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# Workshop on Bootstrap Methods and Permutation Tests for Teaching Statistics

### Presented by

Tim Hesterberg

#### Wednesday, May 16, 2007 • 8:30am - 4:30pm

The Consortium for the Advancement of Undergraduate Statistics Education (CAUSE) will sponsor a 1-day workshop on bootstrap methods and permutation tests for teaching statistics.

In addition to meals during the day of the workshop, participants will receive a registration fee waiver for the United States Conference on Teaching Statistics (USCOTS), which will begin on the evening of Thursday, May 17 and run through Saturday, May 19, 2007.

### Target Audience

Participants in this workshop should be teaching or planning to teach introductory level undergraduate statistics courses in a two-year or four-year college or university, or the Advanced Placement high school statistics course.

### Abstract

Statistical concepts such as sampling distributions, standard errors, and P-values are difficult for many students. It is hard to get hands-on experience with these abstract concepts. In this workshop we'll learn how to use bootstrapping and permutation tests (BPT), for use in statistical practice and teaching. BPT provide output we may graph in familiar ways (like histograms) to help students and clients understand sampling variability, standard errors, p-values, and the Central Limit Theorem (CLT)-not just in the abstract, but for the data set and statistic at hand.

BPT also free students from dependence on formula-based methods. Early in Stat 101 we teach that robustness is important, and that students should look at medians, not just means. Yet later in the course, and too often in statistical practice, we ignore those lessons, and use simple means with Normal-based inferences, even though the corresponding assumptions are violated. BPT provide ways to calculate standard errors, confidence intervals, and hypothesis tests for a wide variety of statistics, without formulas. Or they can be used to check formulas, and help students gain intuition about whether an answer they calculate with a formula is reasonable.

Teaching materials using BPT are available for use with some introductory statistics texts, such as Moore and McCabe, Introduction to the Practice of Statistics, see www.insightful.com/Hesterberg/bootstrap.

### Expectations

• Participation in all sessions offered on Wednesday, May 16, 2007

• Attendance at USCOTS

Please note: CAUSEway workshops receive principal funding from a National Science Foundation grant. As part of that award, Science and Mathematics Program Improvement (SAMPI) at Western Michigan University will be conducting an independent evaluation of all CAUSEway activities and workshop participants are expected to fully participate in this evaluation.

### Tim Hesterberg

Tim Hesterberg taught at St. Olaf College and Franklin and Marshall College, then joined Insightful Corp. in 1996 to turn his research on bootstrap methods into widely usable statistical software. He has taught short courses on BPT in such exotic locations as Rochester MN and Little Rock. Oh yes, also Albuquerque, San Francisco, Boston, Chicago, L.A., Washington D.C., Minneapolis, Cincinnati, Portland, Seattle, Toronto, London, Manchester, Basingstoke UK, Bedford UK, Zurich, Basel, and Montpellier. His web site is www.insightful.com/Hesterberg. He enjoys teaching water bottle rockets, and works on environmental preservation, fighting global warming, and scientific integrity in public policy, home.comcast.net/~timhesterberg.

### Workshop outline

We begin with a graphical approach to bootstrapping and permutation testing, illuminating basic statistical concepts of standard errors, confidence intervals, p-values and significance tests. We show graphical and numerical diagnostic checks for the validity of traditional Gaussian-based inferences.

We consider a variety of statistics (mean, trimmed mean, regression, etc.), and a number of sampling situations (one-sample, two-sample, stratified, finite-population), stressing the common techniques that apply in these situations.

Introduction to Bootstrapping

General procedure

Why does bootstrapping work?

Sampling distribution and bootstrap distribution

Bootstrap Distributions and Standard Errors

Distribution of the sample mean

Bootstrap distributions of other statistics

Simple confidence intervals

Two-sample applications

How Accurate Is a Bootstrap Distribution?

Example where things go wrong

Bootstrap Confidence Intervals

Bootstrap percentiles as a check for standard intervals

More accurate bootstrap confidence intervals

Significance Testing Using Permutation Tests

Two-sample applications

Other settings

Course sessions will be a combination of PowerPoint-style presentation, live demonstrations, and hands-on work using statistical software.

The demonstrations will use the free student version of S-PLUS with a resampling library that provides an easy-to-use graphical interface for BPT. However, the focus of this course is on the concepts to be taught, not the software. We use the graphical interface so that participants with no experience with S-PLUS will have no trouble following. The teaching ideas can also be implemented with other software.

### Course materials

Course participants will receive handouts and a copy of Bootstrap Methods and Permutation Tests, Hesterberg, et al., W. H. Freeman, 2003, a supplemental chapter for using BPT for teaching introductory statistics.

### Learning outcomes

Participants will learn how to use resampling methods:

• to compute standard errors
• to check the accuracy of the usual Gaussian-based methods,
• to compute both quick and more accurate confidence intervals,
• for a variety of statistics and
• for a variety of sampling methods, and
• to perform significance tests in some settings.

Participants will also gain an appreciation for the benefits of these methods in teaching statistical concepts.