Class Of Statistics Research Articles

Student knowledge gains in polar literacy and statistics after completing guided inquiry modules in an undergraduate statistics course

Climate change is a major concern to undergraduate students. Understanding climate change relies on an understanding of polar regions. However, courses on polar regions are rare at undergraduate institutions. Polar ENgagement through GUided INquiry (PENGUIN) modules were designed to give students experience with polar research in a variety of standard courses, including physics, computer science, physical chemistry, and economics, through using course-specific and computational tools to analyze polar data. Here, we present a new PENGUIN module taught in a statistics class, in which students apply statistical tools to ice core data to reconstruct past temperature records. Quantitative student responses on pre- and post-surveys were collected in a quasi-experimental context to assess student knowledge gains for a test group of 91 students and a control group of 73 students (who did not complete the module). Test-group students made statistically significant increases of 25 to 46% on all six statistics questions, with a normalized gain of 56%. By contrast, control group statistics knowledge gains ranged from −4 to 25%, with statistically significant increases for only three questions and a normalized gain of 22%. For polar research questions, the test group demonstrated increases in correct responses to polar research questions (11 to 31%), with statistically significant improvements (p < .05) of 22-31% on 3 of 6 polar research questions. These findings support the conclusion that PENGUIN modules can successfully teach course concepts while increasing polar literacy.

Three new corrections for standardized person-fit statistics for tests with polytomous items.

Recent years have seen a growing interest in the development of person-fit statistics for tests with polytomous items. Some of the most popular person-fit statistics for such tests belong to the class of standardized person-fit statistics, , that is assumed to have a standard normal null distribution. However, this distribution only holds when (a) the true ability parameter is known and (b) an infinite number of items are available. In practice, both conditions are violated, and the quality of person-fit results is expected to deteriorate. In this paper, we propose three new corrections for that simultaneously account for the use of an estimated ability parameter and the use of a finite number of items. The three new corrections are direct extensions of those that were developed by Gorney etal. (Psychometrika, 2024, https://doi.org/10.1007/s11336-024-09960-x) for tests with only dichotomous items. Our simulation study reveals that the three new corrections tend to outperform not only the original statistic but also an existing correction for proposed by Sinharay (Psychometrika, 2016, 81, 992). Therefore, the new corrections appear to be promising tools for assessing person fit in tests with polytomous items.

Hitting the High-dimensional notes: an ODE for SGD learning dynamics on GLMs and multi-index models

Abstract We analyze the dynamics of streaming stochastic gradient descent (SGD) in the high-dimensional limit when applied to generalized linear models and multi-index models (e.g. logistic regression, phase retrieval) with general data-covariance. In particular, we demonstrate a deterministic equivalent of SGD in the form of a system of ordinary differential equations that describes a wide class of statistics, such as the risk and other measures of sub-optimality. This equivalence holds with overwhelming probability when the model parameter count grows proportionally to the number of data. This framework allows us to obtain learning rate thresholds for the stability of SGD as well as convergence guarantees. In addition to the deterministic equivalent, we introduce an SDE with a simplified diffusion coefficient (homogenized SGD), which allows us to analyze the dynamics of general statistics of SGD iterates. Finally, we illustrate this theory on some standard examples and show numerical simulations, which give an excellent match to the theory.

The sample is not the population

AbstractGiven sample data, how do you calculate the value of a parameter? While this question is impossible to answer, it is frequently encountered in statistics classes when students are introduced to the distinction between a sample and a population (or between a statistic and a parameter). It is not uncommon for teachers of statistics to also confuse these concepts. An excerpt of a national mathematics examination paper, where a sample is mistaken for the population, is used to illustrate this confusion as well as sample variation and its link to sample size. We discuss two techniques that can be used to explain the difference between a parameter and a statistic. The first is a visual technique in which the variability in calculated statistics is contrasted to the fixed value of the corresponding parameter. Thereafter, we discuss Monte Carlo simulation techniques and explain the contribution that these methods may have.

Oracle inequalities and upper bounds for kernel conditional U-statistics estimators on manifolds and more general metric spaces associated with operators

ABSTRACT U-statistics represent a fundamental class of statistics that emerge from modelling quantities of interest defined by multi-subject responses. These statistics generalize the empirical mean of a random variable X to summations encompassing all distinct k-tuples of observations drawn from X . A significant advancement was made by Stute [ConditionalU-statistics. Ann. Probab. 19 (1991), pp. 812–825], who introduced conditional U-statistics as a generalization of the Nadaraya–Watson estimates for regression functions. Stute demonstrated their robust pointwise consistency towards the conditional function r ( k ) ( φ , t ~ ) = E ( φ ( Y 1 , … , Y k ) ∣ ( X 1 , … , X k ) = t ~ ) , for t ~ ∈ R pk , where φ is a measurable function. In this investigation, we develop oracle inequalities and upper bounds for kernel-based estimators of conditional U-statistics of general order, applicable across a wide range of metric spaces associated with operators. Our analysis specifically targets doubling measure metric spaces, incorporating a non-negative self-adjoint operator characterized by Gaussian regularity in its heat kernel. Remarkably, our study achieves an optimal convergence rate in certain cases. To derive these results, we explore the regression function within a general framework, introducing several novel insights. These findings are established under sufficiently broad conditions on the underlying distributions. The theoretical results serve as essential tools for advancing the field of general-valued data, with potential applications including the examination of conditional distribution functions, relative-error prediction, the Kendall rank correlation coefficient, and discrimination problems – areas of significant independent interest.

Violence against women: a pedagogical proposal for promoting Critical Statistical Literacy

The text is part of a research that aimed to study a pedagogical proposal developed and carried out with high school students from the theoretical perspective of Critical Statistical Literacy. Evidence was sought of the contributions that this theory could bring to the teaching and learning of statistics. The methodological technique used was participant observation, which developed from news published on social media about violence against women. Data collection was carried out using three instruments: video recording of the class; teacher's logbook; and videos created as a final task by students. The analysis indicates that the theoretical perspective adopted and the use of real data in statistics classes contribute to the development of criticality on social issues and statistical literacy. Thus, it became possible to offer conditions for implementing what is partially proposed in the curricular documents guiding Brazilian education.

Implementation of DESMOS as a Teaching Tool in Graphing Functions in the New Normal

Before the implementation of online learning, students graphed functions on paper using either a ballpen or pencil. However, online learning materials including online graphing calculators were being encouraged to be used since the modality had shifted into online learning. DESMOS is one of the online learning materials that can be used in graphing functions. This study aimed to evaluate the effectiveness of the implementation of DESMOS as a graphing tool for teachers and students together with the benefits of this software together with the perceptions towards it. The study was conducted with 23 Grade 11 students taking up Accountancy and Business Management during the classes of Statistics and Probability. The research design used was mixed consisting of comparative statistical techniques and narrative analysis. The interventions involving DESMOS were done virtually through Google Meet. Their skills before and after the interventions involving DESMOS were compared and based on the statistical aspect, there was a significant difference between the skills before and after the interventions with a t-statistical value of -3.78, which was lower than the critical value of -2.074. Besides, the students were able to collaborate in terms of tasks and reflect on what they had learned in DESMOS, and they were able to see DESMOS as an accessible, convenient, and effective graphing tool. DESMOS should be widely used as a teaching tool in graphing functions so students will be able to appreciate technology with mathematics since people are now living in the era of technology.

Trends and adverse pregnancy and birth outcomes associated with stimulant-related disorder diagnosis.

Stimulant-related disorders (SRD), or the continued misuse of illicit or prescribed stimulants, during pregnancy can have adverse health effects for mothers and infants. This study aimed to measure prevalence and trends of SRD diagnosis in pregnancy, and associations between SRD diagnosis and adverse maternal and infant health outcomes, among pregnant individuals in California. Retrospective cohort study. California, USA. Pregnant individuals from the Study of Outcomes in Mothers and Infants (SOMI) with singleton live births between 2012 and 2020 (n = 3 740 079). SRD diagnosis (excluding cocaine) and maternal (gestational diabetes, gestational hypertension [gHTN], severe maternal morbidity [SMM]) and infant (very preterm birth [gestational age <32 weeks], preterm birth [gestational age 32-37 weeks], neonatal intensive care unit [NICU] admission, small for gestational age [SGA]) outcomes were classified using International Classification of Disease (ICD) codes and vital statistics. Risk ratios were estimated with modified Poisson log linear regression that accounted for sibling pregnancies. Covariates included maternal sociodemographic characteristics, mental and physical health problems, nicotine use and co-occurrence of other diagnosed substance use disorders. Bias analyses were conducted to address unmeasured confounding and exposure misclassification. SRD diagnosis among pregnant individuals increased from 2012 to 2020 (554 to 748 per 100 000 births). SRD diagnosis was associated with an increased risk of SMM (adjusted risk ratio [aRR] = 2.3; 95% confidence interval [CI] = 2.2-2.5), gHTN (aRR = 1.8; 95% CI = 1.7-1.9), very preterm birth (aRR = 2.2, 95% CI = 2.0-2.5), preterm birth (aRR = 2.1, 95% CI = 2.1-2.2) and NICU admission (aRR = 2.0, 95%CI = 1.9-2.0), and a decreased risk of gestational diabetes (aRR = 0.8; 95% CI = 0.8-0.9). SRD diagnosis was not associated with infants born SGA. Findings were generally robust to unmeasured confounding and misclassification of diagnosis. Stimulant-related disorder diagnosis during pregnancy appears to be associated with an increased risk for select adverse maternal and infant health outcomes including severe maternal morbidity, gestational hypertension, very preterm birth, preterm birth and neonatal intensive care unit admission.

A General Formulation for the Large-Sample Behaviour of a Class of Hypothesis Test Statistics

A General Formulation for the Large-Sample Behaviour of a Class of Hypothesis Test Statistics

A class of nonparametric tests for the two-sample problem based on order statistics

In this paper, a new class of distribution-free statistics based on order statistics from two independent samples is introduced to test the equality of two continuous distributions. The null distributions are obtained, and the symmetry property of the proposed test statistics is studied. The exact power functions of the new class of tests under the Lehmann alternative family are derived. Extensions of the proposed class of test statistics to situations with unequal sample sizes are discussed. We also study the power performance of the proposed test under the location-shift and scale-shift alternatives using Monte Carlo simulations. We observe that the power performance of the new class of test procedures is comparable to some commonly used nonparametric tests under various scenarios, which indicates that the new class of test procedures can be a good alternative to those classic nonparametric tests for the two-sample problem.

An empirical study on sample size for the central limit theorem using Japanese firm data

AbstractIn statistics classes, the central limit theorem has been demonstrated using simulation‐based illustrations. Known population distributions such as a uniform or exponential distribution are often used to consider the behavior of the sample mean in simulated samples. Unlike such simulations, a number of real‐data‐based simulations are here implemented in which the populations are empirical distributions of data selected from Japanese firms. The dataset chosen contains 38 variables familiar to business students, such as sales and assets. The maximum population size of the variables is 2243. One thousand samples with replacement are selected for specific variable–sample size combinations. Hypothesis testing results indicate that the normality hypothesis for the sample mean is rejected for 31 variables at the 0.1% level even with a sample size of 500. It is emphasized that the data for these variables indicate that this should not be a surprise, and emphasize the importance of looking at data.

Universal hard-edge statistics of non-Hermitian random matrices

Random matrix theory is a powerful tool for understanding spectral correlations inherent in quantum chaotic systems. Despite diverse applications of non-Hermitian random matrix theory, the role of symmetry remains to be fully established. Here, we comprehensively investigate the impact of symmetry on the level statistics around the spectral origin—hard-edge statistics—and expand the classification of spectral statistics to encompass all the 38 symmetry classes of non-Hermitian random matrices. Within this classification, we discern 28 symmetry classes characterized by distinct hard-edge statistics from the level statistics in the bulk of spectra, which are further categorized into two groups, namely, the Altland-Zirnbauer0 classification and beyond. We introduce and elucidate quantitative measures capturing the universal hard-edge statistics for all the symmetry classes. Furthermore, through extensive numerical calculations, we study various open quantum systems in different symmetry classes, including quadratic and many-body Lindbladians, as well as non-Hermitian Hamiltonians. We show that these systems manifest the same hard-edge statistics as random matrices and that their ensemble-average spectral distributions around the origin exhibit emergent symmetry conforming to the random-matrix behavior. Our results establish a comprehensive understanding of non-Hermitian random matrix theory and are useful in detecting quantum chaos or its absence in open quantum systems. Published by the American Physical Society 2024

(043) INACCURATE AND INADEQUATE ICD-10 CODING RELATED TO FEMALE SEXUAL HEALTH THREATENS PATIENT CARE, RESEARCH AND BILLING

Abstract Introduction The International Classification of Diseases (ICD) is an international health information system for the collection, processing, classification, and presentation of mortality statistics. The ICD 10th Edition (ICD-10) is a tool for physicians and billing professionals to accurately bill for the care provided. However, physicians who treat female sexual health (FSH) disorders report difficulty in finding appropriate codes for diagnoses and clinical syndromes (Parish et al. 2021). These issues impede the process for appropriate treatment and allotting the correct reimbursement to providers. Additionally, quantitative and qualitative research on FSH is limited due to the lack of accurate ICD codes for FSH disorders in this cohort. Objective This study aims to evaluate the ICD-10 coding system to assess the accuracy and quality of codes related to common FSH disorders. Methods A list of 50 most commonly encountered clinical FSH diagnoses was created based on clinical practice findings and ISSWSH guidelines. The list was compared against existing ICD-10 codes to characterize current FSH disorders that are recognized in ICD-10 and determine which FSH disorders are billable (ICD10data.com categorizes codes as “billable” or “non-billable”) or missing entirely. FSH diagnoses explicitly listed as an independent diagnosis or generally listed were considered ICD-10 coded. Diagnoses were considered to not have an existing code if they were not explicitly listed independently or under a more general term. Results 44% (n=22) of the diagnoses did not have existing ICD-10 codes, and 6% (n=3) of the diagnoses had appropriate ICD-10 codes but were not billable (Figure 1, Table 1). FSH diagnoses such as “clitoral adhesions”, “clitorodynia” and “persistent genital arousal disorder” were not coded in ICD-10. Many diagnoses were grouped under general terms - pelvic floor pain disorders were grouped under “R10.2: Pelvic and peroneal pain” which included both male and female diagnoses. Other codes had significant diagnostic overlap - “vulvodynia” was separately cataloged as “N94.810: vulvar vestibulitis”, “N94.818: Other vulvodynia” and “N94.819: vulvodynia, unspecified”. There were numerous common FSH diagnoses with incomplete, inaccurate, or outdated ICD codes. Conclusions These findings highlight the pressing need for an expanded, comprehensive, and precise set of ICD codes dedicated to FSH disorders. Without appropriate coding for 50% of FSH diagnoses, clinical care, research, and healthcare billing are severely impeded. It is much more difficult for physicians to accurately classify and bill for their procedures, which may create problems with clinical documentation leading to delayed treatment and poor clinical outcomes. For example, existing codes for “vulvodynia,” a common disorder affecting 16% of women, are vague and unclear, which lacks practicality for charting and billing purposes. Additionally, the limitations of ICD coding make it nearly impossible to research specific disorders, as they can not be searched in databases like TriNetX. These limitations may explain the large gaps in the literature regarding FSH disorders. Additionally, electronic medical records often have outdated ICD codes, further creating obstacles for clinicians. The current gap in classification, including ICD-10 coding and medical records, must be addressed to advance the understanding and management of FSH disorders. Disclosure No.

Multi-Server Multi-Function Distributed Computation.

The work here studies the communication cost for a multi-server multi-task distributed computation framework, as well as for a broad class of functions and data statistics. Considering the framework where a user seeks the computation of multiple complex (conceivably non-linear) tasks from a set of distributed servers, we establish the communication cost upper bounds for a variety of data statistics, function classes, and data placements across the servers. To do so, we proceed to apply, for the first time here, Körner's characteristic graph approach-which is known to capture the structural properties of data and functions-to the promising framework of multi-server multi-task distributed computing. Going beyond the general expressions, and in order to offer clearer insight, we also consider the well-known scenario of cyclic dataset placement and linearly separable functions over the binary field, in which case, our approach exhibits considerable gains over the state of the art. Similar gains are identified for the case of multi-linear functions.

Functional literacy development of junior schoolchildren based on digital educational resources

Relevance. In the context of the reorganisation of the educational process policy of the Republic of Kazakhstan, the issue of teaching primary school children to develop functional literacy becomes urgent, which is an important step for modernising the educational system of the Republic of Kazakhstan and ensuring the competitiveness of the young generation. Purpose. The study aims to develop and experimentally verify the model of functional literacy development of junior schoolchildren based on digital educational resources. Methodology. The study employed analysis, comparison, systematisation, classification, generalisation, experiment, and methods of mathematical statistics. Results. The concepts of �functional literacy�, �development of functional literacy of junior schoolchildren�, and �development of functional literacy based on digital educational resources� were defined. The research was conducted in general education schools �School-lyceum No. 66� and �School No. 16� (Karaganda). As part of the experiment, the development of the functional literacy of junior schoolchildren model was carried out, namely the implementation of components with selected methods of their formation and pedagogical conditions, which was used to improve the educational process in primary schools of the Republic of Kazakhstan. Conclusions. The results of the conducted experiment formed promising directions for improving the educational process aimed at the development of functional literacy in the Republic of Kazakhstan through the formation of components, as well as pedagogical conditions and the development of methods of their implementation. The practical significance of the study consists in the development and implementation of the model, components, pedagogical conditions and methods of development of functional literacy of junior schoolchildren in the Republic of Kazakhstan. Keywords: primary education; methodology of training organisation; meta-subject results; components; pedagogical conditions of training; digital technologies

Student perceptions of weekly synchronous team quizzes in an online statistics course

In a fully online college introductory statistics class, we incorporated a flexible synchronous course component to provide instructor immediacy and support students who are lacking sufficient prior knowledge when a new topic is introduced. We describe a learning cycle with weekly team quizzes inspired by the readiness assurance process of team-based learning; we interviewed eight students for their perceptions of the course structure. Team quizzes are designed to provide regular formative assessment and feedback in real-time with the goal of improving student satisfaction and success in the course. Overall, students reported that the weekly synchronous sessions contributed to a strong sense of belonging to peers and the instructor, were helpful for their learning and helped them successfully complete the course. Implications for practice or policy: Instructors can use regular synchronous team quizzes in a fully online course to improve student engagement, connectedness, persistence and learning. Instructors can use team quizzes for regular formative assessment and feedback and to facilitate just-in-time intervention.

Comfort in active learning spaces – students’ perceptions and preferences

ABSTRACT Evidence suggests that Active Learning (AL) and Active Learning Spaces (ALSs) have the potential to improve student learning outcomes. In this study, the student experiences of AL and ALSs in four classes in mathematics and statistics at a Norwegian university are examined through classroom observations, surveys, and interviews. The student interviews are analysed using constant comparative method, which resulted in one main category and three sub-categories presenting what the students perceived to be significant factors that impacted their learning experiences in the ALSs and how these factors affected their motivation to engage with the subject. The main category is called Engagement and Comfort, and the three sub-categories are called Students’ Varying Preferences, Student-student Communication, and Teachers’ Communication. Students’ motivation was looked at through an Approach-Avoidance Theory lens. Crucial to the student experiences was that some students felt deeply uncomfortable in the ALSs, which prevented them from engaging and benefitting from the ALSs. This research highlights how students’ comfort in the ALSs is essential to ensure their engagement and suggests many aspects that can support students’ comfort. Future research and professional development programmes built upon the reflections here can be used to support improved educational quality.

Efficient Corrections for Standardized Person-Fit Statistics.

Many popular person-fit statistics belong to the class of standardized person-fit statistics, T, and are assumed to have a standard normal null distribution. However, in practice, this assumption is incorrect since T is computed using (a) an estimated ability parameter and (b) a finite number of items. Snijders (Psychometrika 66(3):331-342, 2001) developed mean and variance corrections for T to account for the use of an estimated ability parameter. Bedrick (Psychometrika 62(2):191-199, 1997) and Molenaar and Hoijtink (Psychometrika 55(1):75-106, 1990) developed skewness corrections for T to account for the use of a finite number of items. In this paper, we combine these two lines of research and propose three new corrections for T that simultaneously account for the use of an estimated ability parameter and the use of a finite number of items. The new corrections are efficient in that they only require the analysis of the original data set and do not require the simulation or analysis of any additional data sets. We conducted a detailed simulation study and found that the new corrections are able to control the Type I error rate while also maintaining reasonable levels of power. A real data example is also included.

Confounded Local Inference: Extending Local Moran Statistics to Handle Confounding

Local statistical analysis has long been of interest to social and environmental scientists who analyze geographic data. Research into local spatial statistics experienced a step-change in the mid-1990s, which provided a large class of local statistical methods and models. The local Moran statistic is one commonly used local indicator of spatial association, able to detect both areas of similarity and observations that are very dissimilar from their surroundings. From this, many further local statistics have been developed to characterize spatial clusters and outliers. These statistics have seen limited adoption because they do not sufficiently model the relationships involved in confounded spatial data, where the analyst seeks to understand the local spatial structure of a given outcome variable that is influenced by one or more additional factors. Recent innovations used to do joint multivariate local analysis also do not model this kind of conditional local structure in data. This article provides tools to rigorously characterize confounded local inference and a new and different class of multivariate conditional local Moran statistics that can account for confounding. To do this, we return to the Moran scatterplot as the critical tool for local Moran-style covariance statistics. Extending this concept, a new method is available directly from a “Moran-form” multiple regression. We show the empirical and theoretical properties of this statistic, show how some existing heuristic approaches arise naturally from this framework, and show how the use of conditional inference can change interpretations in an empirical analysis of rent and housing stock in a rapidly changing neighborhood.

Status in a psychological statistics class: The role of academic and status-based identities in college students’ subjective social status

Great effort has been invested in increasing STEM achievement among students, but feelings of low status among underrepresented or otherwise vulnerable students may be creating additional challenges. The present study assessed how perceptions of social status within the classroom—termed subjective social status—aligned with objective course performance and differed by sex, first-generation status, work status, and race/ethnicity among 713 students enrolled across three introductory statistics classes. Findings indicated that final exam score was moderately related to ratings of subjective social status, suggesting that factors besides objective course performance may influence classroom subjective social status. When asked to explain how they evaluated their standing in the course, students reported five main themes, including both academic achievement with respect to exam scores and their understanding of course content. When examining differences by status-based identities in subjective social status, we found that female and first-generation students had lower subjective social status compared to their male and continuing-generation peers, although results were less robust for first-generation status. Likewise, working students reported lower subjective social status relative to non-working students, despite showing no difference in final exam score. In contrast, although Asian/Asian American students outperformed Latine students, there were no differences in reports of subjective social status between Asian/Asian American, Latine, and white students. Taken together, results suggest that factors beyond course performance may relate to students’ subjective social status, and subjective social status may contribute to disparities in academic performance, especially by sex and work status.