A simulation study was carried out to assess the effects of using different testing frameworks and different statistical estimators in constructing a vertical scale. The adaptive multistage testing framework (MST) was comprised of five test forms which were administered across three testing occasions. The single form testing framework (SFT) was comprised of one form at each of the three testing occasions. Maximum likelihood estimation (MLE) and Bayesian Expected a-posteriori (EAP) estimators were used to estimate each simulee's ability at three "testing'' occasions. Item response theory (IRT) true scores, or domain scores, were used as the score scale. This was done to facilitate the use of growth scores between testing occasions. It was hypothesized that testing framework and estimation procedures would influence the recovery of the known domain score for each simulee across the three testing occasions and growth values between testing occasions. Average absolute deviation (AAD) values indicated that the MST framework offered a slight reduction in error when compared to the SFT framework in estimating IRT domain scores. The pattern of errors in estimation indicated that the MST framework provided more accurate estimates across the range of ability. The MST framework also offered a slight reduction in error when estimating IRT growth scores. Horizontal distances between test administrations indicted that EAP estimation produced uneven departures from known horizontal distances, but MLE did not. This was true for both the SFT and MST framework. Also, when the distributions of IRT domain scores were considered, the MLE estimation method was more consistent with the distribution of known domain scores.Overall, the MST framework performed better than did the SFT framework with respect to reduced estimation error and approximating the known IRT domain score.

For unidimensional item response theory (UIRT) models, three linking methods, which are the separate, concurrent, and fixed parameter calibration methods, have been developed and widely used in applications such as vertical scaling, differential item functioning, computerized adaptive testing (CAT), and equating. By contrast, even though a few studies have compared the separate and concurrent calibration methods for full multidimensional IRT (MIRT) models or applied the concurrent calibration method to vertical scaling using the bifactor model, no study has yet provided technical descriptions of the concurrent and fixed parameter calibration methods for any MIRT models. Thus, the purpose of this dissertation was to extend the concurrent and fixed parameter calibration methods for UIRT models to the two-tier item factor analysis model. In addition, the relative performance of the separate, concurrent, and fixed parameter calibration methods was compared in terms of the recovery of item parameters and accuracy of IRT observed score equating using both real and simulated datasets. The separate, concurrent, and fixed parameter calibration methods well recovered the item parameters, with the concurrent calibration method performing slightly better than the other two linking methods. Despite the comparable performance of the three linking methods in terms of the recovery of item parameters, however, some discrepancy was observed between the IRT observed score equating results obtained with the three linking methods. In general, the concurrent calibration method provided equating results with the smallest equating error, whereas the separate calibration method provided equating results with the largest equating error due to the largest standard error of equating. The performance of the fixed parameter calibration method depended on the proportion of common items. When the proportion was , the fixed parameter calibration method provided more biased equating results than the concurrent calibration method because of the underestimated specific slope parameters. However, when the proportion of common items was 40%, the fixed parameter calibration method worked as well as the concurrent calibration method.

This dissertation presents the results of an experiment that measured the learning outcomes associated with three different pedagogical approaches to introductory physics labs. These three pedagogical approaches presented students with the same apparatus and covered the same physics content, but used different lab manuals to guide students through distinct cognitive processes in conducting their laboratory investigations. We administered post-tests containing multiple-choice conceptual questions and free-response quantitative problems one week after students completed these laboratory investigations. In addition, we collected data from the laboratory practical exam taken by students at the end of the semester. Using these data sets, we compared the learning outcomes for the three curricula in three dimensions of ability: conceptual understanding, quantitative problem-solving skill, and laboratory skills. Our three pedagogical approaches are as follows. Guided labs lead students through their investigations via a combination of Socratic-style questioning and direct instruction, while students record their data and answers to written questions in the manual during the experiment. Traditional labs provide detailed written instructions, which students follow to complete the lab objectives. Open labs provide students with a set of apparatus and a question to be answered, and leave students to devise and execute an experiment to answer the question. In general, we find that students performing Guided labs perform better on some conceptual assessment items, and that students performing Open labs perform significantly better on experimental tasks. Combining a classical test theory analysis of post-test results with in-lab classroom observations allows us to identify individual components of the laboratory manuals and investigations that are likely to have influenced the observed differences in learning outcomes associated with the different pedagogical approaches. Due to the novel nature of this research and the large number of item-level results we produced, we recommend additional research to determine the reproducibility of our results. Analyzing the data with item response theory yields additional information about the performance of our students on both conceptual questions and quantitative problems. We find that performing lab activities on a topic does lead to better-than-expected performance on some conceptual questions regardless of pedagogical approach, but that this acquired conceptual understanding is strongly context-dependent. The results also suggest that a single “Newtonian reasoning ability" is inadequate to explain student response patterns to items from the Force Concept Inventory. We develop a framework for applying polytomous item response theory to the analysis of quantitative free-response problems and for analyzing how features of student solutions are influenced by problem-solving ability. Patterns in how students at different abilities approach our post-test problems are revealed, and we find hints as to how features of a free-response problem influence its item parameters. The item-response theory framework we develop provides a foundation for future development of quantitative free-response research instruments. Chapter 1 of the dissertation presents a brief history of physics education research and motivates the present study. Chapter 2 describes our experimental methodology and discusses the treatments applied to students and the instruments used to measure their learning. Chapter 3 provides an introduction to the statistical and analytical methods used in our data analysis. Chapter 4 presents the full data set, analyzed using both classical test theory and item response theory. Chapter 5 contains a discussion of the implications of our results and a data-driven analysis of our experimental methods. Chapter 6 describes the importance of this work to the field and discusses the relevance of our research to curriculum development and to future work in physics education research.

Item response theory (IRT) is a newer and improved theory compared to the classical measurement theory. The fully Bayesian approach shows promise for IRT models. However, it is computationally expensive, and therefore is limited in various applications. It is important to seek ways to reduce the execution time and a suitable solution is the use of high performance computing (HPC). HPC offers considerably high computational power and can handle applications with high computation and memory requirements. In this work, we have modified the existing fully Bayesian algorithm for 2PNO IRT models so that it can be run on a high performance parallel machine. With this parallel version of the algorithm, the empirical results show that a speedup was achieved and the execution time was reduced considerably.

Item response theory (IRT) is a newer and improved theory compared to the classical measurement theory. The fully Bayesian approach shows promise for IRT models. However, it is computationally expensive, and therefore is limited in various applications. It is important to seek ways to reduce the execution time and a suitable solution is the use of high performance computing (HPC). HPC offers considerably high computational power and can handle applications with high computation and memory requirements. In this work, we have applied two different parallelism methods to the existing fully Bayesian algorithm for 2PNO IRT models so that it can be run on a high performance parallel machine with less communication load. With our parallel version of the algorithm, the empirical results show that a speedup was achieved and the execution time was considerably reduced.

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Multiscaled experimental investigations of heat transfer from nanoscales to macroscales are requisite to progress in energy technologies. In nuclear applications, material properties can undergo significant alteration due to destructive interaction with irradiating particles at microstructural levels that affect bulk properties. Correlating material microstructure to bulk material properties remains a crucial hurdle for obtaining first-principles-based, full-scale material property predictive capability. Ion-irradiated material studies provide valuable insight into material behavior under irradiation conditions that can be correlated to neutron irradiation effects. Through such studies, the need of costly (money and time) studies of neutron interaction with materials can be mitigated significantly. One of the challenges associated with studies of ion-irradiated materials is that the affected layer, or penetration depth, is typically very thin (~0.1-100μm for laboratory accelerators). Few investigations have been reported of ion-irradiation effects on thermal transport properties, in part, due to the challenge associated with measurements at the spatial scales of the zones of interest. This study expands the current knowledge base regarding thermal transport in ion-irradiated materials through the use of a multiscaled experimental approach using thermal wave methods. In a manner not previously explored, four thermal wave methods are used to characterize the proton-irradiated layer in ZrC including scanning thermal microscopy, spatial-scanning front-detection photothermal radiometry (PTR), lock-in IR thermography (lock-in IRT), and tomographic, frequency-based PTR. For the first time, the in-depth thermal conductivity profile of an ion-irradiated sample is measured directly. The profiles obtained by each of the spatial scanning methods are compared to each other and the numerical prediction of the ion-damage profile. The complementary nature of the various techniques validates the measured profile and the measured degradation of thermal conductivity in the ZrC sample showing the viability of such complementary studies.

In this report we give a brief introduction to Item Response Theory models and multilevel models. The general assumptions of two classical Item Response Theory, 1PL and 2PL models are discussed. We follow the discussion by introducing a multilevel level framework for these two Item Response Theory Models. We explain Bock and Aitkin's (1981) work to estimate item parameters for these two models. Finally we illustrate these models with a LSAT exam data and two statistical softwares; R project and Stata. / text

The main purpose of this study was to construct different vertical scales based on various combinations of calibration methods and proficiency estimators to investigate the impact different choices may have on these properties of the vertical scales that result: grade-to-grade growth, grade-to-grade variability, and the separation of grade distributions. Calibration methods investigated were concurrent calibration, separate calibration, and fixed a, b, and c item parameters for common items with simple prior updates (FSPU). Proficiency estimators investigated were Maximum Likelihood Estimator (MLE) with pattern scores, Expected A Posteriori (EAP) with pattern scores, pseudo-MLE with summed scores, pseudo-EAP with summed scores, and Quadrature Distribution (QD). The study used datasets from the Iowa Tests of Basic Skills (ITBS) in the Vocabulary, Reading Comprehension (RC), Math Problem Solving and Data Interpretation (MPD), and Science tests for grades 3 through 8. For each of the research questions, the following conclusions were drawn from the study. With respect to the comparisons of three calibration methods, for the RC and Science tests, concurrent calibration, compared to FSPU and separate calibration, showed less growth and more slowly decreasing growth in the lower grades, less decrease in variability over grades, and less separation in the lower grades in terms of horizontal distances. For the Vocabulary and MPD tests, differences in both grade-to-grade growth and in the separation of grade distributions were trivial. With respect to the comparisons of five proficiency estimators, for all content areas, the trend of pseudo-MLE ≥ MLE > QD > EAP ≥ pseudo-EAP was found in within-grade SDs, and the trend of pseudo-EAP ≥ EAP > QD > MLE ≥ pseudo-MLE was found in the effect sizes. However, the degree of decrease in variability over grades was similar across proficiency estimators. With respect to the comparisons of the four content areas, for the Vocabulary and MPD tests compared to the RC and Science tests, growth was less, but somewhat steady, and the decrease in variability over grades was less. For separation of grade distributions, it was found that the large growth suggested by larger mean differences for the RC and Science tests was reduced through the use of effect sizes to standardize the differences.

The purposes of this study were to develop a mathematics achievement test for the seventh graders in Tainan based on the Grade 1-9 Curriculum, and to explore the difference in performance for variables of gender, tutoring, scale of school, public-private school and textbook version. The population of this study consisted of the eight graders in Tainan City. Three samples were drawn for this study: the first tryout sample¡]n=402¡^, the second tryout sample¡]n=455¡^and the norm sample¡]n=870¡^. The Mathematics Achievement Test for Seventh Graders developed by the researcher was used. The data were analyzed in two dimensions: 1. items and test with methods of CTT and IRT; and 2. the difference in performance for variables of gender, tutoring, scale of school, public-private school and textbook version with statistical testing methods. The results of this study were listed below: I. Item and Test Analysis: 1.Regarding the difficulty and discrimination of CTT, the average difficulty of interval scale¡]¡µ¡^of items was 12.14, the mean of percentage passing and discrimination were 0.58 and 0.52, respectively. 2.According to the result of the reliability examination, the Cronbach value of internal consistency was 0.85, the test-retest reliability indicated 0.86, the split-half reliability showed 0.86. 3.The evidences of validity about this test were well content-related, criterion-related, construct-related. As for the result of the validity examination, the content validity of this test was through experts¡¦ review and judgment. The criterion validity was based on significantly positive correlation of the monthly test scores for each school. The construct validity had established in two ways of the internal consistency and the different groups analysis. 4.Analyzing items with IRT, 3PL model, the mean of discrimination (a), difficulty (b) and guessing(c) are 1.23, 0.14 and 0.21, respectively. 5. DIF was present for the item 17 between gender groups. 6. The correlations of item difficulty values between IRT and CTT were 0.97¡ã1.00, the correlations of item discrimination were 0.21¡ã0.95. The correlation between ability parameters of IRT model and total score of CTT ranged from 0.98 to 1.00. The result of indices between IRT and CTT revealed high correlations. 7. This test established a percentile rank and T-score norms. II. Testing of the performance differences with significance level£\=0.01: 1.The student¡¦s performances were significantly different between gender groups, and the female exceeded male. 2.The performances of the students who accepted tutoring after school hours were better than the others¡¦ performances significantly. 3. The student¡¦s performances in the public and private school were significantly different, and the private school outperformed the public school. 4.The performances of the students in private school were better than the performances of the students¡]both accepting tutoring and not ¡^in public school. And in public school, the performances of the students accepting tutoring were better than the students not accepting tutoring. 5.As for the school scale, the large is better than the small, and the middle is better than the small at statistical significant level. 6.In the textbook version, this test found that the performance of student using the version Nani surpassed the performance of student using the version Hanlin, and the version Jenlin outshined the version Hanlin. Finally, based on the results and findings of this study, numerous suggestions for the practical use of the test and future researches were provided.