Elementary Statistics Research Articles

Analysis of r×c Tables containing Outliers

We examine the problem of accommodating outliers in tables of measurement data when there are no replications. The suggested strategy for the determination of the cells that contain outliers and for handling them analytically is easily understood and implemented in practice and presented in even the most elementary statistics course along with the course’s ANOVA material.

ChatGPT-generated help produces learning gains equivalent to human tutor-authored help on mathematics skills.

Authoring of help content within educational technologies is labor intensive, requiring many iterations of content creation, refining, and proofreading. In this paper, we conduct an efficacy evaluation of ChatGPT-generated help using a 3 x 4 study design (N = 274) to compare the learning gains of ChatGPT to human tutor-authored help across four mathematics problem subject areas. Participants are randomly assigned to one of three hint conditions (control, human tutor, or ChatGPT) paired with one of four randomly assigned subject areas (Elementary Algebra, Intermediate Algebra, College Algebra, or Statistics). We find that only the ChatGPT condition produces statistically significant learning gains compared to a no-help control, with no statistically significant differences in gains or time-on-task observed between learners receiving ChatGPT vs human tutor help. Notably, ChatGPT-generated help failed quality checks on 32% of problems. This was, however, reducible to nearly 0% for algebra problems and 13% for statistics problems after applying self-consistency, a "hallucination" mitigation technique for Large Language Models.

The useful and not so paradoxical inspection paradox

We offer ways that the inspection paradox can be usefully presented, even in the most elementary statistics courses, and provide guidance about how it can be revisited subsequently in the same course and in succeeding courses. Numerous situations in which the inspection paradox might occur are mentioned, and mathematically simple demonstrations are furnished in order to help convince students of the paradox’s veracity. Although remedial actions for the paradox are given, the main point of view is that the two sampling procedures leading to this apparent paradox are simply alternative methods that yield differing, but bona fide, measures and interpretations for the populations from which the data were obtained. Suggestions for student projects and undergraduate research are given.

Effects of K-W-L Instructional Strategy on Academic Performance of Pupils in Primary Mathematics and English in Owerri North Lga of Imo State, Nigeria

The purpose of this study was to find out if learners taught algebraic expression/elementary statistics in Mathematics and parts of speech in English Language using K-W-L instructional strategy will have better academic performance than those taught with the conventional Teacher method at 0.05 alpha levels. The researchers used quasi-experimental design which adopted the pretest, post-test Experimental group method. The area of study was Owerri North LGA Imo State, Nigeria. The population of the study was all Primary 5 learners in Owerri North Public schools. Purposive sampling technique was used to select three primary schools and simple random sampling technique was used to select classes in each of the schools. The sample of the study was 120 primary learners. The data collection instruments for the study were treatment 1 (K-W-L instructional strategies), treatment 2, (TCM [Teacher conventional method), Treatment 3 (combined TCM & K-W-L), multiple-choice questions for each subject chosen from past FSLCE and Common entrance questions. Two research questions and one null hypothesis guided the study. Mean, standard deviation and ANCOVA were the statistical tools used to analyze the data. The findings of the study revealed that the group taught with combined TCM & K-W-L achieved higher academically than the group taught with only TCM or K-W-L. The study also discovered that K-W-L instructional strategy is gender friendly. It was recommended that primary school teachers should be encouraged to use K-W-L instructional strategy to facilitate learners’ performance in algebraic expression, elementary statistics and parts of speech. Furthermore Basic Education Stake holders should organize regular workshops and seminars to train and retrain teachers on the use of 21st century teaching strategies.

Cryptology as a Way to Teach Advanced Discrete Mathematics

We present a detailed description of a Cryptography and Computer Security course that has been offered at Knox College for the last 15 years. While the course is roughly divided into two sections, Cryptology and Computer Security, our emphasis here is on the Cryptology section. The course puts the cryptologic material into its historical context and also includes reference to ciphers used and discussed in literature. Through lectures and assignments on cryptanalysis, the course motivates students to learn a variety of topics in advanced discrete mathematics, including discrete probability, elementary statistics, number theory, and abstract algebra. The students have found this approach motivating and we believe our experiences are relevant to instructors teaching this material in a variety of different courses and institutions.

Stereotype threat and gender differences in statistics

Stereotype threat (ST) has been extensively explored as an explanation for gender disparities in achievement and participation in mathematics. However, there is a lack of research evaluating ST in statistics. The present study evaluated the impact of ST on gender differences in student performance, self-efficacy, and anxiety in statistics using a four-group, quasi-experimental design. Specifically, 102 elementary statistics students at a university in the Southeast United States were randomly assigned to one of four ST conditions including an explicit ST condition, an implicit ST condition, a reverse ST condition, and a nullified ST condition. Results indicated that there were no gender differences by ST condition in statistics self-efficacy, test anxiety, and performance. Analyses of student responses to open-ended questions indicated that females were more likely than males to report that they had fewer opportunities to achieve in statistics. Implications of our findings and suggestions for future research are discussed.

Elementary Statistics Projects Using Covid Data

This article describes five elementary statistics projects involving the Covid-19 data made available to the public in csv files by the Centers for Disease Control and Prevention. The first project examined data available at the beginning of the covid surge in New York City in spring, 2020, and used the correlation coefficient to estimate the total number of deaths that could be expected as the spike ran its course. The second project is an easy one on the concept of excess deaths and on the mechanics of extracting parts of a data file that answer relevant questions. The data is from a spike in deaths in the particularly bad flu surge in the winter of 2017–2018. The third and fourth projects ask the student to fit a logistic growth curve to observed cumulative numbers of deaths in a spike, like the Covid spikes in New York City and Wisconsin and the nationwide 2017–2018 flu spike. The method is a simple linear regression with transformed variables. The fifth project involves hypothesis testing and judging when a Poisson model might be useful. The paper also documents difficulties and adaptations of the sort familiar to all teachers who have taught during the Covid-19 pandemic.

Teacher-Made Videos as Learning Tool in Elementary Statistics during the Pandemic: A Developmental Research

The COVID-19 pandemic has affected education institutions around the world which has forced them to abruptly shift to online learning to address educational challenges with limited resources. Hence, this developmental research aimed to develop teacher-made videos as a learning tool for online learning in elementary statistics. This was utilized as an asynchronous lecture material during the pandemic and its acceptability was evaluated using the ADDIE Model. However, this paper focused only on the development and evaluation phase. It included 104 freshmen university students and five experts as participants of the study. Mean, standard deviation, frequency count, correlation analysis, and test of difference were used as data analysis tools. The developed videos consist of the following elements: title, learning objectives, overview, content discussion, assessment, and answer key. The teacher-made videos were highly acceptable in terms of learning objectives, content, organization and presentation, format and design, learning activities, and assessment as evaluated by the students and experts. In addition, when the participants were grouped according to sex and specialization, their overall acceptability mean did not exhibit significant differences. It was also found that the evaluation factors in the acceptability questionnaire all have a strong, positive correlation with the overall acceptability mean. Thus, technology-enhanced instructional materials like videos and other learning media are helpful learning resources in maximizing learning outcomes amid the pandemic.

실용통계와 대학 기초통계학과의 수직적 연계성에 관한 연구

Objectives The purposes of this study are to study vertical articulation between practical statistics and elementary statistics of the University and to provide the implication of development of subjects for statistics.
 Methods The vertical articulation between practical statistics and elementary statistics of university are studied based on Song et. al(1991)’s criterion such as repetition, development and gap.
 Results As a result of studying vertical articulation, the ratios of repetition and gap are relatively higher than that of development.
 Conclusions The fact the ratio of gap is relatively higher than that of development makes students difficult to study statistics in university. To close the gap between high school and university education, supplementary learning materials or new statistics-related courses need to be developed.

Penugasan Tutor Sebaya dengan Metode Pinalti

This research focuses on the assignment of peer tutors in the Mathematics Study Program, Mathematics Department, FMIPA Unpatti. The purpose of this study was to obtain the completion of peer tutor assignments with the penalty method. The penalty method is a method used to solve the problem of unbalanced assignments. The processed two parts, namely finding the initial solution and finding the optimal solution. The column penalty method or the row penalty method is used to get the initial solution. In this study, the row penalty method is used because the number of rows is less than the number of columns, and the optimal solution is sought. The data used are student names, courses, and final grades. The results obtained using the Penalty method are that David becomes a tutor in the Statistical Method course, Alfito becomes a tutor in the Operations Research course, Christin becomes a tutor in the Linear Program course, Gabriella becomes a tutor in the Analytical Geometry course and Navila becomes a tutor in the course Elementary Statistics.

Algorithmic fairness in computational medicine.

SummaryMachine learning models are increasingly adopted for facilitating clinical decision-making. However, recent research has shown that machine learning techniques may result in potential biases when making decisions for people in different subgroups, which can lead to detrimental effects on the health and well-being of specific demographic groups such as vulnerable ethnic minorities. This problem, termed algorithmic bias, has been extensively studied in theoretical machine learning recently. However, the impact of algorithmic bias on medicine and methods to mitigate this bias remain topics of active discussion. This paper presents a comprehensive review of algorithmic fairness in the context of computational medicine, which aims at improving medicine with computational approaches. Specifically, we overview the different types of algorithmic bias, fairness quantification metrics, and bias mitigation methods, and summarize popular software libraries and tools for bias evaluation and mitigation, with the goal of providing reference and insights to researchers and practitioners in computational medicine.

Work on new method to find initial basic feasible solution of transportation problem in contrast to existing methods

In the present paper, we focused on finding an initial basic feasible solution for transportation problems. The new method is compared to four different proposed mean methods namely, Proposed Arithmetic Mean (PAM), Proposed Harmonic Mean (PHM), Proposed Geometric Mean (PGM) and Proposed Quadratic Mean (PQM) methods along with existing traditional methods like North West Corner Method (NWCM), Least Cost Method (LCM) and Vogel Approximation Method (VAM). Also, the deviation percentage of the outcomes has been figured out in contrast to distinct methods. The approach thus developed, involves elementary arithmetic and statistics, which could be of keen interest even for beginners and is beneficial to decision makers dealing with the problem of supply chain as well as logistics. Suitable examples are given for examining optimality and to validate the results obtained.

An Evaluation of College Students’ Perceptions of Statisticians

The widely used Draw a Scientist Test was revised to focus on statistics and 110 Elementary Statistics students were asked to draw a statistician. In addition, to better understand students’ drawings and have some relative comparison, 173 College Algebra students were asked to draw a mathematician. A detailed analysis of students’ images and students’ demographic information was conducted using descriptive statistics, categorical data analysis, logistic regressions, and hierarchical cluster analysis. Results showed that students tend to perceive statisticians and mathematicians as primarily White and male. However, female students were more likely than male students to draw a female statistician and mathematician. Two themed clusters emerged from the hierarchical cluster analysis for both the math and statistics students. We discuss the implications of the results for teaching and future research.

Synthesis of Data Science Competency for Higher Education Students

The research aims to Data Science Performance Synthesis for Higher Education Students and Data Science Performance Suitability Assessment for Higher Education Students. The research instruments include 1) data science performance synthesis tables, 2) expert interviews in data science performance assessments, 3) expert questionnaires to assess the consistency of data science performance. Analytical methods include 1) analyzing the frequency obtained from the content analysis table, 2) synthesis of content from interviews, 3) analyzing performance consistency, and components of data science performance, from data science synthesis for higher education students, finding that data performance for higher education students consists of five performances: 1) programming skills, 2)elementary statistics, 3) fundamentals of data science, 4) data preparation, and 5) Big data analytics.

Local Instructional Theory Topik Dua Tipe Kesalahan dalam Pengujian Hipotesis

Two types of errors are one of the important topics in hypothesis testing. Studying the two types of errors is not only studying how the procedure determines the probability of making an error, but it is very important to study the theoretical concepts of the two types of errors. To achieve this goal, a learning design is needed that can facilitate students to construct their own concepts of the two types of errors. The learning design developed is local instructional theory resulting from the cyclic process of hypothetical learning trajectory. The type of research used is design research using the model developed by Gravemeijer and Cobb. The test subjects used in this study were students of the Ma thematics Education Study Program, FMIPA UNP who took the Elementary Statistics Course in the July – December 2019 semester. This research resulted in a very practical local instructional theory used to facilitate students in carrying out horizontal and vertical mathematization processes, so that students are able to construct their own concepts of two types of errors in hypothesis testing.

The Composite Covariance of a Kalman Filter Estimation

A Kalman filter estimation of the state of a system is merely a random vector that has a normal, also called Gaussian, distribution. Elementary statistics teaches any Gaussian distribution is completely and uniquely characterized by its mean and covariance (variance if univariate). Such characterization is required for statistical inference problems on a Gaussian random vector. This mean and composite covariance of a Kalman filter estimate of a system state will be derived here. The derived covariance is in recursive form. One must not confuse it with the “error covariance” output of a Kalman filter. Potential applications, including geological ones, of the derivation are described and illustrated with a simple example.

The optimal correlation detector?

SUMMARY Correlation detectors are now used routinely in seismology to detect occurrences of signals bearing close resemblance to a reference waveform. They facilitate the detection of low-amplitude signals in significant background noise that may elude detection using energy detectors, and they associate a detected signal with a source location. Many seismologists use the fully normalized correlation coefficient C between the template and incoming data to determine a detection. This is in contrast to other fields with a longer tradition for matched filter detection where the theoretically optimal statistic C2 is typical. We perform a systematic comparison between the detection statistics C and C|C|, the latter having the same dynamic range as C2 but differentiating between correlation and anticorrelation. Using a database of short waveform segments, each containing the signal on a 3-component seismometer from one of 51 closely spaced explosions, we attempt to detect P- and S-phase arrivals for all events using short waveform templates from each explosion as reference signals. We present empirical statistics of both C and C|C| traces and demonstrate that C|C| detects confidently a higher proportion of the signals than C without evidently increasing the likelihood of triggering erroneously. We recall from elementary statistics that C2, also called the coefficient of determination, represents the fraction of the variance of one variable which can be explained by another variable. This means that the fraction of a segment of our incoming data that could be explained by our signal template decreases almost linearly with C|C| but diminishes more rapidly as C decreases. In most situations, replacing C with C|C| in operational correlation detectors may improve the detection sensitivity without hurting the performance-gain obtained through network stacking. It may also allow a better comparison between single-template correlation detectors and higher order multiple-template subspace detectors which, by definition, already apply an optimal detection statistic.

Remembering What Produced the Data: Individual and Social Reconstruction in the Context of a Quantified Self Elementary Data and Statistics Unit

Given growing interest in K-12 data and data science education, new approaches are needed to help students develop robust understandings of and familiarity with data. The model of the quantified self—in which data about one’s own activities are collected and made into objects of study—provides inspiration for one such approach. By drawing on what one already knows about their self and their prior experiences, it may be possible to bootstrap students’ abilities to interpret and make sense of data. Taking that possibility seriously, this article describes some of the gains observed in students’ statistical reasoning following a quantified self, wearables-based elementary statistics unit and provides a theoretical framework drawing from cognitive psychology, embodiment, and situative perspectives to characterize how prior experience is used as a resource in data sense-making when the data are about students’ own physical experiences. This framework centralizes and interrogates the work of “remembering” prior experiences and articulates how remembering is involved in interpreting quantified self data. Specifically, the framework emphasizes that remembering in service of data interpretation is a reconstructive act that draws from both general and specific embodied resources and that the work of reconstructive remembering in the classroom is both individual and multi-participant work. To demonstrate measured learning gains and illustrate the framework, written assessment results and descriptive cases of student and teacher discussions about quantified self data from two sixth-grade classes participating in a classroom design experiment are provided. Both a discussion of and recommendations for ethical considerations related to quantified self data in education are also provided.

Confidence Intervals of COVID-19 Vaccine Efficacy Rates

This tutorial uses publicly available data from drug makers and the Food and Drug Administration to guide learners to estimate the confidence intervals of COVID-19 vaccine efficacy rates with a Bayesian framework. Under the classical approach, there is no probability associated with a parameter, and the meaning of confidence intervals can be misconstrued by inexperienced students. With Bayesian statistics, one can find the posterior probability distribution of an unknown parameter, and state the probability of vaccine efficacy rate, which makes the communication of uncertainty more flexible. We use a hypothetical example and a real baseball example to guide readers to learn the beta-binomial model before analyzing the clinical trial data. This note is designed to be accessible for lower-level college students with elementary statistics and elementary algebra skills.

The Relationship Between Learning Mode and Student Performance in an Undergraduate Elementary Statistics Course in the United States

Faculty have conducted many studies on the relationship between learning mode and student performance but few researchers have evaluated final grades, grade distribution, and pass rates in a sophomore introductory statistics course with a non-traditional student population who self-selected the learning mode from among different course sections. Accordingly, we examined 307 end-of-course grades from four different modes of instruction: (a) online, (b) videosynchronous learning classroom, (c) videosynchronous learning home, and (d) traditional classroom in an introductory statistics course. All data on grades, which included pass rate and grade distribution, were collected from the nine-week January 2019 term. All learning modes used the same text, syllabus, assignments, quizzes, and tests. In this study, learning mode was not significantly related to end-of-course score, final grade distribution, or pass rate. Future researchers should explore the impacts of gender, instructor quality, different term lengths, and the standardized use of textbooks and syllabi on student performance when exploring the impact of learning mode on grades, grade distribution, and pass rates.