Skip to main content

2000 | Buch | 2. Auflage

Permutation Tests

A Practical Guide to Resampling Methods for Testing Hypotheses

verfasst von: Phillip Good

Verlag: Springer New York

Buchreihe : Springer Series in Statistics

insite
SUCHEN

Über dieses Buch

In 1982, I published several issues of a samdizat scholarly journal called Random­ ization with the aid of an 8-bit, I-MH personal computer with 48K of memory (upgraded to 64K later that year) and floppy disks that held 400 Kbytes. A decade later, working on the first edition of this text, I used a 16-bit, 33-MH computer with 1 Mb of memory and a 20-Mb hard disk. This preface to the second edition comes to you via a 32-bit, 300-MH computer with 64-Mb memory and a 4-Gb hard disk. And, yes, I paid a tenth of what I paid for my first computer. This relationship between low-cost readily available computing power and the rising popularity of permutation tests is no coincidence. Simply put, it is" faster today to compute an exact p-value than to look up an approximation in a table of the not-quite-appropriate statistic. As a result, more and more researchers are using Permutation Tests to analyze their data. Of course, some of the increased usage has also come about through the increased availability of and improvements in off-the-shelf software, as can be seen in the revisions in this edition to Chapter 12 (Publishing Your Results) and Chapter 13 (Increasing Computation Efficiency).

Inhaltsverzeichnis

Frontmatter
Chapter 1. A Wide Range of Applications
Abstract
The chief value of permutation tests lies in their wide range of applications.
Phillip Good
Chapter 2. A Simple Test
Abstract
In this chapter, we consider the assumptions that underlie the permutation test and take a look at some of the permutation test’s formal properties—its significance level, power, and robustness. This first look is relatively nonmathematical in nature. A formal derivation is provided in Chapter 14.
Phillip Good
Chapter 3. Testing Hypotheses
Abstract
In this chapter, you learn how to approach and resolve a series of testing problems of increasing complexity, specifically, tests for location and scale parameters in one, two, and k samples. You learn how to derive confidence intervals for the unknown parameters, and you learn to increase the power of your tests by sampling from blocks of similar composition.
Phillip Good
Chapter 4. Experimental Designs
Abstract
In this chapter, we explore the use of permutation methods for analyzing the results of complex experimental designs that may involve multiple control variables, covariates, and restricted randomization.
Phillip Good
Chapter 5. Multivariate Analysis
Abstract
The value of an analysis based on simultaneous observations on several variables—height, weight, blood pressure, and cholesterol level, for example, is that it can be used to detect subtle changes that might not be detectable, except with very large, prohibitively expensive samples, were you to consider only one variable at a time.
Phillip Good
Chapter 6. Categorical Data
Abstract
In many experiments and in almost all surveys, many if not all the results fall into categories rather than being measurable on a continuous or ordinal scale: e.g., male vs. female, black vs. Hispanic vs. oriental vs. white, in favor vs. against vs. undecided. The corresponding hypotheses concern proportions: “Blacks are as likely to be Democrats as they are to be Republicans.” Or, “the dominant genotype ‘spotted shell’ occurs with three times the frequency of the recessive.” In this chapter, you learn to test hypotheses like these that concern categorical and ordinal data.
Phillip Good
Chapter 7. Dependence
Abstract
The title of this chapter, “dependence,” reflects our continuing emphasis on the alternative rather than on the null hypothesis. As you discover anew in this chapter, the permutation test is invaluable1 whether you wish to focus on one or two specific hypotheses of dependence or provide protection against a broad spectrum of alternatives.
Phillip Good
Chapter 8. Clustering in Time and Space
Abstract
In this chapter, you learn how to detect clustering in time and space and to validate clustering models. We use the generalized quadratic form in its several guises including Mantel’s U and Mielke’s multiresponse permutation procedure to work through a series of applications in atmospheric science, epidemiology, ecology, and archeology.
Phillip Good
Chapter 9. Coping with Disaster
Abstract
In this chapter, you receive practical guidelines for coping with the many catastrophes that confront the applied statistician:
  • subjects who miss an appointment,
  • subjects who disappear completely and mysteriously in the middle of an experiment,
  • incomplete questionnaires,
  • covariates after the fact,
  • outlying observations whose extreme and questionable values suggest they may have been recorded incorrectly,
  • off-scale and other censored values that cannot be determined with precision,
  • and even studies that must be brought to a rapid and untimely conclusion well in advance of the scheduled date.
Phillip Good
Chapter 10. Which Statistic? Solving the Insolvable
Abstract
Many common statistical problems defy conventional parametric analysis simply because the distributions of the resultant test statistics are not well tabulated, or, worse, we settle for a less-than-optimal statistic simply because a table for the lessthan-optimal statistic is readily available—the chi-square statistic (Section 6.3) and its misapplication to sparse contingency tables is one obvious example.
Phillip Good
Chapter 11. Which Test Should You Use?
Abstract
In this chapter, we provide you with an expert system to use in choosing an appropriate testing technique. Your expert system comes to you in two versions—a professional’s handbook with detailed explanations of the choices and a short “quick-reference” version at the end of the chapter.
Phillip Good
Chapter 12. Publishing Your Results
Abstract
McKinney et al [1989] report that more than half the published articles that apply Fisher’s exact test do so improperly. Our own survey of some 50 biological and medical journals supports their findings. This chapter provides you with a positive prescription for the successful application and publication of the results of resampling procedures. First, we consider the rules you must follow to ensure that your data can be analyzed by statistical and permutation methods. Then, we describe two commercially available computer programs that can perform a wide variety of permutation analyses. Finally, we provide you with five simple rules to prepare your report for publication.
Phillip Good
Chapter 13. Increasing Computational Efficiency
Abstract
With today’s high-speed computers, drawing large numbers of subsamples with replacement (the bootstrap) or without (the permutation test) is no longer a problem, unless or until the entire world begins computing resampling tests. To prepare for this eventuality, and because computational efficiency is essential in the search for more powerful tests, a primary focus of research in resampling today is the development of algorithms for rapid computation.
Phillip Good
Chapter 14. Theory of Permutation Tests
Abstract
In this chapter, we establish the underlying theory of permutation tests. The content is heavily mathematical, in contrast to previous chapters, and a knowledge of calculus is desirable.
Phillip Good
Backmatter
Metadaten
Titel
Permutation Tests
verfasst von
Phillip Good
Copyright-Jahr
2000
Verlag
Springer New York
Electronic ISBN
978-1-4757-3235-1
Print ISBN
978-1-4757-3237-5
DOI
https://doi.org/10.1007/978-1-4757-3235-1