In this paper we describe an interactive activity that illustrates simple linear regression. Students collect data and analyze it using simple linear regression techniques taught in an introductory applied statistics course. The activity is extended to illustrate checks for regression assumptions and regression diagnostics taught in an intermediate applied statistics course.
This study compares students' performance and attitudes in a hybrid (blend of online and face-to-face) model of Elementary Statistics and a traditional (face-to-face) model of the same course. Performance was measured by test, quiz, project, and final exam grades. Attitude was measured by the results of a course survey administered at the end of the semester. Both models of the course required the same textbook and statistical computer package, were taught by the same instructor, and had similar demographic characteristics such as gender, major, and classification. Significant differences were found in an extra credit grade comprised of points earned on interactive worksheets, and attitudes toward the course. There was no significant difference in students' performance as measured by grades. The value of hybrid courses as a viable option in distance education and their potential benefits to students and the educational institution are discussed.
This article describes an innovative curriculum module the first author created on the two-way exchange between statistics and applied ethics. The module, having no particular mathematical prerequisites beyond high school algebra, is part of an undergraduate interdisciplinary ethics course which begins with a 3-week introduction to basic applied ethics taught by a philosophy professor (the second author), and continues with 3-week modules from professors in various other disciplines. The first author's module's emphasis on conceptual and critical thinking makes it easily adaptable to service-level courses as well as readily expandable for more mathematically sophisticated audiences. Through in-class explorations and discussions, the module made connections to contemporary topics such as the death penalty, equal pay for equal work, and profiling. This article shares examples, resources, strategies and lessons learned for instructors wishing to develop their own modules of various lengths.
In this paper, we present an interactive teaching approach to introduce the concept of optimal design of experiments to students. Our approach is based on the use of spreadsheets. One advantage of this approach is that no complex mathematical theory is needed nor that any design construction algorithm has to be discussed at the introductory stage. Another benefit is that the students build all necessary matrices for concrete examples starting from a sensible initial design. By modifying the initial design by trial and error, they can try to improve the properties of the parameter estimators interactively. For problems in which finding the optimal design is not evident, they can use optimization software which is readily available in the spreadsheet software.
Courses in clinical epidemiology usually include acquainting students with a single 2X2 table. All diagnostic test characteristics are explained using this table. This pedagogic approach may be misleading. A new didactic approach is hereby proposed, using two tables, each with specific analogous notations (uppercase and lowercase) and derived equations. This approach makes it easier to discuss the use of Bayes' Theorem and the two stages of analyses, i.e., using sensitivity to calculate predictive values. Two different types of false negative rates and false positive rates are discussed.
In teaching undergraduate time series courses, we have used a mixture of various statistical packages. We have finally been able to teach all of the applied concepts within one statistical package; R. This article describes the process that we use to conduct a thorough analysis of a time series. An example with a data set is provided. We compare these results to an identical analysis performed on Minitab.
Recently, Nathan (1986) criticized Bar-Hillel and Falk's (1982) analysis of some classical probability puzzles on the grounds that they wrongheadedly applied mathematics to the solving of problems suffering from "ambiguous informalities". Nathan's prescription for solving such problems boils down to assuring in advance that they are uniquely and formally soluble--though he says little about how this is to be done. Unfortunately, in real life problems seldom show concern as to whether their naturally occurring formulation is or is not ambigous, does or does not allow for unique formalization, etc. One step towards dealing with such problems intelligently is to recognize certain common cognitive pitfalls to which solvers seem vulnerable. This is discussed in the context of some examples, along with some empirical results.
The Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) states in Standard 11 for grades 9 through 12 that students should have oportunities to "use experimental and theoretical probabilities to represent and solve problems involving ncertainty." Standard 1 emphasizes the importance of students' learning to "formulate problems from situations within and outside mathematics." This article discusses a simply stated problem involving uncertainty that students can investigate experimentally or theoretcially. The problem places students in the role of problem formulator by giving them opportunities to generate various interesting problems of their own on the basis of a given situation. By changing certain characteristics of the original problem, students can be introduced to some fundamental concepts of decision making in two -player games.
For a quick and overall assessment of data sets, graphical methods are used extensively. Graphic statistics are devices for representing or summarizing numerical data or information. In this paper, some relatively new techniques, frequently referred to as methods of exploratory data analysis, are dicussed and illstrated with numerical examples.
Widespread availability of desk-top computing allows psychologists to manipulate complex multivariate datasets. While researchers in the physical and engineering sciences have dealt with increasing data complexity by using scientific visualization, reseearchers in the behavioral sciences have been slower to adopt these tools (Butler, 1993). To address this descrepancy, this paper defines scientific visualization, presents a theoretical framework for understanding visulaization, and reviews a number of multivariable visualization techniques in light of this framework.