Single-case and Small-n Experimental Designs: A Practical Guide To Randomization Tests

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Single-case and Small-n Experimental Designs: A Practical Guide To Randomization Tests
John B. Todman , and Pat Dugard
Manufacturer: Lawrence Erlbaum
ProductGroup: Book
Binding: Hardcover

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ASIN: 0805835547

This book is a practical guide to help researchers draw valid causal inferences from small-scale clinical intervention studies. It should be of interest to teachers of, and students in, courses with an experimental clinical component, as well as clinical researchers.

Inferential statistics used in the analysis of group data are frequently invalid for use with data from single-case experimental designs. Even non-parametric rank tests provide, at best, approximate solutions for only some single-case (and small-n ) designs. Randomization (Exact) tests, on the other hand, can provide valid statistical analyses for all designs that incorporate a random procedure for assigning treatments to subjects or observation periods, including single-case designs. These Randomization tests require large numbers of data rearrangements and have been seldom used, partly because desktop computers have only recently become powerful enough to complete the analyses in a reasonable time. Now that the necessary computational power is available, they continue to be under-used because they receive scant attention in standard statistical texts for behavioral researchers and because available programs for running the analyses are relatively inaccessible to researchers with limited statistical or computing interest.

This book is first and foremost a practical guide, although it also presents the theoretical basis for Randomization tests. Its most important aim is to make these tests accessible to researchers for a wide range of designs. It does this by providing programs on CD-ROM that allow users to run analyses of their data within a standard package (Minitab, Excel, or SPSS) with which they are already familiar. No statistical or computing expertise is required to use these programs. This is the "new stats" for single-case and small-n intervention studies, and anyone interested in this research approach will benefit.

Although the title is "Simulation", don't get the idea that this is a typical traditional text like say Fishman. Thompson covers many of the same topics but in different and interesting ways. For example the chapter on random quadrature covers most of the Monte Carlo techniques that one can find in Hammersley and Handscomb but he demonstrates the methods as ways to approximate integrals of functions. Although this was an early application of the Monte Carlo method, it is not what we typically do in simulation. But these techniques are still useful and regaining popularity when intensive computing is involved as comes about with bootstrap or Markov chain Monte Carlo. He also shows graphically the pitfalls of some pseudorandom number generators but does not get carried away in the quest to test randomness, a trap that too many of our colleagues fall into.

As Pieter van Gelder pointed out in his review, Thompson stimulates us with some examples of how Monte Carlo methods can readily attack solutions to differential equations such as in the gambler's ruin, the Dirichlet problem and the Fokker-Planck equation.

Thompson's strength is his knowledge of nonparametric density estimation and stochastic processes. Areas in which he has done a great deal of research.

Several authors including Thompson and Dudewicz have noted that the nonparametric bootstrap suffers some because of its discrete jumpy nature. If the distribution that one is sampling from is known to be continuous then smoothing the empiric distribution before resampling makes sense. Dudewicz refers to this approach as "the generalized bootstrap". Thompson and Taylor put a great deal of effort into such a resampling algorithm and named it SIMDAT. Section 5.3 addresses this approach. Thompson also presents SIMEST an algorithm that develops a likelihood function through simulation to then find parameter estimates that approximately maximize this likelihood. He demonstrates this with an oncological example of a stochastic model for tumor growth.

Other very practical and interesting examples of simulation in the text are rank testing for high-dimensional multivariate statistical process control, models for stocks (using geometric Brownian motion)and other problems in finance.

A whole chapter, Chapter 10 is devoted to resampling-based testing of hypotheses and Chapter 9 "Bayesian Approaches" covers Gibbs sampling and Markov chain Monte Carlo. Ideas of experimental design and response surface optimization are covered in Chapters 10 and 11.

Unusual for a statistics text is Chapter 8 that deals with the mathematics of Chaos theory.

Chapter 12 should not be overlooked. This puts many of the techniques together in the study of the AIDS epidemic. This is an endeavor that Professor Thompson has put a great deal of research effort into and his finding about the effects of the homosexual bath houses is very informative and enlightening.

This is a great book for statistician, operation research analysts, scientists and engineers. It contains some valuable material and philosophy that you will find nowhere else!

I recommend that the reader go through the preface. It is not the standard preface that outlines the text but rather it introduces arguments justifying the approach. In the preface he describes the Monty Hall problem. This is a wonderful problem for illustrating the subtleties of probability theory. Many mathematicians (including thee famous Paul Erdos) were led to incorrect solutions through probabilistic arguments. Although a careful mathematical treatment would lead to the correct answer, Professor Thompson points out that the easiest way to be convinced of the correct answer is to simulate the game.

The text is fairly technical and is meant for the applied statistician with a strong mathematical and statistical background. For the right audience it is a very entertaining book.

The philosophy is very similar to the philosophy of Efron and other resampling statisticians who see the value in the use of intensive computing to replace analytical methods when the analysis is difficult. The book covers many of the computer-intensive methods that are currently popular including the EM algorithm, Markov Chain Monte Carlo (Gibbs Sampling) and resampling methods including bootstrap. Monte Carlo methods are introduced early (after discussing pseudo random number generation) along with various techniques for variance reduction in the simulations. Then a variety of models and interesting practical examples are presented.

The presentation is not very systematic which may be unsettling for some readers. However, I think it is worth the effort. Any statistician with a broad range of consulting experience will appreciate and relate to Thompson's ideas.

Hollow Chocolate Bunnies of the Apocalypse (Gollancz)

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Hollow Chocolate Bunnies of the Apocalypse (Gollancz)
Robert Rankin
Manufacturer: Orion Books Limited
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Binding: Paperback

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ASIN: 0575074019

Toy Town—older, bigger, and certainly not wiser. The Old Rich, who have made their millions from the royalties on their world-famous nursery rhymes, are being murdered one by one. A psychopath is on the loose, and he must be stopped at any cost. It’s a job for Toy Town’s only detective—but he’s missing, leaving only Eddie Bear, and his bestest friend Jack, to track down the mad killer.

Puns like epées, wild imaginings - both dark and very, very funny.......2007-09-23