Elementary Statistics Research Articles

Вероятностная модель функционирования автоматизированной системы управления электрооборудованием промышленных предприятий Вьетнама при возникновении аварии

Introduction. Ensuring fire safety of industrial facilities depends on how correctly the automated systems for detecting and extinguishing a fire are selected, how quickly and efficiently the necessary preventive measures are taken to minimize the likelihood of a fire and damage from it. Assessment of the degree of risk of injury to people and damage caused by accidents is associated with the task of predicting the indicators of reliability and residual life of a functioning system. The most important issue is the establishment of the permissible periods for the further operation of residual current devices at a specific value of the risk of an accident. One of the features of industrial facilities is the presence of a large number of electrical equipment that creates the risk of major accidents accompanied by fires and explosions. Timely detection of the pre-fire state of electrical equipment is ensured through the use and development of an automated control system for electrical equipment. Goals and objectives. Assessment of the degree of risk of injury to people and damage to them in case of accidents when predicting reliability indicators in an automated control system for electrical equipment. Methods. To obtain the results, general scientific and special methods of scientific knowledge were used: analysis, synthesis, generalization, which were based on the provisions of the theory of probability, the theory of reliability. Research results. An assessment of the occurrence of an emergency is carried out based on elementary statistics and discrete Poisson distribution. Conclusions. The use of an automated control system for electrical equipment upon detection of leakage currents allows increasing the level of fire safety of industrial enterprises, as well as determining the life cycle of residual current devices during its operation. Keywords: accident, analysis, fire, explosion, risk, statistics, reliability, electrical equipment

中外合作办学中双语课程过程化考核的实践及思考——以《基础统计学》为例

中外合作办学中双语课程过程化考核的实践及思考——以《基础统计学》为例

Using COVID-19 Vaccine Efficacy Data to Teach One-Sample Hypothesis Testing

In late November 2020, there was a flurry of media coverage of two companies’ claims of 95% efficacy rates of newly developed COVID-19 vaccines, but information about the confidence interval was not reported. This paper presents a way of teaching the concept of hypothesis testing and the construction of confidence intervals using numbers announced by the drug makers Pfizer and Moderna publicized by the media. Instead of a two-sample test or more complicated statistical models, we use the elementary one-proportion z-test to analyze the data. The method is designed to be accessible for students who have only taken a one-semester elementary statistics course. We will justify the use of a z-distribution as an approximation for the confidence interval of the efficacy rate. Bayes’s rule will be applied to relate the probability of being in the vaccine group among the volunteers who were infected by COVID-19 to the more consequential probability of being infected by COVID-19 given that the person is vaccinated.

The Mathematics of A Watershed Year

In 2011, Sonoma State University developed a STEM first-year experience (supported by NSF STEP grant 1068445) that combines general education requirements in mathematics, biology, and critical thinking. The mathematics content includes topics from precalculus and elementary statistics, with a particular focus on using functions and modeling with mathematics, and serves as an alternative pathway to calculus. In this article, we share sample activities and student work to describe the philosophy, pedagogy, and mathematics content of the course. We also share pre- and post-survey results of student attitudes towards math, and data on student achievement in subsequent classes and persistence in pursuing STEM degrees. Coming up on its 8th iteration, the course serves 60 incoming freshmen each year and has become an integral part of the School of Science and Technology's recruitment and retention efforts.

Mentoring model based on the levelling of probabilistic thinking to develop problem solving ability

This study aims to describe the probabilistic thinking level of mathematics education students in the topics of sample space, event, and the probability of the event. Many studies have produced different levels of probabilistic thinking, allowing for another new leveling structure of the probabilistic thinking.This study used a qualitative descriptive method involving 112 mathematics education students of Universitas Ahmad Dahlan who took elementary statistics subject in the second semester of 2017/2018 academic year as its subjects. The data analysis was conducted by describing the answers based on the probabilistic thinking leveling indicator.The results of the first stage of this study found a new leveling structure in probabilistic thinking, namely six levels of probabilistic thinking: (1) Level 0 (pre-subjective), with 23 students (20.54%); (2) Level 1 (subjective), with 18 students (16.07%); (3) Level 2 (transition), with 16 students (14.29%); (4) Level 3 (informal quantitative), with 17 students (15.18%); (5) Level 4 (formal quantitative), with 14 students (12.50%); and (6) Level 5 (numerical), with 24 students (21.43%). The second phase of the research will focus on the appropriate mentoring model based on the findings of this first stage research, improve the students’ ability to solve problems, and raise their level of probabilistic thinking to the next levels.

PENINGKATAN DISPOSISI MATEMATIKA MAHASISWA STKIP PESISIR SELATAN PADA MATA KULIAH STATISTIKA DASAR DENGAN PENERAPAN PROBLEM BASED LEARNING

Disposition is a character or personality that is needed for an individual to succeed. Students need a mathematical disposition to persevere in the face of problems, take responsibility in their learning, and develop good work habits in mathematics. However, the mathematical disposition of STKIP Pesisir Selatan students while attending basic statistics lectures is still far from expectations. This is seen from the results of a questionnaire that 56% of students who do not like elementary statistics courses. In addition they lack confidence in solving problems in mathematics. For this reason, a learning model is needed to overcome them. One model that can be used is problem based learning. With learning like this will form the tendency of students to be diligent, conscientious, never give up, see a problem from a variety of different perspectives to get a solution so that when the student successfully resolves a given problem, it will give a sense of pleasure, satisfaction and confidence appears. The purpose of this study is to find out how to increase the mathematical disposition of STKIP Pesisir Selatan students in basic statistics courses before and after learning problem based learning and whether the improvement is significant. All populations were sampled, namely students of mathematics and ICT education courses taking basic statistics courses in the even semester 2018/2019. This type of research is Quasi Exspriment with One Group Pretest-Posttest Design. The research data were obtained from a questionnaire given before and after the experiments were carried out. Data analysis used N-gain test to measure the increase in mathematical disposition and continued by paired sample t test to see the significance of the increase. The results of the analysis show that the increase in mathematical disposition of STKIP Pesisir Selatan students with the application of problem based learning in basic statistical subjects has increased quite well, but the increase that occurred was not significant.

Attitudes toward Using and Teaching Confidence Intervals: A Latent Profile Analysis on Elementary Statistics Instructors

The use of confidence intervals (CIs) for making a statistical inference is gaining popularity in research communities. To evaluate college statistics instructors’ readiness to teach CIs, this study explores their attitudes toward teaching CIs in elementary statistics courses, and toward using CIs in inferential statistics. Data were collected with a survey that classifies instructors’ attitudes on the basis of three previously established pedagogical components: affective, cognitive, and behavioral. Based on the survey responses from 270 participants, we created three profiles (subgroups) via latent profile analysis, and identified each profile’s pattern of attitudes toward CIs and common characteristics of the instructors that fit each profile. In addition, we compared the profiles across groupings created by six variables: gender, academic background, statistics teaching experience, subject preference, degree level, and desire to improve teaching. The results of the latent profile analysis support three profiles within the population of statistics instructors, and the results of the comparative analysis of teacher characteristics indicate that the six variables are moderate to strong predictors of the grouping of the sample into three profiles.

MedEx - Data Analytics for Medical Domain Experts in Real-Time.

Translational research in the medical sector is dependent on clear communication between all participants. Visualization helps to represent data from different sources in a comprehensible way across disciplines. Existing tools for clinical data management are usually monolithic and technically challenging to set up, others require a transformation into specific data models while providing mostly non-interactive visualizations or being specialized to very particular use cases. Statistical programming languages (R, Julia) on the other hand offer great flexibility in data analytics, but are harder to access for clinicians with little to no programming expertise. Our software, the Medical Data Explorer (MedEx), aims to fill this gap as light-weight, intuitive, web-based solution with simple data import routes. We couple a modern dynamic web interface with an in-memory database solution for near real-time responsiveness. MedEx provides multiple visualization options (Scatterplot, correlation heatmap, bar chart, grouped boxplot, grouped histogram, coplot) to get an easy overview on the loaded data as well as to perform pattern discovery and elementary statistics. We demonstrate the utility of MedEx, by example, on data from the cardiology research warehouse of Heidelberg University Hospital. In summary, our tool empowers clinicians to conduct their own interactive exploratory data analysis.

IMPROVING STUDENT’S LEARNING ACHIEVEMENT ON MATHEMATICS THROUGH COOPERATIVE LEARNING TYPE THINK PAIR SHARE (TPS)

This study aims to find out the significant effect of cooperative learning type Think Pair Share (TPS) in improving students’ learning achievement on the subject of elementary statistics. This is a quasi experimental study involving all students who take elementary statistics subject at the Department of Mathematics Education, Universitas Muhammadiyah Surakarta. The subjects of this study were devided into 2 groups, namely the experimental group taught using cooperative learning type Think Pair Share (TPS) and the control group taught using conventional learning. Each group is taught with the same topic, namely hypothesis testing. In this study, the data collection was done by test and observation. Whereas, the data analysis was conducted using one way ANOVA (Analysis of Variance) with five percent of significant level. Based on the analysis, it can be concluded that there is a significant effect of learning methods on students’ learning achievement on statistics. The learning mathematics with cooperative learning type Think Pair Share (TPS) can improve students’ learning achievement on statistics

Visualizing and Understanding Hypothesis Testing Using Dynamic Software

This article illustrates ways that dynamic software using some sophisticated techniques in Excel can be used to demonstrate fundamental ideas related to hypothesis testing to increase student understanding of the concepts and methods in elementary statistics courses. The article considers hypothesis tests for the population mean with large or small samples, for the population proportion, for the difference of means, and for the difference of proportions. In each instance, spreadsheets are used that draw repeated random samples of selected sizes from a variety of underlying populations and display the sample means or sample proportions graphically. In the process, students come to see how the decision of rejecting or failing to reject the null hypothesis clearly depend on the sample drawn, which in turn depends on the size of the sample and the shape of the underlying population.

Character Education Strengthening of Students Through The Mathematical Disposition Strategy on Statistics Elementary

This study aims to improve the strengthening of student character education through a mathematical disposition strategy in Elementary Statistics. The sample of this study was 30 students of the 3rd semester of Biology Education. The research method used was experimental and the research firm was quasi-experimental. Data collection techniques are measurement techniques, namely initial ability tests and mathematical disposition scales. The results of this study indicate that character education can be enhanced or strengthened by a mathematical disposition strategy. That is by increasing high confidence in solving problems, not easily discouraged and asking questions, having prepared before starting learning such as reading the material or other references, knowing the role of mathematics related with everyday life and knowing that success in mathematics subjects can support progress in other disciplines.

Narrow big data in a stream: Computational limitations and regression

We consider the on-line model for a data stream: data points are waiting in a queue and are accessible one-by-one by a special instruction. When a data point is processed, it is dropped forever. The data stream is assumed to be so long that it cannot be stored in memory in full: the size of memory is assumed to be polynomial in the dimension of data, but not the number of observations. This is a natural model for Narrow Big Data. First we prove a negative theorem illustrating that this model leads to serious limitations: we show that some elementary statistics, such as sample quantiles, cannot be computed in this model (the proof is based on a Kolmogorov complexity argument). This raises a crucial question which data-analytic procedures can be implemented in the stream data model and which cannot be performed at all, or only approximately (with some loss of information). After the negative results, we turn our attention to several positive results from multivariate linear regression with Narrow Big Data. We prove that least-squares based estimators and regression diagnostic statistics, such as statistics based on the residual sum of squares, can be computed in this model efficiently. The class of statistics efficiently computable in the stream data model also includes two-stage procedures involving auxiliary regressions, such as White’s heteroscedasticity test of Breusch–Godfrey autocorrelation test (which may be surprising because the procedures, as defined, seem to require a data point to be processed several times). The computation is done exactly: we do not use preprocessing steps involving data compression techniques with information loss (such as sampling or grouping) for a reduction of the size of the data set.

A Factor analysis of students’ attitudes towards statistics in Higher Learning Institution Malaysia

Attitudes toward statistics have received a great attention by academic and researcher in statistics and mathematics education. This paper investigates students’ attitudes towards statistics in one of the Malaysia higher education institution and determined the factors that explain the attitude of students toward statistics. Stratified sampling method was used to select 274 respondents from 18 classes Elementary Statistics course. The attitudes toward statistics were measured using the Survey Attitude Towards Statistics (SAT-36) scale. Factor analysis was applied to identify the factors on students’ attitude toward statistics. Findings from factor analysis revealed that seven factors that explain the attitude of the students were self-determination, cognitive competence, effort, value of statistics in professional life, difficulty, statistical solving and value of statistics in everyday life. The results suggested that statistics should be demonstrated in more practical way for developing more positive attitude towards statistics. This could further promote the learning process and students’ ability to apply the statistical concepts.

The Elementary Statistics of Majority Voting

The Elementary Statistics of Majority Voting

Elementary Statistics on Trial—The Case of Lucia de Berk

In the conviction of Lucia de Berk an important role was played by a simple hypergeometric model, used by the expert consulted by the court, which produced very small probabilities of occurrences of certain numbers of incidents. We want to draw attention to the fact that, if we take into account the variation among nurses in incidents they experience during their shifts, these probabilities can become considerably larger. This points to the danger of using an oversimplified discrete probability model in these circumstances.

Empirical evidence of deep learning in learning communities

PurposeThe purpose of this paper is to investigate whether learning communities (LCs), defined as a cohort of students jointly enrolled in two distinct courses, increase “deep learning” in either or both courses. This study focuses on the impact of learning communities in quantitative courses.Design/methodology/approachThe hypothesis is tested using a unique data set including individual student performance and characteristics collected from students enrolled in an LC of Principles of Microeconomics and Elementary Statistics. The sample also includes students enrolled in each course separately which allows for testing between groups. The final exam in each course contained questions designed specifically to test deep learning. The design facilitates the use of multivariate regression analysis to examine the correlation between learning in communities and deep learning, holding constant other possible elements of student success.FindingsDespite perceptions among the sample student population that learning increases in both courses as a result of the LC format, the empirical evidence does not reveal any statistically significant increase in deep learning as a result of learning in community. However, the sample is more introverted than the average college student which may meaningfully impact the results.Research limitations/implicationsThere are a number of important motivations for implementing an LC program that are not measured here. These include an increased sense of community among students, breadth (rather than depth) of knowledge, and awareness of the interconnectedness of learning across disciplines. However, to the extent that university instructors are motivated to ensure learning in their own discipline, this resource-intensive strategy may not be the most suitable approach in quantitative courses.Originality/valueLearning communities continue to be a popular pedagogical technique and curriculum requirement, particularly at teaching-focused universities. This research offers an empirical approach to measuring one aspect of their value which is typically left to conceptual or qualitative study.

Practicality of Elementary Statistics Module Based on CTL Completed by Instructions on Using Software R

This research is a development research using 4-D design model (define, design, develop, and disseminate). The results of the define stage are analyzed for the needs of the following; Syllabus analysis, textbook analysis, student characteristics analysis and literature analysis. The results of textbook analysis obtained the description that of the two textbooks that must be owned by students also still difficulty in understanding it, the form of presentation also has not facilitated students to be independent in learning to find the concept, textbooks are also not equipped with data processing referrals by using software R. The developed module is considered valid by the experts. Further field trials are conducted to determine the practicality and effectiveness. The trial was conducted to the students of Mathematics Education Study Program of STKIP PGRI which was taken randomly which has not taken Basic Statistics Course that is as many as 4 people. Practical aspects of attention are easy, time efficient, easy to interpret, and equivalence. The practical value in each aspect is 3.7; 3.79, 3.7 and 3.78. Based on the results of the test students considered that the module has been very practical use in learning. This means that the module developed can be used by students in Elementary Statistics learning.

Development of introduced species Malus Mill. (Rosaceae Adans.) in South Karelia

This study contains findings of research carried out at the Botanical Garden of Petrozavodsk State University (South Karelia, central taiga subzone) in April – October in the period from 1986 to 2012. The subjects of the studies were introduced plants of three species of Malus Mill.: dwarf apple – Malusbaccata (L.) Borkh., wild apple – Malussylvestris Mill., and Niedzwetzky’s apple – Malusniedzwetzkyana Dieck. ex Koehne. Phenological observations were carried out once in 3 days by the N. Bulygin technique (1979). The phenophase was considered to have occurred if it was observed in at least 30% of the shoots of all specimens of the species under study. All samples were checked for compliance with the normal probability law. The correlation coefficients and differences between the mean values ​​were verified to determine their reliability. Elementary statistics obtained demonstrate, among other things, that the experiment’s accuracy rate is fairly high (4–6%), while the variation coefficient is small (18–22%). It was found that M.baccata trees begin and end most of their phenophases approximately 5–10 days earlier than the other studied species. Furthermore, in the beginning and middle of the growing period, phonological phases of M.baccata proceed at colder weather compared to the other studied Malus species. At the end of the growing period, these differences among the species level off. Of all the studied climatic factors, air temperature has the most measurable positive influence on the development of Malus species in Karelia. Daily average air humidity and precipitation have a less prominent influence on еру phenophases of the studied Malus species. The course and strength of such influence depend on the peculiarities of the phenophase itself. All the studied introduced Malus species show a high degree of introduction prospect (82−93 points) and can be successfully used in Karelia for gardening and landscaping purposes.

Assessment of statistical education in Indonesia: Preliminary results and initiation to simulation-based inference

Start in this paper, we assess our traditional elementary statistics education and also we introduce elementary statistics with simulation-based inference. To assess our statistical class, we adapt the well-known CAOS (Comprehensive Assessment of Outcomes in Statistics) test that serves as an external measure to assess the student’s basic statistical literacy. This test generally represents as an accepted measure of statistical literacy. We also introduce a new teaching method on elementary statistics class. Different from the traditional elementary statistics course, we will introduce a simulation-based inference method to conduct hypothesis testing. From the literature, it has shown that this new teaching method works very well in increasing student’s understanding of statistics.

The Turtleback Diagram for Conditional Probability

We elaborate on an alternative representation of conditional probability to the usual tree diagram. We term the representation `turtleback diagram' for its resemblance to the pattern on turtle shells. Adopting the set theoretic view of events and the sample space, the turtleback diagram uses elements from Venn diagrams---set intersection, complement and partition---for conditioning, with the additional notion that the area of a set indicates probability whereas the ratio of areas for conditional probability. Once parts of the diagram are drawn and properly labeled, the calculation of conditional probability involves only simple arithmetic on the area of relevant sets. We discuss turtleback diagrams in relation to other visual representations of conditional probability, and detail several scenarios in which turtleback diagrams prove useful. By the equivalence of recursive space partition and the tree, the turtleback diagram is seen to be equally expressive as the tree diagram for representing abstract concepts. We also provide empirical data on the use of turtleback diagrams with undergraduate students in elementary statistics or probability courses.