Journal of mathematics and statistics最新文献

Ordinal Logistic Regression Analysis in Effective Teaching Practices 有效教学实践中的正态逻辑回归分析

Journal of mathematics and statistics Pub Date : 2024-01-01 DOI: 10.3844/jmssp.2024.13.17

Hongwei Wang

{"title":"Ordinal Logistic Regression Analysis in Effective Teaching Practices","authors":"Hongwei Wang","doi":"10.3844/jmssp.2024.13.17","DOIUrl":"https://doi.org/10.3844/jmssp.2024.13.17","url":null,"abstract":": The Association of College and University Educators (ACUE) course in effective teaching practices has been applied to an undergraduate mathematics class at Texas A and M International University (TAMIU) for the past two years (Spring 2022, Fall 2022 and Spring 2023). Practices such as ensuring equitable access to learning, embracing diversity in the classroom, providing useful feedback and teaching powerful note-taking skills were applied throughout the whole semester in class. This study focuses on the comparison between the same class in Spring 2022 when ACUE’s effective teaching practices were not present and the classes in which ACUE was present in Fall 2022 and Spring 2023; in total, 89 students from two classes were analyzed with identification data removed. Ordinal logistic regression is used to analyze how effective teaching practices are related to students' final grades by analyzing students' grades, assignment submissions and class participation in different classes. Fisher’s exact test is applied to data analysis to check how effective teaching practices affect class participation; results show that for students who were from the class with ACUE practices, the odds of being more likely (i.e., “very” with a value of 2 or “somewhat likely” with a value of 1 versus “unlikely” with a value of 0) to have a passing grade is 1.92 times that of students who were from the class without ACUE practices, holding constant all other variables such as homework assignments and class participation. The impact of effective teaching practices is statistically significant on class participation (p-value = 0.04); this study concurs with the previous studies that ACUE’s effective teaching practices have positively improved students’ performance and should be applied to college classrooms. Ordinal logistic regression was the first time applied in analyzing","PeriodicalId":92671,"journal":{"name":"Journal of mathematics and statistics","volume":"12 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140517780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Generalized Statistical Inference for Quantiles of Two-Parameter Gamma Distribution 双参数伽马分布定量的广义统计推断

Journal of mathematics and statistics Pub Date : 2024-01-01 DOI: 10.3844/jmssp.2024.1.12

Malwane Ananda

{"title":"Generalized Statistical Inference for Quantiles of Two-Parameter Gamma Distribution","authors":"Malwane Ananda","doi":"10.3844/jmssp.2024.1.12","DOIUrl":"https://doi.org/10.3844/jmssp.2024.1.12","url":null,"abstract":": Gamma distribution is a widely used distribution to analyze data in many disciplines such as hydrology, meteorology, environmental monitoring, lifetime testing and reliability. In this study, we look at the statistical inference for the quantiles of two-parameter gamma distribution. The testing and estimation of gamma quantile are required especially in areas such as flood frequency analysis and life testing. For this problem, all the statistical inference methods available in the statistical literature are approximate methods. In this study, we propose two methods to tackle this problem. The first method is an exact statistical inference procedure utilizing the generalized p-value technique. The procedure is exact in the sense that it is based on exact probability statements rather than based on approximations. The second procedure is based on the parametric bootstrap approach. We apply the proposed methods to several examples with real data sets and compare the results with other existing methods. A limited simulation study is given to compare the performance of the proposed methods with other existing methods. Overall, according to the simulation results, in terms of size and power, these two new methods perform well over the other existing methods whether it is related to lower or higher quantiles.","PeriodicalId":92671,"journal":{"name":"Journal of mathematics and statistics","volume":"22 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140517749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

q-Deformed Statistics from Position-Dependent Mass Schrödinger Equationa 位置依赖质量Schrödinger方程的变形统计量

Journal of mathematics and statistics Pub Date : 2023-01-01 DOI: 10.3844/jmssp.2023.20.27

Jesus Morales Rivas, Jose Juan Peña Gil, J. García Ravelo

{"title":"q-Deformed Statistics from Position-Dependent Mass Schrödinger Equationa","authors":"Jesus Morales Rivas, Jose Juan Peña Gil, J. García Ravelo","doi":"10.3844/jmssp.2023.20.27","DOIUrl":"https://doi.org/10.3844/jmssp.2023.20.27","url":null,"abstract":"An algebraic approach is used to obtain the canonical form of the position-dependent mass Schrödinger equation from where a couple of canonical quantum variables, the q-deformed operators for the position xq, and the hermitian linear momentum operator pq are derived. In this q-deformed coordinate space, the commutator remains invariant namely [xq, pq] = iħ. By taking advantage of these q-deformed variables, one gets to a q-deformed exponential function expq(x) as well as its corresponding q-deformed logarithm function lnq(x). From these q-deformed mathematical relations and from the fact that thermodynamic properties such as the internal energy U, entropy S, free energy F, heat capacity C, and others are related to the partition function Z and ln(Z), it is proposed their generalizations in terms of the q-deformed exponential and q-deformed logarithmic functions. As a result, the structure of Legendre transformations between these statistical properties remains invariant. The usefulness of the proposal is exemplified by considering two specific position-dependent mass distributions. In the same way, other possibilities could be used to generalize the statistical properties straightforwardly.","PeriodicalId":92671,"journal":{"name":"Journal of mathematics and statistics","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135058046","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Comparing the Diagnostics Accuracy of CD4+ T-Lymphocyte Count and Percent as a Surrogate Markers of Pediatric HIV Disease. 比较CD4+ t淋巴细胞计数和百分比作为儿科HIV疾病替代标志物的诊断准确性

Journal of mathematics and statistics Pub Date : 2019-01-01 Epub Date: 2019-04-03 DOI: 10.3844/jmssp.2019.55.64

Musie Ghebremichael, Haben Michael, Jack Tubbs, Elijah Paintsil

{"title":"Comparing the Diagnostics Accuracy of CD4+ T-Lymphocyte Count and Percent as a Surrogate Markers of Pediatric HIV Disease.","authors":"Musie Ghebremichael, Haben Michael, Jack Tubbs, Elijah Paintsil","doi":"10.3844/jmssp.2019.55.64","DOIUrl":"https://doi.org/10.3844/jmssp.2019.55.64","url":null,"abstract":"<p><p>The percentage CD4+ T-lymphocytes is used to monitor pediatric HIV disease. However, in resource-limited settings, enumerating the percentage of CD4+ T-lymphocytes is hampered by the lack of laboratory infrastructure and trained technicians. In this paper, we investigated the performances of the percentage and absolute CD4+ T-lymphocytes as markers of pediatric HIV disease progression using data from HIV-infected children enrolled through the Yale Prospective Longitudinal Pediatric Cohort study. A Lehmann family of Receiver Operating Characteristic (ROC) curves were used to estimate and compare the performance of the two biomarkers in monitoring pediatric HIV disease progression. The area under the ROC (AUC) curve and its empirical estimator have previously been used to assess the performance of biomarkers for a cross-sectional data. However, there is a paucity of literature on the AUC for correlated longitudinal biomarkers. Previous works on the estimation and inference of the AUC for longitudinal biomarkers have largely focused on independent biomarkers or failed to consider the effect of covariates. The Lehmann approach allowed us to estimate the AUC of the aforementioned correlated longitudinal biomarkers as functions of explanatory variables. We found that the overall performance of the two biomarkers was comparable. The area under the ROC curves for CD4+ T cell count and percentage were 0.681 [SE = 0.029; 95% CI: 0.624-0.737] and 0.678 [SE = 0.024; 95% CI:0.630-0.725], respectively. Our results suggest that absolute CD4+ T-lymphocyte counts could be used as a proxy for percentage of CD4+ T-lymphocytes in monitoring pediatric HIV in resource-limited settings.</p>","PeriodicalId":92671,"journal":{"name":"Journal of mathematics and statistics","volume":"15 1","pages":"55-64"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.3844/jmssp.2019.55.64","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37318134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 6