Basic Concepts Of Probability Research Articles

Informed consent-patients' understanding of risk.

The central concept of informed consent is communication of the chance of a successful outcome. The risks and benefits are probabilistic concepts derived from populations; they do not map with any certainty to the individual. We tested patients' comprehension of basic probability concepts that are needed for informed consent. Patients (n=478) completed five questions designed to test risk estimates that are relevant to informed consent. The questions posed non-medical scenarios to avoid patients associating them with their clinical care. The questionnaire was in English and was only offered to patients whose nurse felt that they had sufficient English literacy to understand the questions. Out of a possible total of five correct answers, Asian patients scored lowest, and significantly less than Pākehā/Europeans (average total score 2.6±1.7 vs 3.6±1.4, p<0.001, 95% confidence interval 0.5 to 1.38). The total score for Māori/Pasifika was intermediate (3.2±1.4), yet they had the lowest deprivation index. This discordant finding may be due to poorer English literacy among Asian participants. On multiple linear regression, Asian ethnicity and advancing age were the independent predictors of a low score. Socio-economic deprivation decile and sex were not. When answering questions constructed according to best practice, many (but not all) patients have reasonable risk comprehension. Further improvement could target older patients, those of Asian ethnicity and probably all patients where English is a second language. Liberal use of interpreters is suggested.

Patient Understanding of Risk: A Survey of Probability Literacy

The central concept of informed consent is communication of the chance of a successful outcome. It is not easy or intuitive to map a population-derived risk estimate to an individual. We tested patient comprehension of basic probability concepts needed for informed consent. Patients (n=478) completed five questions testing risk estimates relevant to informed consent. To avoid patients associating them with their clinical care, the questions posed non-medical scenarios. Correct answers varied from 36% for Q3 to 83% for Q5. A total of 64% of patients could not say that 1:10 is a higher frequency than 1:100 or 1:1,000. Age and ethnicity were independent predictors of overall score, whereas sex and socioeconomic decile were not. Māori/Pasifika scored significantly worse than Pakeha/European (total score 3.2 vs 3.6, p<0.001). Asian patients scored worse than Māori/Pasifika (2.6 vs 3.2, p<0.001) even though Asian patients’ socioeconomic decile was the highest of all groups; this may have been a language issue. Many patients do not sufficiently grasp risk to understand informed consent. Increased comprehension may be achieved by a combination of written documents, unhurried verbal explanations, with time for questions. Risk presented as “two in a 1,000 chance of a serious complication” may be better comprehended if spelt out fully to patients as “out of every 1,000 patients undergoing this procedure, around two may experience a serious complication”. Communication should be culturally appropriate; and, in a language preferred by the patient.

DEVELOPMENT AND EVALUATION OF A PROFESSIONAL DEVELOPMENT PROGRAM ON DESIGNING PARTICIPATORY ACTION RESEARCH PROJECTS FOR BASIC EDUCATION TEACHERS

Anchored on Evans’ professional development (PD) model, this study aimed to develop, implement, and evaluate a professional development program on designing participatory action research (PAR) projects for basic education teachers. The teachers are from Junior and Senior High School teaching English, Mathematics, and Science. The PD program consisted of ten in-person training sessions and virtual consultations which happened in between training on AR problem conceptualization and methodology for a 14-week period. Using the mixed-methods sequential explanatory (QUAN à qual) design, the study started with a professional needs assessment participated by 18 teachers from a secondary school as a basis for the planned PD program. The teachers underwent training sessions to develop a group or participatory AR proposal as evidence of their professional growth and program outcome. At the end of the program, the English, Mathematics, and Science teachers, respectively, developed and presented their AR proposals on the (a) design and evaluation of a gamified-based instruction towards improving vocabulary skill, (b) video-based instruction in teaching basic concepts of probability, and (c) investigating the effect of contextualized learning materials in developing students’ conceptual understanding of atoms. The post-assessment results, supported by interviews, revealed that the teachers displayed behavioural, attitudinal, and intellectual developments in AR. Based on the Department of Education’s criteria for evaluating PAR proposals, all three proposals were rated acceptable for implementation by a panel of evaluators. In conclusion, the PD design and evaluation framework were important factors that enabled the participating teachers to transform their AR competencies toward developing PAR proposals for improving teaching and research in their schools.

ANALYSIS OF SOCIO-ECONOMIC SYSTEMS USING QUANTUM-LIKE MATHEMATICAL MODELS BASED ON STATUS FUNCTIONS. PART I

The basic concepts of classical probability, negative probability, fuzzy sets are considered with appropriate analogies of the quantum mechanical approach to create mathematical models for describing social phenomena. It also briefly describes the features of the application of the theory of intentionality, which uses the concept of institutionality for social phenomena. At the same time, institutionality is understood as a property of consciousness directed at objects and states of affairs in the real world. The concept of collective institutionality is singled out, which forms social facts arising from the collective impact of members of society. The concept of status is given, which denotes a set of characteristic values of a subject or object that determine its position in the system. The features and scope for fuzzy models are described, which are used for the mathematical description of linguistic terms and intentionality in estimating the probabilities of events in fuzzy set theory. In addition, the concept of negative probability and the possibility of using it to describe social events are described. The following is an example illustrating the concept of a complex-valued function and its use to measure the characteristics of socio-economic processes. In conclusion, the concept of status functions is introduced for comparison with membership functions and wave functions.

Age declines in numeracy: An analysis of longitudinal data.

Numeracy, the ability to understand and use basic probability and numerical concepts, is associated with diverse positive outcomes across the lifespan. Prior cross-sectional research on numeracy has generally found a negative association with age, but positive correlations with male gender, education attainment, and measures of fluid and crystallized intelligence have been more robust. Age effects on cognitive functioning are well established, but little is known about longitudinal trends of numeracy into older age. The present study investigates longitudinal age effects on numeracy using a sample of 524 adults (2008 Agerange = 20-78) from the RAND American Life Panel. Participants completed a numeracy measure in both 2008 and 2019, a span of 11 years. Using a linear mixed-effect model to predict numeracy scores, a significant interaction between the year of testing and the quadric age term shows a decline in numeracy scores beginning in later middle age, a trend that falls in between those previously found for crystallized and fluid cognitive abilities. Numeracy declines are somewhat mitigated for males and those with higher education, but the interaction of the two variables did not return a clear pattern of results. Prior research has shown that numeracy is positively related to the quality of health and financial decisions and, ultimately, more positive health and economic outcomes. The implications of age declines in numeracy are discussed in relation to health and financial decision-making, tasks that remain relevant into old age. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

An Application of Quantum Logic to Experimental Behavioral Science

In 1933, Kolmogorov synthesized the basic concepts of probability that were in general use at the time into concepts and deductions from a simple set of axioms that said probability was a σ-additive function from a boolean algebra of events into [0, 1]. In 1932, von Neumann realized that the use of probability in quantum mechanics required a different concept that he formulated as a σ-additive function from the closed subspaces of a Hilbert space onto [0,1]. In 1935, Birkhoff &amp; von Neumann replaced Hilbert space with an algebraic generalization. Today, a slight modification of the Birkhoff-von Neumann generalization is called “quantum logic”. A central problem in the philosophy of probability is the justification of the definition of probability used in a given application. This is usually done by arguing for the rationality of that approach to the situation under consideration. A version of the Dutch book argument given by de Finetti in 1972 is often used to justify the Kolmogorov theory, especially in scientific applications. As von Neumann in 1955 noted, and his criticisms still hold, there is no acceptable foundation for quantum logic. While it is not argued here that a rational approach has been carried out for quantum physics, it is argued that (1) for many important situations found in behavioral science that quantum probability theory is a reasonable choice, and (2) that it has an arguably rational foundation to certain areas of behavioral science, for example, the behavioral paradigm of Between Subjects experiments.

Venn diagrams and probability in clinical research

Statistics is the science dealing with the collecting, summarizing and interpreting of associations in research data, and has a leading role in medical research. This article is an introductory publication in a series devoted to biomedical statistics. The aim of this article is to acquaint the readers with the basic concepts of Venn diagrams, probability and set theory, which are required to further understand descriptive and inferential statistics. First, we discuss the applications of Venn diagrams in current clinical research. Then we discuss the definitions of sample space, events, basic set operations (union and intersection) and their implementation in the classical approach to probability theory. All examples are introduced with Venn diagrams to illustrate the cases.

The `Quantum Game Show': a very simple explanation of Bell's Theorem in Quantum Mechanics

In this article give a very simple presentation of Bell's inequality by comparing it to a 'quantum game show', followed by a simple description of Aspect's 1985 experiment involving entangled photons which confirms the inequality. The entire article is non-technical and requires no mathematical background other than high school mathematics and an understanding of basic concepts in probability. The physics involved in Aspect's experiment is also explained.

Optimal Power Dispatch and Reliability Analysis of Hybrid CHP-PV-Wind Systems in Farming Applications

Renewable energy sources (RES) are seen as potential alternative energy sources for rural communities to meet energy demand where electricity supply is inaccessible. Wind and Photo-Voltaic (PV) power is seen as mature and sustainable alternatives for rural electrification. This paper discusses the optimal power dispatch for hybrid combined heat and power (CHP), wind, PV and battery systems with a view to determining the operation of the hybrid system for farming applications. This is accomplished by considering the basic power system probability concepts to assess the performance of the reliability indices. The proposed mathematical model seeks to minimize the system operation costs from CHP. The developed model was validated on five case studies with the same load profile, solar radiation, wind speed and CHP generating unit parameters and solved using a CPLEX solver embedded in Algebraic Modelling Language. The sensitivity analysis performed indicates that the hybrid system achieved a higher reliability as compared to other case studies. The result shows 48% of energy cost reduction is achievable when considering the proposed hybrid CHP, wind, PV and battery system as compared to energy supply via CHP.

Playing Settlers of Catan Enhances Student Learning of Probability in Liberal Arts Mathematics

ABSTRACT Playing board games is known to improve pre-school student numeracy and many board games are used to motivate and explore concepts in probability. This study investigates whether college students in liberal arts mathematics courses assigned to play the board game Settlers of Catan develop a stronger grasp of basic probability concepts than those assigned more traditional homework problems via an analysis of pre- and post-assessments and final exam questions.

Using Stochastic Approaches for Teaching Mass Transfer Unit Operations: The Monte Carlo Method

Mass transfer separations are of extreme importance to professionals working in the chemical industry. For this reason, chemical engineering and industrial chemistry students are both taught these unit operations at the final years of their study programs. The traditional way of carrying out their design is based on the use of deterministic models, most often involving ordinary differential equations. However, the macroscopic result of many existing chemical processes is due to the effect of statistical molecular motion. Hence, the use of stochastic or random approaches enables the issue to be addressed with just basic probability concepts aided by computer software. Based on these ideas, this article explores the implementation of Monte Carlo simulations for addressing two case studies related to mass transfer processes (batch distillation and gas membrane separation) and presents a comparative evaluation with respect to traditional deterministic methods. The easiness and accuracy of the method allow the conclusion that Monte Carlo simulations may facilitate understanding and add another dimension to students’ computational skills without detriment to the result’s quality. The case studies presented may also enrich the instructors’ educational competence, providing them with an alternative view of the matter.

Investigating Preservice Middle School Mathematics Teachers’ Competencies in Statistics and Probability in Terms of Various Variables

In this study, probabilities of preservice middle school mathematics teachers’ possession of four fundamental cognitive skills required for learning and teaching statistics and probability topics were examined by using the log-linear cognitive diagnostic model, which is one of the cognitive diagnostic models. Moreover, the probabilities of preservice teachers’ possession of these skills were investigated according to gender, university ranking, and grade level variables. Hence, it was examined whether there was a significant relationship between the probabilities of having each skill and these variables. A Statistical Reasoning Test, which was developed by Arican and Kuzu in 2019, measured preservice teachers’ possession of four critical skills was used in collecting the data. These four skills included representing and interpreting data, drawing inferences about populations based on samples, selecting and using appropriate statistical methods to analyze data, and understanding and applying basic concepts of probability. In the 2016-2017 academic year, the test was applied to 456 preservice teachers selected from four different universities in Turkey, and probabilities of their possession of each attribute were calculated. Later, the relationship between the preservice teachers’ test scores and gender was examined by using the Mann-Whitney U test, and the relationship between their test scores and ranking of the attended university and grade level were examined using the Kruskal Wallis-H test. Although probabilities of the preservice teachers’ possession of these four skills did not significantly differ according to gender, some significant differences were detected for university ranking and grade level variables.

The earliest teaching and learning of probability in Singapore, the US, and Indonesia from the perspectives of textbooks analysis

This study analyzed how the earliest teaching and learning of probability was organized in Singapore, the US, and Indonesia through an analysis of textbook as an intended mathematics curriculum. An analytical framework was developed comprising four perspectives: representational forms, cognitive demand levels, contextual features, and organization of topics and its uniqueness. This study disclosed that the organization of the earliest teaching and learning of probability in the three countries focused on approximately similar topics, such as basic concepts of probability and probability measurements, although they were intended for different educational levels. Nevertheless, the uniqueness of the organization indicated that students in the three countries may receive different opportunity-to-learn in the earliest teaching and learning of probability in schools. In addition, Singaporean textbook had more exposure to higher-cognitive demand levels and written forms, while the US textbook put more concerns on lower-level demands and visual forms, Indonesian textbook included more proportions of lower- cognitive demand levels and written forms. Moreover, the three textbooks provided considerable opportunity to engage in real-life situations. Considering these results, more studies analyzing other standards-based textbooks and teaching practices might be needed to have further understanding of the organization of probability teaching and learning in schools.

Developing an Optimal Strategy for a Maximization Dice Game

Many dice games have been used to illustrate basic probability concepts in college mathematics and statistics classrooms (see, for example, [1, 5]). There has been growing interest in developing op...

Diagnosing Preservice Teachers’ Understanding of Statistics and Probability: Developing a Test for Cognitive Assessment

This study investigates preservice middle school mathematics teachers’ understanding of statistics and probability and provides a cognitive diagnostic assessment of their strengths and weaknesses on these subjects. A statistical reasoning test that included 15 multiple-choice and 5 open-ended items was developed from the perspective of the log-linear cognitive diagnosis model, which is a general form of the cognitive diagnosis models. The statistical reasoning test was applied to 456 preservice teachers from 4 universities in 3 different regions of Turkey. The collected data were analyzed using the Mplus 6.12 software, and diagnostic feedback on the preservice teachers’ responses was provided based on the findings. The analysis suggested that although many preservice teachers were able to represent and interpret the given data, most experienced difficulty in drawing inferences about populations based on samples, selecting and using appropriate statistical methods, and understanding and applying the basic concepts of probability. In addition, preservice teachers had difficulty answering open-ended items. Implications for teaching are also discussed.

A Qualitative Research on the Difficulties and Failures about Probability Concepts of High School Students

This research aimed to examine the difficulties and failures of eleventh-grade students regarding probability concepts. With this aim, ten different open-ended probability problems were asked to the 142 eleventh-grade students. Each of these problems requires using different basic probability concepts. It is qualitative research, and the data gathered in this study were analyzed using by descriptive analysis method. The findings indicated that many of these students had difficulties in solving probability problems and failed to apply different probability concepts to these problems. Notably, it was stated that many students had difficulties in finding all the probabilities without any missing in these problems. Besides, it is essential to develop reasoning skills since the students usually used trial-and-error method and prediction to solve probability problems.

Meteorologists’ Interpretations of Storm-Scale Ensemble-Based Forecast Guidance

AbstractDuring the 2017 Spring Forecasting Experiment in NOAA’s Hazardous Weather Testbed, 62 meteorologists completed a survey designed to test their understanding of forecast uncertainty. Survey questions were based on probabilistic forecast guidance provided by the NSSL Experimental Warn-on-Forecast System for ensembles (NEWS-e). A mix of 20 multiple-choice and open-ended questions required participants to explain basic probability and percentile concepts, extract information using graphical representations of uncertainty, and determine what type of weather scenario the graphics depicted. Multiple-choice questions were analyzed using frequency counts, and open-ended questions were analyzed using thematic coding methods. Of the 18 questions that could be scored, 60%–96% of the participants’ responses aligned with the researchers’ intended response. Some of the most challenging questions proved to be those requiring qualitative explanations, such as to explain what the 70th-percentile value of accumulated rainfall represents in an ensemble-based probabilistic forecast. Additionally, participants providing answers not aligning with the intended response oftentimes appeared to consider the given information with a deterministic rather than probabilistic mindset. Applications of a deterministic mindset resulted in tendencies to focus on the worst-case scenario and to modify understanding of probabilistic concepts when presented with different variables. The findings from this survey support the need for improved basic and applied training for the development, interpretation, and use of probabilistic ensemble forecast guidance. Future work should collect data for a larger sample size to examine the knowledge gaps across specific user groups and to guide development of probabilistic forecast training tools.

A New Numerical Method for DNA Sequence Analysis Based on 8-Dimensional Vector Representation

Background: The multiple sequence alignment (MSA) algorithms are the traditional ways to compare and analyze DNA sequences. However, for large DNA sequences, these algorithms require a long time computationally. Objective: Here we will propose a new numerical method to characterize and compare DNA sequences quickly. Method: Based on a new 2-dimensional (2D) graphical representation of DNA sequences, we can obtain an 8-dimensional vector using two basic concepts of probability, the mean and the variance. Results: We perform similarity/dissimilarity analyses among two real DNA data sets, the coding sequences of the first exon of beta-globin gene of 11 species and 31 mammalian mitochondrial genomes, respectively. Conclusion: Our results are in agreement with the existing analyses in our literatures. We also compare our approach with other methods and find that ours is more effective.

Touching beliefs: Using touchscreen technology to elicit subjective expectations in survey research.

When making decisions under uncertainty, individuals may form subjective expectations about probabilities of events relevant for their choice. Accurate measurement of subjective expectations is critical for high-quality data needed to analyze individual behavior. This paper reports the development and validity of a new method of eliciting point subjective expectations in developing countries. We developed a touchscreen-based application that combines an animated slider along with dynamic images that change relative sizes based on the probability indicated by the respondent. We compare our method to the more traditional approach of using beans as visual aids. First, we find that respondents have a sound understanding of basic concepts of probability. Second, we test for equality of the distributions elicited with the different methods and find them highly comparable. Third, we provide evidence that respondents report a more favorable opinion about the slider method and more willingness to complete long surveys using the slider rather than beans. Our findings suggest that the slider could be a viable elicitation method for empirical researchers who aim to collect data on subjective expectations in developing countries.

Probabilistic Based Reliability Assessment Concepts for Composite Power Systems

The ability of a power system to maintain sufficient supply of electricity at all operating condition reflects its reliability. It is a measure of the systems or components adequacy and security in achieving its role at all times. This work presents system adequacy with respect to reliability following discussions on the basic probability concepts relevant for the reliability assessment of a functional composite power system (hierarchical level II). The concept has been illustrated with a simple composite system of three components; generator, transformer and transmission line. Proceeding on the assumption that components exist in one of the two-state model and not in multi-states, the steady state transition diagram was developed in order to identify system states and the transition rates between states on account of the failure or restoration of a system component. With system states and interstate transition rates identified, state and event probabilities determined, reliability indices that describes the adequacy of such composite systems can be evaluated.