Teaching

  • Five case studies based on real situations and real data are presented for use in courses on research methodology and data analysis. Departing from the typical case study approach, students are asked to act as consultants to resolve the issues placed before them, prior to being given a solution. In generic terms, students are given a description of a real problem and a real dataset relevant to solving that problem and are asked for their advice on how the problem may be solved. This approach motivates students to take ownership of the problem at hand and provides them with the opportunities and experiences to use the tools of their education actively, rather than to merely acquire them.

  • The simplest forms of regression and correlation involve formulas that are incomprehensible to many beginning students. The application of these techniques is also often misunderstood. The simplest and most useful description of the techniques involves the use of standardized variables, the root mean square operation, and certain distance measures between points and lines. On the standardized scale, the simple linear regression coefficient equals the correlation coefficient, and the distinction between fitting a line to points and choosing a line for prediction is made transparent. The typical size of prediction errors is estimated in a natural way by summarizing the actual prediction errors incurred in the dataset by use of the regression line for prediction. The connection between correlation and distance is simplified. Despite their intuitive appeal, few textbooks make use of these simplifications in introducing correlation and regression.

  • We explore the varied uses of the uniform distribution on [theta - 1/2, theta + 1/2] as an example in the undergraduate probability and statistics sequence or the mathematical statistics course. Like its cousin, the uniform distribution on [0, theta], this density provides tractable examples from the topic of order statistics to hypothesis tests. Unlike its cousin, which appears in many probability and statistics books, this uniform is less well known or used. We discuss maximum likelihood estimators, likelihood ratio tests, confidence intervals, joint distributions of order statistics, use of Mathematica®, sufficiency, and other advanced topics. Finally, we suggest a few exercises deriving likelihood ratio tests when the range is unknown as well, or for the uniform on [theta - rho, theta + rho].

  • There are many common misconceptions regarding factor analysis. For example, students do not know that vectors representing latent factors rotate in subject space, rather than in variable space. Consequently, eigenvectors are misunderstood as regression lines, and data points representing variables are misperceived as data points depicting observations. The topic of subject space is omitted by many statistics textbooks, and indeed it is a very difficult concept to illustrate. An animated tutorial was developed in an attempt to alleviate this problem. Since the target audience is intermediate statistics students who are familiar with regression, regression in variable space is used as an analogy to lead learners into factor analysis in the subject space. At the end we apply the Gabriel biplot to combine the two spaces. Findings from a textbook review, a survey, and a "think aloud" protocol were taken into account during the program development and are discussed here.

  • By putting emphasis on applications in two basic statistics courses for chemistry students and chemical engineering students we have enhanced student motivation and increased student activity. In addition to a traditional in-class exam, the students complete a take-home project where statistical problems relevant to chemists are discussed. We give several examples of the course and project material. The main difference between the two courses is that the first is optional, attracting approximately 15 students, while the second is compulsory with approximately 100 students. We discuss how the different requirements affect the learning situation and how separate strategies of teaching have to be developed for the small class and large class situations, respectively.

  • Over the past 25 years or so there has been a growing interest and amount of research work into the teaching of probability and statistics. This interest and research has been reflected in the five International Conferences on Teaching Statistics, the establishment of journals such as Teaching Statistics and the Journal for Statistics Education as well as an increasing number of articles in other journals and papers at other conferences. Initially the emphasis was on school pupils but, increasingly, there has been an emphasis on teaching undergraduates.<br>In their bibliography, Sahai, et al (1996) list 2367 references up until the year 1994. With so much published work it is difficult for newcomers to the field to know where to start. The following list of basic references attempts to pull together the various strands of research about undergraduate teaching so that new lecturers will be able to get a quick overview of current thinking and where it has come from. The many older references are to give an historical context and reflect the influences on today's practice.<br>As in all such summary bibliographies there is a lot of subjectivity in the choice of what to include. It was difficult to decide whether or not to include textbooks. In the end I decided to include a few that had been particularly influential on the way statistics is taught at undergraduate level. I have not included any of the very interesting references that are specific to the school level because this would have made what was intended to be a short list even longer than it has become. The list has been circulated amongst a lot of people working in the field of statistical education and I have benefited from their advice. In the final analysis, though, the final decision was mine and any errors and omissions are mine. I would welcome correspondence about any important contributions that are missing and any references that I have included that you think should not be.

  • This paper describes a computer managed instruction package for teaching introductory or advanced statistics. The instructional package is described and anecdotal information concerning its performance and student responses to its use over two semesters are given. (Author/BL)

  • Describes the operation of a graduate level statistics course based on computer-assisted instruction (CAI). Course content and student reactions are discussed, course evaluations are reported, problems involved with moving the courseware to different computer systems are described, and the CAI run-time system is explained. (10 references) (LRW)

  • Describes primary and supplementary textbooks for a course on nonparametric statistics for students in behavioral sciences, lists conceptual and applied articles using these techniques, and recommends the use of the SPSS-X computer package. All of these materials have been received favorably by the students. (PsycLIT Database Copyright 1993 American Psychological Assn, all rights reserved)

  • Discusses experiences in elementary statistics that involve describing data by measures of central tendency and dispersion and that are appropriate for students in secondary schools. Includes background information, instructional strategies, procedures, and a ready-to-duplicate student worksheet. (JN)

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