Students often come to their first statistics class with the preconception that statistics is confusing and dull. This problem is compounded when even introductory techniques are steeped in jargon. One approach that can overcome some of these problems is to align the statistical techniques under study with elements from students’ everyday experiences. The use of simple physical analogies is a powerful way to motivate even complicated statistical ideas. In this article, I describe several analogies, some well known and some new, that I have found useful. The analogies are designed to demystify statistical ideas by placing them in a physical context and by appealing to students’ common experiences. As a result, some frequent misconceptions and mistakes about statistical techniques can be addressed.
Key Words: Expectation; Graphical displays; Hypothesis testing; Influence diagnostics; Regression models; Structure mapping; "Teaching-With-Analogies."
I recently introduced an advanced statistical methods course into our curriculum with a two-tiered prerequisite system - students were required to have taken
either an introductory statistics course
or Calculus II. As a result, this course served as a first course in statistics for some quantitatively strong students and a follow-up course for others. I used a case study approach to introduce and motivate ideas to students new to statistics while engaging and challenging students for whom some ideas were review. Given constraints on resources which exist at smaller schools, a data-centered course such as this offered a good first experience in statistics for math students, one which piqued their interest and set a solid foundation for further study. In addition, the mixed audience led to an intellectually exciting class atmosphere for all students in the class. A quantitative assessment of students’ understanding of important statistical concepts is described to provide insight into whether or not students with no statistical experience can comprehend and apply basic ideas as well as if they had taken an introductory statistics class.
Key Words: Applied regression; Case studies; Conceptual understanding; Mathematics majors; Prerequisites.
A number of programs written for the TI-83 Plus calculator are
demonstrated in this article to illustrate this graphing calculator's surprisingly advanced
statistical capabilities. Examples include residual plots for analysis of variance,
pairwise comparison in
one-factor experimental design, statistical inference for simple linear regression and
confidence intervals for contrasts used in experimental design. These and a number of other
programs are available for download. Advances in graphing
calculator statistical programs, such as those described in this article, allow instructors
and students in introductory applied graduate level statistics courses to perform
sophisticated statistical data diagnostic and inference procedures during class time in an
ordinary class room.
Key Words: Contrast; One-factor experimental design; Residual plot; Simple linear regression; TI-83 Plus graphing calculator.
The dice game HOG has been used successfully in a variety of educational situations as an activity that not only introduces students to concepts in probability, statistics, and simulation but
also fosters student interest in these concepts.
This article presents several areas in the statistics curriculum where important concepts can be dealt with in a hands-on
way. These areas include probability as decision making, experimental versus theoretical probability,
expected value, and optimization.
This article explains the rules for HOG, gives examples of students’ understanding, develops the probability theory, and identifies a “best” strategy for playing the game. This “best” strategy is developed in the context of fair six-sided dice and then generalized to fair s-sided dice.
Key Words: Expected value; Optimization; Probability.
As part of the University of Newcastle’s Total Quality Management (TQM) course, students study Experimental Design (ED) and Statistical Process Control (SPC) within the framework of the scientific approach to process improvement. A sufficient balance of theory and application is required to keep Business and Management students, most with a largely non-quantitative background, interested and aware of the need and method to correctly implement ED and SPC in industry. Tools to facilitate a basic understanding of the importance of the 3Rs, namely,
Randomization, Replication, and
Blocking, as well as highlighting the potential for mistakes or inefficient calibration techniques are essential in the learning process. This paper describes the use of a particular tool, called the "Ballistat," to illustrate TQM concepts, which enables students to obtain the hands-on experience needed to control processes in industry.
Key Words: Blocking; Linear Regression; Randomization; Replication; Statistical process control; Total quality management.
Teaching Bits: A Resource for Teachers of Statistics
This department features information sampled from a variety of sources that may be of
interest to teachers of statistics. Deb Rumsey abstracts information from the literature on
teaching and learning statistics, while Bill Peterson summarizes articles from the news and
other media that may be used with students to provoke discussions or serve as a basis for
classroom activities or student projects.
Body girth measurements and skeletal diameter measurements, as well as age, weight, height and gender, are given for 507 physically active
individuals - 247 men and 260 women. These data can be used to provide statistics students practice in the art of data analysis. Such analyses range from simple descriptive displays to more complicated multivariate analyses such as multiple regression and discriminant analysis.
Key Words: Anthropometry; Discriminant analysis; Ergonomics; Forensic science; Multiple regression.