Computer Simulations to Clarify Key Ideas of Statistics

A "Reverse Order" Elementary Statistics Course

Students in elementary statistics traditionally see experiments and data as words and numbers in a text. They receive little exposure to the important statistical activities of sample selection, data collection, experimental design, development of statistical models, the need for randomization, selection of factors, etc. They often leave the first course without a firm understanding of the role of applied statistics or of the statistician in scientific investigations. In an attempt to improve elementary statistics education, we have developed a statistics laboratory similar to those of other elementary science courses. We will discuss our experiences in teaching a laboratory component with the traditional elementary statistics course. In each lab session, students, working in teams, discuss the design of an experiment, carry out the experiment, and analyze their data using Minitab on a Macintosh or MS-DOS based computer. The students then individually either answer a series of short answer questions or write a formal scientific report. The labs are designed to be relatively inexpensive and portable. They do not require a prior background in science, statistics or computing.

One of the main themes of statistics courses is to teach about variability, as well as location. This is especially important for non-statistics students, who often overlook variability. We consider particularly the problem of comparing variability among k samples (k > 2) that are not necessarily drawn from Gaussian populations. This can also be viewed as testing for homoskedasticity of samples. We examine tools for this problem from the perspective of their suitability for inclusion in elementary statistics courses for students of non-mathematical subjects. The ideas are illustrated by an example that arose in a student project.Supplemental data for this article can be accessed on the publisher's website.

The book covers the topics usually included in undergraduate Statistics courses: graphical and numerical description of data, probability, discrete and continuous variables and distributions, sampling and sampling distribution, estimation, hypothesis testing, simple regression, ANOVA, and maximum likelihood method. It is the philosophy that is unusual: we try to prove most facts, without sacrificing intuition. As a result, the reader can see the true motivation behind statistical constructions and the logical links between them. The book is particularly suitable for Statistics courses of the London School of Economics and University of London. The electronic (pdf) copy of the book is extremely easy to use on electronic devices because it contains almost 400 hyperlinks. You can start reading the book from the middle. Whenever knowledge of the previous material is required, you will see a link which will take you to the relevant place in the text. After reading it, just press the back button in your pdf reader and continue reading where you took off. The main statistical phenomena and variables are modeled and illustrated in Excel. The book is written with the view that the reader is preparing to take Econometrics. In particular, it contains a chapter called "Bridge to econometrics". In a separate chapter we describe Excel and Mathematica statistical functions that allow one to do without statistical tables. Many topics are provided with Excel and Mathematica examples and videos and developed further on the author's web site http://raisingthebar.nl/, which is regularly updated.

Chapter 9 - Sampling distributions, or why exploratory analyses are not enough

The Statistics Anxiety Rating Scale has 51 items, each scored on a 5-point rating scale to measure statistics anxiety with six subscales, Worth of Statistics, Interpretation Anxiety, Test and Class Anxiety, Computational Self-concept, Fear of Asking for Help, and Fear of Statistics Teachers. Psychometric properties included analyses of construct and concurrent validities an internal consistency and test-retest reliability. 221 college students (74% women; M age=28 yr.) in elementary statistics courses at several southwestern state universities participated. The findings are consistent with previous reports and indicate adequate concurrent validity, internal consistency, and split-half reliability, but for construct validity confirmatory factor analysis yielded marginal support.

This month, we bring you some “Technology Tips” that are related to probability and statistics. We begin with a contribution by Bishnu Naraine and Peiyi Zhao: an exploration that uses The Geometer's Sketchpad to discuss the broken-stick problem, which is also known as the spaghetti problem. This totally geometric solution nicely complements the analytic solution of the same problem, given in “The Spaghetti Problem Problem,” by Dennis Ippolito, which appeared on pages 422–26 of the May 2000 issue of the Mathematics Teacher. Next is a feature by Allen Holmes that discusses obtaining an explicit definition for a recursively defined sequence by using the built-in statistics regression ability of graphing calculators to model the equation of the sequence. Then a short program by John Jose for the TI-83 and TI-83 Plus graphing calculator helps investigate the law of large numbers by simulating the results of a simple two-dice experiment. Finally our “Surfing note” features a Web site that is devoted to statistics. It contains many resources for an elementary statistics course.

This article illustrates ways that dynamic software using some sophisticated techniques in Excel can be used to demonstrate fundamental ideas related to regression and correlation analysis to increase student understanding of the concepts and methods in elementary statistics courses and in courses at the college algebra/precalculus level that stress ideas on curve fitting techniques.

A collaborative, statistics education research project (Lovett, 2001) is discussed. Some results of the project were applied in the computer lab sessions of my elementary statistics course. I detail the process of applying these research results, as well as the use of knowledge surveys. Furthermore, I give general suggestions to teachers who want to put educational research results into effective use in their own classes.

Based on the current research status, this paper proposes a deep learning model named Covid-DenseNet for COVID-19 detection from CXR (computed tomography) images, aiming to build a model with smaller computational complexity, stronger generalization ability, and excellent performance on benchmark datasets and other datasets with different sample distribution features and sample sizes. The proposed model first extracts and obtains features of multiple scales from the input image through transfer learning, followed by assigning internal weights to the extracted features through the attention mechanism to enhance important features and suppress irrelevant features; finally, the model fuses these features of different scales through the multi-scale fusion architecture we designed to obtain richer semantic information and improve modeling efficiency. We evaluated our model and compared it with advanced models on three publicly available chest radiology datasets of different types, one of which is the baseline dataset, on which we constructed the model Covid-DenseNet, and the recognition accuracy on this test set was 96.89%, respectively. With recognition accuracy of 98.02% and 96.21% on the other two publicly available datasets, our model performs better than other advanced models. In addition, the performance of the model was further evaluated on external test sets, trained on data sets with balanced sample distribution (experiment 1) and unbalanced sample distribution (experiment 2), identified on the same external test set, and compared with DenseNet121. The recognition accuracy of the model in experiment 1 and experiment 2 is 80% and 77.5% respectively, which is 3.33% and 4.17% higher than that of DenseNet121 on external test set. On this basis, we also changed the number of samples in experiment 1 and experiment 2, and compared the impact of the change in the number of training set samples on the recognition accuracy of the model on the external test set. The results showed that when the number of samples increased and the sample features became more abundant, the trained Covid-DenseNet performed better on the external test set and the model became more robust. Compared with other advanced models, our model has achieved better results on multiple datasets, and the recognition effect on external test sets is also quite good, with good generalization performance and robustness, and with the enrichment of sample features, the robustness of the model is further improved, and it has better clinical practice ability.

In statistical inference, many students have a difficult time learning the sample mean, sampling distribution, and the central limit theorem, even though these are key concepts in statistics. This study aimed to identify and correct prospective mathematics teachers’ misconceptions about the sample mean and sampling distribution during the statistical inference process in an introductory statistics course at two Korean universities. It also aimed to develop an exploratory lesson by applying Keller’s ARCS (attention, relevance, confidence, and satisfaction) model so that the prospective teachers could better understand the sample mean and sampling distribution and correct their misconceptions. The exploratory lesson was implemented, observed, and analyzed. The findings showed that the exploratory lesson had positive effects on prospective teachers’ attention, relevance, confidence, and satisfaction. In addition, through communication and discussion with their peers, they could better understand the concepts, discover new facts, and correct their misconceptions in the exploration process of the lesson. Thus, this study provided empirical evidence to show that an exploratory statistics lesson using Keller’s ARCS model can be an effective lesson model for teaching statistical inference.

The overuse of lecture-based approaches for instruction in university courses may have limited student access to knowledge, particularly the transfer of complex concepts, such as central limit theorem in statistics. This study seeks to contribute to empirical research regarding the effectiveness of serious educational games (SEGs) to increase undergraduates’ conceptual understanding and affective interest in statistics. An experimental design was used to test the efficacy of an SEG, Deadly Distribution, which simulates a real-world context to learn and interact with statistics concepts, compared to traditional notes and homework problems, as supplements to instruction in addition to class lectures. Students who played the game had similar increases in academic growth of conceptual knowledge as students who studied traditional course material. Furthermore, this treatment group had a significant increase in affective outcomes compared to the control group. These findings extend the current literature, which is mixed and sparse, on the effectiveness of SEGs in the undergraduate classroom. In an undergraduate introductory statistics course, an SEG might be an effective substitute for traditional study time of course materials outside of class to increase their affect toward the subject matter and produce similar gains for students who might not otherwise study.

Our institution is heavily invested in improving the learning outcomes of our students, especially in core courses like statistics which is taken by majority of freshmen students. As such, we have been reviewing our existing pedagogy and exploring novel ways to improve students experience in statistics course. In this study we compare web-based vs paper-based traditional homework models and their impact on students’ performance in an undergraduate statistics course. In web-based model, students used MyStatLab to complete the homework assignments along with additional resources offered by this platform. On the other hand, in paper-based model students used traditional approach in completing the homework and was manually graded by the instructor. Our analysis indicated that there is no statistically significant difference in students’ final course grades between the two modalities. Additionally, we conducted a chi-square test of independence and found no statistically significant relationship between students’ final course grades and homework models. However, our analysis concluded that student performance and perceptions improved with online homework model compared to the traditional model. Keywords: Web-based online homework, Traditional homework, Student performance, Undergraduate Statistics DOI: 10.7176/JEP/13-27-09 Publication date: September 30 th 2022

This study qualitatively investigates the nature of the challenges that a student who is highly successful in mathematics faces in learning college-level elementary statistics. The study draws on the constructs of eagerness, flexibility and willingness to characterize the necessary disposition for critical thinking that is essential in learning statistics. The case study is based on data collected through a survey assessment and a follow-up interview with a mathematics major enrolled in an elementary college statistics course at the time of the study. The qualitative analysis relies on the student's verbal descriptions of the challenges he was experiencing in the course. The findings suggest that while his strong inclination towards inquisitive learning and strong understanding of mathematical concepts supported this student's mathematics learning, the same characteristics might have been causing him difficulties in learning college-level elementary statistics.

Neural networks (NNs) are efficient tools for rapidly obtaining geoelectric models to solve magnetotelluric (MT) inversion problems. Training an NN with strong predictive power requires numerous training samples to prevent underfitting. To reduce the computational burden of generating a large number of training samples, this work analyzes the influence of the sample features and distribution on the training effect for an NN and proposes an efficient method of sample generation. This innovative method consists of three steps: 1) geoelectrically simplifying the features; 2) removing unnecessary features on the basis of realistic geological characteristics; and 3) mapping the samples to a higher-dimensional space. Numerical examples based on simple stratified models show that the number of samples can be reduced to below one-millionth of the original number while improving the predictive effect of the NN. The performance and effectiveness for processing more complex structures are verified by the inversion results obtained for a public data set, COPROD2. We conclude that this advanced method can generate high-quality training samples at a greatly reduced computational cost. The analysis of the sample features and distribution not only advances the state of research on the use of machine learning in geophysical inversion but also is a forward-looking study on the mechanisms of underfitting, tracing the source of these phenomena back to the training samples used.