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. ## Undergraduate Curriculum## What Teachers Should Know about the Bootstrap: Resampling in the Undergraduate Statistics CurriculumarXiv, 2014, 83 pages, 23 figures. The scripts and datasets are here: scriptsData14115279.tar.gz Abstract: I have three goals in this article: - To show the enormous potential of bootstrapping and permutation tests to help students understand statistical concepts including sampling distributions, standard errors, bias, confidence intervals, null distributions, and P-values.
- To dig deeper, understand why these methods work and when they don't, things to watch out for, and how to deal with these issues when teaching.
- To change statistical practice---by comparing these methods to common t tests and intervals, we see how inaccurate the latter are; we confirm this with asymptotics. n >= 30 isn't enough---think n >= 5000. Resampling provides diagnostics, and more accurate alternatives. Sadly, the common bootstrap percentile interval badly under-covers in small samples; there are better alternatives.
The tone is informal, with a few stories and jokes. ## 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 ## Diez, Barr and Cetinkaya-Rundel: Introductory Statistics with Randomization and SimulationThis is on OpenIntro. This intro stat book uses randomization tests (permutation tests) to introduce hypothesis testing. The treatment of the bootstrap in the first edition is lacking-they find that the bootstrap percentile interval is poor in small samples (true), and don't go deeper. See my 2014 arXiv article below for a deeper discussion. 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+.
resample for R. The newest version is at r-packages or on CRAN, http://cran.fhcrc.org/web/packages/resample.The bootstrap package is smallest, the boot package offers the most analytical capabilities, and the resample package is easiest to use. The R version of resample is a partial copy of the S+ version, but I'll add to it over time. The S+ version includes a menu interface, and offers some capabilities not in the other packages. For a quick comparison of all, see bootstrapComparison.txt. For a comparison of ease of use of boot and resample, see resamplePoster1407.pdf. ## 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/ |