Randomization Tests

Randomization Tests

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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.show more

Product details

  • Hardback | 376 pages
  • 157.5 x 236.2 x 25.4mm | 657.72g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • Revised
  • 4th Revised edition
  • 2 black & white illustrations, 66 black & white tables
  • 1584885890
  • 9781584885894
  • 1,406,070

Review quote

"...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 Societyshow more

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 Intelligibility Respect for the Validity of Randomization Tests Versatility Practicality Precursors of Randomization Tests Other Applications of Permutation Tests Questions and Exercises Notes References 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 Introduction 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 References Between-Subjects Designs Introduction 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 Outliers Questions and Exercises References 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 References 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 SIGMAt2 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 Outliers 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 References 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 References Correlation 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 References 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 References 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 References 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 Correlation 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 References 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 Complications Questions and Exercises References 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 (A -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 References 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 References 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 Referencesshow more

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