This paper describes an interactive project developed to use for teaching statistical sampling methods in an introductory undergraduate statistics course, an Advanced Placement (AP) statistics course, or, with adaptation, in a statistical sampling course or a statistical simulation course. The project allows students to compare the performance of simple random sampling, stratified random sampling, systematic random sampling, and cluster random sampling in an archaeological setting.
This paper begins by describing two hands-on activities developed for teaching basic statistical concepts to junior high students. Through generating, collecting, displaying, and analyzing data, students are given the opportunity to explore a variety of descriptive statistical techniques and develop an understanding of the distinction between theoretical, subjective, and empirical (or experimental) probabilities. These activities are then extended to introduce the sampling distribution of a sample proportion. The extension is appropriate for use in grades 9 through 12, in an Advanced Placement (AP) Statistics course, or in an introductory statistics course at the undergraduate level.
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.
This dataset contains information on life expectancies in various countries of the world and the densities of people per television set and of people per physician in those countries. The example has proven very useful for helping students to discover the fundamental principle that correlation does not imply causation. The data also give students an opportunity to explore data transformations and to consider whether a causal connection is necessary for one variable to be a useful predictor of another.
Classical estimators for the parameter of a uniform distribution on the interval are often discussed in mathematical statistics courses, but students are frequently left wondering how to distinguish which among the variety of classical estimators are better than the others. We show how classical estimators can be derived as Bayes estimators from a family of improper prior distributions. We believe that linking the estimation criteria in a Bayesian framework is of value to students in a mathematical statistics course, and we believe that the students benefit from the exposure to Bayesian methods. In addition, we compare classical and Bayesian interval estimators for the parameter Phi and illustrate the Bayesian analysis with an example.
In this paper, I will define statistical literacy (what it is and what it is not) and discuss how we can promote it in our introductory statistics courses, both in terms of teaching philosophy and curricular issues. I will discuss the important elements that comprise statistical literacy, and provide examples of how I promote each element in my courses. I will stress the importance of and ways to move beyond the "what" of statistics to the "how" and "why" of statistics in order to accomplish the goals of promoting good citizenship and preparing skilled research scientists.
In linear regression problems in which an independent variable is a total of two or more characteristics of interest, it may be possible to improve the fit of a regression equation substantially by regressing against one of two separate components of this sum rather than the sum itself. As motivation for this "separation principle," we provide necessary and sufficient conditions for an increased coefficient of determination. In teaching regression analysis, one might use an example such as the one contained herein, in which the number of wins of Major League Baseball teams is regressed against team payrolls, for the purpose of demonstrating that an investigator can often exploit intuition and/or subject-matter expertise to identify an efficacious separation.
We describe our experiences and express our opinions about a non-introductory statistics course covering data analysis. In addition to the methods of statistics, the course emphasizes the process of data analysis, the communication of results, and the role of statistics in the accumulation of scientific evidence. Since it is impossible to provide explicit instructions for all data analytic situations, the course attempts to impart a body of tools, a spirit of approach, and enough thoroughly covered case studies to give students the skills and confidence to apply this craft on their own.
StatVillage is a hypothetical city based on real data that is suitable as a teaching aid for an introductory class in survey sampling. It uses a World Wide Web-based interface to allow the students to actively select sampling units; it then returns the corresponding data for further analysis. The underlying data are actual census records extracted from public use microdata files.
We describe a World Wide Web-accessible workshop designed for students in an introductory statistics course that uses a capture-recapture experiment to illustrate the concept of a sampling distribution. In addition to the usual "sampling bowl" experiment, the workshop contains a computer simulation program written in XLISP-STAT that will allow students to further investigate the properties of the estimator.