We consider the effect on estimation of simultaneous variable centering
and interaction effects in linear regression. We technically define, review,
and amplify many of the statistical issues for interaction models with
centering in order to create a useful and compact reference for teachers,
students, and applied researchers. In addition, we investigate a sequence
of models that have an interaction effect and/or variable centering and
derive expressions for the change in the regression coefficients between
models from both an intuitive and mathematical perspective. We demonstrate
how these topics may be employed to motivate discussion of other important
areas, e.g., misspecification bias, multicollinearity, design of experiments,
and regression surfaces. This paper presents a number of results also
given elsewhere but in a form that gives a unified view of the topic.
The examples cited are from the area of medical statistics.
Key Words: Beta coefficients; Introductory statistics;
Medical statistics; Misspecification bias; Multicollinearity; Multiple
The first day of a course has great potential to set the tone for the
entire course, planting the seeds for habits of mind and questioning and
setting in motion expectations for classroom discourse. Rather than let
the first meeting contain little besides going over the syllabus, the
instructor (Lesser) decided to use two sustained open-ended scenarios
to put in place from the start the problem-based inquiry learning approach
he wanted to use throughout most of the course. After reviewing the literatures
involved, this paper shares a description of the lesson's design and instructional
cycle and a discourse analysis of that lesson's implementation. Strategies
identified by the case study analysis include varying participation structures,
well-crafted problems, and the instructor's role as facilitator and co-learner.
Key Words: Counterintuitive; Cognitive conflict; Discourse;
First day of class; Simpson's paradox; Representation; Teachers.
The study presents and applies the 4MAT theoretical framework to educational
planning to transform a biostatistics course into a problem-based learning
experience. Using a four-question approach, described are specific activities/materials
utilized at both the class and course levels. Two web-based instruments
collected data regarding student satisfaction with the course and perception
of the field of biostatistics (Attitudes Toward Statistics Survey). Student
satisfaction and perception increased significantly following implementation
of the new curriculum as compared to previous ratings. The results indicated
that students felt more strongly that the seminars were well-organized,
encouraged participation/discussion and integrated concepts across the
curriculum. Additionally, recommendations for implementation are provided
regarding problem-based learning techniques and the adaptation of our
approach to more general settings are addressed.
Key Words: Active learning; Student attitudes; Curriculum
assessment; Course evaluation.
In this article we describe a semester-long project, based on the popular
video game series Guitar Hero, designed to introduce upper-level undergraduate
statistics students to statistical research. Some of the goals of this
project are to help students develop statistical thinking that allows
them to approach and answer open-ended research questions, improve statistical
programming skills, and investigate computational statistical methods,
such as resampling methods and power simulations. We outline the steps
of the project, including developing a method to address the research
question ("Are missed notes grouped together in parts of a song?"), statistical
programming (implemented in R), collecting data, estimation, and hypothesis
testing - including statistical power. The project, as described in this
article, was intended as a semester-long project for Mathematical Statistics
students, but would work equally well as a capstone project. We discuss
modifications to make this project appropriate for different courses,
including graduate-level courses. The appendix includes the handouts provided
to the students, several songs recorded by our class, some of the methods
created by the students, and R code for implementing various aspects of
Key Words: Active Learning; Bootstrap Methods; Permutation
Tests; Resampling Methods; Course Project; Simulation.
Interviews with Statistics Educators
Joan Garfield is Professor of Educational Psychology at the University
of Minnesota. She is a Fellow of the American Statistical Association,
a Fellow of the American Educational Research Association, and a recipient
of ASA's Founders Award. She received the United States Conference On
Teaching Statistics Lifetime Achievement Award in 2007. The following
interview took place via email on October 16 - 26, 2011.
We located 38 articles that have been published from January 2011 through October 2011 that pertained
to statistics education. In this column, we highlight a few of these articles that represent a variety of
different journals that include statistics education in their focus. We also provide information about the
journal and a link to their website so that abstracts of additional articles may be accessed and viewed.
CAUSEweb (www.causeweb.org) and MERLOT (www.merlot.org) are online resources for statistics educators.
MERLOT has peer-reviewed applets, videos, simulations, tutorials, and activities which work well for either
online or traditional classes. CAUSEweb has many of these resources (plus others, including jokes, cartoons,
songs, and quotes), but also serves as a contact point for professional development opportunities such as conferences,
workshops, and webinars
Data Sets and Stories
This paper presents a data set describing the sale of individual residential
property in Ames, Iowa from 2006 to 2010. The data set contains 2930 observations
and a large number of explanatory variables (23 nominal, 23 ordinal, 14
discrete, and 20 continuous) involved in assessing home values. I will
discuss my previous use of the Boston Housing Data Set and I will suggest
methods for incorporating this new data set as a final project in an undergraduate
Key Words: Multiple Regression; Linear Models; Assessed
Value; Group Project.