The bootstrap and permutation tests offer ways to help students better understand concepts such as sampling distributions, standard errors, confidence intervals, P-values, and statistical significance. Here are notes about books and software for teaching using resampling. ## Mathematical Statistics## Chihara and Hesterberg: Mathematical Statistics with Resampling and RMathematical Statistics with Resampling and R by Laura Chihara and Tim Hesterberg (Wiley, 2011) uses permutation tests and bootstrapping to introduce these concepts and to motivate more classical mathematical approaches. For more information, see ## OverviewResampling helps students understand the meaning of sampling distributions, sampling variability, P-values, hypothesis tests, and confidence intervals. This groundbreaking book shows how to apply modern resampling techniques to mathematical statistics. Extensively class-tested to ensure an accessible presentation, Mathematical Statistics with Resampling and R utilizes the powerful and flexible computer language R to underscore the significance and benefits of modern resampling techniques. The book begins by introducing permutation tests and bootstrap methods, motivating classical inference methods. Striking a balance between theory, computing, and applications, the authors explore additional topics such as: - Exploratory data analysis
- Calculation of sampling distributions
- The Central Limit Theorem
- Monte Carlo sampling
- Maximum likelihood estimation and properties of estimators
- Confidence intervals and hypothesis tests
- Regression
- Bayesian methods
Mathematical Statistics with Resampling and R is an excellent book for courses on mathematical statistics at the upper-undergraduate and graduate levels. It also serves as a valuable reference for applied statisticians working in the areas of business, economics, biostatistics, and public health who utilize resampling methods in their everyday work. ## Introductory Statistics
The bootstrap and permutation tests offer ways to help students
better understand concepts such as sampling distributions, standard
errors, confidence intervals, and P-values. ## Lock^5: Statistics: Unlocking the Power of DataThis intro stat book uses randomization (resampling) to introduce statistical concepts.
The publisher's page is here. See the related note about StatKey below. More formally, this is ## Single chapters for Moore et. al booksBootstrap Methods and Permutation Tests (BMPT)
by Hesterberg, Moore, Monaghan, Clipson, and Epstein
was
written as an introduction to these methods, with a focus on the
pedagogical value.
There are different versions of BMPT, written as supplemental chapters for two different books, but all can be used independently as an introduction to bootstrap methods and permutation tests.
The first version (
The second version (
The third version (
The fourth version ( ## S+ data packages and supplements for PBS and IPSThere are S+ packages to accompany both versions, containing datasets, example scripts, and documentation.For BMPT/PBS download PBSdata.zip. For BMPT/IPS5e download IPSdata.zip. For BMPT/IPS6e download IPSdata6.zip. Download the appropriate package, unzip, then follow instructions in INSTALL.txt. To use these packages, you need S+ and S+Resample, see below. For a general introduction to S+, see the S-PLUS Guide for Moore and McCabe's Introduction to the Practice of Statistics, Fifth Edition. This works best with the IPS5e version of the data package. ## Bootstrap/Resampling Software## StatKeyThe Lock^5 team have developed web apps to encourage the use of simulation methods (e.g. bootstraps intervals and randomization tests) to help students in introductory statistics courses understand the basic ideas of statistical inference. The result, called StatKey, is now freely available at http://lock5stat.com/statkey. I've seen a demo, this could be very useful, with or without their book. There are procedures for generating bootstrap distributions for a mean, median, standard deviation, proportion, difference in means, difference in proportions, slope, and correlation as well as constructing randomization distributions to test hypotheses about most of the same parameters. In each of these situations students see a representation of the original sample, individual bootstrap/randomization samples, and a summary dotplot of the results for lots of simulated samples. Students can easily interact with the bootstrap or randomization distribution to find summary statistics, find percentiles, or check tail probabilities. ## S+ and R softwareThere are three general-purpose packages for resampling in R and S+:bootstrap for
R
and
S+,
boot for
R
and
S+, and
S+Resample for S+.
The bootstrap package is smallest, the boot package offers the most analytical capabilities, and the S+Resample package is easiest to use, especially on Windows, and offers some capabilities not in the other packags. For a quick comparison of S+Resample, bootstrap and boot, see comparison.txt. S+ is the commercial predecessor to R. S+Resample ships with S+; the other packages must installed. There is a free student version of S+ available from http://www.onthehub.com/tibco. This is an older version of S+, without S+Resample preinstalled. To install it in S+, install the pkgutils package, then use that to install S+Resample: install.pkgutils() library(pkgutils) install.packages("resample") ## Short Course: Bootstrap Methods and Permutation TestsThis is an introduction to the bootstrap, permutation tests, and other resampling methods. For a course description and details see bootstrap-short-course. I have given this course in various formats, ranging from a two-day hands-on course to half-day lecture-only, public or private, in Albuquerque, Boston, Chicago, Cincinnati, L.A., Little Rock, Miami, Minneapolis, Portland, Rochester MN, San Francisco, Washington D.C., Basel, Basingstoke UK, Bedford UK, London, Manchester, Montpellier FR, Toronto, and Zurich.Since I am no longer at Insightful (now Tibco) I won't give this course as frequently. Contact me if you are interested in arranging a course. ## Articles and Technical Reports:For other articles (including references to published articles related to this software) see articles/ |