Statistical Concepts Research Articles

Conversations with Gábor J. Székely

Gábor J. Székely was born in Budapest, Hungary on February 4, 1947. He graduated from Eötvös Loránd University (ELTE) with an M.S. degree in 1970, and a Ph.D. degree in 1971. He received his Candidate Degree from the Hungarian Academy of Sciences in 1976, and the Doctor of Science Degree (D. Sc.) from the Hungarian Academy of Sciences in 1986. Székely joined the Department of Probability Theory of ELTE in 1970. In 1989, he became the founding chair of the Department of Stochastics of the Budapest Institute of Technology (Technical University of Budapest). In 1995, he moved to the United States as a tenured full professor at Bowling Green State University (BGSU) in Bowling Green, Ohio. Before that, in 1990–1991, he was the first Lukacs Distinguished Professor at BGSU. Székely had several visiting positions, for example, at the University of Amsterdam in 1977 and at Yale University in 1989. Between 2006 and 2022, he served as a Program Director in the Statistics Program of the Division of Mathematical Sciences at the U.S. National Science Foundation. Székely has about 250 publications, including 6 books in several languages. In 1988, he received the Rollo Davidson Prize from Cambridge University, jointly with Imre Z. Ruzsa for their work on algebraic probability theory. In 2010, Székely became an Elected Fellow of the Institute of Mathematical Statistics mostly for his works dealing with physics concepts in statistics like energy statistics and distance correlation. He had the fortune to know and work with world-class mathematicians and statisticians like (in chronological order of their first meetings): P. Erdős, A. Rényi, Y. Linnik, B. de Finetti, A. N. Kolmogorov, H. Robbins, G. Pólya, L. Shepp, G. Wahba, C. R. Rao, B. Efron, P. Bickel and E. Seneta.

Embodied nonlinear dynamics of cognitive performance.

Study participants are typically unable to generate binary button-press sequences that pass as classically random sequences, such as from successive "fair coin" flips. Instead, their sequences repeat or alternate between responses too often. These deviations from randomness are commonly explained in terms of limitations or idiosyncrasies in cognitive processing. This article tests a novel hypothesis that randomness departures in participant-generated binary sequences are driven by coordination dynamics; alternating and repeating sequences are related to bimanual coordination attractors. Participants (N = 128) were asked to generate sequences that were representative of a random sequence, by successively pressing either of two buttons across 1,600 trials. Statistical analyses identify the binary button-press dynamics with a discrete sine-circle version of the Haken, Kelso, Bunz bimanual coordination model. Permutation analyses revealed the most common one- to five-trial subsequences were identified with the most dynamically stable coordinative relationships, consistent with bimanual coordination predictions. The sequences were consistent with scaling noises. Thus, participants' sequences departed from classical randomness by virtue of membership in a more inclusive category of variability that subsumes classical randomness. Recurrence quantification analysis revealed the mixture of stochasticity and determinism in the sequences was better approximated by the sine-circle model than by phase-randomized surrogate data sets that preserved both the power spectral densities and distributions of each participant's sequence. A relationship between randomness production and two-alternative forced-choice performance is established that constrains response time distribution models. The article's organization illustrates a nonreductive approach to inference for cognitive systems, inspired by statistical physics concepts such as renormalization group theory and universality. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Teaching Statistical Inference Through a Conceptual Lens: A Spin on Existing Methods with Examples

Using software to teach statistical inference in introductory courses opens the door for methods and practices that are more conceptually appealing to students. With an increasing number of fields requiring competency in statistics including data science, natural and social sciences, public health and more, it is crucial that we as instructors deliver the basic concepts of statistics effectively. In line with guidelines presented in the GAISE College Report, this article demonstrates intuitive approaches to teaching proportion and mean inference that take advantage of statistical software and emphasize conceptual understanding. The article recommends putting aside asymptotic-based methods for proportion inference and using the exact binomial method. Regarding mean inference, we propose a more contextualized and simplified process that uses the distribution of the sample mean directly and avoids standardized statistics such as z or t. In both the proportion and mean inference contexts, we discuss the benefits of the proposed approaches and provide detailed examples that demonstrate the methods using the Rguroo statistical software.

STUDI THE HIDDEN CURRICULUM DALAM MEMBANGUN KARAKTER SISWA DAN MENINGKATKAN KECERDASAN SPIRITUAL DI MI TARBIYATUS SHIBYAN

The approach used in this research is a psychological and sociological approach. The type of research is field research, which is a type of research based on data obtained directly from research sites in the field and is descriptive analytic in nature.In this study the authors raise important points of discussion in the area of how schools are trying through the application of a hidden curriculum to build student character and improve spiritual intelligence at MI Tarbiyatus ShibyanQualitative descriptive is a method used by researchers in order to carry out in-depth data analysis.The concept of implementing a hidden curriculum is to include character values that are included in all subjects. The character values that are instilled are religious values, independent values, values of appreciating achievement, values of curiosity, values of love for the motherland and creative values.Characterizations in elementary schools can encourage the development of students' spiritual intelligence by emphasizing religious values and discipline. The main concept of character education is based on the school's vision, mission and goals, which are related to curriculum and academic subjects, school culture both in the teacher's environment and in the student's environment as well as self-management through identification and development programs. student interests and talents. The concept of teaching character statistics is implemented through a hidden curriculum, including character statistics in all subjects. The character values contained are religious values, independent values, achievement appreciation values, curiosity values, patriotism values, and constructive values.

Using quantile regression and relative entropy to assess the period of anomalous behavior of marine mammals following tagging.

Tagging of animals induces a variable stress response which following release will obscure natural behavior. It is of scientific relevance to establish methods that assess recovery from such behavioral perturbation and generalize well to a broad range of animals, while maintaining model transparency. We propose two methods that allow for subdivision of animals based on covariates, and illustrate their use on narwhals (Monodon monoceros) and bowhead whales (Balaena mysticetus), captured and instrumented with Acousonde™ behavioral tags, but with a framework that easily generalizes to other marine animals and sampling units. The narwhals were divided into two groups based on handling time, short ( min) and long ( min), to measure the effect on recovery. Proxies for energy expenditure (VeDBA) and rapid movement (jerk) were derived from accelerometer data. Diving profiles were characterized using two metrics (target depth and dive duration) derived from depth data. For accelerometer data, recovery was estimated using quantile regression (QR) on the log-transformed response, whereas depth data were addressed using relative entropy (RE) between hourly distributions of dive duration (partitioned into three target depth ranges) and the long-term average distribution. Quantile regression was used to address location-based behavior to accommodate distributional shifts anticipated in aquatic locomotion. For all narwhals, we found fast recovery in the tail of the distribution (<3 h) compared with a variable recovery at the median (∼1-10 h) and with a significant difference between groups separated by handling time. Estimates of bowhead whale recovery times showed fast median recovery (<3 h) and slow recovery at the tail (>6 h), but were affected by substantial uncertainty. For the diving profiles, as characterized by the component pair (target depth, dive duration), the recovery was slower (narwhals-long: h; narwhals-short: h; bowhead whales: <9h) and with a difference between narwhals with short vs long handling times. Using simple statistical concepts, we have presented two transparent and general methods for analyzing high-resolution time series data from marine animals, addressing energy expenditure, activity, and diving behavior, and which allows for comparison between groups of animals based on well-defined covariates.

IMPLEMENTATION OF DECISION TREE AND SUPPORT VECTOR MACHINE ON RAISIN SEED CLASSIFICATION

In everyday life there are many complex and global problems, especially in terms of decision making. Machine learning (ML) which is built from the concepts of computer science statistics and mathematics can automatically solve problems without guidance from ordinary users. Decision tree (DT) and support vector machine (SVM) are two supervised learning methods among several classification algorithms in ML. Both algorithms are the most popular classification techniques due to their ability to change a complex decision-making process into a simple process. In this study, the accuracy of the DT and SVM algorithms is studied on classifying raisin seeds into the Besni class and the Kecimen class based on existing features. The raisin data are divided into training and testing data, and the evaluation of the two methods is done using the testing data. The results of the evaluation are compared based on the accuracy, sensitivity, specificity, and kappa levels of the DT and SVM algorithms. The results on classifying raisin seeds data show that the SVM algorithm is superior to DT, therefor the number of positive observations is more precise in the prediction.

베이지안 통계를 활용한 특수교육 중재전략의 효과성 평가 방안 탐색

It is important to examine the extent which special education interventions are effective in terms of practical significance. However, because, until now, domain statistical practice in the area of special education is frequentist statistics, there are some limitations of investigating practical significance. In this paper, bayesian statistics was considered as an alternative approach for investigating practical significance. Bayesian statistics is a method of statistics inference in which proability is the most important concept. Therefore, it allows us to focus on the importance of practical significance in special education research. This paper provided the basic concepts of the bayesian statistics and then use a practical example on how to evaluate the effectiveness of special education intervention using bayesian statistics. Results of this study support the evidence that bayesian statistics could be one of alternative approaches for evaluating the effects of interventions in the area of special education. Finally, considerations for future research are discussed.

Research on the Impact Mechanical Properties of Real-Time High-Temperature Granite and a Coupled Thermal–Mechanical Constitutive Model

Studying the mechanical behavior of rocks under real-time high-temperature conditions is of great significance for the development of energy caverns, nuclear waste disposal projects, and tunneling engineering. In this study, a real-time high-temperature impact compression test was conducted on Sejila Mountain granite to explore the effects of temperature and external load on its mechanical properties. Based on the concepts of damage mechanics and statistics, a coupled thermal-mechanical (T-M) damage constitutive model was established, which considers the temperature effect and uses the double-shear unified strength as the yield criterion. The parameter expressions were clarified, and the accuracy and applicability of the model were verified by experimental data. The research results indicated that high temperatures had an obvious damaging and deteriorating effect on the strength of the granite, while an increase in impact velocity had an enhancing effect on the strength of the granite. The established constitutive model theoretical curve and test curve showed a high degree of agreement, indicating that the coupled T-M model can objectively represent the evolution process of damage in rocks and the physical meaning of its parameters is clear.

PENGEMBANGAN BAHAN AJAR GAMIFIKASI BERBASIS CONTEXTUAL TEACHING LEARNING (CTL) BERBANTU ANDROID

This development research aims to determine the development process of CTL-based gamification teaching materials assisted by android for seventh grade students on the subject of Statistics in MTs. MA'ARIF 1 Punggur which is valid and practical for use in learning. The type of research used is research development or Research and Development (R&amp;D). The model used by researchers is the 4-D model developed by Thiagarajan (1974). The results of the development process of the Android-assisted CTL-based gamification module in this study consisted of 4 stages, namely (1) Define, the results of this analysis are that the textbook lacks in illustrating images and the book is only available in the school library Then the concept analysis results obtained in the form of a statistical material concept map. After that, a task analysis was carried out, namely in the form of KI and KD related to statistics material and finally, the analysis of the learning objectives of the results obtained in the form of graduation achievement indicators in the statistics material. (2) Design, the design uses Powerpoint software, I-Spring Suite 8 software is used to convert (.pptx) to (.html5) and Website 2 APK Bulder software is used to convert (.html5) into applications (.apk). (3) development, based on the results of the validation of the three experts, namely material experts, design, and language gamification modules based on Android-assisted Contextual Teaching and Learning that have been developed, obtain an average percentage of validity of 77.72% which indicates the interpretation is valid and the practicality test results are obtained. Practicality percentage of 82.17% which shows the interpretation very practical. Then it can be identified that the Android-assisted Contextual Teaching and Learning (CTL) based gamification module is declared valid and practically used in learning. (4) desseminate limited product distribution, namely in class VIIB Mts. Ma'arif 1 Punggur.

Asynchronous student engagement in analysis of climate data achieves learning objectives related to climate change understanding, statistical competence, and climate anxiety

Learning in asynchronous online environments has gained importance over the last several decades, and educational environment shifts from the COVID-19 pandemic appear to have increased this need. Science educators and students need information about which approaches work in the asynchronous environment where informal feedback tends to be reduced, compared to other teaching modalities. In this study, we asynchronously implemented a learning module across 5 institutions that guided students (N = 199) from prescriptive data analysis through guided inquiry and eventually to open inquiry. The module focuses on the science behind climate change. Students work with the same authentic data sets used by professional scientists to examine geologic history and causes of climate change. By analyzing contemporary atmospheric carbon dioxide and temperature data and then using the 800,000-year record available from the Vostok ice core proxy record of atmospheric properties, students identify the causes of climate change and discover the unprecedented nature of recent atmospheric changes. Using a pre/post-module assessment, we demonstrate improvement in students’ understanding of climate change processes and statistical methods used to analyze data. However, there was no evidence that the module develops students’ scientific reasoning about the relationship between causation and correlation. Students maintained that correlation is not causation, even when a robust causal mechanism (i.e., the greenhouse effect) explains the link between atmospheric carbon dioxide and temperature. Finally, our analysis indicated that generally, anxiety about climate change was reduced during the module, such that students become less anxious about the climate change the more they learn about it. However, science-denying students experienced much higher anxiety about climate change than students who accepted the scientific consensus about climate change. Climate science-dissenting students were so few in this study that a statistical comparison was not possible, but this intriguing finding warrants further investigation of the role of anxiety in science denial. Mainly, this study demonstrates how asynchronous online learning environments can indeed support the achievement of learning objectives related to conducting authentic science, such as increasing understanding of climate change and statistical concepts, all while not provoking anxiety about climate change.

Revealing attitude toward statistics among MA TEFL students: A Systemic Functional Linguistics perspective

Higher education students’ attitudes toward statistics are of great importance as these may affect student performance and achievement in statistics learning. Despite some interest in attitude towards statistics among higher education students in language-related fields and the broader area of tertiary-level education, the different types of existing attitudes toward statistics might remain uncovered. Applying the Attitude system as an analytical framework, this study explores how higher education students use linguistic resources to indicate statistics-related attitude before, during and after learning. The narratives of learning statistics were obtained from a group of MA TEFL students (n=25) who participated in an introductory course on basic statistical concepts and procedures, among others. The study makes visible a great variety and a considerable variation of linguistic means which students use to express statistics-related attitude as Judgement, Appreciation and Affect, emerging over time. As such, this study advances methodological practices and training in the field.

Methodological progress note: Machine learning methods in healthcare research.

Methodological progress note: Machine learning methods in healthcare research.

Statistical Rules in Scientific Reports (The basics)

Objective: Scientific papers usually contain information and data that we call them statistics. We expect statistics to provide us with a suitable description of the data by summarizing. Scientific journals have specific frameworks for this work in mention to writers and readers can understand statistical concepts with a common terminology. In this paper we guide reader to write a scientific issue without any confusion and crowding and we propose some notes to report a scientific descriptive statistics, and make a table properly and draw a visual graph.

Exploring the statistical nature of independent chromosome segments

Previous research in genomics developed the concept of independent chromosome segments and suggested that genomic prediction works on capturing the segment effects rather than on LD to individual QTL. The number of independent chromosome segments (Me) was posited as 4NeL, a function of effective population size (Ne) and genome length (L) in Morgans (M). The objective of this study was to determine whether the physical segments are approximately consecutive haplotype blocks of length ¼ M, with the number of haplotype blocks for each physical location equal to Ne. In a simulated population, the number of animals randomly selected as reference animals is represented as Na. For all animals, the genome was split into equal-sized segments represented as Ns. For each specific location, segments of non-reference animals were assigned the most similar segment of one reference animal. Genomic analyses estimated the value of the segment effects, and breeding values were a sum of all segment effects for a specific animal. Accuracies of segment effects were calculated by correlating the true breeding values (TBV) and the breeding values based on segments. Segment effect accuracies were compared with the true accuracy calculated by the correlation of TBV and genomic estimated breeding values (GEBV) computed using GBLUP. Accuracies were maximized at Na=Ne, Ns=4 L, but they were not as high as in GBLUP. Accuracies may be smaller using the statistical concept of segments due to approximations based on computing limitations, as the origin of each segment and the recombination sites were unknown in the simulation. Therefore, random animals served as reference animals, and each non-reference animal received the most similar segment of a reference animal instead of a linear combination of such segments. Genomic selection acts partially on ¼ M long chromosome segments, and using the statistical definition of segments moderately explains the accuracy. More complex simulations are needed to investigate the issue thoroughly.

Three Principles for Modernizing an Undergraduate Regression Analysis Course

As data have become more prevalent in academia, industry, and daily life, it is imperative that undergraduate students are equipped with the skills needed to analyze data in the modern environment. In recent years there has been a lot of work innovating introductory statistics courses and developing introductory data science courses; however, there has been less work beyond the first course. This article describes innovations to Regression Analysis taught at Duke University, a course focused on application that serves a diverse undergraduate student population of statistics and data science majors along with nonmajors. Three principles guiding the modernization of the course are presented with details about how these principles align with the necessary skills of practice outlined in recent statistics and data science curriculum guidelines. The article includes pedagogical strategies, motivated by the innovations in introductory courses, that make it feasible to implement skills for the practice of modern statistics and data science alongside fundamental statistical concepts. The article concludes with the impact of these changes, challenges, and next steps for the course. Portions of in-class activities and assignments are included in the article, with full sample assignments and resources for finding data in the supplemental materials. Supplementary materials for this article are available online.

“Your truth isn’t the Truth”: Data activities and informal inferential reasoning

This paper investigates data activities in an afterschool setting, offering a deeper understanding of the social nature of students’ informal inferences by investigating how informal inferences are negotiated in group interactions, influenced by social norms, and how statistical concepts come into play in learners’ informal inferential reasoning (IIR). Analyses take up a multi-sited orientation to investigate how youth used quantitative and contextual resources during a research activity to make meaning of data and negotiate emergent social tensions. Findings show how data activities that are part of informal inferential reasoning, such as collection, interpretation, generalization, inference, and representation unfolded as social, political, and personal. Implications call for designs for learning that better support working with data and understanding real-world phenomena and sociopolitical issues in ways that leverage youths’ experiences, enabling them to take part in social action as critical community actors.

Modeling how fast teacher trainees master statistical concepts in verification of the learning curve theories

This study was undertaken to model and evaluate how fast Ghanaian teacher trainees master statistical concepts, in verification of the learning curve theory. The target population was all the 2020/2021 academic year level 300 teacher trainees in Ghana. However, St. Joseph’s College of Education (JOSCO), Bechem, was selected out of proximity from the 46 colleges of education in Ghana. At JOSCO, the Science/Mathematics, Agriculture/ICT and the Social Studies classes were randomly selected from the five level 300 classes and all the students in the three classes served as the experimental units. In effect, a ten-week period experimental tuition and evaluation on Educational Statistics was conducted and the data on the percentage of statistical concepts mastered by the teacher trainees were collected for the study. Tabular and graphical analyses on the data were carried out for the verification of the learning curve theory. Ordinary differential equations were used to derive the model for the prediction of the percentage of statistical concepts mastered by the teacher trainees. Graphical and numerical residual analyses were also conducted for the model adequacy checking. In all, the learning curve was successfully verified and the derived model was also found to be adequate for the prediction of the percentage of statistical concepts mastered by the teacher trainees at any point in time. This happens to be the first time research has been successfully conducted to verify the learning curve theory in statistical concept build-up in the colleges of education in Ghana.

A statistical approach to predict fatigue failure of leaf springs manufactured with nanotube incorporated epoxy‐woven glass fiber composites

AbstractIn this study, a statistical approach was developed to predict fatigue failure of laminated composite leaf springs prepared with carbon nanotube (CNT) filled epoxy/woven glass fibers. Electrical resistance change method and the Weibull analysis were adopted to develop a statistical approach. The electrical conductivity for successful application of health monitoring of leaf springs was achieved by dispersing 0.4 wt% of CNTs into epoxy resin. In‐situ monitoring of damage in composite leaf springs during fatigue tests applied as cyclic flexural deflection was carried out at nine different displacement ratios. The critical fatigue cycle and the corresponding change in electrical resistance were determined at each displacement ratio. Then, the critical electrical resistance change to cyclic fatigue was found 0.15% with 95% reliability by the Weibull analysis. The average fatigue life and the average strength loss corresponding to the 0.15% resistance change ratio were found to be 48.33% and 9.88%, respectively. The reported statistical concept based on the monitoring of change in electrical resistance during deflection can be successfully employed as a useful tool to predict safety limits of composite structures subjected to fatigue loading, especially in aerospace industry.

Psychological profile and prerequisites for the formation of the killer’s personality

The relevance of the study is conditioned upon the elevated level of crime and scientific interest in determining the prerequisites for murders that are individual in nature, develop into a series of hidden intentions and have complex consequences for the life of society. Clarifying the psychological causes of serious crimes is important for preventive work in the defined area. The purpose of this study was to determine the personality traits of murderers, to identify the prerequisites for the formation of criminal behaviour, to investigate the classification and rating of serial crimes by cruelty and methods, to analyse statistical data on the commission of murders. In the study of the nature of serial murders, the following methods were used: the method of analysis and synthesis, the biographical method, the statistical method, and the generalization method. Using theoretical analysis, the psychological root causes of homicide drives, their main features and methods of implementation, and gender characteristics regarding the strength of committing a crime were identified; the data obtained were confirmed by real statistical indicators. The study highlighted the problem of increasing criminal cases caused by the mental state of the individual. The features of the psychology of the killer were covered, and the influence of childhood and life circumstances on the formation of the internal urge to commit murder was substantiated. The factors that encourage violence were identified. The types of serial killers were identified, and the “handwriting” of crime execution was analysed. The essence of impulsive and serial murder was delineated, and the concept of moral statistics as a provocative factor in committing a crime was covered. A psychological portrait of a serial killer was formed. Features of early research at the level of physiology and genetics were established. The presented theoretical material not only serves as an informational resource but can also be used in carrying out preventive measures related to early education, the methods of which have a preventive and correctional impact.

Common statistical concepts in the supervised Machine Learning arena.

One of the core elements of Machine Learning (ML) is statistics and its embedded foundational rules and without its appropriate integration, ML as we know would not exist. Various aspects of ML platforms are based on statistical rules and most notably the end results of the ML model performance cannot be objectively assessed without appropriate statistical measurements. The scope of statistics within the ML realm is rather broad and cannot be adequately covered in a single review article. Therefore, here we will mainly focus on the common statistical concepts that pertain to supervised ML (i.e. classification and regression) along with their interdependencies and certain limitations.