This paper describes an interactive activity developed for illustrating hypothesis tests on the mean for paired or matched
samples. The activity is extended to illustrate assessing normality, the Wilcoxon signed rank test, Kaplan-Meier survival
functions, two-way analysis of variance, and the randomized block design.
Key Words:Active learning; Assessing normality; Blinding; Confounding variable; Kaplan-Meier survival
function; Paired difference experiment; Randomization; Randomized block design; Right-censored data; Two-way analysis of
variance; Wilcoxon signed rank test.
This article explores the uses of a simulation model (the two bucket story)—implemented by a stand-alone computer program,
or an Excel workbook (both on the web)—that can be used for deriving bootstrap confidence intervals, and simulating various
probability distributions. The strengths of the model are its generality, the fact that it provides a powerful approach
that can be fully understood with very little technical background, and the fact that it encourages an active approach to
statistics—the user can see the method being acted out either physically, or in imagination, or by a computer. The article
argues that this model and other similar models provide an alternative to conventional approaches to deriving probabilities
and making statistical inferences. These simulation approaches have a number of advantages compared with conventional
approaches: their generality and robustness; the amount of technical background knowledge is much reduced; and, because the
methods are essentially sequences of physical actions, it is likely to be easier to understand their interpretation and
Key Words:Active learning; Approaches to statistical thinking; Bootstrapped confidence intervals;
Computer simulation; Probability distributions; Resampling.
This paper describes a project with the goal of exposing both elementary school and undergraduate students to the concepts
associated with the experimental method, from the formulation of a researchable question to the analysis and interpretation
of the results. Under the guidance of their university mentors, fourth and fifth grade students formulated a research
question, designed an experiment to answer that inquiry, recorded the appropriate measurements, calculated the necessary
statistics, created visual displays of their results, and interpreted their findings at a student-centered Numeracy
Key Words:Active learning; Elementary statistics education, Numeracy.
We compare students in online and lecture sections of a business statistics class taught simultaneously by the same
instructor using the same content, assignments, and exams in the fall of 2001. Student data are based on class grades,
registration records, and two surveys. The surveys asked for information on preparedness, reasons for section choice, and
evaluations of course experience and satisfaction. Using descriptive statistics, regression analysis and standard
hypothesis tests, we test for significant differences between the online and lecture sections with regard to performance
and satisfaction with the course as well as motivation and preparedness for taking an online course. We report several
differences, including better performance by online students.
Key Words:Distance education; Internet course; Online education.
This article uses a case study of 2001 town and city data that we analyzed for Boston Magazine. We use this
case study to demonstrate the
challenges of creating a valid ranking structure. The data consist of three composite indices for 147 individual
townships in the Boston metropolitan area representing measures of public safety; the environment; and health. We report
the data and the basic ranking procedure used in the magazine article, as well as a discussion of alternative ranking
procedures. In particular, we demonstrate the impact of additional adjustment for the size of population, even when per
capita data are used. This case study presents an opportunity for discussion of fundamental data analysis concepts in all
levels of statistics courses.
Key Words:Data Analysis; Demographics; Graphics.
Three basic theorems concerning expected values and variances of sums and products of random variables play an important
role in mathematical statistics and its applications in education, business, the social sciences, and the natural sciences.
A solid understanding of these theorems requires that students be familiar with the proofs of these theorems. But while
students who major in mathematics and other technical fields should have no difficulties coping with these proofs, students
who major in education, business, and the social sciences often find it difficult to follow these proofs. In many textbooks
and courses in statistics which are geared to the latter group, mathematical proofs are sometimes omitted because students
find the mathematics too confusing. In this paper, we present a simpler approach to these proofs. This paper will be useful
for those who teach students whose level of mathematical maturity does not include a solid grasp of differential calculus.
Key Words:Covariance; Joint probability distribution; Means; Variances.
Datasets and Stories
Textbooks and websites today abound with real data. One neglected issue is that statistical investigations often require
a good deal of “cleaning” to ready data for analysis. The purpose of this dataset and exercise is to teach students to
use exploratory tools to identify erroneous observations. This article discusses the merits of such an exercise and
provides a team project, problem data, cleaned data for instructors, and reflections on past experiences. The main goal
is to give instructors a prepared project for their students to perform realistic data preparation and subsequent analysis.
The data for this project involve categorical and continuous variables for subjects age 65 and over testing calcium,
inorganic phosphorus, and alkaline phosphatase levels in the blood. The project described in this article involves
summary analysis, but the cleaned data could also be used for projects on independent samples t-tests, analysis of
variance, or regression.
Key Words:Activity-based learning; Data cleaning; Team projects.
Statistics textbooks for undergraduates have not caught up with the
enormous amount of analysis of Internet data that is taking place
these days. Case studies that use Web server log data or Internet
network traffic data are rare in undergraduate Statistics education.
And yet these data provide numerous examples of skewed and bimodal
distributions, of distributions with thick tails that do not follow
the usual models studied in class, and many other interesting
statistical curiosities. This paper summarizes the results of
research in two areas of Internet data analysis: users' web browsing
behavior and network performance. We present some of the main
questions analyzed in the literature, some unsolved problems, and
some typical data analysis methods used. We illustrate the questions
and the methods with large data sets. The data sets were obtained
from the publicly available pool of data and had to be processed and
transformed to make them available for classroom exercises. Students
in Introductory Statistics classes as well as Probability and
Mathematical Statistics courses have responded to the stories behind
these data sets and their analysis very well. The message in the
stories can be conveyed at a descriptive or a more advanced level.
Key Words:Exponential; Internet traffic; Inverse Gaussian; Maximum
likelihood; Negative Binomial; Poisson; Web server log data.