Coefficient Of Scalability Research Articles

Validity and Reliability of Physical Sports and Health Education's Learning Assessment of Self Defense Material for Class VII Junior High School Student

Instruments adhering to appropriate standards are crucial in gauging the conclusive outcomes of learning activities. This ensures that student learning achievements are accurately identified, serving as evaluation benchmarks for subsequent educational programs. The present research endeavors to develop an assessment instrument for Physical Education and Health (PJOK) learning, specifically focusing on self-defense material designed for seventh-grade junior high school students. This instrument is envisaged as a valuable tool to assist educators in conducting assessments, leading to the optimization of learning skills evaluation outcomes. The research methodology employs the Research and Development approach, referencing the ADDIE development model. The analysis stage involves observation and interviews, instrument design, product development, as well as Focus Group Discussions (FGD) with learning evaluation experts. Additionally, instrument product trials are conducted to examine validity and reliability. The research involves 66 seventh-grade junior high school students as participants. The validity test was carried out using the Reproducibility Coefficient and Scalability Coefficient according to the Guttman scale test, while the reliability test used Kuder Richardson (K-R) 20. The validity test results showed that all variables had values ​​> 0.90 for the reproducibility coefficient and > 0.60 for the scalability coefficient so it is said to be valid. The reliability test results showed a value of > 0.60 for K-R 20 so it is considered reliable. In conclusion, the PJOK learning assessment instrument for self-defense material emerges as a reliable and valid tool. Educators can confidently integrate this instrument into their assessments, leveraging its proven to be valid and reliable.

Seeing Beyond Words: An Investigation of Students' Opinions on Interactive Murals for Vocabulary Teaching

This study investigates the ways in which students view interactive murals as part of the vocabulary teaching and learning process in the classroom. A qualitative methodology and survey were administered to 22 elementary school students. The three components of the questionnaire were as follows: the pedagogical content of the feature of interactive mural, and motivation in using the murals. The questionnaire was administered to a research sample of 22 students who were specifically selected for the study. With a coefficient of scalability (CS) of at least 0.60 and a coefficient of reproducibility (CR) of at least 0.90, the data were deemed to meet the unidimental and cumulative features after being analyzed using the Guttman scale. The results revealed that the mean CS score was 0.91, indicating that the coefficients of scalability were deemed good, and the mean CR score from the three indicators was 0.90, indicating that the CR results were valid. Considering the mean recapitulation rate among the students was 16,33%, the students’ perception was positive. The results, which showed that students’ perceptions of the interactive smural’s use as a technology in the classroom were positively correlated with their use of learning resources. It was possible for the students to acquire new teaching tools, such as interactive murals. Murals werehave been suggested as a potentially engaging substitute for traditional classroom media, particularly when teaching vocabulary. In summary, by documenting the diverse perspectives, this research not only sheds light on the perceived advantages of interactive murals but also emphasizes how these visual aids can be utilizedused to create captivating and productive vocabulary learning opportunities. The findings have implications for teachers, curriculum developers, and legislators who want to improve vocabulary instruction in the classrooms by incorporating interactive and visually appealing elements of murals.

Validation of the Identification of Medication Adherence Barriers Questionnaire (IMAB-Q); a Behavioural Science-Underpinned Tool for Identifying Non-Adherence and Diagnosing an Individual's Barriers to Adherence.

To validate the Identification of Medication Adherence Barriers Questionnaire (IMAB-Q) as a tool to guide practitioners to identify patients who require support to take their medicines as prescribed, their key barriers to adherence and select relevant behaviour change techniques. Adults prescribed medication for cardiovascular disease prevention were recruited from nine community pharmacies in England. Participants completed the IMAB-Q comprising 30 items representing potential barriers to adherence developed from our previous mixed methods study (scoping review and focus groups) underpinned by the Theoretical Domains Framework. Participants also self-reported their adherence on a visual analogue scale (VAS) ranging from perfect adherence (100) to non-adherence (1). A subgroup of 30 participants completed the IMAB-Q twice to investigate test-retest reliability using weighted Kappa. Mokken scaling was used to investigate IMAB-Q structure. Spearman correlation was used to investigate IMAB-Q criterion validity compared to the VAS score. From 1407 invitations, 608 valid responses were received. Respondents had a mean (SD) age of 70.12 (9.9) years and were prescribed a median (IQ) 4 (3, 6) medicines. Worry about unwanted effects (n = 212, 34.5%) and negative emotions evoked by medicine taking (n = 99, 16.1%) were most frequently reported. Mokken scaling did not organise related IMAB-Q items according to the TDF domains (scalability coefficient H = 0.3 to 0.6). Lower VAS self-reported adherence correlated with greater IMAB-Q reported barriers (rho = -0.14, p = 0.001). Test-retest reliability of IMAB-Q items ranged from kappa co-efficient 0.9 to 0.3 (p < 0.05). The IMAB-Q is valid and reliable for identifying people not adhering and their barriers to adherence. Each IMAB-Q item is linked to a TDF domain which in turn is linked to relevant behaviour change techniques. The IMAB-Q can therefore guide patients and practitioners to select strategies tailored to a patient's identified barriers.

Task and Ego Orientation in Sport Questionnaire: A Mokken Scale Analysis

Athletes’ goal orientations have been associated with a wide array of sport-related behaviors, thoughts, and perceptions. The two main goal orientations defined in the achievement goal theory framework are task and ego orientations. The task and ego orientation questionnaire (TEOSQ) was developed to assess levels of task and ego goal orientations in sport-related settings and is widely used in research in the field of sport psychology. Its use in research rests on the assumption that sum scores of the TEOSQ can be used to order individuals by their levels of the two goal orientations. In this study, the soundness of this assumption is evaluated using Mokken scale analysis (MSA). TEOSQ responses from 749 football players were used in the analysis. Both the monotone homogeneity model and the double monotonicity model were fitted. The scalability coefficients for both the task and ego orientation subscales were 0.45 indicating a moderately good scalability. Invariant item ordering did not hold for either of the two subscales. There is definite room for improvement in the TEOSQ. Several improvement suggestions are made and further research directions are discussed.

Validation of public health center resilience questionnaire in flood-prone areas of East Java province, Indonesia

Background. Public Health Center is the front line that plays a major role in disaster preparedness and management, so efforts are needed to increase the resilience of the Public Health Center to ensure that the Public Health Center remains resilient, safe and continues to operate in the event of a disaster. To prevent the impact of paralysis of health services at the Public Health Center, a tool is needed to measure the resilience of the Public Health Center. Objective. This research aims to identify indicators of Public Health Center resilience which were synthesized from various sources. Methods. This research was a cross-sectional study among 30 Public Health Centers in flood-prone areas of East Java Province that experienced floods from September to October 2021. Confirmatory factor analysis was used to assess the suitability of the structural model of Public Health Center resilience. The validity of the questionnaire has been tested using the Coefficient of Reproducibility and Coefficient of Scalability with values of Kr = 0.903 and Ks = 0.903 so that it is declared valid. Results. The results showed that the reliability value = 0.843&gt;0.7, which indicates adequate reliability. All items in the Health Center Resilience questionnaire have a factor loading greater than 0.32 and obtained AVE &gt; 0.5, which indicates good convergent validity, and CR obtained &gt; 0.7 means that the questions in the questionnaire are reliable. Conclusion. In conclusion, there are 13 indicators that make up the significant Public Health Center Resilience questionnaire.

Analysis of SOR Framework Concerning Online Shopping Value and Web Satisfaction on E-Commerce

Online shopping transactions on e-commerce in Indonesia are increasing. E-commerce players continue to attempt and develop strategies to attract users in shopping online. This research analyze through the SOR (Stimulus, Organism, Response) framework on the driving factors for e-commerce users, especially Shopee in making online purchases regarding online shopping value and web satisfaction provided on Shopee services, problems related to the high number of e-commerce shopping. and the amount of impulsive spending money in the large number from big sale programs that are displayed. The approach of this research was qualitative through descriptive analysis of the results of questionnaires obtained by 385 respondents in Indonesia using the Guttman Scale and interviewing 10 informants as supporting empirical data. The results of this study was reproducibility coefficient is 0.94 and a scalability coefficient is 0.63, with reliable test using the Richard Kuderson formula (KR20) is 0.2 which was declared valid and reliable. In addition, the most important driving factor for purchase intention was obtained from this study, namely the free shipping feature with a percentage of 48.1%. Recommendations for future research is to focus on research on the peak moments of online shopping, such as the Ramadan big sale, and the celebration of the national shopping day and others. In addition, expanding respondents and informants, in order to expand the study and re-design related to the framework used.

The Big Three Perfectionism Scale-Short Form: An item response theory analysis of Italian workers.

BackgroundThe present study examined the psychometric properties of the Big Three Perfectionism Scale–Short Form (BTPS-SF) using Rasch and Mokken item response theory (IRT) analyses, which have not previously been applied to the BTPS-SF.Materials and methodsA total of 401 Italian workers (Mage = 46.78; SD = 10.1; male = 48.9%; female = 51.1%) completed the BTPS-SF questionnaire. We conducted confirmatory factor analyses of the BTPS-SF and IRT analyses using the generalized partial credit model (GPCM) and Mokken scale analysis. Discrimination and difficulty parameters were calculated. The Loevinger coefficient of scalability was computed. Item characteristic curves (ICC), test information function (TIF), and differential item functioning (DIF) for gender were calculated.ResultsA three-factor solution revealed the best fit. Thus, IRT analyses were performed for each BTPS-SF factor: rigid perfectionism (RP), self-critical perfectionism (SP), and narcissistic perfectionism (NP). All the items showed Loevinger coefficients from medium to strong and discrimination parameters from medium to very high. No DIF for gender was found.ConclusionThe Big BTPS-SF shows good psychometric properties for Italian workers. Future research is warranted to examine the findings in workers from different countries.

Cross-cultural validity of the WHO-5 Well-Being Index and Euthymia Scale: A clinimetric analysis

BackgroundThe assessment of psychological well-being and euthymia represents an emerging issue in clinical psychology and psychiatry. Rating scales and indices such as the 5-item version of the World Health Organization Well-Being Index (WHO-5) and the Euthymia Scale (ES) were developed but insufficient attention has been devoted to the evaluation of their cross-cultural validity. This is the first study using Clinimetric Patient-Reported Outcome Measures (CLIPROM) criteria to assess cross-cultural validity and sensitivity of five different versions of the WHO-5 and ES. MethodsA multicenter cross-sectional study involving a total of 3762 adult participants from different European (i.e., Italy, Poland, Denmark) and non-European (i.e., China, Japan) countries was conducted. Item Response Theory models (Mokken and Rasch analyses) were applied. ResultsMokken coefficients of scalability were found to range from 0.42 to 0.84. The majority of the versions of the WHO-5 fitted the Rasch model expectations. Paired t-tests revealed that the Italian and Danish WHO-5 versions were unidimensional. Person Separation Reliability indices showed that the Polish, Danish, and Japanese ES versions could reliably discriminate between subjects with different levels of euthymia. LimitationsA convenience sampling was used, thus limiting the generalizability of study findings. In addition, no measures of negative mental health were administered. ConclusionsWHO-5 can be used in international studies for cross-cultural comparisons since it covers transcultural components of subjective well-being. Findings also suggest that the ES can be used as a cross-cultural screening tool since it entailed the clinimetric property of sensitivity.

The Strategy of Workforce Management Based on Risk Assessment of Manual Handling Work with Suitability of Work Environment in Makasar Industrial Area, Indonesia

BACKGROUND: A good work environment suitability has a major impact on health and safety, and it encourages a more productive workforce. When it is incompatible with labor, it can lead to unintended impacts and various risks. AIM: We aimed to investigate the strategy of workforce management based on risk assessment of manual handling work with suitability of work environment in Makasar industrial area, Indonesia. METHODS: Twenty three workforce samples are selected from Makassar Industrial Area (KIMA), Indonesia. The risk of manual handling work is assessed based on the suitability of the work environment to the workforce’s response using Guttman scale, in which the answer YES = 1 means there is a risk, while the answer NO = 0 means there is no risk. However, the scales are the reproducibility coefficient ≥ 0.90 and scalability coefficient ≥0.60, and Guttman scale score is calculated from Tn = total answers of “YES” for the KPI in the scale. Meanwhile, the SWOT-4Q is used to analyze the strategy of industry supervisor samples. RESULTS: For the workforce, eight of nine risk assessments do not show risk, and only “high vibration intensity in the workplace,” with a percentage of 78.26%, affects the excessive condition. The strategy used by the supervisors in quadrant I is in accordance with the strength of the risk assessment and has a great opportunity to reduce risk. The management maximally exploits the big opportunity of the manual handling work. CONCLUSIONS: The results showed that most of the workforce did not experience the risk of manual handling work with the suitability of the work environment. In addition, industrial supervisors should implement a growth strategy because they can enlarge the industry by taking advantage of the advantages of manual handling work to maximize the exploitation of large manual handling work opportunities.

Pathways for primary care practice adoption of patient engagement strategies.

To identify potential orderings of primary care practice adoption of patient engagement strategies overall and separately for interpersonally and technologically oriented strategies. We analyzed physician practice survey data (n=71) on the adoption of 12 patient engagement strategies. Mokken scale analysis was used to assess latent traits among the patient engagement strategies. Three groupings of patient engagement strategies were analyzed: (1) all 12 patient engagement strategies, (2) six interpersonally oriented strategies, and (3) six technologically oriented strategies. We did not find scalability among all 12 patient engagement strategies, however, separately analyzing the subgroups of six interpersonally and six technologically oriented strategies demonstrated scalability (Loevinger's H coefficient of scalability [range]: interpersonal strategies, H=0.54 [0.49-0.60], technological strategies, H=0.42 [0.31, 0.54]). Ordered patterns emerged in the adoption of strategies for both interpersonal and technological types. Common pathways of practice adoption of patient engagement strategies were identified. Implementing interpersonally intensive patient engagement strategies may require different physician practice capabilities than technological strategies. Rather than simultaneously adopting multiple patient engagement strategies, gradual and purposeful practice adoption may improve the impact of these strategies and support sustainability.

Quantifying the patient´s perspective in neuromyelitis optica spectrum disorder: Psychometric properties of the SymptoMScreen questionnaire.

BackgroundThe assessment of self-reported outcomes in neuromyelitis optica spectrum disorder (NMOSD) is limited by the lack of validated disease-specific measures. The SymptoMScreen (SyMS) is a patient-reported questionnaire for measuring symptom severity in different domains affected by multiple sclerosis (MS), but has not been thoroughly evaluated in NMOSD. The aim of this study was to assess the psychometric properties of the SyMS in a sample of patients with NMOSD.MethodsA non-interventional, cross-sectional study in adult subjects with NMOSD (Wingerchuk 2015 criteria) was conducted at 13 neuroimmunology clinics applying the SyMS. A non-parametric item response theory procedure, Mokken analysis, was performed to assess the underlying dimensional structure and scalability of items and overall questionnaire. All analyses were performed with R (v4.0.3) using the mokken library.ResultsA total of 70 patients were studied (mean age: 47.5 ± 15 years, 80% female, mean Expanded Disability Status Scale score: 3.0 [interquartile range 1.5, 4.5]). Symptom severity was low (median SyMS score: 19.0 [interquartile range 10.0, 32.0]). The SyMS showed a robust internal reliability (Cronbach’s alpha: 0.90 [95% confidence interval 0.86, 0.93]) and behaved as a unidimensional scale with all items showing scalability coefficients > 0.30. The overall SyMS scalability was 0.45 conforming to a medium scale according to Mokken’s criteria. Fatigue and body pain were the domains with the highest scalability coefficients. The SyMS was associated with disability (rho: 0.586), and physical and psychological quality of life (rho: 0.856 and 0.696, respectively).ConclusionsThe SyMS shows appropriate psychometric characteristics and may constitute a valuable and easy-to-implement option to measure symptom severity in patients with NMOSD.

Examining the Dimensionality and Monotonicity of an Attitude Dataset based on the Item Response Theory Models

In the current study, the factor structure of an attitude scale was analyzed by using the two different item response theory models that allow modeling non-monotonic item response curves. The current study utilized the two models to examine whether the two-factor solution of factor analysis may be caused by method effect, or by the failure of the analysis in describing and fitting the dataset because of the monotonicity assumption. This study was conducted on a dataset obtained from 355 undergraduate students who were studying at the Middle East Technical University. The data were obtained by carrying out the Attitude Scale Towards Foreign Languages as Medium of Instruction, which was developed by Kartal and Gülleroğlu (2015). The fit of the scale items to the generalized graded unfolding model was examined based on the item response curves, item parameters, item fit statistics and fit graphics. For Mokken scaling, scalability coefficients were calculated, dimensionality analyzes were conducted by using the Automated Item Selection Procedure. The monotonicity assumption was investigated based on the rest-score group methods. The results of the current study revealed that items of the attitude scale fit to the unidimensional models that do not assume monotone increasing item response curves for all items, while the factor analysis suggested a two-factor solution for the data. Researchers are recommended to utilize statistical techniques that can identify any possible violation of the monotonicity assumption and model items having non-monotonic response curves to examine dimensionality of their data.

A two-step, test-guided Mokken scale analysis, for nonclustered and clustered data

PurposeMokken scale analysis (MSA) is an attractive scaling procedure for ordinal data. MSA is frequently used in health-related quality of life research. Two of MSA's prime features are the scalability coefficients and the automated item selection procedure (AISP). The AISP partitions a (large) set of items into scales based on the observed item scores; the resulting scales can be used as measurement instruments. There exist two issues in MSA: First, point estimates, standard errors, and test statistics for scalability coefficients are inappropriate for clustered item scores, which are omnipresent in quality of life research data. Second, the AISP insufficiently takes sampling fluctuation of Mokken’s scalability coefficients into account.MethodsWe solved both issues by providing point estimates and standard errors for the scalability coefficients for clustered data and by implementing a Wald-based significance test in the AISP algorithm, resulting in a test-guided AISP (T-AISP), that is available for both nonclustered and clustered test scores.ResultsWe integrated the T-AISP into a two-step, test-guided MSA for scale construction, to guide the analysis for nonclustered and clustered data. The first step is performing a T-AISP and select the final scale(s). For clustered data, within-group dependency is investigated on the final scale(s). In the second step, the strength of the scale(s) is determined and further analyses are performed. The procedure was demonstrated on clustered item scores obtained from administering a questionnaire on quality of life in schools to 639 students nested in 30 classrooms.ConclusionsWe developed a two-step, test-guided MSA for scale construction that takes into account sample fluctuation of all scalability coefficients and that can be applied to item scores obtained by a nonclustered or clustered sampling design.

The proportion of non-depressed subjects in a study sample strongly affects the results of psychometric analyses of depression symptoms.

BackgroundRecent studies have uncovered a peculiar finding: that the strength and dimensionality of depression symptoms’ inter-relationships vary systematically across study samples with different average levels of depression severity. Our aim was to examine whether this phenomenon is driven by the proportion of non-affected subjects in the sample.MethodsCross-sectional data from the “Cohort Study on Substance Use Risk Factors” was analyzed. Self-reported depression symptoms were assessed via the Major Depressive Inventory. Symptom data were analyzed via polychoric correlations, principal component analysis, confirmatory factor analysis, Mokken scale analysis, and network analysis. Analyses were carried out across 22 subsamples containing increasingly higher proportions of non-depressed participants. Results were examined as a function of the proportion of non-depressed participants.ResultsA strong influence of the proportion of non-depressed participants was uncovered: the higher the proportion, the stronger the symptom correlations, higher their tendency towards unidimensionality, better their scalability, and higher the network edge strengths. Comparing the depressed sample with the general population sample, the average symptom correlation increased from 0.29 to 0.51; variance explained by the first eigenvalue increased from 0.36 to 0.56; fit measures from confirmatory one-factor analysis increased from 0.81 to 0.97; the H coefficient of scalability increased from 0.26 to 0.48; and the median network edge increased from 0.00 to 0.07.ConclusionsResults of psychometric analyses vary substantially as a function of the proportion of non-depressed participants in the sample being studied. This provides a possible explanation for the lack of reproducibility of previous psychometric studies.

The Cumulative Structure of Personal and Instrumental ADL. A Study of Elderly People in a Health Service District

Katz' Index of ADL has been supplemented by five well-defined instrumental activities, namely cooking, washing, transportation, cleaning, and shopping. Eighty-five persons, mainly elderly, who had consecutively consulted a district occupational therapist, were assessed in their homes in order to study the reliability, the scalability, and the validity of the expanded index. The inter-observer reliability was high. The coefficient of scalability was well above the acceptance level, indicating construct validity. No person was dependent in personal ADL and totally independent in instrumental ADL. Persons who were dependent in both personal and instrumental ADL were older and lived in sheltered accommodation more often than persons who were dependent only in instrumental ADL, indicating external validity. This study shows that there was a cumulative relationship between certain well-defined instrumental activities and between personal and instrumental activities. This supplemented index can be useful for assessing and differentiating the need for personal assistance and homecare among disabled elderly people.

Assessment of activities of daily living in the elderly. A study of a population of 76-year-olds in Gothenburg, Sweden

The cumulative structure of personal daily activities (Katz' Index of ADL) and four well-defined instrumental activities (cooking, transportation, shopping, and cleaning) have been studied in a population of 76-year-olds (N = 659) in Gothenburg, Sweden. Sixty-five percent of the population were independent, 22% were dependent in instrumental activities, and 13% were dependent in both instrumental and personal activities. No person was dependent in personal ADL and independent in instrumental ADL. The internal consistency and the coefficient of scalability were well above the acceptance level, which indicated an internal reliability and validity of the new scale. The frequency of personal and home-assistance care, type of accommodation, self-assessment of self-care and domestic activities were compared with the level of dependence in ADL and indicated external validity. This cumulative instrument of ADL can be used to describe and compare the level of disability in elderly populations and to define the need for personal assistance in home care among disabled persons.

Liselere Geçiş Sistemi: Yerel Yerleştirmeye Yönelik Guttman Tutum Ölçeği Geliştirilmesi

The foundation of transition from elementary education to secondary education is rooted in exams as well as the success gained from those exams. Although students were placed into a secondary education institution based on their exam scores in the previous exam system, with the newly-implemented ‘Entrance System for High Schools’ (shortly LGS in Turkish), there are two different student placements under consideration: (1) centralized placement, and (2) local placement. The purpose of the current study is to develop an attitude scale based on Guttman Scaling in order to investigate the attitudinal behaviors of the parents in the current education system. In line with this objective, a draft scale, consisting of ten items were administered to 241 parents whose children were placed into a high school in the 2017-2018 academic year. In the direction of the responses provided by the parents, four items were removed from the scale. Reliability test was conducted on the residual six items. The coefficient of reproducibility was calculated as 0,986 and scalability coefficient was 0,925, which is considered as acceptable for the reliability of the current scale. It was concluded that Guttman Scaling for local placement (i.e., address-based placement) is a reliable research tool for measuring attitudes towards placements in secondary education.

Validity and Reliability Test of the Indonesian Version of the Boredom Prone Scale (BPS) in Medical Student

Introduction. Boredom is defined as a state of relatively low arousal and dissatisfaction, which is attributed to inadequately stimulating situations. Everyone tends to experience boredom. Boredom Proneness Scale is one of many scales that can measures boredom proneness. BPS hasn't been adapted from the original language (English) in Indonesia. Methods. This study uses validity and reliability approach. Process of education divided into the adaptation process and psychometric analysis process. Psychometric analysis of the BPS Indonesian Version consists of Item Content Validity Analysis (I-CVI) &amp; Scale Content Validity Index (S-CVI). BPS Indonesian Version was spread twice amongst students of Medicine Program Faculty of Medicine Batch 2016─2018. Psychometric analysis of Boredom Proneness Scale Indonesian Version as the Guttman Scale was done by counting the coefficient of reproducibility (CR) and coefficient of scalability (CS). The adaptation process obtained BPS Indonesian Version. Results. Based on nine experts' appraisal in experts panel, minimum I-CVI is 0,83 (minimally accepted index 0,78) on the 10th scale, and S-CVI is 0,98 (minimally accepted index 0,90). CR of BPS Indonesian Version is 0,589 (first) and 0,594 (second) which defines BPS Indonesian Version is not valid. CS of BPS Indonesian Version is obtained as 0,177 (first) and 0,188 (second) which defines BPS Indonesian Version is not appropriate to be used in the study. Conclusion. BPS Indonesian Version is not appropriate to be used in measuring boredom proneness in students.

Standard errors of two‐level scalability coefficients

For the construction of tests and questionnaires that require multiple raters (e.g., a child behaviour checklist completed by both parents) a novel ordinal scaling technique is currently being further developed, called two-level Mokken scale analysis. The technique uses within-rater and between-rater coefficients to assess the scalability of the test. These coefficients are generalizations of Mokken's scalability coefficients. In this paper we derived standard errors for the two-level coefficients and for their ratios. The coefficients, the estimates, the estimated standard errors and the software implementation are discussed and illustrated using a real-data example, and a small-scale simulation study demonstrates the accuracy of the estimates.

Bias of Two-Level Scalability Coefficients and Their Standard Errors.

Two-level Mokken scale analysis is a generalization of Mokken scale analysis for multi-rater data. The bias of estimated scalability coefficients for two-level Mokken scale analysis, the bias of their estimated standard errors, and the coverage of the confidence intervals has been investigated, under various testing conditions. It was found that the estimated scalability coefficients were unbiased in all tested conditions. For estimating standard errors, the delta method and the cluster bootstrap were compared. The cluster bootstrap structurally underestimated the standard errors of the scalability coefficients, with low coverage values. Except for unequal numbers of raters across subjects and small sets of items, the delta method standard error estimates had negligible bias and good coverage. Post hoc simulations showed that the cluster bootstrap does not correctly reproduce the sampling distribution of the scalability coefficients, and an adapted procedure was suggested. In addition, the delta method standard errors can be slightly improved if the harmonic mean is used for unequal numbers of raters per subject rather than the arithmetic mean.