Class Of Statistics Research Articles

Grasping the STARS: A comprehensive study on statistics—Anxiety levels among engineering students

Engineering students often face the challenge of comprehending and applying statistical concepts to evaluate and assess research. This research seeks to investigate the factor structure of Statistics Anxiety Rating Scale (STARs), which comprises six domains with 51 items. The questionnaire was administered to engineering students currently enrolled in a statistics class, and the data were analyzed using Statistical Package for the Social Sciences. The study sheds light on the factors that contribute to students’ statistics anxiety when taking a statistics course. The findings highlight the elements that influence statistics anxiety, educators and institutions can develop targeted interventions and support mechanisms to enhance students’ statistical competence and overall learning experience. This research not only addresses the unique challenges faced by engineering students but also holds implications for fostering statistical literacy across various disciplines.

Examining the Impact of Statistical Features on Grade 11 Students' Performance in Statistics Using Calculators

This research investigates how feature characteristics affect the academic achievement of Grade 11 students in the field of statistics, with a particular emphasis on the role played by the use of calculators. The control group utilized various scientific calculators that are typically employed in statistics classes. The experimental group utilized the statistical functionalities of the advanced calculator. The objective of this study is to ascertain the impact of statistical characteristics of calculators on the academic achievement of grade 11 students in the field of statistics. The study aimed to determine whether there was a notable disparity between the pretest scores of the two groups. Is there a substantial disparity between the pretest and posttest scores of the groups? Is there a substantial disparity in the gain scores between the two groups? Furthermore, provides a comprehensive assessment of the study. The study's findings indicate a notable disparity in the utilization of various statistical functions on calculators. The experimental group demonstrated superior performance and adeptly utilized the statistical aspects of advanced calculators. The students in the Control group had challenges when attempting to solve the z-test and p-value. The statistical functionality of advanced calculators becomes valuable in advanced statistical topics.

Uniform in number of neighbors consistency and weak convergence of $ k $NN empirical conditional processes and $ k $NN conditional $ U $-processes involving functional mixing data

<abstract><p>$ U $-statistics represent a fundamental class of statistics arising from modeling quantities of interest defined by multi-subject responses. $ U $-statistics generalize the empirical mean of a random variable $ X $ to sums over every $ m $-tuple of distinct observations of $ X $. Stute [182] introduced a class of so-called conditional $ U $-statistics, which may be viewed as a generalization of the Nadaraya-Watson estimates of a regression function. Stute proved their strong pointwise consistency to: $ r^{(m)}(\varphi, \mathbf{t}): = \mathbb{E}[\varphi(Y_{1}, \ldots, Y_{m})|(X_{1}, \ldots, X_{m}) = \mathbf{t}], \; \mbox{for}\; \mathbf{ t}\in \mathcal{X}^{m}. $ In this paper, we are mainly interested in the study of the $ k $NN conditional $ U $-processes in a functional mixing data framework. More precisely, we investigate the weak convergence of the conditional empirical process indexed by a suitable class of functions and of the $ k $NN conditional $ U $-processes when the explicative variable is functional. We treat the uniform central limit theorem in both cases when the class of functions is bounded or unbounded satisfying some moment conditions. The second main contribution of this study is the establishment of a sharp almost complete Uniform consistency in the Number of Neighbors of the constructed estimator. Such a result allows the number of neighbors to vary within a complete range for which the estimator is consistent. Consequently, it represents an interesting guideline in practice to select the optimal bandwidth in nonparametric functional data analysis. These results are proved under some standard structural conditions on the Vapnik-Chervonenkis classes of functions and some mild conditions on the model. The theoretical results established in this paper are (or will be) key tools for further functional data analysis developments. Potential applications include the set indexed conditional <italic>U</italic>-statistics, Kendall rank correlation coefficient, the discrimination problems and the time series prediction from a continuous set of past values.</p></abstract>

Permutation tests of multivariate location using data depth

ABSTRACT We provide two classes of affine invariant statistics based on data depth to test the equality of mean vectors in multivariate paired data. The proposed tests are defined based on the depth values of the deepest point of the sample relative to the negative of the multivariate sample and the expected median under the null hypothesis. The tests are implemented through the idea of the permutation procedure. No distributional assumption is imposed on the data, except that the permutation test assumes a centrally symmetric distribution of the paired data. A simulation study compares the new tests to some competitors. The results show that the new tests are highly competitive for a wide variety of distributional models. More specifically, the results show that the tests based on the halfspace, simplicial, and projection depth functions perform well compared to other methods and are the most robust. A real data example illustrating the use of the tests is also presented.

Ergodic properties of Brownian motion under stochastic resetting.

We study the ergodic properties of one-dimensional Brownian motion with resetting. Using generic classes of statistics of times between resets, we find respectively for thin- or fat-tailed distributions the normalized or non-normalized invariant density of this process. The former case corresponds to known results in the resetting literature and the latter to infinite ergodic theory. Two types of ergodic transitions are found in this system. The first is when the mean waiting time between resets diverges, when standard ergodic theory switches to infinite ergodic theory. The second is when the mean of the square root of time between resets diverges and the properties of the invariant density are drastically modified. We then find a fractional integral equationdescribing the density of particles. This finite time tool is particularly useful close to the ergodic transition where convergence to asymptotic limits is logarithmically slow. Our study implies rich ergodic behaviors for this nonequilibrium process which should hold far beyond the case of Brownian motion analyzed here.

Program Construction Method for Sequential Statistics Class Algorithm Based on Bidirectional Scanning Induction

The program construction process is based on rigorous mathematical reasoning, which leads to a fully correct algorithmic program via step-by-step refinement of the program specifications. The existing program construction methods' refinement process is partly based on individual subjective speculation and analysis, which lacks a precise guidance method. Meanwhile, efficiency factors have usually been ignored in the construction process, and most of the constructed abstract programs cannot be run directly by machines. In order to solve these problems, a novel program construction method for the sequence statistical class algorithms based on bidirectional scan induction is proposed in this paper. The method takes into account the efficiency factor and thus improves the Morgan's refinement calculus. Furthermore, this paper validates the method's feasibility using an efficiency-sensitive sequential statistics class algorithm as a program construction example. The method proposed in this paper realizes the correctness construction process from program specifications to efficient executable programs.

On the weak convergence and the uniform-in-bandwidth consistency of the general conditional $U$-processes based on the copula representation: multivariate setting

$U$-statistics represent a fundamental class of statistics from modeling quantities of interest defined by multi-subject responses. $U$-statistics generalise the empirical mean of a random variable $X$ to sums over every $m$-tuple of distinct observations of $X$. Stute [Conditional U -statistics, Ann. Probab., 1991] introduced a class of estimators called conditional $U$-statistics. In the present work, we provide a new class of estimators of conditional $U$-statistics. More precisely, we investigate the conditional $U$-statistics based on copula representation. We establish the uniform-in-bandwidth consistency for the proposed estimator. In addition, uniform consistency is also established over $\varphi \in \mathscr{F}$ for a suitably restricted class $\mathscr{F}$, in both cases bounded and unbounded, satisfying some moment conditions. Our theorems allow data-driven local bandwidths for these statistics. Moreover, in the same context, we show the uniform bandwidth consistency for the nonparametric Inverse Probability of Censoring Weighted estimators of the regression function under random censorship, which is of its own interest. We also consider the weak convergence of the conditional $U$-statistics processes. We discuss the wild bootstrap of the conditional $U$-statistics processes. These results are proved under some standard structural conditions on the Vapnik-Chervonenkis class of functions and some mild conditions on the model.

In Pursuit of Campus-Wide Data Literacy: A Guide to Developing a Statistics Course for Students in Nonquantitative Fields

Data literacy for students in nonquantitative fields is important as statistics become the grammar of research and how the world’s decisions are made. Statistics courses are typically offered by mathematics or statistics departments or by social and natural sciences such as economics, political science, psychology, and biology. Here we discuss how to construct a statistics course for students in nonquantitative fields, with a goal of integrating statistical material with students’ substantive interests, using student-focused teaching methods and technology to increase student involvement. We demonstrate this kind of hybrid course with the example of an introductory applied statistics class, taught at both the University of Toronto’s Anne Tanenbaum Center for Jewish Studies and the United States Naval Academy.

Development of an Integrated Statistics E-Module with Flipbook and Augmented Reality

Numeration is an important aspect of learning mathematics. Numeration is the ability to apply mathematical symbols to solve everyday problems. The importance of numeration contradicts the conditions in the field, which show that students in the statistics class have not been able to solve problems related to numeracy properly due to a lack of multi-representational skills. This truth is evident from the opening observations made in statistics class revealed that, out of 37 pupils, only 12 were successful in converting verbal and graphic representations into symbolic ones to solve statistical issues correctly. In the meantime, 17 out of 25 students failed because they did not comprehend the issues represented graphically. The SPSS practice video barcode and software of studio.essemblrword.com has been used in statistical module development research to find a solution to this issue. All of these programs are integrated into e-modules, which are packaged in flipbook form. Define, design, develop, and disseminate steps of the 4-D model are used in the development process. In this study, a questionnaire was employed as a data gathering tool. Both qualitative and quantitative data were collected. The findings demonstrated that the produced module met the extremely feasible criteria for content feasibility (85.78%), linguistic feasibility (88.61%), presentation feasibility (84.82%), and visual feasibility (84.72%). Keywords: Statistic E-Module, Multiple Representation, Augmented Reality

Flexible nonlinear inference and change-point testing of high-dimensional spectral density matrices

This paper studies a flexible approach to analyze high-dimensional nonlinear time series of unconstrained dimension based on linear statistics calculated from spectral average statistics of bilinear forms and nonlinear transformations of lag-window (i.e. band-regularized) spectral density matrix estimators. That class of statistics includes, among others, smoothed periodograms, nonlinear statistics such as coherency, long-run-variance estimators and contrast statistics related to factorial effects as special cases. Especially, we introduce the class of nonlinear spectral averages of the spectral density matrix. Having in mind big data settings, we study a sampling design which includes a sparse sampling scheme. Gaussian approximations with optimal rate are derived for nonlinear time series of growing dimension for these frequency domain statistics and the underlying lag-window (cross-) spectral estimator under non-stationarity. For change-testing (self-standardized) CUSUM statistics are examined. Further, a specific wild bootstrap procedure is proposed to estimate critical values. Simulation studies and an application to SP500 financial returns are provided in a supplement to this paper.

Modern Teaching Methods in Action in Statistics Classes in West Bengal

The overall research study has focused on the current teaching methods in the statistics domain in the Indian state of West Bengal. Different teaching styles have been evaluated in this study along with existing gaps in the current teaching method. It has been observed that traditional teaching method is still practiced by teachers and professors in WB. However, the participants accepted that “project-based learning” can be more effective in terms of technical skill development. In addition, teachers should move forward from lecture-based classes to active learning techniques that can optimise students' engagement and the standard of learning. In this study, it has been founded that the usage of modern teaching approaches primarily leads to knowledge-based application that depends on both students and educators so that their time can be utilized effectively.

3 in 1 Effect When Using Adventure Based Learning Approach in Basic Statistics Class

3 in 1 Effect When Using Adventure Based Learning Approach in Basic Statistics Class

Assessing Landslide Susceptibility along India’s National Highway 58: A Comprehensive Approach Integrating Remote Sensing, GIS, and Logistic Regression Analysis

The NH 58 area in India has been experiencing an increase in landslide occurrences, posing significant threats to local communities, infrastructure, and the environment. The growing need to identify areas prone to landslides for effective disaster risk management, land use planning, and infrastructure development has led to the increased adoption of advanced geospatial technologies and statistical methods. In this context, this research article presents an in-depth analysis aimed at developing a landslide susceptibility zonation (LSZ) map for the NH 58 area using remote sensing, GIS, and logistic regression analysis. The study incorporates multiple geo-environmental factors for analysis, such as slope aspect, curvature, drainage density, elevation, fault distance, flow accumulation, geology, geomorphology, land use land cover (LULC), road distance, and slope angle. Utilizing 50% of the landslide inventory data, the logistic regression model was trained to determine correlations between causal factors and landslide occurrences. The logistic regression model was then employed to calculate landslide probabilities for each mapping unit within the NH 58 area, which were subsequently classified into relative susceptibility zones using a statistical class break technique. The model’s accuracy was verified through ROC curve analysis, resulting in a 92% accuracy rate. The LSZ map highlights areas near road cut slopes as highly susceptible to landslides, providing crucial information for land use planning and management to reduce landslide risk in the NH 58 area. The study’s findings are beneficial for policymakers, planners, and other stakeholders involved in regional disaster risk management. This research offers a comprehensive analysis of landslide-influencing factors in the NH 58 area and introduces an LSZ map as a valuable tool for managing and mitigating landslide risks. The map also serves as a critical reference for future research and contributes to the broader understanding of landslide susceptibility in the region.

The framework of parametric and nonparametric operational data analytics

This paper introduces the general philosophy of the Operational Data Analytics (ODA) framework for data‐based decision modeling. The fundamental development of this framework lies in establishing the direct mapping from data to decision by identifying the appropriate class of operational statistics. The efficient decision making relies on a careful balance between data integration and decision validation. Through a canonical decision making problem under uncertainty, we show that the existing approaches (including statistical estimation and then optimization, retrospective optimization, sample average approximation, regularization, robust optimization, and robust satisficing) can all be unified through the lens of the ODA formulation. To make the key concepts accessible, we demonstrate, using a simple running example, how some of the existing approaches may become equivalent under the ODA framework, and how the ODA solution can improve the decision efficiency, especially in the small sample regime.

Weighted mean difference statistics for paired data in the presence of missing values.

Missing data is a common issue in many biomedical studies. Under a paired design, some subjects may have missing values in either one or both of the conditions due to loss of follow-up, insufficient biological samples, etc. Such partially paired data complicate statistical comparison of the distribution of the variable of interest between the two conditions. In this article, we propose a general class of test statistics based on the difference in weighted sample means without imposing any distributional or model assumption. An optimal weight is derived from this class of tests. Simulation studies show that our proposed test with the optimal weight performs well and outperforms existing methods in practical situations. Two cancer biomarker studies are provided for illustration.

Stationary Jackknife

Variance estimation is an important aspect in statistical inference, especially in the dependent data situations. Resampling methods are ideal for solving this problem since these do not require restrictive distributional assumptions. In this paper, we develop a novel resampling method in the Jackknife family called the stationary jackknife. It can be used to estimate the variance of a statistic in the cases where observations are from a general stationary sequence. Unlike the moving block jackknife, the stationary jackknife computes the jackknife replication by deleting a variable length block and the length has a truncated geometric distribution. Under appropriate assumptions, we can show the stationary jackknife variance estimator is a consistent estimator for the case of the sample mean and, more generally, for a class of nonlinear statistics. Further, the stationary jackknife is shown to provide reasonable variance estimation for a wider range of expected block lengths when compared with the moving block jackknife by simulation.

The impact of anisotropic redshift distributions on angular clustering

A leading way to constrain physical theories from cosmological observations is to test their predictions for the angular clustering statistics of matter tracers, a technique that is set to become ever more central with the next generation of large imaging surveys. Interpretation of this clustering requires knowledge of the projection kernel, or the redshift distribution of the sources, and the typical assumption is an isotropic redshift distribution for the objects. However, variations in the kernel are expected across the survey footprint due to photometric variations and residual observational systematic effects. We develop the formalism for anisotropic projection and present several limiting cases that elucidate the key aspects. We quantify the impact of anisotropies in the redshift distribution on a general class of angular two-point statistics. In particular, we identify a mode-coupling effect that can add power to auto-correlations, including galaxy clustering and cosmic shear, and remove it from certain cross-correlations. If the projection anisotropy is primarily at large scales, the mode-coupling depends upon its variance as a function of redshift; furthermore, it is often of similar shape to the signal. In contrast, the cross-correlation of a field whose selection function is anisotropic with another one featuring no such variations — such as CMB lensing — is immune to these effects. We discuss explicitly several special cases of the general formalism including galaxy clustering, galaxy-galaxy lensing, cosmic shear and cross-correlations with CMB lensing, and publicly release a code to compute the biases.

Reducing statistics anxiety and academic procrastination among Israeli students: A pilot program

AbstractMany college students consider statistical courses as frightening and demanding, yielding high anxiety and low competence, and correlating with maladaptive academic behaviors and low achievement. With undergraduate students, the present pre‐post study compared a supportive online teaching program utilizing mandatory statistical exercises (n = 37) with a no intervention, optional exercise statistics class (n = 32). We evaluated whether our statistics teaching intervention decreased test anxiety and academic procrastination and increased academic self‐efficacy and academic achievements. Results indicated a decrease in academic procrastination and test anxiety at course end for intervention group and an increase in test anxiety for control group. At the end of the course intervention group reported higher academic self‐efficacy and achievements. Teaching statistics using mandatory supportive activities might contribute to more positive psychological outcomes (eg, higher academic self‐efficacy and lower academic procrastination) and higher academic achievements.

How Fun Overcame Fear: The Gamification of a Graduate-Level Statistics Course

Innovative instructional methods can help improve student engagement and learning outcomes when teaching difficult subjects, such as statistics. This instructional innovation article illustrates how gamification can be applied in management education to improve students’ learning experience, engagement, and acquisition of knowledge. Our purpose is to demonstrate how gamification is not only a powerful way to build on the use of games and game thinking in our field, but also a versatile application of education technology that could potentially enhance the way management knowledge is taught. Furthermore, it is a low-risk way for management educators to join and contribute to the larger virtual revolution. We document the process of combining the Technology, Pedagogy, and Content Knowledge (TPACK) competency framework and the Mechanics, Dynamics, and Aesthetics (MDA) design framework to create both theoretically and practically motivated gamification designs in a graduate-level statistics class. With student data and feedback, we demonstrate that gamification helped create a positive learning experience, facilitated interactions in the course, and assisted the learning of statistical knowledge. We offer suggestions and concrete examples for interested educators to implement gamification in their courses.

Dragons and data

Abstract How do you convince the maths-anxious that statistics can be fun? Sarah R. Christofides shows how she uses simulated data to fire up her introductory statistics classes