Dissertations / Theses on the topic 'Rasch model analysis'
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1
Yoshida, Keitaro. "Evaluation of RELATE Using Rasch Analysis." BYU ScholarsArchive, 2010. https://scholarsarchive.byu.edu/etd/2343.
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The importance of valid and reliable couple assessment has been increasing with growth in research on couple and family relationships as well as in therapeutic and educational interventions for couples and families. However, self-report instruments–the most popular type of couple assessment–have been criticized at least partly due to limitations in Classical Test Theory (CTT) which has been used solely in developing and evaluating couple assessments for decades. In an effort to address the limitations in the sole use of CTT in developing self-report couple assessments, the present study integrated a modern test theory called Item Response Theory (IRT) and evaluated the properties of subscales in the RELATionship Evaluation (RELATE) using the existing data from 4,784 participants. Using the Rasch rating scale or partial credit model which is one of the IRT models, the author demonstrated that some of the RELATE subscales had items and response categories that functioned less optimally or in an unexpected way. The results suggested that some items misfit the model or overlapped with other items, many scales did not cover the entire range of the measured construct, and response categories for many items malfunctioned. The author made recommendations on possible remedies that could be adopted to improve the function of individual scales and items.
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Harrell, Leigh Michelle. "Accuracy of Global Fit Indices as Indictors of Multidimensionality in Multidimensional Rasch Analysis." Diss., Virginia Tech, 2009. http://hdl.handle.net/10919/29656.
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Most research on confirmatory factor analysis using global fit indices (AIC, BIC, AICc, and CAIC) has been in the structural equation modeling framework. Little research has been done concerning application of these indices to item response models, especially within the framework of multidimensional Rasch analysis. The results of two simulations studies that investigated how sample size, between-dimension correlation, and test length affect the accuracy of these indices in model recovery using a multidimensional Rasch analysis are described in this dissertation. The first study analyzed dichotomous data, with model-to-data misfit as an additional independent variable. The second study analyzed polytomous data, with rating scale structure as an additional independent variable. The interaction effect between global fit index and between-dimension correlation had very large effect sizes in both studies. At higher values of between-dimension correlation, AIC indicated the correct two-dimension generating structure slightly more often than does the BIC or CAIC. The correlation by test length interaction had an odds ratio indicating practical importance in the polytomous study but not the dichotomous study. The combination of shorter tests and higher correlations resulted in a difficult-to-detect distinction being modeled with less statistical information. The correlation by index interaction in the dichotomous study had an odds ratio indicating practical importance. As expected, the results demonstrated that violations of the Rasch model assumptions are magnified at higher between-dimension correlations. Recommendations for practitioners working with highly correlated multidimensional data include creating moderate length (roughly 40 items) instruments, minimizing data-to-model misfit in the choice of model used for confirmatory factor analysis (MRCMLM or other MIRT models), and making decisions based on multiple global indices instead of depending on one index in particular.Ph. D.
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Bourke, Mary P. "Measuring nursing educators' beliefs about diversity in personal and professional contexts : Rasch model diagnostics and scale analysis /." [Bloomington, Ind.] : Indiana University, 2007. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3303325.
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Thesis (Ph.D.)--Indiana University, Dept. of Education, 2007.Title from PDF t.p. (viewed Nov. 3, 2008). Source: Dissertation Abstracts International, Volume: 69-02, Section: B, page: 0928. Adviser: Jesse Goodman.
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Liu, Mingyang Liu. "Differential Item Functioning in Large-scale Mathematics Assessments: Comparing the Capabilities of the Rasch Trees Model to Traditional Approaches." University of Toledo / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1513266587329066.
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Knutson, Nichole Marie. "APPLYING THE RASCH MODEL TO MEASURE AND COMPARE FIRST- GENERATION AND CONTINUING-GENERATION COLLEGE STUDENTS’ ACADEMIC SELF-EFFICACY." UKnowledge, 2011. http://uknowledge.uky.edu/epe_etds/1.
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Students who are the first in their families to attend college are less likely to earn a college degree as compared to their continuing-generation peers. In efforts to increase college graduation rates for first-generation college students, support programs designed to assist first-generation college students are increasing in numbers. These first- generation programs are relying on existing research to build effective curriculums. Even though an extensive body of literature exists in the fields of self-efficacy and first- generation college students, research investigating the self-efficacy of first-generation college students are extremely limited. The research is further limited when examining academic self-efficacy and generational status. The purpose of this study is to investigate if parental levels of education affect college students’ self-reported levels of academic self-efficacy. The following research questions guided this study: 1) Do survey response hierarchies differ between first-generation college students and their continuing- generation counterparts on a scale that measures academic self-efficacy?, 2) Do levels of item endorsability vary based upon parental levels of education? and 3) Do the results produced from the college student survey support the existing literature on first- generation college students and academic-self-efficacy? Quality control indicators were utilized to assess the soundness of the instrument and to ensure that the rating scale functioned appropriately. Variable maps were used to compare and contrast student responses and item hierarchies. Pairwise differential item functioning (DIF) was used to examine item endorsability based upon levels of parental education. Results encourage practitioners to be mindful of the importance of data-informed decision making.
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Stammen, Andria. "The Development and Validation of the Middle School-Life Science Concept Inventory (MS-LSCI) Using Rasch Analysis." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1523631816773049.
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Maier, Marco J., and Ingrid Koller. "Supplement to Koller, Maier, & Hatzinger: "An Empirical Power Analysis of Quasi-Exact Tests for the Rasch Model: Measurement Invariance in Small Samples"." WU Vienna University of Economics and Business, 2014. http://epub.wu.ac.at/4340/1/Report127.pdf.
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This document is a supplementary text to "An Empirical Power Analysis of
Quasi-Exact Tests for the Rasch Model: Measurement Invariance in Small
Samples" by Koller, Maier, & Hatzinger (to be published in Methodology,
ISSN-L 1614-1881), which covers all technical details regarding the
simulation and its results.
First, the simulation scenarios and the introduction of differential item
functioning (DIF) are described. Next, the different populations'
distributions that were investigated are discussed, and finally, actual
type-I-error rates and empirical power are displayed for all simulated
scenarios. (authors' abstract)Series: Research Report Series / Department of Statistics and Mathematics
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Wang, Wenjia. "Item Response Theory in the Neurodegenerative Disease Data Analysis." Thesis, Bordeaux, 2017. http://www.theses.fr/2017BORD0624/document.
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Les maladies neurodégénératives, telles que la maladie d'Alzheimer (AD) et Charcot Marie Tooth (CMT), sont des maladies complexes. Leurs mécanismes pathologiques ne sont toujours pas bien compris et les progrès dans la recherche et le développement de nouvelles thérapies potentielles modifiant la maladie sont lents. Les données catégorielles, comme les échelles de notation et les données sur les études d'association génomique (GWAS), sont largement utilisées dans les maladies neurodégénératives dans le diagnostic, la prédiction et le suivi de la progression. Il est important de comprendre et d'interpréter ces données correctement si nous voulons améliorer la recherche sur les maladies neurodégénératives. Le but de cette thèse est d'utiliser la théorie psychométrique moderne: théorie de la réponse d’item pour analyser ces données catégoriques afin de mieux comprendre les maladies neurodégénératives et de faciliter la recherche de médicaments correspondante. Tout d'abord, nous avons appliqué l'analyse de Rasch afin d'évaluer la validité du score de neuropathie Charcot-Marie-Tooth (CMTNS), un critère important d'évaluation principal pour les essais cliniques de la maladie de CMT. Nous avons ensuite adapté le modèle Rasch à l'analyse des associations génétiques pour identifier les gènes associés à la maladie d'Alzheimer. Cette méthode résume les génotypes catégoriques de plusieurs marqueurs génétiques tels que les polymorphisme nucléotidique (SNPs) en un seul score génétique. Enfin, nous avons calculé l'information mutuelle basée sur la théorie de réponse d’item pour sélectionner les items sensibles dans ADAS-cog, une mesure de fonctionnement cognitif la plus utilisées dans les études de la maladie d'Alzheimer, afin de mieux évaluer le progrès de la maladieNeurodegenerative diseases, such as Alzheimer’s disease (AD) and Charcot Marie Tooth (CMT), are complex diseases. Their pathological mechanisms are still not well understood, and the progress in the research and development of new potential disease-modifying therapies is slow. Categorical data like rating scales and Genome-Wide Association Studies (GWAS) data are widely utilized in the neurodegenerative diseases in the diagnosis, prediction and progression monitor. It is important to understand and interpret these data correctly if we want to improve the disease research. The purpose of this thesis is to use the modern psychometric Item Response Theory to analyze these categorical data for better understanding the neurodegenerative diseases and facilitating the corresponding drug research. First, we applied the Rasch analysis in order to assess the validity of the Charcot-Marie-Tooth Neuropathy Score (CMTNS), a main endpoint for the CMT disease clinical trials. We then adapted the Rasch model to the analysis of genetic associations and used to identify genes associated with Alzheimer’s disease by summarizing the categorical genotypes of several genetic markers such as Single Nucleotide Polymorphisms (SNPs) into one genetic score. Finally, to select sensitive items in the most used psychometrical tests for Alzheimer’s disease, we calculated the mutual information based on the item response model to evaluate the sensitivity of each item on the ADAS-cog scale
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Brown, Kathleen Annette. "An Iterative Needs Assessment/Evaluation Model for a Japanese University English-language Program." Diss., Temple University Libraries, 2009. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/66807.
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CITE/Language ArtsEd.D.
The focus of this study is the development and implementation of the Iterative Needs Assessment/Evaluation Model for use as part of an English curriculum reform project at a four-year university in Japan. Three questions were addressed in this study: (a) what model components were necessary for use in a Japanese university setting; (b) what survey instruments would work with such a model; and (c) what needs would the stakeholders in the project report? The site for the study was a mid-sized private, four-year university in Japan. Set as an instrumental case study (Stake, 1998), multiple methods and sources were employed. Stakeholders in the project included university students (n = 1533), teaching staff (n = 33), university administrators and staff (n = 5), and domain experts (n = 7). Data collection included the use of questionnaires, unstructured and semi-structured interviews, and systems and materials analyses. Questionnaires were developed and analyzed using Rasch analysis. The Needs Assessment/Evaluation Model was assessed using a modified version of the Checklist for Judging the Adequacy of an Evaluation Design (Sanders & Nafziger, 1985). Implementation of a full iteration of the Model indicated that use of the Iterative Needs Assessment/Evaluation Model could guide the development and evaluation of the English language program. As part of the study, valid survey instruments that can continue to aid the assessment of needs for and evaluation of the courses were developed. Data from multiple sources indicated a difference in the perception of needs between stakeholders. The processes followed through the development and application of the Iterative Needs Assessment/Evaluation Model served to incorporate these different perceptions into a cohesive language program curriculum.
Temple University--Theses
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Paprzycki, Peter Pawel. "Developing a Methodological Framework for the Analysis of Perceptions: A Case Study of the National Public Opinion Survey “The EU in the Eyes of Asia-Pacific”." University of Toledo / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1430493813.
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Robson, Graham George. "A MODEL OF SITUATIONAL CONSTRUCTS ACCOUNTING FOR WILLINGNESS TO COMMUNICATE AT A JAPANESE UNIVERSITY." Diss., Temple University Libraries, 2015. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/362956.
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Language ArtsEd.D.
Many researchers have highlighted the need for students to have a willingness to communicate (WTC) in second and foreign language classrooms. WTC is important because it is believed that WTC leads to eventual communication both inside and outside the classroom. Previous research into WTC has centered mainly on the use of structural models and trait, self-reported measurements of WTC, but recent research has shown that WTC is also heavily dependent on the situation. However, very few studies recognize this and have, thus, not employed situational measurements of WTC. After a thorough review of WTC literature, 13 pertinent constructs were modified to reflect the situation in the foreign language classroom. These were related to constructs of the classroom, beliefs about communication; self-determined motivation; self-perceived competence; communication anxiety and willingness to communicate. A preliminary study employing exploratory factor analysis and Rasch analysis, followed by a main study conducted with and confirmatory factor analysis and Rasch analysis were undertaken with first- and second-year Japanese university students. The factor analysis was used to investigate the underlying structures of the factors and the Rasch analysis was used to determine fit, category functioning and dimensionality. Nine reliable and unidimensional factors were brought forward from the main study, which were Classroom Efficacy Factor and Classroom Affective Factor as the two classroom factors; Intrinsic Motivation for Communication, Introjected Regulation for Communication and External Regulation for Communication as the three self-determined motivation constructs, and finally, Self-Perceived Competence, Communicative Anxiety and Willingness to Communicate split in two subconstructs of pair/work and whole class activities. The second half the study was the formulation of a structural equation model using the above constructs to predict situational WTC. The model also included an often under-utilized resource, the teacher, who assessed the learners’ actual communication to identify if WTC leads to language use. All the fit indices in the final model (N = 376) were good, and the model included three additional paths. The model indicated that classroom constructs led to motivation and self-perceived competence, which predicted confidence. Motivation led directly to WTC and indirectly to WTC through confidence. Lastly, WTC predicted actual communication. The constructs in this study can be applied in other studies of situational WTC. This study helps to both expand our understanding of constructs affecting situational WTC and actual communication, and provides more validity to the construct of situational WTC. It also reaffirms the importance of what happens in the classroom, which is main arena for communication in the EFL setting.
Temple University--Theses
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Haji, Harun Hajah Zurina. "Evaluating the teaching and learning of fractions through modelling in Brunei : measurement and semiotic analyses." Thesis, University of Manchester, 2011. https://www.research.manchester.ac.uk/portal/en/theses/evaluating-the-teaching-and-learning-of-fractions-through-modelling-in-brunei-measurement-and-semiotic-analyses(b03b0a49-80a9-4ba0-a43c-d7201b180158).html.
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This thesis is submitted to the University of Manchester for the degree of Doctor of Philosophy (PhD). This study developed an experimental small group teaching method in the Realistic Mathematics Education tradition for teaching fractions using models and contexts to year 7 children in Brunei (N=89) whose effectiveness was evaluated using a treatment-control design: the E1 group was given the experimental lessons, the E2 group who was given “normal” lessons taught by the experimenter, and a whole class (E3) group which acted as the control group. The experimental teaching was video recorded and subject to semiotic analysis, aiming to describe the objectifications that realized ‘learning of fractions’ by the groups.The research addresses two research questions:1. How effective was the experimental teaching in helping learners make sense of fractions, with respect to equivalence of fractions and flexibility of unitizing?2. What were the semiotic learning and teaching processes in the experimental group of the RME-like lessons? This study used a mixed method approach with a quasi-experimental design (QED) for the quantitative side, and a semiotic analysis for the qualitative side. Quantitatively, the experimental teachings proved to be relatively effective with an effect size of 0.6 from the pre- to the delayed post-teaching test, compared to the E2 and the control groups.The basic findings pertaining to the semiotic analyses were:a. The mediation of the production of fractions in terms of length, from the production of fractions in terms of the number of parts which led to equivalence of fractions;b. The use of language and gesture help to objectify the equivalence of fractions and the flexibility of unitizing–in some case it involved gesturing to the self;c. The role of the Hour-Foot clock (HFC) as a model in a realistic context; andd. The complexity of the required chains of objectifications reflects the difficulties of the topic.
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Hamilton, Erin Kinzel. "Multiscale and meta-analytic approaches to inference in clinical healthcare data." Diss., Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/47600.
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The field of medicine is regularly faced with the challenge of utilizing information that is complicated or difficult to characterize. Physicians often must use their best judgment in reaching decisions or recommendations for treatment in the clinical setting. The goal of this thesis is to use innovative statistical tools in tackling three specific challenges of this nature from current healthcare applications.
The first aim focuses on developing a novel approach to meta-analysis when combining binary data from multiple studies of paired design, particularly in cases of high heterogeneity between studies. The challenge is in properly accounting for heterogeneity when dealing with a low or moderate number of studies, and with a rarely occurring outcome. The proposed approach uses a Rasch model for translating data from multiple paired studies into a unified structure that allows for properly handling variability associated with both pair effects and study effects. Analysis is then performed using a Bayesian hierarchical structure, which accounts for heterogeneity in a direct way within the variances of the separate generating distributions for each model parameter. This approach is applied to the debated topic within the dental community of the comparative effectiveness of materials used for pit-and-fissure sealants.
The second and third aims of this research both have applications in early detection of breast cancer. The interpretation of a mammogram is often difficult since signs of early disease are often minuscule, and the appearance of even normal tissue can be highly variable and complex. Physicians often have to consider many important pieces of the whole picture when trying to assess next steps. The final two aims focus on improving the interpretation of findings in mammograms to aid in early cancer detection.
When dealing with high frequency and irregular data, as is seen in most medical images, the behaviors of these complex structures are often difficult or impossible to quantify by standard modeling techniques. But a commonly occurring phenomenon in high-frequency data is that of regular scaling. The second aim in this thesis is to develop and evaluate a wavelet-based scaling estimator that reduces the information in a mammogram down to an informative and low-dimensional quantification of the innate scaling behavior, optimized for use in classifying the tissue as cancerous or non-cancerous. The specific demands for this estimator are that it be robust with respect to distributional assumptions on the data, and with respect to outlier levels in the frequency domain representation of the data.
The final aim in this research focuses on enhancing the visualization of microcalcifications that are too small to capture well on screening mammograms. Using scale-mixing discrete wavelet transform methods, the existing detail information contained in a very small and course image will be used to impute scaled details at finer levels. These "informed" finer details will then be used to produce an image of much higher resolution than the original, improving the visualization of the object. The goal is to also produce a confidence area for the true location of the shape's borders, allowing for more accurate feature assessment. Through the more accurate assessment of these very small shapes, physicians may be more confident in deciding next steps.
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Alqarni, Abdulelah M. Dr. "THE RELATIONSHIP BETWEEN STUDENT EVALUATIONS AND TEACHER QUALITY IN HIGH SCHOOL IN SAUDI ARABIA: ITEM RESPONSE THEORY ANALYSIS AND MULTILEVEL MODELING." Kent State University / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=kent1424789095.
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Wilson, Therese Maree. "Statistical reasoning at the secondary tertiary interface." Thesis, Queensland University of Technology, 2006. https://eprints.qut.edu.au/16358/3/Therese%20Wilson%20Thesis.pdf.
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Each year thousands of students enrol in introductory statistics courses at universities throughout Australia, bringing with them formal and informal statistical knowledge and reasoning, as well as a wide range of basic numeracy skills, mathematical inclinations and attitudes towards statistics, which have the potential to impact on their ability to develop statistically. This research develops and investigates measures of each of these components for students at the interface of secondary and tertiary education, and investigates the relationships that exist between them, and a range of background variables. The focus of the research is on measuring and analysing levels and abilities in statistical reasoning for a range of students at the tertiary interface, with particular interest also in investigating their basic numeracy skills and how these may or may not link with statistical reasoning allowing for other variables and factors. Information from three cohorts in an introductory data analysis course, whose focus is real data investigations, provides basis for the research. This course is compulsory for all students in degree programs associated with all sciences or mathematics.
The research discusses and reports on the development of questionnaires to measure numeracy and statistical reasoning and the students' attitudes and reflections on their prior school experiences with statistics. Students' attitudes are found to be generally positive, particularly with regard to their self-efficacy. They are also in no doubt as to the links that exist between mathematics and statistics.
The Numeracy Questionnaire, developed to measure pre-calculus skills relevant to an introductory data analysis course which emphasises real data investigations, demonstrates that many students who have completed a basic algebra and calculus senior school subject struggle with skills which are in the pre-senior curricula. Direct examination of the responses helps to understand where and why difficulties tend to occur. Rasch analysis is used to validate the questionnaire and assist in the description of levels of skill. General linear models demonstrate that a student's numeracy score depends on the result obtained in senior mathematics, whether or not the student is a mathematics student, gender, whether or not higher level mathematics has been studied, self-efficacy and year. The research indicates that either the pre-senior curricula need strengthening or that exposure to mathematics beyond the core senior course is required to establish confidence with basic skills particularly when applied to new contexts and multi- step situations.
The Statistical Reasoning Questionnaire (SRQ) is developed for use in the Australian context at the secondary/tertiary interface. As with the Numeracy Questionnaire, detailed examination of the responses provides much insight into the range and features of statistical reasoning at this level. Rasch analyses, both dichotomous and polychotomous, are used to establish the appropriateness of this instrument as a measuring tool at this level. The polychotomous, Rasch partial credit model is also used to define a new approach to scoring a statistical reasoning instrument and enables development and application of a hierarchical model and measures levels of statistical reasoning appropriate at the school/tertiary interface.
General linear models indicate that numeracy is a highly significant predictor of statistical reasoning allowing for all other variables including tertiary entrance score and students' backgrounds and self-efficacy. Further investigation demonstrates that this relationship is not limited to more difficult or overtly mathematical items on the SRQ.
Performance on the end of semester component of assessment in the course is shown to depend on statistical reasoning at the beginning of semester as measured by the partial credit model, allowing for all other variables. Because of the dominance of the relationship between statistical reasoning (as measured by the SRQ) and numeracy on entry, some further analysis of the end of semester assessment is carried out. This includes noting the higher attrition rates for students with less mathematical backgrounds and lower numeracy.
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Wilson, Therese Maree. "Statistical reasoning at the secondary tertiary interface." Queensland University of Technology, 2006. http://eprints.qut.edu.au/16358/.
Full textAbstract:
Each year thousands of students enrol in introductory statistics courses at universities throughout Australia, bringing with them formal and informal statistical knowledge and reasoning, as well as a wide range of basic numeracy skills, mathematical inclinations and attitudes towards statistics, which have the potential to impact on their ability to develop statistically. This research develops and investigates measures of each of these components for students at the interface of secondary and tertiary education, and investigates the relationships that exist between them, and a range of background variables. The focus of the research is on measuring and analysing levels and abilities in statistical reasoning for a range of students at the tertiary interface, with particular interest also in investigating their basic numeracy skills and how these may or may not link with statistical reasoning allowing for other variables and factors. Information from three cohorts in an introductory data analysis course, whose focus is real data investigations, provides basis for the research. This course is compulsory for all students in degree programs associated with all sciences or mathematics. The research discusses and reports on the development of questionnaires to measure numeracy and statistical reasoning and the students' attitudes and reflections on their prior school experiences with statistics. Students' attitudes are found to be generally positive, particularly with regard to their self-efficacy. They are also in no doubt as to the links that exist between mathematics and statistics. The Numeracy Questionnaire, developed to measure pre-calculus skills relevant to an introductory data analysis course which emphasises real data investigations, demonstrates that many students who have completed a basic algebra and calculus senior school subject struggle with skills which are in the pre-senior curricula. Direct examination of the responses helps to understand where and why difficulties tend to occur. Rasch analysis is used to validate the questionnaire and assist in the description of levels of skill. General linear models demonstrate that a student's numeracy score depends on the result obtained in senior mathematics, whether or not the student is a mathematics student, gender, whether or not higher level mathematics has been studied, self-efficacy and year. The research indicates that either the pre-senior curricula need strengthening or that exposure to mathematics beyond the core senior course is required to establish confidence with basic skills particularly when applied to new contexts and multi- step situations. The Statistical Reasoning Questionnaire (SRQ) is developed for use in the Australian context at the secondary/tertiary interface. As with the Numeracy Questionnaire, detailed examination of the responses provides much insight into the range and features of statistical reasoning at this level. Rasch analyses, both dichotomous and polychotomous, are used to establish the appropriateness of this instrument as a measuring tool at this level. The polychotomous, Rasch partial credit model is also used to define a new approach to scoring a statistical reasoning instrument and enables development and application of a hierarchical model and measures levels of statistical reasoning appropriate at the school/tertiary interface. General linear models indicate that numeracy is a highly significant predictor of statistical reasoning allowing for all other variables including tertiary entrance score and students' backgrounds and self-efficacy. Further investigation demonstrates that this relationship is not limited to more difficult or overtly mathematical items on the SRQ. Performance on the end of semester component of assessment in the course is shown to depend on statistical reasoning at the beginning of semester as measured by the partial credit model, allowing for all other variables. Because of the dominance of the relationship between statistical reasoning (as measured by the SRQ) and numeracy on entry, some further analysis of the end of semester assessment is carried out. This includes noting the higher attrition rates for students with less mathematical backgrounds and lower numeracy.
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Duku, Eric K. "Assessing Early Child Development: Issues of Measurement Invariance and Psychometric Validity." Thèse, Université d'Ottawa / University of Ottawa, 2013. http://hdl.handle.net/10393/24097.
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The measurement of reliable and valid indicators of early child development is necessary for assessing phenomena and is useful in the monitoring of ongoing efforts to eradicate inequalities in the social determinants of health. There is an increasing awareness of the contextual, cultural, and developmental influences on constructs used in early child development (ECD) research. Using a measurement perspective, this dissertation examined the issue of measurement invariance and psychometric validity in early child development research. A construct violates the principle of invariance when two persons from different populations who are theoretically identical on the construct being measured have different scores on it.
This dissertation consists of three journal-style manuscripts (published or under review) that were used as examples to address the importance of the issue of measurement invariance and psychometric validity in ECD research using data from two unique areas: autism and executive functioning. The three data sets were collected on pre-school children with parents and or teachers as informants and were chosen to represent different levels of data collection – clinical, community, and population. These data sets allowed for the examination of measurement invariance by type of informant, sex, and age of child. The results from the three studies illustrate the importance of assessing measurement invariance in ECD and whether or not the instruments examined can be used to assess sub-group differences with confidence.
A lack of measurement invariance found for two of the studies, suggests that observed group differences in latent constructs could be attributed, in part, to measurement bias. More importantly, bias in the measurement of the constructs of severity of social impairment symptoms in autism, and executive functioning across groups could have an impact on services such as patient treatment. These biases could also influence public policy development, particularly when there may be an underlying need for a cross-group approach where belief systems may affect the meaning and structure of constructs.
In summary, measurement invariance should be a prerequisite for making any meaningful comparisons across groups. A requirement of establishing measurement invariance should be included in the guidelines for comparative research studies as a necessary first step before an instrument is adopted for use.
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Rowles, Phillip Bruce. "Constructing a Polysemous Academic Vocabulary Extent Test Via Polytomous Rasch Model Measurement Analyses." Diss., Temple University Libraries, 2015. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/363274.
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Language ArtsEd.D.
Educational measurement research faces an unresolved dilemma: competently meeting the longstanding demand for improved vocabulary strength (depth) aspect assessments. My original contribution to knowledge in the written receptive vocabulary knowledge construct research domain is twofold. My first contribution is proposing an a priori metasynonymy awareness hypothesis based on a vocabulary strength aspect extension of O’Connor’s (1940) written receptive vocabulary acquisition developmental stage theory. My second contribution is designing and constructing a vocabulary extent (the nexus between vocabulary size (breadth) and strength aspects) test. The test, called the Polysemous Academic Vocabulary Extent Test, utilizes ordered triple rank (OTR) responses and a complementary six-tier incremental scoring guide rubric. An example test item includes a sentence stem with a bold keyword and three options, such as: All the reviews of the movie were positive. positive: a) sure b) good c) enviro
Temple University--Theses
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McEwen, Mary R. "The Effects of Incomplete Rating Designs on Results from Many-Facets-Rasch Model Analyses." BYU ScholarsArchive, 2018. https://scholarsarchive.byu.edu/etd/6689.
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A rating design is a pre-specified plan for collecting ratings. The best design for a rater-mediated assessment both psychometrically and from the perspective of fairness is a fully-crossed design in which all objects are rated by all raters. An incomplete rating design is one in which all objects are not rated by all raters, instead each object is rated by an assigned subset of raters usually to reduce the time and/or cost of the assessment. Human raters have varying propensities to rate severely or leniently. One method of compensating for rater severity is the many-facets Rasch model (MFRM). However, unless the incomplete rating design used to gather the ratings is appropriately linked, the results of the MFRM analysis may not be on the same scale and therefore may not be fairly compared. Given non-trivial numbers of raters and/or objects to rate, there are numerous possible incomplete designs with various levels of linkage. The literature provides little guidance on the extent to which differently linked rating designs might affect the results of a MFRM analysis. Eighty different subsets of data were extracted from a pre-existing fully-crossed rating data set originally gathered from 24 essays rated by eight raters. These subsets represented 20 different incomplete rating designs and four specific assignments of raters to essays. The subsets of rating data were analyzed in Facets software to investigate the effects of incomplete rating designs on the MFRM results. The design attributes related to linkage that were varied in the incomplete designs include (a) rater coverage: the number of raters-per-essay, (b) repetition-size: the number of essays rated in one repetition of the sub-design pattern, (c) design structure: the linking network structure of the incomplete design, and (d) rater order: the specific assignments of raters to essays. A number of plots and graphs were used to visualize the incomplete designs and the rating results. Several measures including the observed and fair averages for raters and essays from the 80 MFRM analyses were compared against the fair averages for the fully-crossed design. Results varied widely depending on different combinations of design attributes and rater orders. Rater coverage had the overall largest effect, with rater order producing larger ranges of values for sparser designs. Many of the observed averages for raters and essays more closely approximated the results from the fully-crossed design than did the adjusted fair-averages, particularly for the more sparsely linked designs. The stability of relative standing measures was unexpectedly low.
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Elderfield, Jessica. "Comparing single-level and multi-level regression models in analysing Rasch measures of numeracy." Thesis, Edith Cowan University, Research Online, Perth, Western Australia, 2008. https://ro.ecu.edu.au/theses/180.
Full textAbstract:
This thesis describes a research study that investigated the empirical differences between two competing regression methods used to produce value-added performance indicator information for the monitoring of school effectiveness, and the practical consequences for schools when using this information for school improvement and accountability purposes. The two regression methods under review were single-level Means-on-Means regression and Multilevel Modelling. The study involved data from 24 government secondary schools with a total of 2862 students in 132 Year 8 classes in Western Australia. The dependent variable was a Rasch-created linear measure of Year 8 Numeracy from data of a Mathematics assessment, specially designed by the Department of Education. The main independent variable was a Rasch-created, linear measure of Year 7 Numeracy from student data of the Western Australian Literacy and Numeracy Assessment. Students' scored responses on items from both assessments were calibrated on a common Western Australian Monitoring Standards in Education linear scale which enabled: (1) the movement of a student's performance to be measured over time; and, (2) the application of subsequent statistical analyses from which valid inferences could be made. There were four other independent variables: (1) gender (male or fema1e); (2) ethnic group (Aborigina1 and Torres Strait Islander, or non-Aboriginal and Torres Strait Islander status); (3) language background (English or other than English); and the schoo1-level variable; and (4) school socioeconomic status.
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Elwood, James Andrew. "Enriching Structural Models of L2 Willingness to Communicate: The Role of Personality, Ego Permeability, and Perceived Distance." Diss., Temple University Libraries, 2011. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/134212.
Full textAbstract:
CITE/Language ArtsPh.D.
Willingness to communicate (WTC) in a second language (L2) is crucial to the development of communicative speaking skills. This study is a cross-sectional investigation of the role in models of second language (L2) willingness to communicate of three personality variables hitherto underresearched in the L2 field: extroversion, ego permeability (one's capacity to tolerate ambiguity), and perceived distance from one's core persona. A sample of 252 Japanese university students responded to a set of instruments used to measure individual difference variables and personality variables; the instruments were drawn from the fields of L2 acquisition and psychology as well as a 5-item instrument designed to measure perceived distance in a series of participatory L2 speaking activities. Confirmatory factor analysis, Rasch analysis, and structural equation modeling were utilized to validate the respective instruments. The International Posture instrument was best represented by a two-factor configuration consisting of Intergroup Approach-Avoidance Tendency and Intercultural Friendship Orientation, while the L2 Communicative Confidence was altered to consist of three factors (L2 Anxiety, Perceived L2 Communicative Competence, and Extroversion). The hypothesized additions of Ego Permeability and Perceived Distance failed to improve the measurement models, and the original Ego Permeability variable functioned poorly in this context. The MacIntyre and Charos (1996) model had marginal fit to the data even after undergoing considerable respecification. The models of Yashima (2002) and Yashima, Zenuk-Nishide, and Shimizu (2004) were found to have good fit as originally conceptualized, but the addition of Extroversion and paths from International Posture and L2 Communicative Anxiety improved the fit of both models. Collectively, the results indicate that extroversion plays an important role in models of L2 WTC and that the basic models of Yashima and colleagues are robust. These findings provide crucial insights into the process of L2 WTC, an important factor in the students' acquisition of communicative competence.
Temple University--Theses
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Ru, Chen-Yi, and 陳奕如. "Bayesian Analysis of Multidimensional Rasch Model." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/t68nsb.
Full textAbstract:
碩士中原大學
應用數學研究所
106
The test theory can be divided into classical test theory (CTT) and item response theory(IRT). But there are problems with sample dependence and test dependence in CTT. Therefore, this study is based on the IRT. In the IRT, it can be divided into binary scoring and multinomial scoring. In addition to the difference in scoring, it can be divided into unidimensional model and multidimensional model after subdivision. This article mainly uses the multidimensional two-parameter logistic model (M2PLM) in binary scoring. This research is aimed at the freshmen who have just entered the freshman year in Chung Yuan Christian University in 2013 years. An English entrance test was conducted for students. The total number of students taking the exam is 3,138. The statistical method used is Bayesian analysis. The estimated values calculated by the Markov Chain Monte Carlo method to analyze what each representative is. The M2PLM is an extnsion of the two-parameter logistic model (2PLM). The difference between the two is that the student ability in 2PLM has only one aspect, and M2PLM has multiple aspects. And this research is to split the ability into two aspects. It can be observed from the different aspects of discrimination to identify which topics are more effective in distinguishing the ability. Finally, a 2PLM and a M2PLM are used to make a further exploration to examine the special places.
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Meng-Pao, Tseng, and 曾盟堡. "The Analysis of Standard Dance''s Judge for Using Many-facet Rasch Model." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/44994239395170730565.
Full textAbstract:
碩士國立體育學院
體育研究所
89
The purpose of this study was to analyze the judge’s rating in terms of item response theory. The data of the evaluation of standard dance’s judge in the final of the 13th Asian Games was analyzed. The FACETS software was used to analyze three-facet Rasch model. Through IRT we could describe and classify the performance of the judge. Furthermore, the judge’s unexpected response was also tested and overtook. The conclusion was that item response theory could better analyze judge’s evaluation precisely.
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Castro, Ana Rosa Galvão de. "Head and neck cancer: rasch analysis in quality of life assessment." Master's thesis, 2018. http://hdl.handle.net/10284/7332.
Full textAbstract:
A patologia oncológica de cabeça e pescoço (POCP) representa 3% de todos os
tumores malignos diagnosticados mundialmente. A POCP inclui várias localizações como:
cavidade oral, faringe, laringe e glândulas salivares. A POCP causa impacto negativo no
doente oncológico e afecta várias funções. A avaliação da Qualidade de Vida Relacionada
com a Saúde (QdVRS) é essencial para melhor compreender e explorar a autopercepção do
doente oncológico de cabeça e pescoço.
Contudo, a QdVRS é considerada um Patient Reported Outcome (PRO) de carácter
subjectivo e multidimensional justificando a necessidade de criar medidas confiáveis, e
adequadas.
O nosso objectivo consistiu em optimizar e melhorar a avaliação da QDVRS com
recurso a modelos matemáticos. Identificaram-se as questões difíceis do EORTC QLQ C-30
e a habilidade do paciente em responder discutindo o conceito de dificuldade em contextos
de saúde.
Foi analisada uma base de dados obtida na Unidade de Cabeça e Pescoço do Instituto
Português de Oncologia do Porto. Usou-se o WinRasch software package- versão de
demonstração.
Os doentes oncológicos de cabeça e pescoço (n=75) foram selecionados no momento
de diagnóstico e agrupados pelo estadiamento da doença. Foi comparado o modelo
conceptual com a análise do Modelo de Rasch (correlação point-measure; dificuldade ou
desafio de acordo com os dados; curvas de probabilidade relacionadas com a variável
latente; infit e outfit).
A análise de Rasch suportou na generalidade o modelo conceptual do EORTC QLQ
C30 nos doentes oncológicos avaliados. Detetaram-se 3 items problemáticos (Q7, Q20, Q28).
Um total de 3 doentes demonstraram resultados fora do esperado baseado na análise.
O Modelo de Rasch aplicado a QdVRS em POCP tem aumentado a precisão e
complementado as técnicas estatísticas tradicionais. Esta abordagem optimiza os PRO e
facilita a sua incorporação na prática clínica em oncologia.Head and neck cancer (HNC) represents 3% of all cancer cases worldwide. HNC includes several upper body locations: oral cavity, pharynx, larynx or salivary glands. HNC is the most distressing human cancer disturbing cervicofacial region and affecting several functions. Health Related Quality of Life (HRQoL) assessment in HNC is essential to better understand and explore the HNC patient’s perceptions. Nevertheless, HRQoL is considered a subjective and multidimensional dynamic Patient Reported Outcome justifying the need to build reliable, robust and adequate measures. Our objective was to optimize and improve HRQoL assessment using mathematical models identifying the EORTC QLQ-C30 questions difficulty and the patients’ ability to answer discussing the concept of difficulty in health context. A database obtained in Oporto Oncology Portuguese Institute, Head and Neck Unit, was explored. It was used the WinRasch software package - demonstration version. HNC patients (n=75) were selected at the time of diagnosis and grouped according to the stage of disease. We compare our construct theory and Rasch Model analysis (point-measure correlation; difficulty or challenge according to the data; probability curves related to the latent variable; infit and outfit). Rasch analysis supported generally the theoretical constructs of the EORTC QLQ C30 in HNC patients evaluated. RM analyses detected three problematic items (Q7, Q20, Q28). A total of 3 respondents demonstrated misfit pattern at constructs based on Rasch analysis. Rasch Model applied to HRQoL in HNC as improving precision and complementing traditional statistical techniques. This approach is improving PRO and enabling its incorporation in oncological clinical practice.
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Tsai, Chia-Hao, and 蔡嘉豪. "Rule Usage Analysis for Proportional Reasoning and Probability Reasoning based on Latent Class Analysis and Mixed Rasch Model." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/92284589062812282102.
Full textAbstract:
碩士國立臺中教育大學
數學教育學系在職進修教學碩士學位班
96
The purpose of this study is to apply latent class analysis (LCA) and mixed Rasch model (MRM) to analyze the rule usage of proportional reasoning and probability reasoning for pupils. Latent classes are acquired according to response pattern so that the classification of rule usage is clearly displayed. As to the test of proportional reasoning, there are 25 items. In addition, probability reasoning test consists of 10 items. The sample includes fourth, fifth and sixth graders who are from elementary school in central district in Taiwan. The results show that there is various characteristics among groups, and there is similar characteristics for students within same group. There are six classes for proportional reasoning and there are three classes for probability reasoning test. Each response pattern of class could be explained by rule pattern. There is obvious difference of rule usage among grade, but there is no difference between gender. The findings of this research should be helpful for problem solving rule and could be used as references for remedial instruction. Finally, some recommendations and suggestions for future research are provided.
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Miguel, José Manuel Pacheco. "Teoria de Resposta ao Item. Representação e utilidade do modelo logístico de traço latente na psicometria actual." Doctoral thesis, 2014. http://hdl.handle.net/10316/24834.
Full textAbstract:
Tese de doutoramento em Psicologia, na área de especialização de Avaliação Psicológica, apresentada à Faculdade de Psicologia e Ciências da Educação da Universidade de CoimbraO modelo de Rasch é o modelo mais simples da teoria de resposta ao item (TRI) e constitui uma abordagem potencialmente útil ao nível da construção e refinamento psicométrico de instrumentos de avaliação psicológica. Trata-se de um modelo logístico de um parâmetro da TRI no qual a quantidade de traço latente existente na pessoa e a quantidade do mesmo traço latente reflectido nos vários itens do instrumento podem ser estimados de forma independente e comparados directamente entre si, uma vez que sujeitos e itens foram medidas numa mesma métrica comum, a escala logit. Esta, definida em unidades de probabilidades logarítmicas, é uma escala intervalar na qual a unidade dos intervalos entre as localizações conjuntas pessoas-itens têm um valor ou um significado consistente. O objectivo da presente dissertação visou a apresentação das potencialidades do modelo de Rasch, comparativamente à abordagem da teoria clássica dos testes (TCT), quando aplicado ao caso específico de instrumentos de avaliação psicológica que recorrem a itens politómicos aos quais os sujeitos respondem numa escala do tipo de Likert, designado Rating Scale Model (RSM). Metodologia Para concretizar este objectivo, relativo à aplicação do Rasch RSM, foram conduzidos quatro estudos psicométricos com amostras independentes de alunos do ensino secundário. O primeiro estudo, com alunos do 12º ano de escolaridade (N = 265), foi realizado com a Career Decision Self-Efficacy Scale — Short Form (CDSESF). No segundo e terceiro estudos, com alunos dos 10º, 11º e 12º anos de escolaridade, procedeu-se à análise da Positive and Negative Affect Schedule (PANAS), numa abordagem TCT com recurso à análise factorial exploratória/confirmatória (AFE/ VI AFC) (N = 528) e à modelação Rasch (N = 519), respectivamente. Finalmente, no quarto e último estudo, também com alunos dos 10º, 11º e 12º anos de escolaridade (N = 508), fez-se a análise Rasch da Rosenberg Self-Esteem Scale (RSES). Em cada um dos estudos, para além das medidas dos itens, foram ainda recolhidos dados para caracterização sociodemográfica das amostras. Resultados Dos resultados obtidos, salientam-se aqueles que se revestem de maior importância para os objectivos estipulados. No âmbito dos três estudos realizados com o Rasch RSM, os resultados alcançados permitiram reunir evidência psicométrica que corrobora, para a CDSE-SF, a PANAS e a RSES a respectiva: (1) validade de conteúdo (i.e., o bom ajustamento dos dados ao modelo permitiu que a parametrização dos sujeitos e a calibração dos itens tenha sido feita com elevada precisão na); (2) validade estrutural (i.e., unidimensionalidade e ausência de DIF), e (3) validade substantiva (i.e., as categorias da escala de resposta funcionam de forma adequada). Os resultados do único estudo baseado na TCT, com a PANAS, revelaram dificuldade de ajustamento do modelo aos dados que só parcialmente conseguiram replicar a estrutura factorial original do instrumento. Conclusões Os resultados sugerem que o RSM proporciona um quadro de referência útil para o refinamento psicométrico dos instrumentos de avaliação psicológica. Da sua aplicação resulta que, no caso específico das versões Portuguesas da CDSE-SF, da PANAS e da RSES, os seus respectivos itens são representativos e relevantes para os domínios dos construtos avaliados (e.g., validade de conteúdo), têm correspondência com os construtos definidos em cada um dos instrumentos (e.g., validade estrutural) e são avaliados através de escalas de resposta cujo diagnóstico ao funcionamento empírico das respectivas categorias revelou adequação das mesmas (e.g., validade substantiva).
Rasch model is the simplest Item Response Theory (ITR) model and constitutes a potentially useful approach at both the construction and refinement psychometric levels of psychological assessment instruments. It is an ITR one parameter logistic model in which the quantity of the latent trait existing in the person and the quantity of the same latent trait reflected in the various items of the instrument can be independently estimated and compared, because both items and subjects are measured using the same common metric, the logit scale. This scale, defined in logarithmic probabilities units, is an interval scale, in which the interval units between the response categories have a consistent value or significance. The goal of this dissertation is focused on the presentation of the Rasch model potentiality as compared with the classical test theory (CTT) approach when applied to the specific case of psychological assessment instruments that recur to polytomous items to which the subjects respond using a Likert type rating scale - the Rating Scale Model (RSM). Methodology In order to achieve this goal, related to the application of the Rasch RSM, four psychometric studies were carried out with independent samples of students attending secondary education. The first study, with a sample of 12th grade students (N = 265), was carried out using the Career Decision Self-Efficacy Scale — Short Form (CDSE-SF). In the second and third studies, comprising students attending respectively the 10th, 11th and 12th grades, we ran an analysis of the Positive and Negative Affect Schedule (PANAS), using both exploratory/confirmatory factor analysis (EFA/ CFA), and Rasch modeling (N = 519), respectively. Finally, in the fourth and last study, also comprising 10th, 11th and 12th grade students (N = VIII 508), a Rasch analysis of the Rosenberg Self-Esteem Scale (RSES) was made. In each of these four studies, in addition to the items’ measurements, data needed for the sociodemographic characterization of the samples were collected. Results From the results obtained we highlight those that are more relevant to the goals previously stated. Within the three studies carried out with the RSM the results obtained gathered psychometric evidence that confirms, concerning the CDSESF, the PANAS and the RSES, their respective: 1) content validity (i.e. the good adjustment of the data to the model allowed both the parameterization of the subjects and the calibration of the items to be made with high precision); 2) structural validity (i.e. unidimensionality and lack of DIF) and; 3) substantive validity (i.e. the categories of the response scale function adequately). The results of the only study which was based on CTT, and in which the PANAS was used, revealed some adjustment difficulties of the model to the data, which only partially replicated the original factorial structure of the instrument. Conclusions The results suggest that the RSM provides a reference framework useful for the psychometric refinement of psychological assessment instruments. In fact, from its application it can be concluded that, in the specific case of the Portuguese versions of the CDSE-SF, the PANAS and the RSES, their respective items are representative and relevant for the domains of the constructs under assessment (e.g. content validity), have correspondence with the constructs defined in each of the instruments (e.g. structural validity), and are assessed using response scales whose diagnostic to the empirical functioning of their respective categories revealed their adequacy (e.g. substantive validity).
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Yeh, Yi-Chun, and 葉懿諄. "Rasch model analysis for studying psychometric characteristics of the WHOQOL-BREF in community-dwelling older people." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/00746376524497432767.
Full textAbstract:
碩士中國醫藥大學
環境醫學研究所碩士班
94
Objectives: Item response theory (IRT) offers one of the best alternatives for optimizing scales and performing item analysis. The Rasch family of model which was one of item response theory was used to analyze the psychometric characteristics of brief version of World Health Organization Quality of life (WHOQOL-BREF) in community-dwelling older people in Taiwan. Methods: One thousand and two hundreds community-dwelling older people living in Shin-Sher Township of Taichung County in 2001, completed the WHOQOL-BREF at their residences either by themselves or with the assistance of an interviewer. The age of these 1200 subjects ranged from 65 to 103 years with an average of 73.4 year, and 59% of the subjects were males. Partial credit model, one of the Rasch family of model, was used to analyze the psychometric characteristics of domains and items of the WHOQOL-BREF. Infit statistics were applied to examine the unidimensionality of each domain; Item calibration of logit unit was to examine the range of item difficulty, redundancy, and hierarchy; and differential item functioning analysis was to examine whether item properties were the same between males and females older people. Results: All of the items within each domain satisfied the assumption of unidimensionality. The range of mean of item difficulty (range) in physical, psychological, social, environmental domain were -1.1~0.48 (1.58), -1.19~1.29 (2.48), -0.77~1.17 (1.94), and -1.08~0.96 (2.04), respectively; the corresponding range (range) of threshold difficulty were -3.86~5.3 (9.16), -6.74~6.78 (13.52), -8.39~9.66 (18.05), and -3.72~4.75 (8.47), respectively; the corresponding range of ability were -6.7~7.76 (14.46), -5.78~8.79 (14.57), -9.34~10.98 (20.32), -5.25~5.41 (10.66), respectively. More item redundancies occurred in environmental domain than those in other domains. Comparison of item hierarchy with the results from the NHRI health survey, found that the two studies had different hierarchy in physical and psychological domains, and a similar hierarchies in social and environmental domains. While “body image” of psychological domain had a significant DIF in age group, “sexual activity” and “friends’ support” of social domain had a significant DIF among gender and age group, there was no apparent DIF in other domains. The reliability indices in physical, psychological, social and environmental domains were 0.76, 0.77, 0.68, and 0.78, respectively. Conclusion: The summated score method is used to measuring personal ability in classical test theory (CTT) analysis and it does not account for the variability of item properties. However, IRT is based on a comprehensive structure of psychometrical theory and provides a foundation for scaling personal ability and item difficulty by using the responses of assessment items. IRT can overcome a lot of limitations of CTT. While our study confirms the suitability of WHOQOL-BREF in older people, it also highlights that there is still a room of improvement for the WHOQOL-BREF in the older people.
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Li, Chien-Chien, and 李蒨蒨. "Analysis of Reading Comprehension Levels of 4th to 6th Grade Students in Pingtung County Using the Rasch Model." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/92298798188746662092.
Full textAbstract:
碩士國立屏東教育大學
教育心理與輔導學系碩士班
102
The study aim at understanding the reading comprehension levels of 4th to 6th grade students in Pingtung County, Taiwan, and at constructing a diagnostic report by using the Rasch model. The first step of this study was to test whether the data conform the one-dimensional Rasch model, and to validate the reading comprehension cognitive levels. Next, students’ reading comprehension performance was analyzed according to the three reading comprehension levels (i.e., locate/recall, integrate/interpret, and critique/evaluate), separated by school size, grade and gender. Finally, diagnostic report for individual student and for class were designed by integrating information obtained from the Rasch analysis. The results are summarized as follows： 1.The test holds satisfactory psychometric properties: (1) Twenty-nine test items were retained according to various fit statistics (i.e., standardized residual t values and differential item functioning) and test content; (2) the 29-item test holds satisfactory psychometric properties (i.e., rating scales are appropriate, items fit the Rasch model, all items are free from gender and grade DIF, and the person separation index is .78); (3) items spread reasonably well along the latent continuum and are aligned with various ability levels 2.Item difficulties vary according to item format and cognitive levels: (1) The three reading cognitive levels show hierarchical structure as expected; (2) item difficulties of the constructed- response items are significantly higher than that of the multiple- choice items. 3.Cognitive level analysis: (1) Although 50% of the students reaches the average difficulty of ‘integrate/interpret’ level, only 40% and 10% of the students reach the mastery levels (defined as having 80% or higher the chance to reach the average difficulty of a particular cognitive level) of ‘locate/recall’ and ‘integrate/interpret’ levels, respectively; (2) Students in large schools outperformed those in medium and small schools on all reading comprehension cognitive levels, and the percentages of reaching the mastery levels of ‘locate/recall’ (44%) and ‘integrate/ interpret’ (15%) are also higher for large schools than those for medium and small schools; (3) students’ reading comprehension performance increases as they move up to higher grade levels, and the percentages of reaching the mastery level of ‘locate/recall’ are 56%, 36% and 23% for 6th, 5th and 4th grade students, separately, while the percentages of reaching the mastery level of ‘integrate/interpret’ are 22%, 9% and 3% for 6th, 5th and 4th grade students, respectively; (4) girls performed significantly better than boys not only on all reading comprehension cognitive levels, but also on the percentages of reaching mastery level; (5) within each grade level, large schools performed better than medium and small schools; yet, the variability is smaller in the large schools. 4.Conversion and application of test scores：(1) The probabilities of answering each item correctly and of reaching a particular cognitive level were computed for each student; (2) norm conversion tables (grade level, gender with in each grade level) were provided to locate students’ relative performance; (3) individual diagnostic report, including scale score, probabilities of reaching each cognitive level, ‘item - person map,’ and summary and suggestions concerning student’s reading comprehension performance, was designed; (4) class diagnostic report, including the distribution of all students reaching each cognitive levels in the ‘item-person map,’ and summary and suggestions concerning class’s reading comprehension performance and teaching practices, was offered. Discussions and suggestions for future research and teaching practices are also provided.
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Cheng, Huey-Ru, and 鄭蕙如. "The Study of mixed Rasch model analysis on mathematical content knowledge and cognitive abilities for junior high school students." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/08157772266504149740.
Full textAbstract:
博士國立臺灣師範大學
教育心理與輔導學系
94
The purpose of this study is to understand the performance of junior high students’ mathematical content knowledge and cognitive abilities. The assessment framework of mathematics will be built and the performance types of students’ mathematical content knowledge and cognitive abilities will be understood based on the Basic Competence Test for Junior High School Students (BCTEST). In the research methods, we collect and analyze the definitions of mathematical content knowledge and cognitive abilities as defined by assessment institutes and use mixed Rasch model to analyze the students’ mathematical response patterns for the BCTEST. The findings were listed as follows: (a) a framework of mathematical content knowledge and cognitive abilities was built based on the BCTEST; (b)students had better performance in data analysis, statistics and probability than in geometry and spatial sense on the mathematical content knowledge; and on the mathematical cognitive abilities performed better in conceptual understanding, procedure knowledge and execution than in problem solving; (c)the results of mixed Rasch model showed that students had different performance in mathematical content knowledge and cognitive abilities who belong to different latent classes. Finally, some suggestions were provided in further instructions and researches based on the results.
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Almeida, Luis Miguel Pires. "Literacia em avaliação de professores desenvolvimento e aplicação do questionário de aferição da literacia em avaliação (QALA)." Doctoral thesis, 2021. http://hdl.handle.net/10437/12800.
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Orientação: Glória de Magalhães RamalhoA avaliação das aprendizagens é uma das mais importantes responsabilidades dos professores, assim como uma das tarefas nas quais os professores despendem mais tempo (Mertler, 2003; Ramesal, 2011). Desta forma, as capacidades em avaliação são uma ferramenta fundamental que todo o professor deve dominar. Ao conjunto de capacidades em avaliação dá-se o nome de literacia em avaliação. O conceito de literacia em avaliação foi primeiramente apresentado por Stiggins (1991) como o conhecimento profundo das questões de avaliação. Do mesmo modo, em 1995, o mesmo autor refere que um educador/professor com literacia em avaliação sabe o que avaliar, a razão de avaliar, como avaliar, quais os possíveis problemas relacionados com a avaliação e como prevenir que esses problemas surjam no processo de ensino e aprendizagem. Para além disso, tem um conhecimento profundo dos efeitos negativos de uma má avaliação. Desta forma, a ausência de capacidades em avaliação, por parte do professor, é um fator que pode pôr em causa tanto a avaliação dos alunos como todo o processo de ensino e aprendizagem. A presente investigação assentou em dois objetivos principais. Em primeiro lugar, pretendeu-se analisar as perceções que os professores, em exercício, tinham dos seus conhecimentos e capacidades em avaliação. Em segundo lugar, procurou-se aferir a literacia em avaliação desses mesmos professores. Destes dois objetivos principais derivaram uma série de objetivos específicos que possibilitaram uma análise mais aprofundada da problemática em investigação. Para tal, foi criado um questionário desenvolvido para o efeito e ao qual designámos de QALA – Questionário de Aferição da Literacia em Avaliação. O QALA foi aplicado a um conjunto de 253 professores do ensino básico e secundário a lecionar na Zona Pedagógica de Lisboa e Península de Setúbal. A análise dos dados seguiu uma abordagem quantitativa do tipo survey. Procedeu-se, em primeiro lugar, a uma avaliação das propriedades psicométricas do QALA com recurso ao modelo Rasch. Posteriormente, foi realizada uma análise descritiva e inferencial, de forma a responder aos objetivos gerais e específicos propostos para a presente investigação. Os resultados alcançados pela aplicação do modelo Rasch, parecem evidenciar boas qualidades psicométricas das 3 partes do QALA. Ficou também evidente que, embora os professores tenham valores positivos em relação às perceções sobre os seus conhecimentos e capacidades em avaliação (Parte 2), nos quatro domínios considerados, os resultados obtidos nas Partes 3 e 4 parecem demonstrar níveis inadequados de literacia em avaliação, o que pode ter implicações negativas em todo o processo de ensino e aprendizagem.
Assessing students’ learning is one of the most important responsibilities a teacher can have, as well as being one of the tasks teachers spend more time doing (Mertler, 2003; Ramesal, 2011). Thus, assessment skills are a primary tool that every teacher should master. The set of assessment skills is known as assessment literacy. The concept of assessment literacy was coined for the first time by Stiggins (1991) as the deep understanding of assessment issues. Similarly, in 1995, the same author refers that an educator/teacher with assessment literacy knows what to assess, the reason to do it, how to do it and the possible problems related with it and how to prevent that those problems occur in the teaching-learning process. Furthermore, the teacher has a deep knowledge about the negative effects of a poor assessment. This way, the lack of assessment skills is a factor that could lead to a poor judgment of the student’s assessment, as well of all the teaching-learning process. The present investigation was based in two main objectives. The first was to analyse the teachers’ perceptions about their knowledge and assessment skills. The second was to measure the assessment literacy from those teachers. These two main objectives originated a set of specific objectives, which enabled a deeper analysis in the investigation. For that purpose, a questionnaire was developed, called QALA - Assessment Literacy Admeasurement Questionnaire. It was implemented to a set of 253 teachers from the basic and secondary education levels teaching in the pedagogical zone of Lisbon and Setubal Peninsula. The data analysis followed a quantitative survey approach. Firstly, was initiated a psychometric assessment of the QALA properties, using the Rasch model. Subsequently, an explanatory inferential analysis was developed, as a way to respond to the specific objectives of the investigation. The achieved results showed by the Rasch Model seem to demonstrate good psychometric skills in the 3 parts of QALA. It was also clear that, although teachers show positive results concerning the perceptions about their knowledge and assessment skills (part 2), in the four considered fields, the results concerning parts 3 and 4 seem to show inadequate levels of literacy skills, which can influence the teaching-learning process negatively.
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Hailaya, Wilham M. "Teacher assessment literacy and student outcomes in the province of Tawi-Tawi, Philippines." Thesis, 2014. http://hdl.handle.net/2440/99098.
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This study examined teachers’ assessment literacy and its probable impact on student achievement and aptitude (the outcome variables) through the intervening variables at the teacher and student levels. It likewise explored the effects of demographic variables on factors at the two levels and on the outcome variables. The study had 582 teacher samples and 2,077 student samples taken from Grade Six, Second Year and Third Year high school classes in the province of Tawi-Tawi, Philippines. It employed a mixed-methods design using quantitative method as a primary approach and qualitative method as a supporting approach. It utilised a number of statistical techniques, including Rasch modeling, structural equation modeling and hierarchical linear modeling, thematic analysis, and through the use of a number of software applications and include SPSS 16.0, LISREL 8.80, and HLM 6.08 to analyse the data. The results revealed that the elementary and secondary school teachers in Tawi-Tawi, Philippines possessed relatively low assessment literacy. In terms of the specific assessment areas, the teachers performed highest on “choosing assessment methods appropriate for instructional decisions” and lowest on “developing assessment methods appropriate for instructional decisions”. The qualitative finding concerning teachers’ knowledge on validity and reliability supported the low assessment literacy results. Moreover, teachers generally indicated that they practised “assessment purpose”, “assessment design”, and “assessment communication” frequently, and “direct transmission method” and “alternative approach” of teaching in more than half of their lessons. Furthermore, the Grade Six, Second Year, and Fourth Year high school students generally exhibited positive “perceptions of assessment” and positive “attitude towards assessment”. Besides, the Grade Six and Second Year high school students obtained below average “academic achievement”, and Fourth Year high school students obtained below average “aptitude”. The results further revealed that teachers’ assessment literacy negatively influenced their teaching practices while their assessment practices positively impacted on their teaching practices. No relationship was evident between their assessment literacy and assessment practices. However, analysis of relevant sub-variables showed some degree of positive effect of assessment literacy on assessment practices. Additionally, the students’ “perceptions of assessment” appeared to positively influence their “attitude towards assessment”. The Grade Six and Second Year high school students’ “perceptions of assessment” and “attitude towards assessment” likewise showed significant positive effects on their “academic achievement”. The Fourth Year high school students’ “perceptions of assessment” and “attitude towards assessment” exerted negative and positive effects, respectively, on their “aptitude”. Some demographic factors had moderating effects on the variables tested. Teachers’ age range (60 years and above), school type, and gender appeared to moderate effects on “academic achievement” while teachers’ age range (below 25 years), academic qualification, and years of teaching experience (16-20 years) had moderating effects on “aptitude”. The study’s results generally serve as empirical evidence and additional information on in-service teachers’ assessment literacy and its relations with other relevant variables. The results have implications for further research using other contextual variables and for the formulation of relevant policies, launching of assessment reform, development of assessment and research programs, and re-examination of assessment component of the Licensure Examination for Teachers. Furthermore, the findings in this study are relevant to pre-service teacher education programs and professional development of elementary and secondary school teachers, especially those from rural communities like Tawi-Tawi in the Philippines.Thesis (Ph.D.) -- University of Adelaide, School of Education, 2014.
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Lye, Che Yee. "Towards a comprehensive model of English as a second language learning and teaching in the Malaysian independent Chinese secondary schools." Thesis, 2016. http://hdl.handle.net/2440/100653.
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Low English proficiency among secondary school students is a major concern in Malaysia, especially in the context of the Malaysian Independent Chinese Secondary Schools since Malaysian students who have spent eleven to thirteen years studying the English language are still not able to master it upon completing secondary schooling. In addition, a significant number of Malaysian graduates are unemployed, and even those who are employed receive complaints from the employers due to their limited English proficiency. It is argued that student-, teacher- and school-level factors may impact on students’ English proficiency. A significant amount of research related to these factors has been conducted, ranging from finding universal trends to identifying differences. These studies have examined the relationships between students’ characteristics, attitudes and motivation, anxiety and self-efficacy as well as conceptions of and approaches to learning; teachers’ characteristics and approaches to teaching; as well as schools’ demographic variables such as instructional time, student-teacher ratio, resources and facilities as well as curriculum and assessment. Researchers have shown that these factors may impact on students’ English proficiency in a single-level model. However, numerous scholars have also argued that these factors may interact with each other and thus focussing on just a single level may not be sufficient to explain the complexity of English language learning and teaching. In addition, limited research has been conducted in the Malaysian context, especially in the Malaysian Independent Chinese Secondary Schools. This research study examines the student-, teacher- and school-level factors, their interrelationships and their impact on students’ English as a second language proficiency. A quantitative research design was used including questionnaires and assessment checklist to collect data from the respondents. The respondents in this study involved the Malaysian Independent Chinese Secondary Schools located at the urban areas in Kuala Lumpur, Selangor, Perak and Penang, the Senior 1 English language teachers, and all Senior 1 students who were taught by these teachers. A number of scales and demographic items related to student-, teacher- and school-level factors were administered for the purpose of this study. All scales except the demographic items employed in this study were validated, calibrated and verified using the Confirmatory Factor Analysis and Rasch Analysis. In addition, as many teachers or raters from different schools and classes were involved in rating students’ English language proficiency, their scores were adjusted by modelling rater judgement through the many facets Rasch analysis. The raw scores obtained from the responses in all scales were anchored to obtain the Weighted Likelihood Estimates for use in subsequent analyses which included the analyses for the student- and teacher-level models as well as the hierarchical linear model. The Structural Equation Modelling approach was employed to examine the student- and teacher-level models. For the student-level model, all scales or variables and demographic items were examined with regards to their interrelationships and how they influenced students’ English language proficiency. For the teacher-level model, the interrelationships of the variables and demographic items were examined. In addition, as data collected were of a hierarchical structure, the relationships among the nested variables in school-, teacher- and student-levels, how these variables influenced students’ English language proficiency, and the cross-level interactions of these variables were examined in the hierarchical linear model. Results of the analyses show that student-, teacher- and school-level variables influence students’ English language proficiency. A significant finding from this study is that students’ motivation, attentiveness in class, the use of deep and surface learning approaches as well as the student-focused teaching approaches and the number of students in schools directly influence students’ English language proficiency. The findings further indicate that students who have higher levels of motivation and attentiveness as well as who use deep learning approaches more tend to have higher English proficiency levels. On the other hand, students who use surface learning approaches more tend to have lower English proficiency levels. The findings also indicate that the more teachers use student-focused teaching approaches and the more students schools have, the more likely students achieve at a higher level in English. Furthermore, while the number of story books in the library moderates the effect of students’ attentiveness on their English proficiency negatively, the emphasis in reading skills moderates positively the effect of student-focused teaching approaches on students’ English proficiency. In addition, teachers’ formal professional development activities positively moderate the effect of students’ motivation on students’ English proficiency. Moreover, multiple interrelationships among the student-level variables are identified in the student-level model. Although not as complicated as the student-level model, the results from the teacher-level model also indicate the interrelationships among the teacher-level variables. Thus, the results of this study support the idea that student-, teacher- and school-level factors interact with each other and impact on students’ English language proficiency. This research is particularly meaningful with regards to its contribution to the theoretical, practical and methodological implications in the English language learning and teaching. These findings suggest new courses of action for designing a suitable curriculum for English learners, strategies for teaching and improving teaching skills as well as a better environment for the learning and teaching of English in the Malaysian Independent Chinese Secondary Schools. The student-, teacher- and school-level factors need to be taken into considerations when one aims to improve students’ English language proficiency.Thesis (Ph.D.) -- University of Adelaide, School of Education, 2016.
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Lacia, Michelle. "Classroom Practices in Mathematics: Effects on Elementary and Secondary School Students' Achievement in Mathematics in Region XII, Philippines." Thesis, 2019. http://hdl.handle.net/2440/121342.
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Students from all levels (elementary to tertiary levels) regard mathematics as a difficult subject. This has been evident in their performances not only in the classroom but also in the local, national and international achievement tests. Students' difficulty in mathematics can be attributed to several factors, one of which is the teacher. The teacher has direct contact with students on a daily basis and therefore been considered to have a direct impact on students' achievement. Studies, such as that of Brophy and Good (1986), Hiebert (1999) and the National Research Council (1999) have found that teacher-level factors are the main contributing factors that influence students' performance. Hence, this study investigated whether teaching and assessment practices (collectively called classroom practices) have influenced students' achievement. Other teacher-level factors, such as teachers' attitudes towards teaching mathematics and efficacy beliefs in mathematics were also examined. School-level and student-level factors were also deemed to have a direct or indirect effect on teachers' classroom practices and students' achievement. This study employed a cross-sectional design. Since this study basically identified and investigated the factors that influence outcomes (e.g. students’ achievement), a quantitative research approach was therefore employed. Survey questionnaires used were first validated. Confirmatory Factor Analysis (CFA) was used in examining the scale structures, while item response theory (IRT) using Rasch model analysis was utilised to examine the scales at the item level. Structural equation modelling (SEM) was employed to ascertain the causal relationship between the variables in each level. Since this study involves three levels of data, school-, teacher- and student- level, a multi-level analysis, particularly, Hierarchical Linear Modeling (HLM) was employed. Findings show that only teachers’ level of education and participation in professional development activities have significant effects on students’ achievement in mathematics. Surprisingly, both teachers' teaching practices and assessment practices did not appear to be significant predictors of students’ achievement. Results at the school-level show that school principals' management or leadership style has a direct positive influence on school climate for learning. School climate, in turn, provides a learning environment that enhances students learning, thus, increasing their performance. Moreover, students’ achievement in mathematics could also be affected by their attitudes towards mathematics, which are measured in this study in terms of their confidence in learning mathematics and usefulness of mathematics. Likewise, students’ beliefs about mathematics appeared to have a positive effect on mathematics achievement. It is interesting to note that students’ mathematics anxiety has no significant effect on their achievement. The findings of the study suggest that students' achievement in mathematics are significantly influenced by multi-level factors, either directly or indirectly. This likewise indicates that school principals, teachers, and students must all be engaged in maintaining a healthy learning environment. It would be beneficial for future research to investigate more deeply on the specific measures of teaching and assessment practices. Implications for educational policies, practice, theory and research are discussed.Thesis (Ph.D.) -- University of Adelaide, School of Education, 2019
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Oko, Jerome. "An investigation into factors affecting Grade 10 and 12 students’ mathematics performance in Port Moresby, Papua New Guinea (PNG)." Thesis, 2021. https://hdl.handle.net/2440/134190.
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Though Papua New Guinea (PNG) has great development potential with its natural resources, the country faces challenges with its education system. One of these challenges is the poor mathematics performance of students at secondary schools. This poor performance is evident both through the significant number of students who cannot continue to Grade 11, and through the simultaneous decline in student enrolment in science related degrees at the university level. That being the case, this study aims to examine the school, teacher and student-level factors and their interrelationships that affect Grade 10 and 12 students’ mathematics results.
A quantitative-dominant mixed-method approach is employed in this study, which has 729 student and 41 teacher participants. The instruments used in this study are: survey questionnaires, mathematics test, and interview questions. The survey questionnaires for students and teachers are adopted from international studies such as Trends in International Mathematics and Science Study (TIMSS) and Programme for International Student Assessment (PISA) and are modified according to the context of this study. The mathematics test questions are adopted and modified from past Grade 10 and 12 national mathematics examination papers, respectively. These survey questionnaires and tests are validated and verified through confirmatory factor analysis and Rasch analysis. Rasch analysis scores obtained from the survey questionnaires and tests are used to examine the relationships between the independent and dependent variables at the teacher and student-levels through the use of Structural Equation Modelling, respectively. Hierarchical Linear Modelling is also employed to examine the direct effects from teacher and student-levels and cross-interaction effects between variables at these two different levels. The interview data at the teacher-level is analysed through thematic approach to capture information that might have been missed in teachers’ survey questionnaires to complement the findings of quantitative (survey) data. A number of significant factors (attitude, motivation, fathers’ occupation, private schools, students’ gender, teachers’ with mathematics major and quality of teaching) that are influencing students’ mathematics results are identified by this study, with mothers’ highest education level found to be the most critical factor. The study concludes that more attention should be given to the factors identified in this study, in order to improve Grade 10 and 12 students’ mathematics results. Overall, this study contributes theoretical, methodological, and practical knowledge to teaching and learning in mathematics education.Thesis (Ph.D.) -- University of Adelaide, School of Education, 2021
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Oliveira, Alexandre Dargains Auricchio de. "A GIS approach to sustainable livestock planning from carbon dynamics analysis: case study of a cattle ranch in Serra da Mantiqueira (Brazil)." Master's thesis, 2020. http://hdl.handle.net/10362/96120.
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Dissertation presented as partial requirement for obtaining the Master’s degree in Geographical Information Systems and ScienceA avaliação da dinâmica do carbono como indicador de serviços ecossistêmicos de regulação climática, através da modelagem de diferentes cenários sobre mudanças de uso e cobertura do solo (LULC), é amplamente utilizada em estudos de conservação ambiental para apoiar processos decisórios atrelados a políticas públicas. Todavia, são raros os estudos em escala local que analisam a relação de impacto e custo-benefício da simulação de cenários agrícolas sustentáveis na prestação de serviços ecossistêmicos. Neste trabalho, realizamos a quantificação, a avaliação econômica e o mapeamento da captura e do estoque de carbono de cenários LULC passados (2007-2017) e futuros (2027), em uma fazenda pecuarista da Serra da Mantiqueira, para entender como diferentes mudanças de paisagens podem impactar o serviço de regulação climática e contribuir economicamente com o setor agrícola. Sob uma abordagem SIG, empregamos técnicas de detecção remota, para elaborar os mapas LULC, ferramentas de modelagem Integrated Valuation of Ecosystem Services and Tradeoffs (InVEST), para a construção dos cenários futuros e para avaliação das dinâmicas de carbono, e ferramentas de modelagem da família Sis para simular a produção resultante do manejo florestal. Todos os cenários avaliados promoveram o aumento da captura e do estoque de carbono na área de estudo, assim como revelaram oportunidades econômicas rentáveis associadas à sua implementação. A introdução de árvores de eucalipto no sistema de produção agropecuário é uma alternativa interessante para a diversificação e aumento de renda, contribuindo para o equilíbrio dos gases de efeito estufa (GEE) da atividade pecuária e agregando valor à produção. Esses resultados são úteis para apoiar o planejamento e o desenvolvimento de políticas de conservação ambiental e de produção agrícola sustentável.
The assessment of carbon dynamics as indicator of climate-regulation ecosystem services (ES) through the modeling of different scenarios on land use and land cover (LULC) changes is widely used in environmental conservation studies to support the decision-making process regarding public policies. However, studies at local scales that address the subject under the farm property perspective, through impact and cost-benefit analyses of simulated sustainable farming scenarios on the provision of ecosystem services, are rare or nonexistent. In this paper, we performed the quantification, valuation and mapping of carbon capture and storage of past (2007-2017) and future LULC (2027) sustainable scenarios in a cattle ranch of Serra da Mantiqueira to understand how different LULC change scenarios may affect the provision of ES and contribute to economic opportunities to the farming sector. Under a GIS-approach, we used remote sensing techniques to LULC mapping, Integrated Valuation of Ecosystem Services and Tradeoffs (InVEST) model for scenario building, carbon assessment and valuation, as well as Sis family software modeling for forest management production. All the sustainable scenarios contributed to the increase of carbon capture and storage in the study area, in addition to showing profitable economic opportunities arising from their implementation. The introduction of eucalyptus trees in livestock and agricultural production systems is an interesting alternative for diversification and income increase, contributing to the balance of greenhouse gases (GHG) from livestock activity and adding value to production. These results are useful to support the development and planning for both environmental conservation policies and sustainable farming production.
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Morin, Maxim. "Expérimentation de la cartographie conceptuelle comme dispositif de collecte de données en vue de l’évaluation des apprentissages." Thèse, 2018. http://hdl.handle.net/1866/21830.
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