Statistical Concepts Research Articles

Preparation of Sampling Plan For the Gravimetric Characterization of Solid Waste From the Municipality of Itaquaquecetuba

Objective: the objective of this study is to utilize a sampling design for the collection of USW samples for gravimetric characterization, with the aim of proposing and standardizing a methodology that allows for the collection of statistically representative samples of this biomass Theoretical Framework: It was based on national and international technical standards that deal with the collection, preparation and sampling of waste. In addition, statistical sampling concepts were used, as well as the National Solid Waste Policy. Method: The methods used in this research include analysis of technical standards (national and international) for municipal solid waste combined with statistical methods of probabilistic sampling. Results and Discussion: As a result, a statistically valid sampling methodology was developed and applied to the waste from the municipality of Itaquaquecetuba, leading to the collection of MSW samples from 35 trucks, which represented the characteristics of the types of wet waste generated in the municipality. This provides essential data for the integrated management of waste in the region. Research Implications: The research proposes a statistically valid sampling plan for the collection and analysis of urban solid waste that can be adapted and used in any region of the country or internationally. Originality/Value: The work contributes to the literature by proposing a statistically valid sampling plan for the collection and sampling of waste, using as a basis the characteristics of urban solid waste generated in Brazil.

Statistical resolution analysis of microwave computational imaging

AbstractThis letter presents a model based on the Cramér–Rao bound theory for calculating the theoretical lower limit of imaging resolution of microwave computational imaging aided by re‐configurable metasurface. The model takes into account two crucial parameters: the signal‐to‐noise ratio and the number of measurements in the imaging process. By simultaneously considering the signal‐to‐noise ratio and the number of measurements, as well as other parameters, the model allows for a comprehensive assessment of the imaging resolution of the imaging system. In addition, both position estimation and intensity estimation are considered, and a new composite statistical resolution concept is proposed, which is more suitable for microwave computational imaging.

The basic statistical concepts and their interrelationships in diagnostic research.

Many medical postgraduate students exhibit a lack of clarity in their understanding of relevant statistical concepts during the conduct of diagnostic studies. This article, grounded in research practice, delves into the role of understanding statistical concepts in diagnostic research. It includes an exploration of sensitivity, specificity, types of statistical errors, and their interrelationships, as well as a discussion on statistical power-an often-overlooked but crucial concept in research. The article elucidates these important concepts with specific examples and illustrations, and addresses an issue of inconsistency related to the receiver operating characteristic curve in research practice. By drawing analogies between basic concepts in diagnostic tests and concepts in statistics, this article helps to enhance researchers' abilities in designing and interpreting clinical diagnostic studies, thereby improving the quality of clinical diagnostic research.

An Introduction to Bayesian Approaches to Trial Design and Statistics for Stroke Researchers.

While the majority of stroke researchers use frequentist statistics to analyze and present their data, Bayesian statistics are becoming more and more prevalent in stroke research. As opposed to frequentist approaches, which are based on the probability that data equal specific values given underlying unknown parameters, Bayesian approaches are based on the probability that parameters equal specific values given observed data and prior beliefs. The Bayesian paradigm allows researchers to update their beliefs with observed data to provide probabilistic interpretations of key parameters, for example, the probability that a treatment is effective. In this review, we outline the basic concepts of Bayesian statistics as they apply to stroke trials, compare them to the frequentist approach using exemplary data from a randomized trial, and explain how a Bayesian analysis is conducted and interpreted.

Students’ local vs. global views of data distributions: a cross-grade-level analysis using eye-tracking

AbstractThe ability to interpret and compare data distributions is an important educational goal. Inherent in the statistical concept of distribution is the need to focus not only on individual data points or small groups of data points (so-called local view), but to perceive a distribution as a whole, allowing to recognize global features such as center, spread, and shape (so-called global view). However, the latter is challenging for students to acquire. This study, involving 68 students in grades 4, 6, and 8, had two main objectives. First, we aimed to examine the potential impact of grade level on how students perceive and compare distributions presented in dot plots. Despite variations in specific pre-knowledge, our findings showed no significant grade-related differences in students’ gaze behavior or their ability to process global features when comparing distributions. This finding suggests that there is no significant developmental trend across grade levels regarding students’ capacity to perceive distributions globally, a critical aim in statistics education. Our second objective was to extend the findings of our previous work regarding the identification of specific eye-tracking measures as indicators of students’ local vs. global views. In line with our hypotheses, differences in gaze behavior between students with a local and global view were determined regardless of their grade level. This robustness across different educational stages underscores the validity of specific eye-tracking measures as reliable indicators for students local vs. global view of data. Our research highlights the potential of eye-tracking for understanding students’ data interpretation approaches in statistics education.

Taking an argumentation approach to statistical investigations: developing student data-ing practices

AbstractResearch literature has provided considerable insight as to how young students might come to deeper understandings of statistical concepts, processes and representations through investigations. However, ‘data-ing’—the critical thinking aspects of decision-making while engaging in statistical investigations—has shown to be more difficult to grasp. Data-ing aspects of statistical investigations identified in literature as particularly challenging include: generating researchable questions, knowing when or how to apply statistical knowledge, seeing a need for evidence to support conclusions, and knowing how to use data as evidence. Argumentation practices necessitate a focus on the use of evidence to logically support a claim, thereby offering potential to focus students on the sufficiency and quality of evidence and the conclusions that can be drawn. As such, argumentation offers potential to support students to engage in data decision-making practices. In the research described here, an argumentation focus was used to guide a statistical investigation with a class of 9–10-year-old students in a suburban Australian school. Analysis of classroom interactions and children's work samples suggested that taking an argument-based focus supported students’ developing capacity to overcome the aforementioned challenges and to engage in critical, decision-making practices with authentic, messy data within the context of the investigation.

Bayesian statistical concepts with examples from rodent toxicology studies.

The theory and practice of statistics comprises two main schools of thought: frequentist statistics and Bayesian statistics. Frequentist methods are most commonly used to analyze animal-based laboratory data, while Bayesian statistical methods have been implemented less widely and may be relatively unfamiliar to practitioners in experimental science. This paper provides a high-level overview of Bayesian statistics and how they compare with frequentist methods. Using examples in rodent toxicity research, we argue that Bayesian methods have much to offer laboratory animal researchers. We advocate for increased attention to and adoption of Bayesian methods in laboratory animal research. Bayesian statistical theory, methods, software, and education have advanced significantly in the last 30 years, making these tools more accessible than ever.

Data simulations for advancing psychological research: Insights, preparations and investigations.

Simulation has become an essential tool in psychological research, offering unique insights into statistical concepts, optimising research project planning and modelling human behaviour and cognition. This tutorial navigates simulations' diverse applications across various research stages. This tutorial begins by demonstrating simulations' impact on understanding statistical concepts. Amidst growing demands for effect size reporting and interpretation, simulations can help clarify the relationship between data and effect sizes, benefiting both educational purposes and advanced research. Simulations play a crucial role in planning psychological research. They provide flexible solutions for power, helping to determine necessary sample sizes and aiding in robust research planning, providing evidence of planned procedures. Simulations are pivotal in exploring human behaviour and cognition, as well as statistical method properties. By forcing researchers to translate verbal theory into formal models, simulation can help specify the assumptions. The paper also discusses improving simulation efficiency, such as using calculation clusters, optimising simulation practices and recognises simulations' limitations. This paper emphasises simulations' versatile role in psychological research. They enable deep insights into complex datasets, streamline project preparation and uncover subtleties in human behaviour, cognition and statistical methodologies.

A Simulation-Based Approach to Teach Interaction Effects in Postgraduate Biostatistics Courses

Simulation-based teaching can be a valuable method for learning statistical concepts. Its practical implementation for health-related subjects is seldomly evaluated. We propose a simulation-based approach to teach interaction effects in a postgraduate biostatistics course. We describe the steps involved in organizing and implementing a simulation-based activity and evaluate its execution. Mainly master and doctoral students in medical sciences (public health/epidemiology) participated to a 3-hr long online workshop on interaction effects. We presented one main learning activity, broken down into six progressive steps, from visualizing an interaction effect to investigating samples leading to erroneous inference. A total of 85 people attended of which 53 filled out an evaluation survey. Most (89%) of the respondents reported that the proposed activities helped them better understand interaction effects. A qualitative content analysis of free-text answers indicated that learning activities focusing on interaction effects in this way were useful for developing an understanding of both the meaning of statistical models and their interpretations. We conclude that a simulation-based approach can be a useful and interactive tool to create a valuable learning experience. The materials provided in this article can serve as a starting point for teachers who wish to implement such a method.

An analysis of direct-to-consumer genetic testing portals and their communication of health risk and test limitations.

Direct-to-consumer (DTC) genetic testing has become incredibly popular for assessing health risk related to specific diseases. However, how this risk is conveyed and whether the limitations of the tests are fully communicated can impact how customers interpret results. Through a qualitative content analysis of three different DTC genetic testing online portals, we examine how companies communicate relative and absolute health risks, the extent to which limitations are communicated, and how this information is presented. Findings suggest that relative risk was more prominently communicated than absolute risk and that it was used to organize and prioritize results. Further, risk information was often communicated using statistical terms and concepts that may not be accessible to all users. Test limitations that were communicated included the inability to diagnose a disease, the importance of lifestyle factors, and that the tests do not account for all genetic variants. Although companies included this information, it was not visually prominent.

The Enhancement of Statistical Literacy: A Cross-Institutional Study Using Data Analysis and Text Mining to Identify Statistical Issues in the Transition to University Education

Statistics modules are included in most university degrees, independent of the degree area, and this means that many students face these modules underprepared and struggle because of a lack of statistics knowledge. The Maths Support Centre (MSC) in the University College Dublin (UCD) provides support for various mathematics-related subjects, with statistics students being the second-largest cohort of visitors. The overall goal of this paper is to identify the common statistical issues students face during the transition from secondary education to tertiary education. The main data set for this study is the data from UCD students who have accessed the UCD MSC since 2015/16 for statistics support; the categorization of statistical concepts has been made with the statistics module description for each statistics subject at the Universidad Rey Juan Carlos (URJC). First, we conducted a categorization of statistical concepts taught in university (based on URJC’s catergorization); after that, UCD MSC tutor comments were categorized and validated, and subsequently descriptive analyses and text mining were used on the UCD MSC comments to achieve a deeper understanding of the statistical issues. The statistical issues presented were categorized as descriptive statistics (22.8%), probability (44%), statistical inference (29.2%), and statistical software (4%). Students struggled with material that was introduced at university level rather than material seen at secondary level. Our findings on students’ main statistical issues contribute to the development of a suite of evidence-based educational applications and games to support undergraduate students internationally in first- and second-year statistical modules.

Statistical physical view of statistical inference in Bayesian linear regression model.

This paper considers similarities between statistical physics and Bayes inference through the Bayesian linear regression model. Some similarities have been discussed previously, such as the analogy between the marginal likelihood in Bayes inference and the partition function in statistical mechanics. In particular, this paper considers the proposal to associate discrete sample size with inverse temperature [C. H. LaMont and P. A. Wiggins, Phys. Rev. E 99, 052140 (2019)2470-004510.1103/PhysRevE.99.052140]. The previous study suggested that incorporating this similarity motivates the derivation of analogs of thermodynamic functions such as energy and entropy. The study also anticipated that those analogous functions have potential to describe Bayes estimation from physical points of view and to provide physical insights into mechanisms of estimation. This paper incorporates a macroscopic perspective as an asymptotics similar to the thermodynamic limit into the previous suggestion. Its motivation stems from the statistical mechanical concept of deriving thermodynamic functions that characterize macroscopic properties of macroscopic systems. This incorporation not only allows analogs of macroscopic thermodynamic functions to be considered but also suggests a candidate for an analog of inverse temperature with continuity, which is partly consistent with the previous proposal to associate the discrete sample size with inverse temperature. On the basis of this suggestion, we analyze analogs of macroscopic thermodynamic functions for a Bayesian linear regression model which is the basis of various machine learning models. We further investigate, through the behavior of these functions, how Bayes estimation is described from the perspective of physics and what kind of physical insight is obtained. As a result, the estimation of regression coefficients, which is the primary task of regression, appears to be described by the physical picture of balance between decreasing energy and increasing entropy as in equilibrium states of thermodynamic systems. More specifically we observe the physical view of Bayes inference as follows: the estimation succeeds where the effect of decreasing energy is dominant at low temperature. On the other hand, the estimation fails where the effect of increasing entropy is dominant at high temperature.

Gamified recreational exercise focused on Markov Chains

The gamified recreational exercise focused on Markov Chains is an innovative methodology that combines learning with play to facilitate the understanding of statistical and mathematical concepts. Markov Chains are models that describe systems that transition between different states, where the probability of moving to a future state depends only on the current state and not on previous ones. By integrating game elements, such as challenges, rewards and competition, we seek to motivate students to actively engage in the learning process. This approach makes learning more engaging and gives participants a hands-on experience of how Markov Chains work in real situations. Exercises may include simulations, board games, or digital applications that represent scenarios where students must make decisions based on probabilities. Through gamification, teamwork and problem solving are encouraged, essential skills in today's world. The gamified recreational exercise is a favorable tool for teaching Markov Chains, it makes learning more dynamic and effective.

Model-agnostic neural mean field with a data-driven transfer function

As one of the most complex systems known to science, modeling brain behavior and function is both fascinating and extremely difficult. Empirical data is increasingly available from ex vivo human brain organoids and surgical samples, as well as in vivo animal models, so the problem of modeling the behavior of large-scale neuronal systems is more relevant than ever. The statistical physics concept of a mean-field model offers a tractable way to bridge the gap between single-neuron and population-level descriptions of neuronal activity, by modeling the behavior of a single representative neuron and extending this to the population. However, existing neural mean-field methods typically either take the limit of small interaction sizes, or are applicable only to the specific neuron models for which they were derived. This paper derives a mean-field model by fitting a transfer function called Refractory SoftPlus, which is simple yet applicable to a broad variety of neuron types. The transfer function is fitted numerically to simulated spike time data, and is entirely agnostic to the underlying neuronal dynamics. The resulting mean-field model predicts the response of a network of randomly connected neurons to a time-varying external stimulus with a high degree of accuracy. Furthermore, it enables an accurate approximate bifurcation analysis as a function of the level of recurrent input. This model does not assume large presynaptic rates or small postsynaptic potential size, allowing mean-field models to be developed even for populations with large interaction terms.

The Importance of Statistics in Medical Healthcare

Abstract: Statistical principles play a fundamental role in shaping the landscape of medical science by providing a structured framework for analyzing data, drawing conclusions, and making informed decisions in healthcare settings. In the realm of medical research, statistical principles are crucial for designing experiments, interpreting results, and ensuring the reliability and validity of findings. Key statistical concepts like hypothesis testing, confidence intervals, regression analysis, and survival analysis are extensively utilized in medical studies to assess the effectiveness of treatments, understand disease patterns, and evaluate healthcare interventions. These principles enable healthcare professionals to make evidence-based decisions, tailor treatments to individual patient needs, and continuously improve the quality of care provided to patients. The role of statistics in medical research starts at the planning stage of a clinical trial or laboratory experiment to establish the design and size of an experiment that will ensure a good prospect of detecting effects of clinical or scientific interest. Statistics is again used during the analysis of data (sample data) to make inferences valid in a wider population. In simple situations computation of simple quantities such as P-values, confidence intervals, standard deviations, standard errors or application of some standard parametric or nonparametric tests may suffice.

Crafting 10 Years of Statistics Explanations: Points of Significance

Points of Significance is an ongoing series of short articles about statistics in Nature Methods that started in 2013. Its aim is to provide clear explanations of essential concepts in statistics for a nonspecialist audience. The articles favor heuristic explanations and make extensive use of simulated examples and graphical explanations, while maintaining mathematical rigor. Topics range from basic, but often misunderstood, such as uncertainty and p-values, to relatively advanced, but often neglected, such as the error-in-variables problem and the curse of dimensionality. More recent articles have focused on timely topics such as modeling of epidemics, machine learning, and neural networks. In this article, we discuss the evolution of topics and details behind some of the story arcs, our approach to crafting statistical explanations and narratives, and our use of figures and numerical simulations as props for building understanding.

Virtual Biostats Day: An Interactive Online Biostatistics Outreach Program Directed at High School Students in Groups Historically Underrepresented in STEM Careers

Persistent underrepresentation of Black and Hispanic Statistics degree holders relative to the U.S. population occurs at all levels in post-secondary education, contributing to the underrepresentation of Black and Hispanic Bio/Statisticians. Attempting to address this inequity before the undergraduate level, Memorial Sloan Kettering (MSK)’s Bridge to Biostats committee was established with the mission to increase awareness of and interest in the field of Biostatistics among high school students in groups underrepresented in STEM fields. We describe in this article an outreach program targeted to underrepresented students in New York City with innate aptitude and interest in STEM subjects, but minimal exposure to Statistics. Virtual Biostats Day is a 1–1/4 hr online exposure program that incorporates interactive elements exploring statistical concepts alongside clear descriptions of the field of Biostatistics and the roles and responsibilities of a Biostatistician. Students are also introduced to professional Biostatisticians who describe their journeys from high school to where they are today. This combination of didactic and active learning has engaged students, even in the online environment. We relate our experience in implementing and presenting our program to students and provide a complete toolkit for other Bio/Statistics departments or organizations interested in engaging in similar outreach work. Supplementary materials for this article are available online.

A numerical approach to radiative ternary nanofluid flow on curved geometry with porous media and multiple slip constraints

AbstractEnergy scarcity is among the biggest global challenges which is aggravating with each passing day due to ever increasing energy demands of contemporary livings as well as industrial requirements verses finite and rapidly depleting fossil reserves of our planet. Improving energy efficiency is one of the effective ways to cope with this challenge. Ternary nanofluids (TNF) are a dynamic novel class of fluids possessing unique thermophysical and other functional characteristics making them the most efficient heat transporting fluids of 21st century. These fluids have promising applications in major manufacturing and processing industries, emerging nanotechnologies and bio‐medical domains. The novel theme of this pragmatic study is analysis of bio‐convective TNF flow by stretchable porous curved surface considering effects of thermal radiation, chemical reaction, magnetic field, and various slip constraints. The modeled partial differential equations (PDEs) governing fluid flow under presumptions are converted to ordinary differential equations (ODEs) by suitable transformation relations. Numerical solutions are presented in graphical sketches and tabular forms using MATLAB bvp4c package for physical interpretations of sundry controlling variables impacts. To gauge veracity of computed results, comparisons with already published results have been presented. Moreover, the statistical concept of Pearson correlation coefficient has been employed to prove strong relationship between slip parameters and physical quantities. Research concludes that thermal efficiency of TNF improves by rising velocity slip, magnetic force, curvature factor, thermal radiation, and thermophoresis effects. Velocity slip and thermal slip improve concentration boundary layer. Gyrotactic microorganisms’ density improves for higher velocity slip, temperature slip while depreciates for larger values of nanoparticle concentration slip and motile organism density slip.

Degrees of Freedom: Search Cost and Self-consistency

Model degrees of freedom ( df ) is a fundamental concept in statistics because it quantifies the flexibility of a fitting procedure and is indispensable in model selection. To investigate the gap between df and the number of independent variables in the fitting procedure, Tibshirani (2015) introduced the search degrees of freedom ( sdf ) concept to account for the search cost during model selection. However, this definition has two limitations: it does not consider fitting procedures in augmented spaces and does not use the same fitting procedure for sdf and df . We propose a modified search degrees of freedom ( msdf ) to directly account for the cost of searching in either original or augmented spaces. We check this definition for various fitting procedures, including classical linear regressions, spline methods, adaptive regressions (the best subset and the lasso), regression trees, and multivariate adaptive regression splines (MARS). In many scenarios when sdf is applicable, msdf reduces to sdf . However, for certain procedures like the lasso, msdf offers a fresh perspective on search costs. For some complex procedures like MARS, the df has been pre-determined during model fitting, but the df of the final fitted procedure might differ from the pre-determined one. To investigate this discrepancy, we introduce the concepts of nominal df and actual df , and define the property of self-consistency, which occurs when there is no gap between these two df ’s. We propose a correction procedure for MARS to align these two df ’s, demonstrating improved fitting performance through extensive simulations and two real data applications.

Parsimonious statistical techniques for the detection of drifts toward dangerous operational conditions in tokamaks

The approaching initial operation of major new tokomaks is rendering more pressing the need for effective disruption prediction techniques. The required tools should be not only accurate but also capable of operating with a minimum number of signals, because in the first campaigns of new devices typically only a very limited number of diagnostics is available. The present work reports the results obtained with two advanced statistical techniques, chaos onset and concept drift (CD). These methods are capable of detecting the plasma drifting towards dangerous regions of the operational space using only global signals such as the plasma current or the locked mode amplitude. The obtained performances meet the requirements of mitigation in devices such as JT60-SA and ITER at the beginning of their operation. The computational times of the chaos onset approach are already of the order of 1 ms on laptop computers, whereas the CD technique requires implementation on FPGAs or GPUs to be compatible with real time requirements.