Randomization Tests: 4th Edition (Hardback) book cover

Randomization Tests

4th Edition

By Eugene Edgington, Eugene Edgington, Patrick Onghena

Chapman and Hall/CRC

376 pages | 2 B/W Illus.

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Hardback: 9781584885894
pub: 2007-02-22
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pub: 2007-02-22
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The number of innovative applications of randomization tests in various fields and recent developments in experimental design, significance testing, computing facilities, and randomization test algorithms have necessitated a new edition of Randomization Tests.

Updated, reorganized, and revised, the text emphasizes the irrelevance and implausibility of the random sampling assumption for the typical experiment in three completely rewritten chapters. It also discusses factorial designs and interactions and combines repeated-measures and randomized block designs in one chapter. The authors focus more attention on the practicality of N-of-1 randomization tests and the availability of user-friendly software to perform them. In addition, they provide an overview of free and commercial computer programs for all of the tests presented in the book.

Building on the previous editions that have served as standard textbooks for more than twenty-five years, Randomization Tests, Fourth Edition includes a CD-ROM of up-to-date randomization test programs that facilitate application of the tests to experimental data. This CD-ROM enables students to work out problems that have been added to the chapters and helps professors teach the basics of randomization tests and devise tasks for assignments and examinations.


“…Overall, this is an interesting and well-written book that provides a useful discussion of the theory, design, and application of randomization tests, illustrated with appropriate examples using experimental data. The end-of-chapter questions and exercises make it useful also as a textbook for college students. It should be of interest for every experimenter who is interested in randomization or permutation tests or is skeptical about the reliability of the assumptions of parametric tests.”

—Andreas Karlsson (Uppsala University), Journal of the Royal Statistical Society

Table of Contents

Statistical Tests That Do Not Require Random Sampling

Randomization Tests

Numerical Examples

Randomization Tests and Nonrandom Samples

The Prevalence of Nonrandom Samples in Experiments

The Irrelevance of Random Samples for the Typical Experiment

Generalizing from Nonrandom Samples


Respect for the Validity of Randomization Tests



Precursors of Randomization Tests

Other Applications of Permutation Tests

Questions and Exercises



Randomized Experiments

Unique Benefits of Experiments

Experimentation without Manipulation of Treatments

Matching: A Precursor of Randomization

Randomization of Experimental Units

Experimental Units

Groups as Experimental Units

Control over Confounding Variables

Between-Subject and Within-Subject Randomization

Conventional Randomization Procedures

Randomization Procedures for Randomization Tests

Further Reading

Questions and Exercises

Calculating P-Values


Systematic Reference Sets

Criteria of Validity for Randomization Tests

Randomization Test Null Hypotheses

Permuting Data for Experiments with Equal Sample Sizes

Monte Carlo Randomization Tests

Equivalent Test Statistics

Randomization Test Computer Programs

Writing Programs for Randomization Tests

How to Test Systematic Data Permutation Programs

How to Test Random Data Permutation Programs

Nonexperimental Applications of the Programs

Questions and Exercises


Between-Subjects Designs


One-Way ANOVA with Systematic Reference Sets

A Simpler Test Statistic Equivalent to F

One-Way ANOVA with Equal Sample Sizes

One-Way ANOVA with Random Reference Sets

Analysis of Covariance

One-Tailed t Tests and Predicted Direction of Difference

Simpler Equivalent Test Statistics to t

Tests of One-Tailed Null Hypotheses for t Tests

Unequal-N One-Tailed Null Hypotheses

Fast Alternatives to Systematic Data Permutation for Independent t Tests

Independent t Test with Random Reference Sets

Independent t Test and Planned Comparisons

Independent t Test and Multiple Comparisons

Loss of Experimental Subjects

Ranked Data

Dichotomous Data


Questions and Exercises


Factorial Designs

Advantages of Randomization Tests for Factorial Designs

Factorial Designs for Completely Randomized Experiments

Proportional Cell Frequencies

Program for Tests of Main Effects

Completely Randomized Two-Factor Experiments

Completely Randomized Three-Factor Experiments

Interactions in Completely Randomized Experiments

Randomization Test Null Hypotheses and Test Statistics

Designs with Factor-Specific Dependent Variables

Dichotomous and Ranked Data

Fractional Factorial and Response Surface Designs

Questions and Exercises


Repeated-Measures and Randomized Block Designs

Carry-Over Effects in Repeated-Measures Designs

The Power of Repeated-Measures Tests

Systematic Listing of Data Permutations

A Nonredundant Listing Procedure

Σt2 as an Equivalent Test Statistic to F

Repeated-Measures ANOVA with Systematic Data Permutation

Repeated-Measures ANOVA with Random Data Permutation

Correlated t Test with Systematic Data Permutation

Fast Alternatives to Systematic Data Permutation for Correlated t Tests

Correlated t Test with Random Data Permutation

Correlated t Test and Planned Comparisons

Correlated t Test and Multiple Comparisons

Rank Tests

Dichotomous Data

Counterbalanced Designs


Factorial Experiments with Repeated Measures

Interactions in Repeated-Measures Experiments

Randomized Block Designs

Randomized Complete Blocks

Incomplete Blocks

Treatments-by-Subjects Designs

Disproportional Cell Frequencies

Test Statistic for Disproportional Cell Frequencies

Data Adjustment for Disproportional Cell Frequency Designs

Restricted-Alternatives Random Assignment

Combining P-Values

Additive Method of Combining P-Values

Combining One-Tailed and Two-Tailed P-Values

Questions and Exercises


Multivariate Designs

Importance of Parametric Assumptions Underlying MANOVA

Randomization Tests for Conventional MANOVA

Custom-Made Multivariate Randomization Tests

Effect of Units of Measurement

Multivariate Tests Based on Composite z Scores

Combining t or F Values over Dependent Variables

A Geometrical Model

Tests of Differences in Composition

Evaluation of Three MANOVA Tests

Multivariate Factorial Designs

Combining Univariate and Multivariate P-Values

Questions and Exercises



Determining P-Values by Data Permutation

Computer Program for Systematic Data Permutation

Correlation with Random Data Permutation

Multivariate Correlation

Point-Biserial Correlation

Correlation between Dichotomous Variables

Spearman’s Rank Correlation Procedure

Kendall’s Rank Correlation Procedure

Questions and Exercises


Trend Tests

Goodness-of-Fit Trend Test

Power of the Goodness-of-Fit Trend Test

Test Statistic for the Goodness-of-Fit Trend Test

Computation of Trend Means

Computer Program for Goodness-of-Fit Trend Test

Modification of the Goodness-of-Fit Trend Test Statistic

Correlation Trend Test

Correlation Trend Test for Factorial Designs

Disproportional Cell Frequencies

Data Adjustment for Disproportional Cell Frequency Designs

Combining of P-Values for Trend Tests for Factorial Experiments

Repeated-Measures Trend Tests

Differences in Trends

Correlation Trend Test and Simple Correlation

Ordered Levels of Treatments

Ranked and Dichotomous Data

Questions and Exercises


Matching and Proximity Experiments

Randomization Tests for Matching

Randomization Tests of Proximity

Matching and Proximity Tests Based on Random Selection of Treatment Levels

Questions and Exercises


N-of-1 Designs

The Importance of N-of-1 Designs

Fisher’s Lady-Tasting-Tea Experiment

The Concept of Choosing as a Random Process

Limitations of the Random Sampling Model for N-of-1 Experiments

Random Assignment Model

Carry-Over Effects

The N-of-1 Randomization Test: An Early Model

Factorial Experiments

Randomized Blocks


Operant Research and Treatment Blocks

ABAB Design

Random Assignment of Treatment Blocks to Treatments

Randomization Tests for Treatment Intervention

Effects of Trends

Randomization Tests for Intervention and Withdrawal

Multiple Schedule Experiments

Power of N-of-1 Randomization Tests

Replicated N-of-1Experiments

N-of-1 Clinical Trial Facilities

Single-Cell and Other Single-Unit Neuroscience Experiments

Books on N-of-1 Design and Analysis

Software for N-of-1 Randomization Tests

Questions and Exercises


Tests of Quantitative Laws

Generic and Specific Null Hypotheses

The Referent of a Law or Model

Test of Incremental Effects

Weber’s Law

Other Psychophysical Laws

Foraging Behavior of Hawks


Questions and Exercises


Tests of Direction and Magnitude of Effect

Tests of One-Tailed Null Hypotheses for Correlated t Tests

Other Tests of One-Tailed Null Hypotheses Using ta or (Ā -B) as Test Statistics

Tests of One-Tailed Null Hypotheses about Differences in Variability

Tests of One-Tailed Null Hypotheses for Correlation

Testing Null Hypotheses about Magnitude of Effect

Testing Null Hypotheses about Specific Additive Effects

Questions and Exercises


Fundamentals of Validity

Randomization Tests as Distribution-Free Tests

Differences between Randomization Test Theory and Permutation Test Theory

Parametric Tests as Approximations to Randomization Tests

Randomization Test Theory

Systematically Closed Reference Sets Permutation Groups

Data-Permuting and Randomization-Referral Procedures

Invariance of Measurements under the Null Hypothesis

General and Restricted Null Hypotheses

Reference Sets for General Null Hypotheses

Reference Subsets for General Null Hypotheses

Reference Subsets for Restricted Null Hypotheses

Reference Subsets for Planned and Multiple Comparisons

Reference Subsets for Factorial Designs

Open Reference Sets: Treatment Intervention and Withdrawal

Closed Reference Sets: Dropouts

Open Reference Sets: Permuting Residuals

Sampling a List of Randomizations

Random Data Permutation: Hypothesis Testing vs. Estimation

Stochastic Closure When Assignments Are Equally Probable

Systematic Expansion of a Random Reference Set

Random Ordering of Measurements within Treatments

Fixed, Mixed, and Random Models

Deriving One-Tailed P-Values from Two-Tailed P-Values with Unequal N

Test Statistics and Adaptive Tests

Stochastic Closure When Assignments Are Not Equally Probable

Questions and Exercises


General Guidelines and Software Availability

Randomization: Multistage Model

Permuting Data: Data-Exchanging Model

Maximizing Power

Randomization Test Computer Programs on the CD

Other Computer Programs


About the Series

Statistics: A Series of Textbooks and Monographs

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General