading and Writing. 2020; 33: 349-375. 10.1007/s11145-019-09962-7</bibtext> </blist> <blist> <bibl id="bib5" idref="ref68" type="bt">5</bibl> <bibtext> Araújo S, Reis A, Petersson KM, Faísca L. Rapid automatized naming and reading performance: A meta-analysis. Journal of Educational Psychology. 2015; 107; 3: 868-883. 10.1037/edu0000006</bibtext> </blist> <blist> <bibl id="bib6" idref="ref7" type="bt">6</bibl> <bibtext> Ballot C, Zesiger P. Effects of word length and frequency on word identification in second- and fifth-grade children as a function of language skills. Journal of Experimental Child Psychology. 2024; 243: 105912. 10.1016/j.jecp.2024.105912</bibtext> </blist> <blist> <bibl id="bib7" idref="ref11" type="bt">7</bibl> <bibtext> Barton JJ, Hanif HM, Eklinder Björnström L, Hills C. The word-length effect in reading: A review. Cognitive Neuropsychology. 2014; 31; 5–6: 378-412. 10.1080/02643294.2014.895314</bibtext> </blist> <blist> <bibl id="bib8" idref="ref141" type="bt">8</bibl> <bibtext> Bartoń, K. (2023). MuMIn: Multi-Model Inference. R package version 1.47.5, https://CRAN.R-project.org/package=MuMIn</bibtext> </blist> <blist> <bibl id="bib9" idref="ref132" type="bt">9</bibl> <bibtext> Bates D, Mächler M, Bolker B, Walker S. Fitting linear mixed-effects models using lme4. Journal of Statistical Software. 2015; 67; 1: 1-48. 10.18637/jss.v067.i01</bibtext> </blist> <blist> <bibtext> Bijeljac-Babic R, Millogo V, Farioli F. A developmental investigation of word length effects in reading using a new on-line word identification paradigm. Reading and Writing. 2004; 17: 411-431. 10.1023/B:READ.0000032664.20755.af</bibtext> </blist> <blist> <bibtext> Brysbaert M, Mandera P, Keuleers E. The word frequency effect in word processing: An updated review. Current Directions in Psychological Science. 2018; 27; 1: 45-50. 10.1177/0963721417727521</bibtext> </blist> <blist> <bibtext> Burani C, Marcolli S, Stella G. How early does morpholexical reading develop in readers of a shallow orthography?. Brain and Language. 2002; 81; 1–3: 568-586. 10.1006/brln.2001.2548</bibtext> </blist> <blist> <bibtext> Carreiras M, Alvarez CJ, de Vega M. Syllable frequency and visual word recognition in Spanish. Journal of Memory and Language. 1993; 32; 6: 766-780. 10.1006/jmla.1993.1038</bibtext> </blist> <blist> <bibtext> Compton DL, Appleton AC, Hosp MK. Exploring the relationship between text–leveling systems and reading accuracy and fluency in second–grade students who are average and poor decoders. Learning Disabilities Research & Practice. 2004; 19; 3: 176-184. 10.1111/j.1540-5826.2004.00102.x</bibtext> </blist> <blist> <bibtext> Conforti S, Marinelli CV, Zoccolotti P, Martelli M. The metrics of reading speed: Understanding developmental dyslexia. Scientific Reports. 2024; 14: 4109. 10.1038/s41598-024-52330-x</bibtext> </blist> <blist> <bibtext> Cuetos F, Barbón A. Word naming in Spanish. European Journal of Cognitive Psychology. 2006; 18; 3: 415-436. 10.1080/13594320500165896</bibtext> </blist> <blist> <bibtext> Cuetos F, Suárez-Coalla P. From grapheme to word in reading acquisition in Spanish. Applied Psycholinguistics. 2009; 30; 4: 583-601. 10.1017/S0142716409990038</bibtext> </blist> <blist> <bibtext> Davies R, Cuetos F, Glez-Seijas RM. Reading development and dyslexia in a transparent orthography: A survey of Spanish children. Annals of Dyslexia. 2007; 57: 179-198. 10.1007/s11881-007-0010-1</bibtext> </blist> <blist> <bibtext> Davies RAI, Arnell R, Birchenough JMH, Grimmond D, Houlson S. Reading through the life span: Individual differences in psycholinguistic effects. Journal of Experimental Psychology: Learning Memory and Cognition. 2017; 43; 8: 1298-1338. 10.1037/xlm0000366</bibtext> </blist> <blist> <bibtext> De Jong PF. What discrete and serial rapid automatized naming can reveal about reading. Scientific Studies of Reading. 2011; 15: 314-337. 10.1080/10888438.2010.485624</bibtext> </blist> <blist> <bibtext> Diamanti V, Grande G, Protopapas A, Melby-Lervåg M, Lervåg A. Preschool morphological awareness and developmental change in early reading ability. Scientific Studies of Reading. 2024. 10.1080/10888438.2024.2370843</bibtext> </blist> <blist> <bibtext> Ehri LC. Learning to read words: Theory, findings, and issues. Scientific Studies of Reading. 2005; 9; 2: 167-188. 10.1207/s1532799xssr0902_4</bibtext> </blist> <blist> <bibtext> Ehri LC, Wilce LS. Development of word identification speed in skilled and less skilled beginning readers. Journal of Educational Psychology. 1983; 75; 1: 3-18. 10.1037/0022-0663.75.1.3</bibtext> </blist> <blist> <bibtext> Ferrand L. Reading aloud polysyllabic words and nonwords: The syllabic length effect reexamined. Psychonomic Bulletin Review. 2000; 7: 142-148. 10.3758/BF03210733</bibtext> </blist> <blist> <bibtext> Forster KI, Forster JC. DMDX: A windows display program with millisecond accuracy. Behavior Research Methods Instruments & Computers. 2003; 35: 116-124. 10.3758/BF03195503</bibtext> </blist> <blist> <bibtext> Georgiou GK, Parrila R. What mechanism underlies the rapid automatized naming–reading relation?. Journal of Experimental Child Psychology. 2020; 194: 104840. 10.1016/j.jecp.2020.104840</bibtext> </blist> <blist> <bibtext> Georgiou GK, Parrila R, Cui Y, Papadopoulos TC. Why is rapid automatized naming related to reading?. Journal of Experimental Child Psychology. 2013; 115; 1: 218-225. 10.1016/j.jecp.2012.10.015</bibtext> </blist> <blist> <bibtext> Georgiou, G. K, Cho, J-R, Deng, C, Altani, A, Romero, S, Kim, M-Y, Wang, L, Wei, W, & Protopapas, A. (2022). Cascaded processing in naming and reading: Evidence from Chinese and Korean. Journal of Experimental Child Psychology, 220. https://doi.org/10.1016/j.jecp.2022.105416</bibtext> </blist> <blist> <bibtext> Hasenäcker J, Schroeder S. Specific predictors of length and frequency effects in German beginning readers: Testing component processes of sublexical and lexical reading in the DRC. Reading and Writing. 2022; 35: 1627-1650. 10.1007/s11145-021-10251-5</bibtext> </blist> <blist> <bibtext> Hudson RF, Pullen PC, Lane HD, Torgesen JK. The complex nature of reading fluency: A multidimensional view. Reading & Writing Quarterly. 2008; 25; 1: 4-32. 10.1080/10573560802491208</bibtext> </blist> <blist> <bibtext> Jones MW, Branigan HP, Kelly ML. Dyslexic and nondyslexic reading fluency: Rapid automatized naming and the importance of continuous lists. Psychonomic Bulletin & Review. 2009; 16: 567-572. 10.3758/PBR.16.3.567</bibtext> </blist> <blist> <bibtext> Joseph HSSL, Nation K, Liversedge SP. Using eye movements to investigate word frequency effects in children's sentence reading. School Psychology Review. 2013; 42; 2: 207-222. 10.1080/02796015.2013.12087485</bibtext> </blist> <blist> <bibtext> Juul H, Poulsen M, Elbro C. Separating speed from accuracy in beginning reading development. Journal of Educational Psychology. 2014; 106; 4: 1096-1106. 10.1037/a0037100</bibtext> </blist> <blist> <bibtext> Karageorgos, P, Richter, T, Haffmans, M. B, Schindler, J, & Naumann, J. (2020). The role of word-recognition accuracy in the development of word-recognition speed and reading comprehension in primary school: A longitudinal examination. Cognitive Development, 56. https://doi.org/10.1016/j.cogdev.2020.100949</bibtext> </blist> <blist> <bibtext> Khelifi R, Sparrow L, Casalis S. Is a frequency effect observed in eye movements during text reading? A comparison between developing and expert readers. Scientific Studies of Reading. 2019; 23; 4: 334-347. 10.1080/10888438.2019.1571064</bibtext> </blist> <blist> <bibtext> Korochkina M, Marelli M, Brysbaert M, Rastle K. The children and young people's books lexicon (CYP-LEX): A large-scale lexical database of books read by children and young people in the United Kingdom. Quarterly Journal of Experimental Psychology. 2024. 10.1177/17470218241229694</bibtext> </blist> <blist> <bibtext> Kuhn MR, Stahl SA. Fluency: A review of developmental and remedial practices. Journal of Educational Psychology. 2003; 95; 1: 3-21. 10.1037/0022-0663.95.1.3</bibtext> </blist> <blist> <bibtext> Kwok RK, Cuetos F, Avdyli R, Ellis AW. Reading and lexicalization in opaque and transparent orthographies: Word naming and word learning in English and Spanish. Quarterly Journal of Experimental Psychology. 2017; 70; 10: 2105-2129. 10.1080/17470218.2016.1223705</bibtext> </blist> <blist> <bibtext> Martens VE, de Jong PF. The effect of word length on lexical decision in dyslexic and normal reading children. Brain and Language. 2006; 98; 2: 140-149. 10.1016/j.bandl.2006.04.003</bibtext> </blist> <blist> <bibtext> Monster I, Tellings A, Burk WJ, Keuning J, Segers E, Verhoeven L. Word properties predicting children's word recognition. Scientific Studies of Reading. 2022; 26; 5: 373-389. 10.1080/10888438.2021.2020795</bibtext> </blist> <blist> <bibtext> New B, Ferrand L, Pallier C. Reexamining the word length effect in visual word recognition: New evidence from the English Lexicon Project. Psychonomic Bulletin & Review. 2006; 13: 45-52. 10.3758/BF03193811</bibtext> </blist> <blist> <bibtext> Protopapas A. CheckVocal: A program to facilitate checking the accuracy and response time of vocal responses from DMDX. Behavior Research Methods. 2007; 39: 859-862. 10.3758/BF03192979</bibtext> </blist> <blist> <bibtext> Protopapas A, Altani A, Georgiou GK. Development of serial processing in reading and rapid naming. Journal of Experimental Child Psychology. 2013; 116: 914-929. 10.1016/j.jecp.2013.08.004</bibtext> </blist> <blist> <bibtext> Protopapas A, Katopodi K, Altani A, Georgiou G. Word fluency as a serial naming task. Scientific Studies of Reading. 2018; 22: 248-263. 10.1080/10888438.2018.1430804</bibtext> </blist> <blist> <bibtext> Protopapas A, Katopodi K, Altani A, Kolotoura I, Ziaka L, Georgiou GK. A process-oriented analysis of speech and silent intervals in responses to serial naming tasks. Journal of Educational Psychology. 2024. 10.1037/edu0000900</bibtext> </blist> <blist> <bibtext> R Core Team. (2023). R: A language and environment for statistical computing. R Foundation for Statistical Computing. https://<ulink href="http://www.R-project.org/">www.R-project.org/</ulink></bibtext> </blist> <blist> <bibtext> Rau AK, Moeller K, Landerl K. The transition from sublexical to lexical processing in a consistent orthography: An eye-tracking study. Scientific Studies of Reading. 2014; 18; 3: 224-233. 10.1080/10888438.2013.857673</bibtext> </blist> <blist> <bibtext> Rodríguez C, van den Boer M, Jiménez JE, de Jong PF. Developmental changes in the relations between RAN, phonological awareness, and reading in Spanish children. Scientific Studies of Reading. 2015; 19; 4: 273-288. 10.1080/10888438.2015.1025271</bibtext> </blist> <blist> <bibtext> Romero S, Georgiou GK, Altani A, Gorgun G, Protopapas A. Beyond word recognition: The role of efficient sequential processing in word- and text-reading fluency development. Scientific Studies of Reading. 2024. 10.1080/10888438.2024.2360189Advance online publication</bibtext> </blist> <blist> <bibtext> Schröter P, Schroeder S. The Developmental Lexicon Project: A behavioral database to investigate visual word recognition across the lifespan. Behavior Research Methods. 2017; 49; 6: 2183-2203. 10.3758/s13428-016-0851-9</bibtext> </blist> <blist> <bibtext> Sebastián, N, Martí, M. A, Carreiras, M. F, & Cuetos, F. (2000). LEXESP, Léxico informatizado del español [Computerized lexicon of Spanish]. Barcelona: Edíciones de la Universitat de Barcelona.</bibtext> </blist> <blist> <bibtext> Seymour PHK, Aro M, Erskine JM. Foundation literacy acquisition in European orthographies. British Journal of Psychology. 2003; 94: 143-174. 10.1348/000712603321661859</bibtext> </blist> <blist> <bibtext> Silva, S, Reis, A, Casaca, L, Petersson, K. M, & Faísc, L. (2016). When the eyes no longer lead: Familiarity and length effects on eye-voice span. Fontiers in Psychology, 7. https://doi.org/10.3389/fpsyg.2016.01720</bibtext> </blist> <blist> <bibtext> Song S, Georgiou GK, Su M, Hua S. How well do phonological awareness and rapid automatized naming correlate with Chinese reading accuracy and fluency? A metaanalysis. Scientific Studies of Reading. 2016; 20; 2: 99-123. 10.1080/10888438.2015.1088543</bibtext> </blist> <blist> <bibtext> Spinelli D, De Luca M, Di Filippo G, Mancini M, Martelli M, Zoccolotti P. Length effect in word naming in reading: The role of reading experience and reading deficit in Italian readers. Developmental Neuropsychology. 2005; 27; 2: 217-235. 10.1207/s15326942dn2702_2</bibtext> </blist> <blist> <bibtext> Tiffin-Richards SP, Schroeder S. Word length and frequency effects on children's eye movements during silent reading. Vision Research. 2015; 113: 33-43. 10.1016/j.visres.2015.05.008</bibtext> </blist> <blist> <bibtext> van den Boer M, de Jong PF. Parallel and serial reading processes in children's word and nonword reading. Journal of Educational Psychology. 2015; 107: 141-151. 10.1037/a0037101</bibtext> </blist> <blist> <bibtext> van den Boer M, Georgiou GK, de Jong PF. Naming of short words is (almost) the same as naming of alphanumeric symbols: Evidence from two orthographies. Journal of Experimental Child Psychology. 2016; 144: 152-165. 10.1016/j.jecp.2015.11.016</bibtext> </blist> <blist> <bibtext> van Heuven, W. J. B, Mandera, P, Keuleers, E, & Brysbaert, M. (2014). Subtlex-UK: A new and improved word frequency database for British English. Quarterly Journal of Experimental Psychology, 67(6), 1176–1190. https://doi.org/10.1080/17470218.2013.850521</bibtext> </blist> <blist> <bibtext> Weekes BS. Differential effects of number of letters on word and nonword naming latency. The Quarterly Journal of Experimental Psychology Section A. 1997; 50; 2: 439-456. 10.1080/713755710</bibtext> </blist> <blist> <bibtext> Ziaka L, Protopapas A. Cognitive control beyond single-item tasks: Insights from pupillometry, gaze, and behavioral measures. Journal of Experimental Psychology: Human Perception and Performance. 2023; 49; 7: 968-988. 10.1037/xhp0001127</bibtext> </blist> <blist> <bibtext> Ziegler JC, Goswami U. Reading acquisition, developmental dyslexia, and skilled reading across languages: A psycholinguistic grain size theory. Psychological Bulletin. 2005; 131; 1: 3-29. 10.1037/0033-2909.131.1.3</bibtext> </blist> <blist> <bibtext> Ziegler JC, Perry C, Jacobs AM, Braun M. Identical words are read differently in different languages. Psychological Science. 2001; 12; 5: 379-384. 10.1111/1467-9280.00370</bibtext> </blist> <blist> <bibtext> Zoccolotti P, De Luca M, Di Pace E, Gasperini F, Judica A, Spinelli D. Word length effect in early reading and in developmental dyslexia. Brain and Language. 2005; 93; 3: 369-373. 10.1016/j.bandl.2004.10.010</bibtext> </blist> <blist> <bibtext> Zoccolotti P, De Luca M, Di Filippo G, Judica A, Martelli ML. Reading development in an orthographically regular language: Effects of length, frequency, lexicality and global processing ability. Reading and Writing. 2009; 22: 1053-1079. 10.1007/s11145-008-9144-8</bibtext> </blist> <blist> <bibtext> Zoccolotti P, De Luca M, Lami L, Pizzoli C, Pontillo M, Spinelli D. Multiple stimulus presentation yields larger deficits in children with developmental dyslexia: A study with reading and RAN-type tasks. Child Neuropsychology. 2013; 19; 6: 639-647. 10.1080/09297049.2012.718325</bibtext> </blist> <blist> <bibtext> Zoccolotti P, De Luca M, Spinelli D. Discrete versus multiple word displays: A re-analysis of studies comparing dyslexic and typically developing children. Frontiers in Psychology. 2015; 6: 1530. 10.3389/fpsyg.2015.01530</bibtext> </blist> </ref> <ref id="AN0190299323-42"> <title> Footnotes </title> <blist> <bibtext> More recently, the Zipf scale has been proposed, which involves a logarithmic transformation that reduces skewness and produces a more easily comprehensible range of values, with high-frequency words around 5‒6 and low-frequency words around 2‒3, consistently interpretable across corpus sizes (van Heuven et al., [59]).</bibtext> </blist> <blist> <bibtext> Previous studies in languages such as English and Dutch have used one-syllable words as short words; however, these are not common in Spanish. This limitation was also noted by Altani et al., [1], [3]; Protopapas et al. ([43]) in their studies in Greek. To address this, they used two-syllable words, matching the naming demands of their two-syllable number words.</bibtext> </blist> </ref> <aug> <p>By Sandra Romero; George K. Georgiou; Angeliki Altani and Athanassios Protopapas</p> <p>Reported by Author; Author; Author; Author</p> </aug> <nolink nlid="nl1" bibid="bib30" firstref="ref1"></nolink> <nolink nlid="nl2" bibid="bib37" firstref="ref2"></nolink> <nolink nlid="nl3" bibid="bib22" firstref="ref3"></nolink> <nolink nlid="nl4" bibid="bib55" firstref="ref4"></nolink> <nolink nlid="nl5" bibid="bib11" firstref="ref5"></nolink> <nolink nlid="nl6" bibid="bib64" firstref="ref6"></nolink> <nolink nlid="nl7" bibid="bib56" firstref="ref8"></nolink> <nolink nlid="nl8" bibid="bib43" firstref="ref9"></nolink> <nolink nlid="nl9" bibid="bib44" firstref="ref10"></nolink> <nolink nlid="nl10" bibid="bib18" firstref="ref13"></nolink> <nolink nlid="nl11" bibid="bib32" firstref="ref14"></nolink> <nolink nlid="nl12" bibid="bib17" firstref="ref16"></nolink> <nolink nlid="nl13" bibid="bib65" firstref="ref18"></nolink> <nolink nlid="nl14" bibid="bib29" firstref="ref19"></nolink> <nolink nlid="nl15" bibid="bib47" firstref="ref20"></nolink> <nolink nlid="nl16" bibid="bib19" firstref="ref21"></nolink> <nolink nlid="nl17" bibid="bib50" firstref="ref22"></nolink> <nolink nlid="nl18" bibid="bib12" firstref="ref26"></nolink> <nolink nlid="nl19" bibid="bib39" firstref="ref29"></nolink> <nolink nlid="nl20" bibid="bib10" firstref="ref39"></nolink> <nolink nlid="nl21" bibid="bib41" firstref="ref40"></nolink> <nolink nlid="nl22" bibid="bib40" firstref="ref42"></nolink> <nolink nlid="nl23" bibid="bib24" firstref="ref43"></nolink> <nolink nlid="nl24" bibid="bib60" firstref="ref44"></nolink> <nolink nlid="nl25" bibid="bib61" firstref="ref51"></nolink> <nolink nlid="nl26" bibid="bib67" firstref="ref53"></nolink> <nolink nlid="nl27" bibid="bib15" firstref="ref54"></nolink> <nolink nlid="nl28" bibid="bib66" firstref="ref61"></nolink> <nolink nlid="nl29" bibid="bib31" firstref="ref64"></nolink> <nolink nlid="nl30" bibid="bib54" firstref="ref69"></nolink> <nolink nlid="nl31" bibid="bib27" firstref="ref70"></nolink> <nolink nlid="nl32" bibid="bib26" firstref="ref71"></nolink> <nolink nlid="nl33" bibid="bib45" firstref="ref72"></nolink> <nolink nlid="nl34" bibid="bib20" firstref="ref75"></nolink> <nolink nlid="nl35" bibid="bib49" firstref="ref78"></nolink> <nolink nlid="nl36" bibid="bib21" firstref="ref82"></nolink> <nolink nlid="nl37" bibid="bib28" firstref="ref91"></nolink> <nolink nlid="nl38" bibid="bib23" firstref="ref92"></nolink> <nolink nlid="nl39" bibid="bib57" firstref="ref96"></nolink> <nolink nlid="nl40" bibid="bib58" firstref="ref99"></nolink> <nolink nlid="nl41" bibid="bib52" firstref="ref102"></nolink> <nolink nlid="nl42" bibid="bib38" firstref="ref103"></nolink> <nolink nlid="nl43" bibid="bib63" firstref="ref104"></nolink> <nolink nlid="nl44" bibid="bib62" firstref="ref105"></nolink> <nolink nlid="nl45" bibid="bib51" firstref="ref110"></nolink> <nolink nlid="nl46" bibid="bib59" firstref="ref111"></nolink> <nolink nlid="nl47" bibid="bib35" firstref="ref121"></nolink> <nolink nlid="nl48" bibid="bib25" firstref="ref129"></nolink> <nolink nlid="nl49" bibid="bib42" firstref="ref130"></nolink> <nolink nlid="nl50" bibid="bib46" firstref="ref131"></nolink> <nolink nlid="nl51" bibid="bib33" firstref="ref139"></nolink> <nolink nlid="nl52" bibid="bib34" firstref="ref140"></nolink> <nolink nlid="nl53" bibid="bib53" firstref="ref156"></nolink> <nolink nlid="nl54" bibid="bib14" firstref="ref157"></nolink> <nolink nlid="nl55" bibid="bib36" firstref="ref158"></nolink> <nolink nlid="nl56" bibid="bib16" firstref="ref170"></nolink> <nolink nlid="nl57" bibid="bib48" firstref="ref171"></nolink> <nolink nlid="nl58" bibid="bib13" firstref="ref178"></nolink>
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An: EJ1499625
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PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Effects of Word Frequency and Length in Discrete and Serial Word Reading
– Name: Language
  Label: Language
  Group: Lang
  Data: English
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Sandra+Romero%22">Sandra Romero</searchLink> (ORCID <externalLink term="http://orcid.org/0009-0008-2959-1779">0009-0008-2959-1779</externalLink>)<br /><searchLink fieldCode="AR" term="%22George+K%2E+Georgiou%22">George K. Georgiou</searchLink> (ORCID <externalLink term="http://orcid.org/0000-0002-9081-992X">0000-0002-9081-992X</externalLink>)<br /><searchLink fieldCode="AR" term="%22Angeliki+Altani%22">Angeliki Altani</searchLink> (ORCID <externalLink term="http://orcid.org/0000-0002-0145-4931">0000-0002-0145-4931</externalLink>)<br /><searchLink fieldCode="AR" term="%22Athanassios+Protopapas%22">Athanassios Protopapas</searchLink> (ORCID <externalLink term="http://orcid.org/0000-0002-7285-8845">0000-0002-7285-8845</externalLink>)
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="SO" term="%22Reading+and+Writing%3A+An+Interdisciplinary+Journal%22"><i>Reading and Writing: An Interdisciplinary Journal</i></searchLink>. 2025 38(10):2897-2928.
– Name: Avail
  Label: Availability
  Group: Avail
  Data: Springer. Available from: Springer Nature. One New York Plaza, Suite 4600, New York, NY 10004. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-460-1700; e-mail: customerservice@springernature.com; Web site: https://link.springer.com/
– Name: PeerReviewed
  Label: Peer Reviewed
  Group: SrcInfo
  Data: Y
– Name: Pages
  Label: Page Count
  Group: Src
  Data: 32
– Name: DatePubCY
  Label: Publication Date
  Group: Date
  Data: 2025
– Name: TypeDocument
  Label: Document Type
  Group: TypDoc
  Data: Journal Articles<br />Reports - Research
– Name: Audience
  Label: Education Level
  Group: Audnce
  Data: <searchLink fieldCode="EL" term="%22Elementary+Education%22">Elementary Education</searchLink><br /><searchLink fieldCode="EL" term="%22Grade+5%22">Grade 5</searchLink><br /><searchLink fieldCode="EL" term="%22Intermediate+Grades%22">Intermediate Grades</searchLink><br /><searchLink fieldCode="EL" term="%22Middle+Schools%22">Middle Schools</searchLink><br /><searchLink fieldCode="EL" term="%22Early+Childhood+Education%22">Early Childhood Education</searchLink><br /><searchLink fieldCode="EL" term="%22Grade+2%22">Grade 2</searchLink><br /><searchLink fieldCode="EL" term="%22Primary+Education%22">Primary Education</searchLink>
– Name: Subject
  Label: Descriptors
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Word+Frequency%22">Word Frequency</searchLink><br /><searchLink fieldCode="DE" term="%22Reading%22">Reading</searchLink><br /><searchLink fieldCode="DE" term="%22Naming%22">Naming</searchLink><br /><searchLink fieldCode="DE" term="%22Vocabulary%22">Vocabulary</searchLink><br /><searchLink fieldCode="DE" term="%22Spanish+Speaking%22">Spanish Speaking</searchLink><br /><searchLink fieldCode="DE" term="%22Elementary+School+Students%22">Elementary School Students</searchLink><br /><searchLink fieldCode="DE" term="%22Grade+5%22">Grade 5</searchLink><br /><searchLink fieldCode="DE" term="%22Grade+2%22">Grade 2</searchLink><br /><searchLink fieldCode="DE" term="%22Syllables%22">Syllables</searchLink><br /><searchLink fieldCode="DE" term="%22Serial+Ordering%22">Serial Ordering</searchLink>
– Name: DOI
  Label: DOI
  Group: ID
  Data: 10.1007/s11145-024-10620-w
– Name: ISSN
  Label: ISSN
  Group: ISSN
  Data: 0922-4777<br />1573-0905
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: When encountering sequences of familiar words ("serial reading"), skilled readers are thought to take advantage of the presentation format by processing multiple words simultaneously in a "cascaded" manner. This is possible when individual words are read "by sight," similar to naming letters or digits. Accordingly, previous studies have shown that as readers become more experienced, fluent reading increasingly parallels serial naming of familiar symbols, while reading individual words ("discrete reading") parallels discrete naming. However, most studies have focused on high-frequency, short words, which are more amenable to cascaded processing; different performance patterns across presentation formats (serial vs. discrete) would be expected for longer, less frequent words. Therefore, in this study, we examined how word frequency and length influence the effect of word presentation format and the relation of word reading with serial and discrete digit naming. We tested 201 Spanish-speaking children in Grades 2 and 5 on serial and discrete digit naming and serial and discrete word reading of eight sets of words varying in length (two vs. four syllables) and frequency (high vs. low). Results showed that the serial word presentation format benefitted reading rates across word sets, particularly for short, high-frequency words and more strongly among fifth graders. Furthermore, the difference between serial and discrete reading and its interaction with word length and frequency were more closely associated with serial naming than discrete naming. The pattern of findings supports the hypothesis that readers employ cascaded processing to the extent individual words in the serial reading task are automatized.
– Name: AbstractInfo
  Label: Abstractor
  Group: Ab
  Data: As Provided
– Name: DateEntry
  Label: Entry Date
  Group: Date
  Data: 2026
– Name: AN
  Label: Accession Number
  Group: ID
  Data: EJ1499625
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=eric&AN=EJ1499625
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1007/s11145-024-10620-w
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 32
        StartPage: 2897
    Subjects:
      – SubjectFull: Word Frequency
        Type: general
      – SubjectFull: Reading
        Type: general
      – SubjectFull: Naming
        Type: general
      – SubjectFull: Vocabulary
        Type: general
      – SubjectFull: Spanish Speaking
        Type: general
      – SubjectFull: Elementary School Students
        Type: general
      – SubjectFull: Grade 5
        Type: general
      – SubjectFull: Grade 2
        Type: general
      – SubjectFull: Syllables
        Type: general
      – SubjectFull: Serial Ordering
        Type: general
    Titles:
      – TitleFull: Effects of Word Frequency and Length in Discrete and Serial Word Reading
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Sandra Romero
      – PersonEntity:
          Name:
            NameFull: George K. Georgiou
      – PersonEntity:
          Name:
            NameFull: Angeliki Altani
      – PersonEntity:
          Name:
            NameFull: Athanassios Protopapas
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2025
          Identifiers:
            – Type: issn-print
              Value: 0922-4777
            – Type: issn-electronic
              Value: 1573-0905
          Numbering:
            – Type: volume
              Value: 38
            – Type: issue
              Value: 10
          Titles:
            – TitleFull: Reading and Writing: An Interdisciplinary Journal
              Type: main
ResultId 1