Thesis advisor: Larry H. Ludlow / The focus on science, technology, engineering, and mathematics fields has noticeably increased in recent decades with the rapid growth in technology. Mathematical knowledge and competence is in many ways a gateway to scientific and technical development, and therefore careers (Prieto & Delgado, 2007). Unfortunately, national and international assessments of mathematics achievement (e.g., Kena et al., 2016; NCES, 2015; OECD, 2013) show that schools in the United States are not helping students achieve acceptable levels of mathematical and numerical proficiency. Therefore, we need to understand how various factors, including mathematics anxiety, affect student performance and persistence in STEM. To do this, a valid and reliable measure of mathematics anxiety is needed. Existing instruments to measure mathematics anxiety have been insufficient in several ways, including in their conceptualization of the construct and use of classical test theory over Rasch measurement theory methods.In this study, an instrument – the Comparative Mathematics Anxiety Scale (CMAS) – was developed to measure the three-dimensional conceptualization of mathematics anxiety that Dr. Caroline Vuilleumier and I originated. A unique, comparative item format adapted from Ludlow et al. (2014, 2019) and Rasch measurement theory (Rasch, 1960/1980) were utilized to mitigate some of the limitations of existing instruments. The overarching research question and three sub-research questions explored whether the CMAS could measure mathematics anxiety in a valid, reliable, and meaningful way. This study employed a seven-step iterative scale development process and was accomplished across three rounds. Ultimately, twenty-three third-person items were developed to capture the emotional-attitudinal, mental-cognitive, and physical-somatic dimensions of mathematics anxiety. Using the Rasch rating scale model, the outcome was the 23-item CMAS that reliably and validly measures increasing levels of three dimensions of mathematics anxiety. The distribution of the items mostly confirmed their hypothesized order and the Rasch measurement theory principles. The scale also provides meaningful interpretations of what a raw score means regarding a student’s experience of emotional-attitudinal, mental-cognitive, and physical-somatic mathematics anxiety. Overall, the findings suggest that the novel approach of combining Rasch measurement theory with third-person items and comparative response options can be successful in developing a scale that measures an important construct. Furthermore, the scale can provide the evidence needed in the provision of interventions and in research to reduce students’ overall experience of mathematics anxiety. / Thesis (PhD) — Boston College, 2021. / Submitted to: Boston College. Lynch School of Education. / Discipline: Educational Research, Measurement and Evaluation.

Background: The use of outcome measures to evaluate upper extremity function after stroke is highly recommended in clinical practice and research. The Chedoke Arm and Hand Activity Inventory (CAHAI) is a recommended measure as it has strong psychometric properties and clinical utility. However, the measure has not been validated in Asia and there are also gaps in the knowledge about the psychometric properties of the CAHAI. Aim & Objectives: This thesis is dedicated to the continued evaluation of the CAHAI with two main objectives: (1) to develop a Singapore version of the CAHAI, and (2) to re-evaluate the original CAHAI using modern test theories. Method: We conducted a study to cross-culturally adapt the CAHAI and evaluated the psychometric properties in a stroke sample in Singapore. Two studies were conducted to re-evaluate the original CAHAI using modern test theories. In the first study, item response theory and Rasch measurement theory were used to evaluate the psychometric properties of the measure. Following which, both measurement theories were used to revise the CAHAI in the second study. Results: Two test items were modified for the Singapore version of the CAHAI, and the measure had good inter-rater reliability (intra-class correlation coefficient = 0.95 – 0.97) and construct validity. The evaluation of the original CAHAI using modern test theories identified three main problems: (1) the scoring scale was not working as intended, (2) local dependency, and (3) the measure was not unidimensional. Revisions to the CAHAI included collapsing the 7-category scale to four categories, deleting two test items, and developing two new shortened versions. Conclusion: The Singapore version of the CAHAI is a valid and culturally relevant outcome measure that can be used to evaluate post-stroke upper extremity function. The original CAHAI was refined into a new 11- and 5-item versions with a 4-category scale which clinicians may find easier to use. / Thesis / Doctor of Philosophy (PhD)

[pt] A medição de fenômenos psicossociais, como a democracia, é um desafio, dada a influência de percepções subjetivas e variáveis difíceis de medir. É fundamental que avaliações de democracia tenham resultados confiáveis e comparáveis, já que exercem um papel vital na análise de realidades políticas e influenciam a tomada de decisões a nível nacional e internacional. Embora elementos centrais da Ciência da Medição permeiem as discussões sobre a medição da democracia, aspectos importantes devem ser abordados para alinhar os métodos usados nesse campo com preceitos fundamentais da metrologia. Estudos recentes sugerem a incorporação da abordagem psicométrica conhecida como o modelo Rasch no sistema metrológico associado a cada atributo, como potencial solução aos desafios de prover medidas comparáveis e confiáveis de grandezas psicossociais. Contudo, esta abordagem ainda não foi explorada na medição da democracia. Este estudo aplica o modelo Rasch ao sistema de medição de democracia do projeto Varieties of Democracy (V-Dem) e à sua base de dados de vinhetas de ancoragem recentemente incorporada. Analisam-se as respostas dos codificadores aos indicadores que constituem o survey do V-Dem sobre Deliberação. O método proposto examina o desempenho do sistema, considerando os avaliadores como o elemento sensor e os indicadores como a estrutura do sistema de medição. As fontes de incerteza de medição são discutidas no modelo do sistema de medição. O estudo revela itens com questões críticas para revisão com base em múltiplos parâmetros, incluindo o funcionamento diferencial dos itens conforme o continente de origem dos avaliadores e dimensões secundárias a afetar o sensor. O tratamento desses elementos pode contribuir à maior confiabilidade da medição de democracia e ao avanço da pesquisa em ciência política. / [en] Measuring psychosocial phenomena, such as democracy, is challenging due to the influence of subjective perceptions and difficult-to-assess variables. It is crucial for democracy assessments to produce reliable and comparable results, as they play a vital role in analysing political realities and influencing decision-making at national and international levels. While essential elements of the Measurement Science are manifest throughout the discussions on democracy measurement, important aspects must be addressed to align the approaches used in this field with fundamental metrology precepts. Recent studies have suggested incorporating the psychometric approach known as the Rasch model into the metrological system associated with each attribute as a potential solution to the challenges of providing comparable and reliable measures of psychosocial traits. However, this approach has yet to be explored in democracy measurement. This study applies the Rasch model to the democracy measuring system from the Varieties of Democracy project (V-Dem) and their recently incorporated anchoring vignettes database. It analyses coders responses to the indicators constituting the V-Dem survey on Deliberation. The proposed method evaluates the system s performance, considering the coders as the sensing element and the indicators as the measuring system s structure. Sources of measurement uncertainty are discussed within the measurement model. The study reveals items associated with critical demands for revision based on multiple parameters, including differential item functioning based on coders continent of origin and secondary dimensions affecting the sensor. Addressing these elements can contribute to enhancing the reliability of democracy assessment and advancing political science research.