Although we use statistical notions daily in making decisions, research in statistics education has focused mostly on formal statistics. Further, everyday culture may influence informal ideas of statistics. Yet, there appears to be minimal literature that deals with the educational implications of the role of culture. This paper will discuss the interaction between statistical cognition and culture, reporting on the effects of culture on secondary students’ statistical ideas. It will draw on examples from my work and that of a few others who have studied cultural influences on statistical ideas to explain how statistics is tied to cultural practices. The paper will consider the issues arising out of the literature and offer suggestions for meeting the challenges

Background: Sampling is a crucial step in health research that directly affects internal and external validity. Selecting the appropriate sampling technique minimizes bias and enhances population representativeness. Objective: To review the concepts, types, strengths, limitations, and applications of probability and non-probability sampling techniques in health research. Discussion: Probability sampling, such as simple random, systematic, stratified, cluster, and multistage, provides equal selection chances for all population members, enabling precise parameter estimation and robust inferential statistical analysis. It is ideal for national disease prevalence surveys, population-based program evaluations, or large-scale clinical trials. Non-probability sampling, including convenience, purposive, quota, and snowball, is faster, cost-effective, and useful for accessing hidden populations, such as marginalized groups or individuals with sensitive health conditions, although it limits result generalizability. Method selection should consider research objectives, population characteristics, available resources, ethics, and the type of data required. In certain contexts, combining both approaches can leverage quantitative rigor with qualitative depth. Conclusion: No single sampling technique is universally superior. Probability sampling is best suited for large-scale quantitative studies or when precise population estimates are required. Non-probability sampling is appropriate for exploratory studies, hard-to-reach populations, or when resources are limited. Combining both approaches can yield qualitatively rich yet quantitatively valid data, strengthening the evidence base for decision-making in health research.

Through hypothesis testing, it is possible to evaluate whether sample data collected based on a circumstance or scenario is statistical significance and can help enhance decision-making processes on such circumstance or scenario. To undertake hypothesis testing, statistics measures and examines random population samples using a variety of statistical tests before establishing values that are compared with test statistics and levels of significance to establish whether they are statistically significant. Both null and alternative hypotheses will be developed based on the provided set of SPSS data related to various aspects of employees’ work environment and a Pearson’s correlation, independent samples t-test and ANOVA will be calculated using SPSS software to determine whether the null hypothesis should be accepted or rejected.

This study analyzes the role of statistical significance testing (SST) in education. Although the basic logic underlying SST 一 a hypothesis is rejected because the observed data would be very unlikely if the hypothesis is true 一 appears so obvious that many people are tempted to accept it, it is in fact fallacious. In the light of its historical background and conceptual development, discussed in Chapter 2, the Fisher’s significance testing, Neyman-Pearson hypothesis testing and their hybrids are clearly distinguished. We argue that the probability of obtaining the observed or more extreme outcomes (p value) can hardly act as a measure of the strength of evidence against the null hypothesis. After discussing the five major interpretations of probability, we conclude that if we do not accept the subjective theory of probability, talking about the probability of a hypothesis that is not the outcome of a chance process is unintelligible. But the subjective theory itself has many intractable difficulties that can hardly be resolved. If we insist on assigning a probability value to a hypothesis in the same way as we assign one to a chance event, we have to accept that it is the hypothesis with low probability, rather than high probability, that we should aim at when conducting scientific research. More important, the inferences behind SST are shown to be fallacious from three different perspectives. The attempt to invoke the likelihood ratio with the observed or more extreme data instead of the probability of a hypothesis in defending the use of р value as a measure of the strength of evidence against the null hypothesis is also shown to be misleading because it can be demonstrated that the use of tail region to represent a result that is actually on the border would overstate the evidence against the ทน11 hypothesis.Although Neyman-Pearson hypothesis testing does not involve the concept of the probability of a hypothesis, it does have some other serious problems that can hardly be resolved. We show that it cannot address researchers' genuine concerns. By explaining why the level of significance must be specified or fixed prior to the analysis of data and why a blurring of the distinction between the р value and the significance level would lead to undesirable consequences, we conclude that the Neyman-Pearson hypothesis testing cannot provide an effective means for rejecting false hypotheses. After a thorough discussion of common misconceptions associated with SST and the major arguments for and against SST, we conclude that SST has insurmountable problems that could misguide the research paradigm although some other criticisms on SST are not really as justified. We also analyze various proposed alternatives to SST and conclude that confidence intervals (CIs) are no better than SST for the purpose of testing hypotheses and it is unreasonable to expect the existence of a statistical test that could provide researchers with algorithms or rigid rules by conforming to which all problems about testing hypotheses could be solved. Finally, we argue that falsificationism could eschew the disadvantages of SST and other similar statistical inductive inferences and we discuss how it could bring education research into a more fruitful situation in which to their practices. Although we pay special attention to mathematics education, the core of the discussion in the thesis might apply equally to other educational contexts

Analysis of non-probability survey samples requires auxiliary information at the population level. Such information may also be obtained from an existing probability survey sample from the same finite population. Mass imputation has been used in practice for combining non-probability and probability survey samples and making inferences on the parameters of interest using the information collected only in the non-probability sample for the study variables. Under the assumption that the conditional mean function from the non-probability sample can be transported to the probability sample, we establish the consistency of the mass imputation estimator and derive its asymptotic variance formula. Variance estimators are developed using either linearization or bootstrap. Finite sample performances of the mass imputation estimator are investigated through simulation studies. We also address important practical issues of the method through the analysis of a real-world non-probability survey sample collected by the Pew Research Centre.US National Science Foundation, Grant/Award Number: 1733572This article is published as Jae Kwang Kim, Seho Park, Yilin Chen, Changbao Wu, Combining Non-Probability and Probability Survey Samples Through Mass Imputation, Journal of the Royal Statistical Society Series A: Statistics in Society, Volume 184, Issue 3, July 2021, Pages 941–963, https://doi.org/10.1111/rssa.1269

The survival of humanity is dependent on the survival of forests and the ecosystems they support, yet annually wildfires destroy millions of hectares of global forestry. Wildfires take place under specific conditions and in certain regions, which can be studied through appropriate techniques. A variety of statistical modeling methods have been assessed by researchers; however, ensemble modeling of wildfire susceptibility has not been undertaken. We hypothesize that ensemble modeling of wildfire susceptibility is better than a single modeling technique. This study models the occurrence of wildfire in the Brisbane Catchment of Australia, which is an annual event, using the index of entropy (IoE), evidential belief function (EBF), and logistic regression (LR) ensemble techniques. As a secondary goal of this research, the spatial distribution of the wildfire risk from different aspects such as urbanization and ecosystem was evaluated. The highest accuracy (88.51%) was achieved using the ensemble EBF and LR model. The outcomes of this study may be helpful to particular groups such as planners to avoid susceptible and risky regions in their planning; model builders to replace the traditional individual methods with ensemble algorithms; and geospatial users to enhance their knowledge of geographic information system (GIS) applications.

After a brief review of ontic and epistemic descriptions, and of subjective, logical and statistical interpretations of probability, we summarize the traditional axiomatization of calculus of probability in terms of Boolean algebras and its set-theoretical realization in terms of Kolmogorov probability spaces. Since the axioms of mathematical probability theory say nothing about the conceptual meaning of randomness one considers probability as property of the generating conditions of a process so that one can relate randomness with predictability (or retrodictability). In the measure-theoretical codification of stochastic processes genuine chance processes can be defined rigorously as so-called regular processes which do not allow a long-term prediction. We stress that stochastic processes are equivalence classes of individual point functions so that they do not refer to individual processes but only to an ensemble of statistically equivalent individual processes. Less popular but conceptually more important than statistical descriptions are individual descriptions which refer to individual chaotic processes. First, we review the individual description based on the generalized harmonic analysis by Norbert Wiener. It allows the definition of individual purely chaotic processes which can be interpreted as trajectories of regular statistical stochastic processes. Another individual description refers to algorithmic procedures which connect the intrinsic randomness of a finite sequence with the complexity of the shortest program necessary to produce the sequence. Finally, we ask why there can be laws of chance. We argue that random events fulfill the laws of chance if and only if they can be reduced to (possibly hidden) deterministic events. This mathematical result may elucidate the fact that not all nonpredictable events can be grasped by the methods of mathematical probability theory

There is an ongoing debate in the survey research literature about whether and when probability and nonprobability sample surveys produce accurate estimates of a larger population. Statistical theory provides a justification for confidence in probability sampling as a function of the survey design, whereas inferences based on nonprobability sampling are entirely dependent on models for validity. This article reviews the current debate about probability and nonprobability sample surveys. We describe the conditions under which nonprobability sample surveys may provide accurate results in theory and discuss empirical evidence on which types of samples produce the highest accuracy in practice. From these theoretical and empirical considerations, we derive best-practice recommendations and outline paths for future research.

A statistical experiment with a filtered probability space is called a filtered experiment. The paper introduces a concept of deficiency for filtered decision problems of one filtered experiment with respect to another. The main theorem is a natural extension of Le Cam (1964, Thm. 3) and establishes a connection between the notion of 'deficiency' and several criteria for comparison of risks. The concept of deficiency developed here is relevant practical purposes of stochastic processes which depend on unknown parameters. The main result applies to statistical problems, like for instance, certain types of stochastic control problems, stopping time problems, and filtering problems

This book has two main aims. The first one (chapters 1-7) is an historically informed review of the philosophy of probability. It describes recent historiography, lays out the distinction between subjective and objective notions, and concludes by applying the historical lessons to the main interpretations of probability. The second aim (chapters 8-13) focuses entirely on objective probability, and advances a number of novel theses regarding its role in scientific practice. A distinction is drawn between traditional attempts to interpret chance, and a novel methodological study of its application. A radical form of pluralism is then introduced, advocating a tripartite distinction between propensities, probabilities and frequencies. Finally, a distinction is drawn between two different applications of chance in statistical modelling which, it is argued, vindicates the overall methodological approach. The ensuing conception of objective probability in practice is the ‘complex nexus of chance’

Simplicity bias is an intriguing phenomenon prevalent in various input-output maps, characterized by a preference for simpler, more regular, or symmetric outputs. Notably, these maps typically feature high-probability outputs with simple patterns, whereas complex patterns are exponentially less probable. This bias has been extensively examined and attributed to principles derived from algorithmic information theory and algorithmic probability. In a significant advancement, it has been demonstrated that the renowned logistic map and other one-dimensional maps exhibit simplicity bias when conceptualized as input-output systems. Building upon this work, our research delves into the manifestations of simplicity bias within the random logistic map, specifically focusing on scenarios involving additive noise. We discover that simplicity bias is observable in the random logistic map for specific ranges of $\mu$ and noise magnitudes. Additionally, we find that this bias persists even with the introduction of small measurement noise, though it diminishes as noise levels increase. Our studies also revisit the phenomenon of noise-induced chaos, particularly when $\mu=3.83$, revealing its characteristics through complexity-probability plots. Intriguingly, we employ the logistic map to illustrate a paradoxical aspect of data analysis: more data adhering to a consistent trend can occasionally lead to \emph{reduced} confidence in extrapolation predictions, challenging conventional wisdom. We propose that adopting a probability-complexity perspective in analyzing dynamical systems could significantly enrich statistical learning theories related to series prediction and analysis. This approach not only facilitates a deeper understanding of simplicity bias and its implications but also paves the way for novel methodologies in forecasting complex systems behavior.

Conditional probability is a key to the subjectivist theory of probability; however, it plays a subsidiary role in the usual conception of probability where its counterpart, namely independence is of basic importance. The paper investigates these concepts from various perspectives in order to shed light on their multi-faceted character. We will include the mathematical, philosophical, and educational perspectives. Furthermore, we will inspect conditional probability from the corners of competing ideas and solving strategies. For the comprehension of conditional probability, a wider approach is urgently needed to overcome the well-known problems in learning the concepts, which seem nearly unaffected by teaching

This study investigates the numerical evolution of an initially internal random wave field characterized by a Gaussian spectrum shape using the Benjamin–Ono (BO) equation. The research focuses on analyzing various properties associated with the random wave field, including the transition to a steady state of the spectra, statistical moments, and the distribution functions of wave amplitudes. Numerical simulations are conducted across different Ursell parameters, revealing intriguing findings. Notably, it is observed that the spectra of the wave field converge to a stationary state in a statistical sense, while exhibiting statistical characteristics that deviate from a Gaussian distribution. Moreover, as the Ursell parameter increases, the positive skewness of the wave field intensifies, and the kurtosis increases. The investigation also involves the computation of the probability of rogue wave formation, revealing deviations from the Rayleigh distribution. Notably, the study uncovers distinct types of internal rogue waves, specifically referred to as the “two sisters” and “three sisters” phenomena.

Decisions about support for predictions of theories in light of data are made using statistical inference. The dominant approach in sport and exercise science is the Neyman-Pearson significance-testing approach. When applied correctly it provides a reliable procedure for making dichotomous decisions for accepting or rejecting zero-effect null hypotheses with known and controlled long-run error rates. Type I and type II error rates must be specified in advance and the latter controlled by conducting an a priori sample size calculation. The Neyman-Pearson approach does not provide the probability of hypotheses or indicate the strength of support for hypotheses in light of data, yet many scientists believe it does. Outcomes of analyses allow conclusions only about the existence of non-zero effects, and provide no information about the likely size of true effects or their practical / clinical value. Bayesian inference can show how much support data provide for different hypotheses, and how personal convictions should be altered in light of data, but the approach is complicated by formulating probability distributions about prior-subjective estimates of population effects. A pragmatic solution is magnitude-based inference, which allows scientists to estimate the true magnitude of population effects and how likely they are to exceed an effect magnitude of practical / clinical importance thereby integrating elements of subjective-Bayesian-style thinking. While this approach is gaining acceptance, progress might be hastened if scientists appreciate the shortcomings of traditional N-P null-hypothesis-significance testing

Current research ideologies in sport science allow for the possibility of investigators producing statistically significant results to help fit the outcome into a predetermined theory. Additionally, under the current Neyman-Pearson statistical structure, some argue that null hypothesis significant testing (NHST) under the frequentist approach is flawed, regardless. For example, a p-value is unable to measure the probability that the studied hypothesis is true, unable to measure the size of an effect or the importance of a result, and unable to provide a good measure of evidence regarding a model or hypothesis. Many of these downfalls are key questions researchers strive to answer following an investigation. Therefore, a shift towards a magnitude-based inference model, and eventually a fully Bayesian framework, is thought to be a better fit from a statistical standpoint and may be an improved way to address biases within the literature. The goal of this article is to shed light on the current research and statistical shortcomings the field of sport science faces today, and offer potential solutions to help guide future research practices.

Modern classrooms have access to a range of potential technologies, ranging from calculators to computers to the Internet. This paper explores some of the potential for such technologies to affect the curriculum and teaching of probability in the secondary school and early undergraduate years, rather than relying on the classical and formal approaches focusing on set theory and counting techniques. Different approaches to probability, including the study of risk, are identified. We describe some of the ways in which the teaching of probability might be supported by the availability of various forms of technology, including calculators, computer software and the Internet. We consider especially the role of simulation as a tool for both teachers and students, focusing on activities that are not possible without the use of technology. Modern technology provides an excellent means of exploring many of the concepts associated with probability. Many of these opportunities for learning were not available before the technology development and access within schools we enjoy today. This paper suggests some of the avenues for exploration, research and development and provides advice on where to get further information and resources

Concerns about the importance of variation in statistics education and a lack of research in this topic led to a preliminary study which explored pre-service teachers’ ideas in this area. The teachers completed a written questionnaire about variation in sampling and distribution contexts. Responses were categorised in relation to a framework that identified levels of statistical thinking. The results suggest that while many of the students appeared to acknowledge variation, they were not able to provide adequate explanations. Although the pre-service teachers have had more real-life experiences involving statistics and have been involved in the study of statistical concepts at secondary school level, they still demonstrated the same misconceptions as those of younger students reported in research literature. While more students showed competence on the sampling question, they were less competent on the distribution task. This could be due to task format or contextual issues. The paper concludes by suggesting some implications for further research and teaching