Assessment of comprehensibility in L2 pronunciation research

L2 pronunciation research has measured L2 learners’ comprehensibility using rating scales with varying granularity, such as 9-point, 100-point, and 1,000-point scales (Chau & Huensch, Reference Chau and Huensch2025; Kostromitina et al., Reference Kostromitina, Sudina and Baghlaf2025). According to Kostromitina et al.’s (Reference Kostromitina, Sudina and Baghlaf2025) methodological review of perception-based L2 pronunciation studies, among the rating scales whose reliability was examined via Cronbach’s alpha, the 9-point scale was the most frequently used (n = 64, 48%), followed by 1,000-point (n = 34, 26%), 7-point (n = 20, 15%), and 5-point scales (n = 11, 8%). A major reason for the widespread adoption of the 9-point scale can be the seminal paper by Munro and Derwing (Reference Munro and Derwing1995), where they asked 18 L1 speakers of English to rate the comprehensibility of 10 L1 Mandarin speakers and two L2 speakers of English with a 9-point scale. In their study, a score of 1 was labeled as extremely easy to understand, while a score of 9 was labeled as impossible to understand. The rest of the score categories (i.e., 2 through 8) were visually presented but came with no performance descriptors. Adapting this 9-point scale in different ways, many studies defined a score of 9 as a representation of comprehensible speech and a score of 1 as incomprehensible speech. For example, Saito et al. (Reference Saito, Macmillan, Mai, Suzukida, Sun, Magne and Murakami2020) labeled a score of 1 as very difficult to understand and a score of 9 as very easy to understand, and Isaacs and Trofimovich (Reference Isaacs and Trofimovich2012) labeled a score of 1 as hard to understand and a score of 9 as easy to understand. This endpoint labeling has been applied to 100-point and 1,000-point scales. Huensch and Nagle (Reference Huensch and Nagle2023) labeled a score of 0 on their 100-point scale as very difficult to understand and a score of 100 as very easy to understand. Saito et al. (Reference Saito, Trofimovich and Isaacs2017) labeled a score of 0 on their 1,000-point scale as difficult to understand and a score of 1,000 as easy to understand. Unlike the 9-point scale, where all possible scores from 1 through 9 are visually presented to raters, 100-point and 1,000-point scales often omit numerical markers, including those for the endpoints. Accordingly, raters were often asked to adjust the location of a slider bar to express their intuitive evaluation of comprehensibility, instead of choosing a discrete, prelabeled score (e.g., Crowther et al., Reference Crowther, Trofimovich, Isaacs and Saito2015; Huensch & Nagle, Reference Huensch and Nagle2021, Reference Huensch and Nagle2023; Saito et al., Reference Saito, Trofimovich and Isaacs2017). These unlabeled scales require raters to construct their own benchmarks and constantly think about what it means to be a score of 5 out of 9 and a score of 50 out of 100, for example, while simultaneously being influenced by their teaching experience and accent familiarity (Saito et al., Reference Saito, Tran, Suzukida, Sun, Magne and Ilkan2019; Tsunemoto et al., Reference Tsunemoto, Trofimovich and Kennedy2023; Winke et al., Reference Winke, Gass and Myford2013), among other individual difference factors.

Validity evidence for these rating scales has been pursued primarily in two ways. First, many researchers examine interrater reliability among raters (e.g., Ali, Reference Ali2023; Bergeron & Trofimovich, Reference Bergeron and Trofimovich2017; Crowther et al., Reference Crowther, Trofimovich, Isaacs and Saito2015; Galante & Thomson, Reference Galante and Thomson2017; Saito et al., Reference Saito, Trofimovich and Isaacs2017; Suzuki & Kormos, Reference Suzuki and Kormos2020; Tergujeff, Reference Tergujeff2021), attempting to validate generalization inference that scores assigned by a rater are generalizable to other raters (Knoch & Chapelle, Reference Knoch and Chapelle2018). Although their methodological review focused on assessment instruments intended for accentedness, comprehensibility, and intelligibility, Kostromitina et al. (Reference Kostromitina, Sudina and Baghlaf2025) found that approximately 48% of the reviewed instruments in L2 pronunciation research reported Cronbach’s alpha and 32% reported intraclass correlation coefficients. Those Cronbach’s alpha values were largely sufficient, ranging from .85 (5-point scale) to .94 (9-point scale). Similarly, intraclass correlation coefficients also ranged from .91 (1,000-point scale) to .97 (100-point scale). This evidence supports the claim that scores obtained from one rater are generalizable to other raters.

Secondly, another line of research examined the relationship between comprehensibility ratings and linguistic correlates in L2 speakers’ performance (Bergeron & Trofimovich, Reference Bergeron and Trofimovich2017; Isaacs & Trofimovich, Reference Isaacs and Trofimovich2012; Saito et al., Reference Saito, Trofimovich and Isaacs2016, Reference Saito, Trofimovich and Isaacs2017; Suzuki & Kormos, Reference Suzuki and Kormos2020; Tsunemoto & Trofimovich, Reference Tsunemoto and Trofimovich2024), validating the explanation inference that scores accurately represent the construct being measured (Knoch & Chapelle, Reference Knoch and Chapelle2018). Isaacs and Trofimovich’s (Reference Isaacs and Trofimovich2012) pioneering study asked 60 L1 speakers of English to assess the comprehensibility of picture description performances elicited from 40 L1 French learners of English. They also analyzed L2 learners’ performance in terms of 19 linguistic features, reporting that comprehensibility ratings were strongly related to both phonological and lexico-grammatical features, such as unique words and word stress errors. This line of research provides evidence that scores reflect differences in the language use observed in speech samples.

However, L2 pronunciation research has provided limited evidence regarding the functioning of a scale. Commonly used reliability indices, such as Cronbach’s alpha and intraclass correlation, do not provide direct evidence because those indices are no more than indicators of rater agreement (Isbell, Reference Isbell, Kang and Ginther2018). When Cronbach’s alpha is used to assess raters’ agreement, different raters are considered to be fixed test items; thus, Cronbach’s alpha indicates the extent to which different raters measure the same construct (i.e., unidimensionality). Regarding intraclass correlation, pronunciation researchers often use two-way consistency, average-measure intraclass correlation known as ICC(2, k) (e.g., Ali, Reference Ali2023; Huensch & Nagle, Reference Huensch and Nagle2023; Isbell, Reference Isbell, Kang and Ginther2018; Nagle & Rehman, Reference Nagle and Rehman2021). This type of intraclass correlation assumes that raters are randomly drawn from a pool of raters and is appropriate when raters’ averaged scores are of interest (Shrout & Fleiss, Reference Shrout and Fleiss1979). ICC(2, k) partitions variance attributable to examinees and variance attributable to raters, better reflecting raters’ consistency than Cronbach’s alpha (Isbell, Reference Isbell, Kang and Ginther2018). While commonly used among L2 pronunciation researchers, both Cronbach’s alpha and intraclass correlation deal with obtained ratings that are decontextualized from the scale design. Suppose that one rater assigns scores of 1, 3, and 9 and another rater assigns scores of 2, 4, and 6 for the same three examinees. Cronbach’s alpha is .86, and ICC(2, k) is .90. However, these ratings can be obtained either with a 9-point scale or with a 100-point scale. When a 9-point scale is used, raters appear to make use of diverse score categories (i.e., functional scale), but they use a narrow range of score categories on a 100-point scale (i.e., dysfunctional scale). As this example illustrates, while Cronbach’s alpha and intraclass correlation inform us about rater agreement, the functionality of a rating scale remains unknown unless ratings are interpreted in relation to the scale design.

Examining scale functioning pertains to evaluation inference that “Observations are evaluated using procedures that provide observed scores with intended characteristics” (Knoch & Chapelle, Reference Knoch and Chapelle2018, p. 483). Validating evaluation inference requires evidence that raters use the given rating scale as intended and that the rating scale functions as intended. For example, when raters are asked to use a 9-point scale, a score of 8 needs to represent more comprehensible speech than that represented by scores up to 7. Isaacs and Thomson’s (Reference Isaacs and Thomson2013) pioneering study tested this assumption by asking 40 novice and experienced raters to use 5-point and 9-point scales to assess comprehensibility of narrative speeches performed by 38 L2 speakers of English. They found that the 9-point scale did not reliably distinguish L2 speakers who were assigned different scores, especially due to raters’ confusion caused by the large number of score categories. Consequently, L2 speakers who were assigned middle score categories were particularly muddled, and speakers who were assigned a score of 2 were also likely to receive a score of 5 on the 9-point scale. Similarly, Isbell (Reference Isbell, Kang and Ginther2018) asked 10 L1 speakers of Korean to use a 9-point scale to assess picture description and read-aloud performances elicited from 36 L2 learners of Korean, finding that the middle scores, such as 4 and 6, were essentially interchangeable with adjacent score categories. More recently, Kermad (Reference Kermad2024) compared 30 untrained raters and 30 trained raters in their use of a 5-point scale while rating prompted speeches performed by 20 L2 learners of English. The study found that untrained raters did not use score categories appropriately, observing that the scores of 3 and 4 were essentially interchangeable. Trained raters, in contrast, used the rating scale as intended, assigning different scores to speakers who displayed speaking performance that differed in comprehensibility. These findings collectively suggest that long rating scales may be overly segmented and thereby impose greater cognitive load on raters, especially due to the presence of potentially redundant mid-points.

Despite potential confusion among raters caused by long rating scales, such scales continue to be used in L2 pronunciation research (Kostromitina et al., Reference Kostromitina, Sudina and Baghlaf2025). Indeed, some studies did not explicitly justify their scale length (e.g., Galante & Thomson, Reference Galante and Thomson2017; Isaacs & Trofimovich, Reference Isaacs and Trofimovich2012; Saito et al., Reference Saito, Tran, Suzukida, Sun, Magne and Ilkan2019), and others justified their scale length on the grounds that previous studies had used the same length (e.g., Ali, Reference Ali2023; Bergeron & Trofimovich, Reference Bergeron and Trofimovich2017; Crowther et al., Reference Crowther, Trofimovich, Isaacs and Saito2015; Suzuki & Kormos, Reference Suzuki and Kormos2020; Thorpe et al., Reference Thorpe, Baker-Smemoe, Hartshorn, McMurry and Wilcox2025; Uchihara et al., Reference Uchihara, Webb, Saito and Trofimovich2023). A few studies provided more concrete justifications, stating that long rating scales were expected to provide raters with sufficient response options (Tergujeff, Reference Tergujeff2021) and to enable scores to be treated as continuous variables (Huensch & Nagle, Reference Huensch and Nagle2021), for example. It is noteworthy that Nagle and Rehman (Reference Nagle and Rehman2021) is one of the few studies that explicitly drew on the rebuttal evidence from Isaacs and Thomson (Reference Isaacs and Thomson2013) and opted for a 7-point scale as an eclectic solution to address the drawbacks of 5-point and 9-point scales. While potentially reflecting the needs of their own research context on one hand, researchers’ arbitrary choice of scale on the other hand makes it difficult to draw solid conclusions due to variations in scale design.

As Isbell (Reference Isbell, Kang and Ginther2018) rightly pointed out, perhaps long rating scales have been tacitly justified because many studies primarily aimed to examine laypeople’s intuitive, impressionistic assessment of comprehensibility. Yet, this persistent methodological convention may also be ascribed to a lack of communication between second language acquisition (SLA) researchers and language testing researchers (Isaacs & Thomson, Reference Isaacs and Thomson2013). In fact, language testing researchers emphasize that rating scales need to undergo a sequence of validation processes that go far beyond calculating interrater reliability (Knoch & Chapelle, Reference Knoch and Chapelle2018). In addition, language testing researchers often use Rasch models that allow closer examination of rater behavior and scale functioning (McNamara et al., Reference McNamara, Knoch and Fan2019), but such an approach has rarely been used in L2 pronunciation research (Kostromitina et al., Reference Kostromitina, Sudina and Baghlaf2025). Although a few studies employed Rasch models, these studies mainly focused on speaker ability and listener severity without fully examining scale functioning (Nagle & Rehman, Reference Nagle and Rehman2021; Shintani et al., Reference Shintani, Saito and Koizumi2019). Clearly, more validity evidence is needed to justify researchers’ use of long rating scales.

Ordered thresholds and threshold distances as psychometric qualities of a rating scale

Two critical assumptions for a functional rating scale are “scale steps are adequate to distinguish among the levels that appear in the scale” and “raters are able to identify differences in performances across score levels” (Knoch & Chapelle, Reference Knoch and Chapelle2018, p. 483). These assumptions have been commonly examined via a Rasch measurement approach (Linacre, Reference Linacre2002), which allows the investigation of two key psychometric properties—ordered thresholds and threshold distances. First, the Rasch-Andrich threshold, or “the location corresponding to the equal probability of observing adjacent categories k-1 and k” (Linacre, Reference Linacre2002, p. 88), needs to increase for higher score categories (Linacre, Reference Linacre1999). Thresholds, also referred to as step calibrations, are estimated by polytomous Rasch models, such as the partial credit model (Masters, Reference Masters1982) and the rating scale model (Andrich, Reference Andrich1978). They indicate the relative probability of receiving a score versus a score one point lower. Negative threshold measures suggest that the higher score category is more likely to be observed than the lower score category, whereas positive threshold measures indicate that the lower score category is more likely to be observed. When threshold measures for higher score categories exceed those for lower score categories across any pairs of two adjacent score categories on a rating scale, such evidence supports the claim that different scores meaningfully reflect differences in L2 speakers’ ability level. Conversely, when threshold measures for lower score categories exceed those for higher score categories, the rating scale is said to exhibit threshold disordering. Threshold disordering indicates that a score category captures an overly limited range of the latent trait or represents a concept that is not well defined in respondents’ minds (Linacre, Reference Linacre2002). In practice, threshold disordering often occurs when a scale has too many categories relative to the ability distribution, or when raters struggle to link certain score categories to specific performance levels.

Another essential condition for a functional rating scale is that obtaining a certain score is sufficiently more difficult than obtaining the score one point lower. When two adjacent categories are equally likely to be chosen for the same examinee, it indicates that the same examinee’s ability can be represented by two score categories that are potentially interchangeable. Threshold distances can be calculated by the difference in logits between the Rasch-Andrich threshold of a score and that of the score one point lower. According to Linacre (Reference Linacre2002), the optimal threshold distance falls within 1.4 to 5.0 logits. Ordered thresholds and threshold distances can also be visually examined in probability curves, which depict the changing likelihood of each score category across examinees’ ability levels. Score categories are said to function properly when each score category displays a distinct peak in its probability curve.

There are two good reasons to assume threshold disordering and narrow threshold distances in the long rating scales used for speech comprehensibility. First, because it is usually difficult for a study to recruit learners with a wide range of proficiency, the sampled learners may display relatively homogeneous comprehensibility that cannot be meaningfully categorized into nine or more score categories. Indeed, Isaacs and Thomson (Reference Isaacs and Thomson2013) reported that raters perceived redundancy of some score categories of their 9-point scale (see also Isbell, Reference Isbell, Kang and Ginther2018; Kermad, Reference Kermad2024). Such redundancy potentially forces raters to choose a score category that does not precisely match the ability level constructed in the raters’ minds (Linacre, Reference Linacre2002). Secondly, for 100-point and 1,000-point scales, raters are asked to assign a score without knowing the exact score they are assigning because numerical values are often hidden on the scale (Bergeron & Trofimovich, Reference Bergeron and Trofimovich2017; Crowther et al., Reference Crowther, Trofimovich, Isaacs and Saito2015; Huensch & Nagle, Reference Huensch and Nagle2021; Nagle et al., Reference Nagle, Trofimovich, O’brien and Kennedy2022; Saito et al., Reference Saito, Trofimovich and Isaacs2017; Trofimovich et al., Reference Trofimovich, Nagle, O’Brien, Kennedy, Taylor Reid and Strachan2020). For example, in Crowther et al.’s (Reference Crowther, Trofimovich, Isaacs and Saito2015) 1,000-point scale, no numerical values were presented except for brief descriptions at the endpoints (i.e., 1 = hard to understand, 1,000 = easy to understand). As such, the relative difficulty of score categories may rest upon not only raters’ intuitive assessment of comprehensibility but also their operation of the slide bar. For example, raters may accidentally place the slide bar at a score of 60 for a speech performance that they think is better than another speech performance they assigned a score of 61 as these two score categories are placed extremely close on the continuum. Indeed, though they used a 1,000-point scale for audio-based measures, such as segmental errors and word stress errors, Saito et al. (Reference Saito, Trofimovich and Isaacs2016) reminded raters that even a slight adjustment of the slider could cause a substantial change in the rating, implying the critical role played by raters’ delicate operation of the slide bar. When threshold disordering and narrow threshold distances are observed, interpreting scores becomes difficult as higher scores do not necessarily represent higher ability levels.

Score category collapsing as a potential solution

One way to address disordered thresholds and narrow threshold distances is score category collapsing, whereby two or more score categories on a rating scale are merged into a single score category (Linacre, Reference Linacre2002). For example, when Rasch models suggest that scores of 2 and 3 are disordered on a 9-point scale (i.e., 123456789), those two score categories can be merged into a single score category, resulting in a new 8-point scale (i.e., 122345678). When scores of 2 and 3 and scores of 7 and 8 are disordered, both pairs can be merged, creating a new 7-point scale (i.e., 122345677). Score category collapsing allows collapsed score categories to represent more distinct ability levels by aggregating minimally different ability levels represented by original score categories. As score categories are collapsed after data collection, L2 pronunciation researchers can still use conventional long rating scales when they design their study, assuring the compatibility of their study with previous studies. Furthermore, while score category collapsing usually requires one to redefine performance descriptors for newly created score categories, comprehensibility rating scales usually come only with the endpoint labeling (e.g., 1 = hard to understand, 9 = easy to understand) and omit descriptors for other score categories. Accordingly, researchers can still interpret obtained scores as listeners’ intuitively perceived comprehensibility of heard speech samples.

Score category collapsing is not a completely new idea in L2 pronunciation research. Isaacs and Trofimovich (Reference Isaacs and Thomson2013) mentioned the possibility of combining the score categories of 3, 4, 5, and 6 in a 9-point scale for comprehensibility, and Isbell (Reference Isbell, Kang and Ginther2018) mentioned the possibility of combining the score category of 7 with adjacent score categories in a 9-point scale for accentedness. However, very few studies have empirically tested its impact on measurement quality, and to my knowledge, Kermad and Bogorevich (Reference Kermad and Bogorevich2022) is the only study. They asked 56 raters, including L1 and L2 speakers of English, to assess speech performances elicited by four tasks—read-aloud, spontaneous speech, elicitation, picture description—which were performed by 15 L2 learners of English. Raters used a 9-point scale (i.e., 123456789) to assess comprehensibility and accentedness. The study collapsed score categories based on statistical information derived from the many-facet Rasch measurement analysis. Specifically, they combined the score categories of 3 and 4 and the score categories of 6 and 7, creating a 7-point scale (i.e., 123345567). They also combined the score categories of 1 and 2, 3 and 4, 6 and 7, and 8 and 9, creating a 5-point scale (i.e., 112234455). The results suggested that the score categories in the 5-point scale represented different ability levels more clearly than those in the 7-point and 9-point scales. Meanwhile, the midpoint of the 5-point scale still did not function well, being muddled with adjacent score categories. While Kermad and Bogorevich’s (Reference Kermad and Bogorevich2022) study demonstrated score category collapsing as a potential solution, they tested only two collapsing patterns, leaving other collapsing patterns to be further explored. In addition, other popular rating scales, such as 100-point and 1,000-point scales, have yet to be examined, though these substantially long rating scales are arguably more likely to confuse raters than a 9-point scale. Expanding Kermad and Bogorevich’s (Reference Kermad and Bogorevich2022) pioneering study, the present study aims to illustrate the impact of score category collapsing on psychometric quality, using 9-point and 100-point scales as illustrative cases.

Research questions

The literature review suggests that many L2 pronunciation studies have conventionally used long rating scales, despite rebuttal evidence such as that presented by Isaacs and Trofimovich’s (Reference Isaacs and Thomson2013) pioneering study. The present study thus aims to raise researchers’ awareness of the potential drawbacks of long rating scales by examining key psychometric properties—ordered thresholds and threshold distances. I chose 9-point and 100-point scales because Saito et al. (Reference Saito, Macmillan, Mai, Suzukida, Sun, Magne and Murakami2020) and Huensch and Nagle (Reference Huensch and Nagle2023) provide well-controlled, rich datasets collected with these two scales (see Methods for more details). I have no intention to exclusively problematize these two scales nor to generalize the present findings to other scales in L2 pronunciation research. Rather, my purpose is to provide empirical evidence that demonstrates the potential limitations of long scales by using 9-point and 100-point scales as illustrative cases. The present study also aims to showcase post hoc score category collapsing as a potential countermeasure against suboptimal scale functioning. With these overarching goals, the present study addresses the following research questions:

Functioning of the original 9-point scale (RQ1)

Table 1 summarizes the statistics regarding the functioning of the nine score categories in Saito et al. (Reference Saito, Macmillan, Mai, Suzukida, Sun, Magne and Murakami2020). The number of times a score category being chosen monotonically increases from 1 (19 times, 2%) to 7 (204 times, 19%) with a slight drop at the scores of 8 (196 times, 18%) and 9 (160 times, 15%). Measure indicates the difficulty of test takers obtaining the score category, suggesting that the difficulty linearly increases as raw scores increase from 1 (–.80 logits) to 9 (2.35 logits). Outfit suggests the extent to which the score category conforms to the specified Rasch model, and values below 2.0 are generally considered acceptable (Linacre, Reference Linacre2002). The nine score categories all meet this criterion. Threshold measures—points at which the likelihood of test takers obtaining two adjacent score categories is equal—monotonically increase as raw scores increase from 2 (–1.54 logits) to 9 (2.07 logits). All distances between adjacent Rasch-Andrich thresholds were positive, suggesting that obtaining higher scores required higher ability levels. However, threshold distances were relatively narrow for score categories from 3 to 7, ranging from .23 to .61 logits. In contrast, threshold distances for 8 and 9 were relatively large, being .82 and .88 logits, though falling short of the recommended lower bound of 1.4 (Linacre, Reference Linacre2002).

Table 1.

Score category statistics of the original 9-point scale

Table 1. Long description

The table consists of 9 rows representing scores 1 through 9 and 8 columns of data.

* Score 1: Count 19, 2 percent, Measure minus 0.80, Outfit 1.4, Threshold Measure N A, Threshold S E N A, Threshold distance N A.

* Score 2: Count 38, 3 percent, Measure minus 0.59, Outfit 1.3, Threshold Measure minus 1.54, Threshold S E 0.25, Threshold distance N A.

* Score 3: Count 78, 7 percent, Measure minus 0.41, Outfit 1.1, Threshold Measure minus 1.30, Threshold S E 0.16, Threshold distance 0.24.

* Score 4: Count 113, 10 percent, Measure minus 0.21, Outfit 1.1, Threshold Measure minus 0.69, Threshold S E 0.11, Threshold distance 0.61.

* Score 5: Count 137, 12 percent, Measure minus 0.02, Outfit 0.9, Threshold Measure minus 0.24, Threshold S E 0.10, Threshold distance 0.45.

* Score 6: Count 155, 14 percent, Measure 0.41, Outfit 0.9, Threshold Measure 0.14, Threshold S E 0.09, Threshold distance 0.38.

* Score 7: Count 204, 19 percent, Measure 0.87, Outfit 0.9, Threshold Measure 0.37, Threshold S E 0.08, Threshold distance 0.23.

* Score 8: Count 196, 18 percent, Measure 1.50, Outfit 0.8, Threshold Measure 1.19, Threshold S E 0.09, Threshold distance 0.82.

* Score 9: Count 160, 15 percent, Measure 2.35, Outfit 0.9, Threshold Measure 2.07, Threshold S E 0.11, Threshold distance 0.88.

Note. Count = the number of times the score category being chosen, Measure = difficulty of test takers obtaining the score, outfit = fit to observed data, Threshold measure = test taker ability at which obtaining two adjacent score categories is equally likely, Threshold SE = standard error of threshold measure, Threshold distance = the difference between two adjacent thresholds.

This suboptimal scale functioning is also evident in the probability curves (Figure 3), where the probability of receiving each score (y-axis; 0.0 to 1.0) is plotted as a function of speakers’ ability (x-axis; –4.0 to 4.0 logits). For example, speakers associated with 1.5 logits on the x-axis likely receive a score of 7. However, many score categories from 2 to 7 fail to display clear peaks. As shown in the curves, speakers around 0 logits are equally likely to receive scores of 3, 4, 5, 6, and 7, which suggests that raters assigned different scores to speakers who did not substantially differ in comprehensibility.

Figure 3.

Probability curves of the original 9-point scale visualizing the probabilities of score categories (y-axis) as a function of examinee ability (x-axis).

Figure 3. Long description

The graph is rendered in a fixed-width character style. The y-axis is labeled Probability on the left, ranging from 0 at the bottom to 1 at the top. The x-axis represents examinee ability, with tick marks at negative 4.0, negative 2.0, 0.0, 2.0, and 4.0.

Nine distinct curves are formed by repeating digits 1 through 9.

* Curve 1 starts at a probability of 1 on the far left (negative 4.0) and follows a logistic decay pattern, sloping downward to reach 0 near the center of the x-axis.

* Curve 9 starts at 0 near the center and follows a logistic growth pattern, reaching a probability of 1 at the far right (4.0).

* Curves 2 through 8 are bell-shaped unimodal distributions that peak at successive intervals along the x-axis.

* Curve 2 peaks in the negative 2.0 region.

* Curve 5 peaks near the 0.0 center point.

* Curve 8 peaks in the 2.0 region.

Asterisks form a solid horizontal baseline at probability 0 and appear at the intersection points where multiple category curves overlap. The density of the numeric characters creates a visual representation of the most likely score category for any given ability level.

Functioning of rating scales derived from score category collapsing (RQ2)

Table 2 presents Rasch-Andrich thresholds and threshold distances for the four rating scales derived from score category collapsing. Threshold measures monotonically increased from low to high score categories for the 3-point and 4-point scales (i.e., ordered thresholds). Meanwhile, in the 5-point scale, the threshold measure for the score category of 3 (.26 logits) was higher than that for the score category of 4 (–.28 logits), indicating disordering between these two score categories (see the Measure column of 112234455 in Table 2). Threshold distances in the 3-point and 4-point scales all fell within the recommended range from 1.4 to 5.0 (Linacre, Reference Linacre2002), suggesting that each score category reflected a distinct difficulty level. In contrast, the 5-point scale contained one negative distance between the score categories of 3 and 4 (–.54 logits), further confirming their disordering.

Table 2.

Score category statistics of the four collapsed scales

Table 2. Long description

The table is structured with a primary column for Score (1 to 5) and four main scale groups labeled 1 1 1 2 2 2 3 3 3, 1 1 2 2 3 4 4 5 5, 1 1 2 2 2 3 3 4 4, and 1 1 2 2 3 3 3 4 4. Each scale group is subdivided into Measure and Distance columns.

* Score 1: All scales show N A for both Measure and Distance.

* Score 2:

- Scale 1 1 1 2 2 2 3 3 3: Measure minus 1.46, Distance N A.

- Scale 1 1 2 2 3 4 4 5 5: Measure minus 1.95, Distance N A.

- Scale 1 1 2 2 2 3 3 4 4: Measure minus 2.76, Distance N A.

- Scale 1 1 2 2 3 3 3 4 4: Measure minus 2.06, Distance N A.

* Score 3:

- Scale 1 1 1 2 2 2 3 3 3: Measure 1.46, Distance 2.92.

- Scale 1 1 2 2 3 4 4 5 5: Measure 0.26, Distance 2.21.

- Scale 1 1 2 2 2 3 3 4 4: Measure 0.40, Distance 3.16.

- Scale 1 1 2 2 3 3 3 4 4: Measure minus 0.59, Distance 1.47.

* Score 4:

- Scale 1 1 1 2 2 2 3 3 3: Empty.

- Scale 1 1 2 2 3 4 4 5 5: Measure minus 0.28, Distance minus 0.54.

- Scale 1 1 2 2 2 3 3 4 4: Measure 2.36, Distance 1.96.

- Scale 1 1 2 2 3 3 3 4 4: Measure 2.65, Distance 3.24.

* Score 5:

- Scale 1 1 2 2 3 4 4 5 5: Measure 1.98, Distance 2.26.

- All other scales are empty for Score 5.

Note. Measure = test taker’s ability at which obtaining two adjacent score categories is equally likely, Distance = the difference between two adjacent thresholds.

Figure 4 presents the probability curves for the four rating scales derived from score category collapsing. Most score categories display distinct peaks, suggesting that those score categories represent distinct ability levels. Meanwhile, the score category of 3 in the 5-point scale remained muddled with adjacent score categories, which suggests that L2 speakers assigned a score of 3 are also likely to receive a score of 2 or 4.

Figure 4.

Probability curves for the 3-point (111222333, top left), 5-point (112234455, top right), 4-point (112223344, bottom left), and 4-point scales (112233344, bottom right).

Figure 4. Long description

A four-panel set of A S C I I plots. Each plot has a vertical Y-axis labeled Probability from 0 to 1 and a horizontal X-axis representing a latent trait scale.

* Top-left panel: 3-point scale (1 1 1 2 2 2 3 3 3). Three bell-shaped curves formed by the numbers 1, 2, and 3. Curve 1 peaks on the left, curve 2 peaks in the center, and curve 3 peaks on the right.

* Top-right panel: 5-point scale (1 1 2 2 3 4 4 5 5). Five overlapping curves labeled 1 through 5. Curves 1 and 5 are at the extremes, while 2, 3, and 4 are narrower and clustered in the center.

* Bottom-left panel: 4-point scale (1 1 2 2 2 3 3 4 4). Four curves where the central curves 2 and 3 show significant overlap and lower peaks compared to the outer curves 1 and 4.

* Bottom-right panel: 4-point scale (1 1 2 2 3 3 3 4 4). Similar to the previous panel but with a different distribution of numeric characters, showing four distinct probability regions across the X-axis from negative 4.0 to positive 4.0.

Comparing the original 9-point scale with the collapsed scales (RQ3)

Figure 5 presents the variable maps for the original 9-point scale and the three collapsed ratings scales that met the criteria for thresholds and probability curves. The leftmost column denotes the common logit scale that applies to the speaker, rater, and scale. The second column presents the distribution of speakers’ ability, where higher values toward the top of the column represent more able speakers. The third column visualizes the distribution of rater severity, where higher values toward the top of the column represent more severe raters. The rightmost column shows each score category and its coverage of measures.

Figure 5.

Variable maps for the original 9-point scale and the collapsed 3-point, 4-point (112223344), and 4-point (112233344) scales.

Figure 5. Long description

A multi-panel figure containing four vertical Wright maps. Each map shares a common vertical axis labeled Measr on the left, ranging from -6 at the bottom to +6 at the top. Each map is divided into four columns: Measr, +speakers, -raters, and Scale.

* Panel 1 (9-point scale): The +speakers column shows a normal distribution of asterisks centered around 0.5 logits. The Scale column shows thresholds for categories 1 through 9 spread from -6 to +6 logits, with category 5 at 0 logits.

* Panel 2 (3-point scale): The +speakers distribution remains similar. The Scale column is collapsed into three categories: 1, 2, and 3. Category 2 is centered at 0, while 1 and 3 are at the extremes.

* Panel 3 (4-point scale 112223344): The Scale column shows four categories. Category 1 is at the bottom, 2 and 3 are clustered around the center, and 4 is at the top. The asterisk density in +speakers is higher, with each asterisk representing 1 speaker instead of 2.

* Panel 4 (4-point scale 112233344): Similar to Panel 3 but with a different collapsing logic for the middle categories. The distribution of raters in the -raters column across all panels shows a concentration of rater IDs (e.g., 1, 2, 3, 4, 5, 6, 7, 8, 9, 10) between -1 and +2 logits.

At the bottom of each map, a legend indicates the scale of the asterisks, such as Measr asterisk equals 2 or asterisk equals 1.

According to these variable maps, it seems that speakers’ abilities became more distinct for the collapsed rating scales. For example, speakers are clustered closely together on the 9-point scale—particularly those with logits between –0.5 and 2.0—whereas the 3-point scale seems to cluster speakers associated with logits of 6.0, 4.5, 3.5, 3.0, and so on. The ranking of rater severity does not seem to differ across the scales. Rater 10 was distinctively severe, while Raters 4 and 5 were lenient. The rest of the raters largely fell within a range from –1.0 to 1.0 logits. As the scale collapsed, each score category covered a wider range of speakers’ ability levels. On the 9-point scale, the score categories from 3 to 6 each covered approximately 0.5 logits at most, whereas the score categories of 7, 8, and 9 each represented a wider range of ability levels. In contrast, the 4-point scale of 112233344 (the rightmost figure) allowed each score category to cover at least 2.0 logits of the speaker’s ability. In short, echoing the observations from their probability curves, these variable maps indicate that the collapsed scales pool minimally different ability levels into one score category and thereby link each score category with a distinctly different ability level.

Table 3 compares the original 9-point scale and the three collapsed rating scales that met the criteria for thresholds and probability curves. It seems that these scales are not substantially different in terms of Cronbach’s alpha and intraclass correlation, as their 95% confidence intervals largely overlap, mostly falling within the range from .80 to .90. As for the model fit, the original 9-point scale and the collapsed 4-point scale of 112223344 explained approximately 60% of the variance, whereas approximately 50% of the variance was explained by the 3-point scale and the other 4-point scale of 112233344. Rasch residuals over |2.0| were minimal across the scales. These explained variances and minimal residuals suggest that the Rasch model adequately fits the observed data across the four scales.

Table 3.

Comparison among the original 9-point, 3-point (111222333), 4-point (112223344), and 4-point (112233344) scales

Table 3. Long description

The table compares the original 9-point scale (123456789), a 3-point scale (111222333), and two variations of 4-point scales (112223344 and 112233344).

* Cronbach alpha: Original .89; 3-point .84; 4-point A .87; 4-point B .86.

* Two-way consistency intraclass correlation: Original .89; 3-point .82; 4-point A .86; 4-point B .84.

* Variance explained by Rasch: Original 63.59%; 3-point 52.82%; 4-point A 60.80%; 4-point B 54.75%.

* Standardized residuals over |2.0|: Original 3.2%; 3-point 3.8%; 4-point A 4.2%; 4-point B 4.5%.

* Strata for person ability: Original 3.13; 3-point 2.97; 4-point A 3.79; 4-point B 3.65.

* Separation reliability for person: Original .91; 3-point .80; 4-point A .87; 4-point B .86.

* Increasing thresholds: All scales show Yes.

* Threshold distances over 1.4: Original No; all others Yes.

* Peaks in probability curves: Original No; all others Yes.

* Raters with infit over 1.5: Original 1; all others 0.

* Strata for rater severity: Original 8.35; 3-point 7.98; 4-point A 11.76; 4-point B 10.75.

* Separation reliability for rater: Original .97; 3-point .97; 4-point A .99; 4-point B .98.

Regarding speaker ability, all the scales were associated with speaker strata of approximately 3, indicating there were three statistically distinguishable ability levels. Separation reliability for person, which can be interpreted as Cronbach’s alpha in classical test theory (Linacre, Reference Linacren.d.), was sufficient, ranging from .80 to .91. As for rater severity, the original 9-point scale and the collapsed 3-point scale found eight rater severity levels, but the 4-point scales found 11 rater severity levels. Separation reliability for rater was high for all four scales, being above .95. These statistics suggest that while the four scales reliably identified three distinct ability levels among speakers, the 4-point scales distinguished rater severity more clearly than the 9-point and 3-point scales.

Person measures or estimated speakers’ ability derived from the collapsed scales were highly correlated with those from the original scale. Pearson’s product-moment correlations were .97 (95% CI[.95, .98]) for the 3-point scale, .99 (95% CI[.98, .99]) for the 4-point scale of 112223344, and .99 (95% CI[.98, .99]) for the 4-point scale of 112233344. These results suggest that ability estimates derived from the collapsed scales were highly compatible with those derived from the original scale. In short, score category collapsing helped score categories to represent more distinct ability levels than those originally represented by the nine score categories, without compromising the psychometric properties of the original 9-point scale.

Functioning of the original 100-point scale (RQ1)

Out of 99 possible threshold distances, 46 distances were positive (i.e., ordered thresholds), and 53 distances were negative (i.e., disordered thresholds). Table 4 presents the 10 score categories that were associated with the highest threshold distances on the 100-point scaleFootnote ⁷. Interestingly, nine of the 10 highest threshold distances were found at score categories that denote one point above multiples of 5 (i.e., 11, 21, 26, 41, 61, 71, 81, 86, 91). This may suggest that raters distinguished scores that are up to exact multiples of 5 (e.g., 20, 60, 70) and scores that denote one point above multiples of 5.

Table 4.

Score category statistics of the 10 score categories associated with the highest threshold distances on the 100-point scale

Table 4. Long description

The table consists of 10 rows representing score categories 11, 13, 21, 26, 41, 61, 71, 81, 86, and 91. The columns are Score, Count, Percentage, Measure, Outfit, Threshold Measure, Threshold S E, and Threshold distance.

* Score 11: Count 17, 1 percent, Measure minus .06, Outfit 1.0, Threshold Measure .96, Threshold S E .07, Threshold distance 1.51.

* Score 13: Count 14, 0 percent, Measure minus .06, Outfit .8, Threshold Measure .60, Threshold S E .07, Threshold distance 1.12.

* Score 21: Count 12, 0 percent, Measure minus .04, Outfit 1.2, Threshold Measure 1.26, Threshold S E .06, Threshold distance 2.60.

* Score 26: Count 20, 1 percent, Measure minus .03, Outfit .8, Threshold Measure .56, Threshold S E .06, Threshold distance 1.47.

* Score 41: Count 26, 1 percent, Measure .00, Outfit .8, Threshold Measure .57, Threshold S E .05, Threshold distance 1.23.

* Score 61: Count 20, 1 percent, Measure .03, Outfit .8, Threshold Measure 1.13, Threshold S E .05, Threshold distance 1.61.

* Score 71: Count 34, 1 percent, Measure .05, Outfit .4, Threshold Measure .68, Threshold S E .05, Threshold distance 1.53.

* Score 81: Count 36, 1 percent, Measure .07, Outfit .9, Threshold Measure .71, Threshold S E .05, Threshold distance 1.39.

* Score 86: Count 36, 1 percent, Measure .09, Outfit .6, Threshold Measure .78, Threshold S E .05, Threshold distance 1.31.

* Score 91: Count 37, 1 percent, Measure .12, Outfit .5, Threshold Measure .80, Threshold S E .06, Threshold distance 1.29.

Note. Count = the number of times the score category being chosen, Measure = difficulty of test takers obtaining the score, outfit = fit to observed data, Threshold measure = test taker’s ability at which obtaining two adjacent score categories is equally likely, Threshold SE = standard error of threshold measure, Threshold distance = the difference between two adjacent thresholds.

Score category collapsing for rectifying threshold disordering and distances (RQ2)

Given that approximately half of the score categories were disordered, score categories were collapsed based on threshold distances under the assumption that large threshold distances suggest the anchoring function of those score categories. Specifically, scores in the ranges 1–10, 11–20, 21–25, 26–40, 41–60, 61–70, 71–80, 81–85, 86–90, and 91–100 were each collapsed into a single score category. This collapsing scheme resulted in a 10-point scale that contains 11 score categories from 0 to 10, with 0 retained as a separate category (see Figure 2). Table 5 summarizes the score category statistics from the MFRM analysis. The threshold measures suggest several disordered categories, such as scores of 3 (.46 logits) and 4 (–1.41 logits) and scores of 8 (1.41 logits) and 9 (.84 logits). Those score categories were also associated with negative threshold distances, including a score of 4 (–1.87 logits) and a score of 9 (–.57 logits).

Table 5.

Score category statistics of the 10-point scale

Table 5. Long description

The table contains 11 rows of data corresponding to scores 0 through 10. The columns are Score, Count, %, Measure, Outfit, Threshold Measure, Threshold S E, and Threshold distance.

* Score 0: Count 54, 2%, Measure minus .74, Outfit 1.5, Thresholds N A.

* Score 1: Count 235, 7%, Measure minus .62, Outfit 1.2, Threshold Measure minus 2.23, Threshold S E .14, Threshold distance N A.

* Score 2: Count 230, 7%, Measure minus .36, Outfit 1.1, Threshold Measure minus .51, Threshold S E .07, Threshold distance 1.72.

* Score 3: Count 107, 3%, Measure minus .31, Outfit .8, Threshold Measure .46, Threshold S E .06, Threshold distance 0.97.

* Score 4: Count 399, 12%, Measure minus .03, Outfit .9, Threshold Measure minus 1.41, Threshold S E .06, Threshold distance minus 1.87.

* Score 5: Count 609, 18%, Measure .19, Outfit 1.0, Threshold Measure minus .30, Threshold S E .05, Threshold distance 1.11.

* Score 6: Count 375, 11%, Measure .46, Outfit .8, Threshold Measure .82, Threshold S E .05, Threshold distance 1.12.

* Score 7: Count 408, 12%, Measure .68, Outfit .9, Threshold Measure .45, Threshold S E .05, Threshold distance minus 0.37.

* Score 8: Count 210, 6%, Measure .87, Outfit .8, Threshold Measure 1.41, Threshold S E .05, Threshold distance 0.96.

* Score 9: Count 237, 7%, Measure 1.05, Outfit 1.0, Threshold Measure .84, Threshold S E .06, Threshold distance minus 0.57.

* Score 10: Count 496, 15%, Measure 1.33, Outfit 1.1, Threshold Measure .46, Threshold S E .06, Threshold distance minus 0.38.

Note. Count = the number of times a score category being chosen, Measure = difficulty of test takers obtaining the score, outfit = fit to observed data, Threshold measure = test taker ability in logit at which obtaining two adjacent score categories is equally likely, Threshold SE = standard error of threshold measure, Threshold distance = the difference between two adjacent thresholds.

To further refine this 10-point scale, another rating scale was created. Specifically, Rasch-Andrich threshold measures and threshold distances were screened in two ways. First, threshold measures and threshold distances were compared for two adjacent score categories from the lowest score category—whether measures and distances associated with higher score categories were higher. Secondly, threshold measures and threshold distances were compared for two adjacent score categories from the highest score category—whether measures and distances associated with lower score categories were lower.

These two screening methods resulted in the slightly different, yet consistent, identification of disordered categories. Neither screening method flagged scores of 1 and 5, which were thus maintained. Scores from 2 to 4 were found to be disordered and were collapsed into a single category. The screening flagged scores from 6 to 10. While collapsing these five score categories into one score category was possible, their associated measures seemed notably different. Specifically, scores of 6 and 7 were associated with notably lower measures (.82 and .45 logits, respectively) than the score of 8, which was associated with a threshold measure of 1.41 logits. While scores of 9 and 10 were similar to scores of 6 and 7 in threshold measures (.84 and .46 logits, respectively), it was thought that the score of 8 denoted an ability level that was somewhat different from ability levels represented by scores of 6 and 7. Accordingly, scores of 6 and 7 were collapsed into one score category, and scores of 8, 9, and 10 were collapsed into another score category. This collapsing transformed the 10-point scale of 012345678910 to a 5-point scale of 01222344555 (see Figure 2).

The 5-point scale did not show any disordered categories, and higher score categories were associated with higher threshold measures (Table 6). However, threshold distances were relatively narrow between score categories of 3 and 4 (.30 logits), compared with the other threshold distances of 1.08 (scores from 1 to 2), 2.08 (scores from 2 to 3), and .90 (scores from 4 to 5) logits.

Table 6.

Score category statistics of the 5-point scale

Table 6. Long description

The table consists of 8 columns: Score, Count, %, Measure, Outfit, Threshold Measure, Threshold S E, and Threshold distance.

* Score 0: Count 54, 2%, Measure minus .93, Outfit 1.6, Thresholds and distance are N A.

* Score 1: Count 235, 7%, Measure minus .62, Outfit 1.1, Threshold Measure minus 2.41, Threshold S E .15, Threshold distance N A.

* Score 2: Count 736, 22%, Measure .19, Outfit 1.0, Threshold Measure minus 1.33, Threshold S E .07, Threshold distance 1.08.

* Score 3: Count 609, 18%, Measure .87, Outfit .9, Threshold Measure .75, Threshold S E .05, Threshold distance 2.08.

* Score 4: Count 783, 23%, Measure 1.63, Outfit 1.0, Threshold Measure 1.05, Threshold S E .05, Threshold distance 0.30.

* Score 5: Count 943, 28%, Measure 2.71, Outfit 1.0, Threshold Measure 1.95, Threshold S E .05, Threshold distance 0.90.

Due to their narrow threshold distance between scores of 3 and 4 in this 5-point scale (.30 logits), these two score categories were collapsed into one score category. This collapsing transformed the 5-point scale of 012345 into a 4-point scale of 012334 (see Figure 2), which maintained the score categories appropriately ordered while also displaying adequately large threshold distances across the score categories (Table 7).

Table 7.

Score category statistics of the 4-point scale

Table 7. Long description

The table consists of eight columns: Score, Count, %, Measure, Outfit, Threshold Measure, Threshold S E, and Threshold distance.

* Score 0: Count 54, 2%, Measure minus 1.00, Outfit 2.0, Threshold Measure N A, Threshold S E N A, Threshold distance N A.

* Score 1: Count 235, 7%, Measure minus .53, Outfit 1.2, Threshold Measure minus 2.56, Threshold S E .15, Threshold distance N A.

* Score 2: Count 736, 22%, Measure .48, Outfit .9, Threshold Measure minus 1.16, Threshold S E .08, Threshold distance 1.40.

* Score 3: Count 1392, 41%, Measure 1.88, Outfit 1.0, Threshold Measure .60, Threshold S E .05, Threshold distance 1.76.

* Score 4: Count 943, 28%, Measure 3.68, Outfit .9, Threshold Measure 3.11, Threshold S E .05, Threshold distance 2.51.

Figure 6 presents the probability curves for the original 100-point scale and the three collapsed scales. The probability curves of the 100-point scale show no clear peaks, suggesting that many different scores represented essentially equivalent ability levels and that the same score represented different ability levels. Combining score categories helped the 10-point scale to display a clear peak of the collapsed score category of 1, which represented ability levels around –2.0 logits. Further merging score categories helped the 5-point scale to display a clear peak for the collapsed score category of 2, which distinctly represented ability levels around 0.0 logits. Finally, the 4-point scale boosted the functioning of the collapsed score category of 3, which uniquely represented ability levels around 2.0 logits. Although these collapsing schemes were implemented based on the statistical information derived from the MFRM analysis, each collapsing scheme happened to target a unique range of ability levels from low-ability speakers (10-point scale), middle-ability speakers (5-point scale), to high-ability speakers (4-point scale).

Figure 6.

Probability curves of the 100-point (top left), 10-point (top right), 5-point (bottom left), and 4-point (bottom right) scales.Footnote ⁸

Figure 6. Long description

A four-panel set of line graphs using A S C I I style characters to plot data. Each graph has a vertical Y axis labeled Probability ranging from 0 to 1 and a horizontal X axis with varying numerical ranges.

* Top-left panel, 100-point scale. The X axis ranges from negative 2.0 to 1.0. A wide U-shaped curve formed by zeros descends from the top left and rises toward the top right. A dense horizontal line of ones and twos sits at the base.

* Top-right panel, 10-point scale. The X axis ranges from negative 4.0 to 4.0. It features multiple overlapping curves formed by digits 0 through 9. The curves for 0 and 9 form the outer U-shape, while intermediate digits create smaller peaks and clusters in the center.

* Bottom-left panel, 5-point scale. The X axis ranges from negative 4.0 to 4.0. Five distinct probability curves are visible, labeled with digits 0 through 5. The curves for 0 and 5 are at the far left and right respectively, while 1, 2, 3, and 4 form overlapping peaks across the middle.

* Bottom-right panel, 4-point scale. The X axis ranges from negative 4.0 to 6.0. Four primary curves labeled 0, 1, 2, 3, and 4 are shown. The distribution is shifted slightly to the right compared to the other panels, with the curve for 4 peaking at the far right of the X axis.

Comparing the original 100-point scale and the collapsed 4-point scale (RQ3)

Figure 7 presents the variable maps of the original 100-point scale and the collapsed 4-point scale. In the original 100-point scale, many speakers and raters are located at 0.0 logits, and many score categories cluster in this same region. In contrast, in the 4-point scale, the score categories of 1, 2, 3, and 4 largely corresponded to speaker abilities below –1.0, around 0.0, around 2.0, and above 3.0 logits, respectively.

Figure 7.

Variable maps of the original 100-point scale (left) and the collapsed 4-point scale (right).

Figure 7. Long description

The image consists of two side-by-side A S C I I style variable maps. Both maps share a vertical Measr axis on the far left ranging from 4 at the top to -3 at the bottom.

Left Panel (100-point scale):

* The Measr axis has major ticks at 4, 3, 2, 1, 0, -1, -2, and -3.

* The plus speakers column shows a dense horizontal line of asterisks concentrated at the 0 mark.

* The minus raters column also shows a dense horizontal line of asterisks at the 0 mark.

* The Scale column on the right shows values 100 at the top, 0 at the bottom, and specific values 98, 90, 49, 9, 2, and 1 clustered around the 0 Measr level.

* A legend at the bottom indicates asterisk equals 4 for speakers and asterisk equals 8 for raters.

Right Panel (4-point scale):

* The Measr axis is identical to the left panel.

* The plus speakers column shows asterisks distributed vertically from approximately 4 down to -0.5, with the highest density between 1 and 3.

* The minus raters column shows a vertical distribution of asterisks from approximately 3 down to -3, with a high concentration between 1 and -1.

* The Scale column on the right shows a simplified 4-point scale with 4 at the top, 3 at Measr 2, 2 at Measr 0, 1 at Measr -2, and 0 at the bottom.

* A legend at the bottom indicates asterisk equals 1 for both speakers and raters.

Table 8 summarizes the comparison between the original 100-point scale and the collapsed 4-point scale. Cronbach’s alpha and intraclass correlation were not substantially different between the two scales. As for the model fit, while the original scale explained more variance than the 4-point scale, there were slightly more unexpected responses for the original scale than for the 4-point scale. The 100-point scale reliably distinguished 10 ability levels, whereas the 4-point scale distinguished nine. The original scale detected eight rater severity levels, whereas the 4-point scale found seven severity levels. Person measures derived from the two scales were highly correlated, with Pearson’s product-moment correlation of .99 (95% CI[.99, 1.00]). Taken together, these findings suggest that the reduction of scale granularity aggregated minimally different ability levels and revealed meaningfully distinct ability levels among speakers without a substantial loss of the information that was originally obtained with the 100-point scale.

Table 8.

Comparison between the original 100-point scale and the collapsed 4-point scale

Table 8. Long description

The table consists of three columns: Criteria, Original 100-point scale, and Collapsed 4-point scale.

* Cronbach’s alpha: .99 [.98, .99] for the 100-point scale and .98 [.97, .99] for the 4-point scale.

* Two-way consistency, average-measure intraclass correlation: .98 [.98, .99] for the 100-point scale and .98 [.97, .99] for the 4-point scale.

* Variance explained by Rasch: 63.50% for the 100-point scale and 56.77% for the 4-point scale.

* Standardized residuals over |2.0|: 3.0% for the 100-point scale and 1.0% for the 4-point scale.

* Strata for person ability: 10.91 for the 100-point scale and 9.21 for the 4-point scale.

* Separation reliability for person: .98 for both scales.

* Increasing thresholds: No for the 100-point scale and Yes for the 4-point scale.

* Threshold distances over 1.4: No for the 100-point scale and Yes for the 4-point scale.

* Peaks in probability curves: No for the 100-point scale and Yes for the 4-point scale.

* Raters with infit over 1.5: 13 for both scales.

* Strata for rater severity: 8.21 for the 100-point scale and 7.21 for the 4-point scale.

* Separation reliability: .97 for the 100-point scale and .96 for the 4-point scale.