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E-raamat: Statistical Hypothesis Testing in Context: Volume 52: Reproducibility, Inference, and Science

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With over 60 years of applied experience, Fay and Brittain present hypothesis testing and compatible confidence intervals, emphasize strategies to address the reproducibility crisis, and provide methods for proper causal interpretation in scientific research. The book presents a full scope of tools and advice on their appropriate use in practice.

Fay and Brittain present statistical hypothesis testing and compatible confidence intervals, focusing on application and proper interpretation. The emphasis is on equipping applied statisticians with enough tools - and advice on choosing among them - to find reasonable methods for almost any problem and enough theory to tackle new problems by modifying existing methods. After covering the basic mathematical theory and scientific principles, tests and confidence intervals are developed for specific types of data. Essential methods for applications are covered, such as general procedures for creating tests (e.g., likelihood ratio, bootstrap, permutation, testing from models), adjustments for multiple testing, clustering, stratification, causality, censoring, missing data, group sequential tests, and non-inferiority tests. New methods developed by the authors are included throughout, such as melded confidence intervals for comparing two samples and confidence intervals associated with Wilcoxon-Mann-Whitney tests and Kaplan-Meier estimates. Examples, exercises, and the R package asht support practical use.

Arvustused

'A necessary book for the applied statistician seeking to understand the theoretical underpinnings of statistical methods and for graduate students knowledgeable about statistical theory but lacking experience in application. The book is chock full of challenging examples that point to the complexities of choice of method. A particularly valuable feature of the book is the authors' description of competing methods coupled with their clarity in explaining and justifying why they prefer one method over others. Fay and Brittain should sit on every statistician's bookshelf.' Janet Wittes, WCG Statistics Collaborative 'Good statistical hypothesis testing and confidence interval construction involves mathematical aspects of finding a good test given a probability model and scientific aspects of determining the appropriateness of a probability model for answering a scientific question. This book provides a lucid discussion of both these mathematical and scientific aspects with compelling scientific examples. I most highly recommend this book.' Dylan Small, University of Pennsylvania 'Congratulations to Fay and Brittain for this wonderful reference book that does what its somewhat unusual title suggests: puts hypothesis testing in the context of science. The vast coverage of topics, extensive bibliography and notes, and easy to understand explanations make 'Statistical Hypothesis Testing in Context: Reproducibility, Inference, and Science' an indispensable tool in the arsenal of any applied or theoretical statistician or biostatistician. I enthusiastically recommend buying the book!' Michael A. Proschan, National Institute of Allergy and Infectious Diseases

Muu info

This coherent guide equips applied statisticians to make good choices and proper interpretations in real investigations facing real data.
Preface xi
1 Introduction 1(7)
1.1 A Cautionary Tale
1(2)
1.2 Science, Reproducibility, and Statistical Inferences
3(2)
1.3 Using the Book
5(1)
1.4 Notes
6(1)
1.5 Problems
6(2)
2 Theory of Tests, p-Values, and Confidence Intervals 8(15)
2.1 Overview
8(1)
2.2 Components of a Hypothesis Test
8(5)
2.3 Confidence Sets: Inverting a Series of Hypothesis Tests
13(4)
2.4 Properties of Hypothesis Tests
17(2)
2.5 Summary
19(1)
2.6 Extensions and Bibliographic Notes
20(1)
2.7 Notes
20(2)
2.8 Problems
22(1)
3 From Scientific Theory to Statistical Hypothesis Test 23(26)
3.1 The Statistician's Role
23(1)
3.2 Causality versus Association
23(5)
3.3 Designing Any Study
28(5)
3.4 Designing an Experimental Study
33(3)
3.5 Designing an Observational Study
36(4)
3.6 A Probability Model for the Study
40(3)
3.7 Statistics Methods Overview
43(2)
3.8 Summary
45(1)
3.9 Extensions and Bibliographic Notes
46(1)
3.10 Notes
47(1)
3.11 Problems
48(1)
4 One-Sample Studies with Binary Responses 49(18)
4.1 Overview
49(1)
4.2 Key Method: Exact Central Method (Clopper-Pearson)
50(1)
4.3 Other Methods for Independent Binary Responses
51(9)
4.4 Designing a One-Sample Binary Response Study
60(2)
4.5 Summary
62(1)
4.6 Extensions and Bibliographic Notes
63(1)
4.7 R Functions and Packages
64(1)
4.8 Notes
65(1)
4.9 Problems
66(1)
5 One-Sample Studies with Ordinal or Numeric Responses 67(17)
5.1 Overview
67(2)
5.2 Exact Test on the Median or Other Quantiles
69(1)
5.3 Tests on the Mean
70(7)
5.4 Testing Other Parameters from One-Sample Numeric Data
77(2)
5.5 Designing a One-Sample Study
79(1)
5.6 Summary
79(1)
5.7 Extensions and Bibliographic Notes
80(1)
5.8 R Functions and Packages
80(1)
5.9 Notes
80(3)
5.10 Problems
83(1)
6 Paired Data 84(20)
6.1 Overview
84(1)
6.2 Sign Test
85(1)
6.3 Wilcoxon Signed-Rank Test
86(4)
6.4 Choosing a Paired-Difference Test under Symmetry
90(4)
6.5 Correlation and Related Types of Association
94(4)
6.6 Agreement Coefficients
98(2)
6.7 Summary
100(1)
6.8 Extensions and Bibliographic Notes
101(1)
6.9 R Functions and Packages
101(1)
6.10 Notes
102(1)
6.11 Problems
103(1)
7 Two-Sample Studies with Binary Responses 104(20)
7.1 Overview
104(2)
7.2 Parameters to Measure Effects
106(2)
7.3 Conditional Tests
108(7)
7.4 Unconditional Tests
7.5 Mid-p Methods
115(1)
7.6 Asymptotic Approximations
116(1)
7.7 Comparison of Binomial Methods
117(2)
7.8 Other Study Designs
119(1)
7.9 Summary
120(1)
7.10 Extensions and Bibliographic Notes
121(1)
7.11 R Functions and Packages
122(1)
7.12 Notes
122(1)
7.13 Problems
122(2)
8 Assumptions and Hypothesis Tests 124(5)
8.1 Overview
124(1)
8.2 Which Test Is More Restrictive?
124(2)
8.3 Multiple Perspective Decision Rules
126(2)
8.4 Summary
128(1)
8.5 Extensions and Bibliographic Notes
128(1)
9 Two-Sample Studies with Ordinal or Numeric Responses 129(32)
9.1 Overview
129(4)
9.2 Inferences on Proportional Odds
133(1)
9.3 Differences in Means
133(8)
9.4 Differences in Medians
141(2)
9.5 Mann-Whitney Parameter
143(8)
9.6 Choosing a Test when Power Concerns Dominate
151(4)
9.7 Summary
155(2)
9.8 Extensions and Bibliographic Notes
157(1)
9.9 R Functions and Packages
157(1)
9.10 Notes
158(1)
9.11 Problems
158(3)
10 General Methods for Frequentist Inferences 161(34)
10.1 Overview
161(1)
10.2 One-Dimensional Parameter
161(3)
10.3 Pivots
164(1)
10.4 Multivariate Normal Inferences
165(1)
10.5 Asymptotic Normality and the Central Limit Theorem
166(2)
10.6 Delta Method
168(1)
10.7 Wald, Score, and Likelihood Ratio Tests
169(5)
10.8 Sandwich Methods
174(2)
10.9 Permutation Tests
176(5)
10.10 Bootstrap
181(4)
10.11 Melding: Combining Confidence Intervals in the Two-Sample Case
185(2)
10.12 Within-Cluster Resampling
187(1)
10.13 Other Methods
188(1)
10.14 Summary
188(2)
10.15 Extensions and Bibliographic Notes
190(1)
10.16 R Functions and Packages
190(1)
10.17 Notes
190(3)
10.18 Problems
193(2)
11 k-Sample Studies and Trend Tests 195(20)
11.1 Overview
195(1)
11.2 Unordered Groups: k-Sample Tests
196(7)
11.3 Ordered Groups: Trend Tests
203(1)
11.4 Follow-Up Tests after Independence Test and Familywise Error Rates
204(1)
11.5 All Pairwise Comparisons
205(3)
11.6 Many-to-One Comparisons
208(1)
11.7 Max-t-Type Procedures
209(1)
11.8 Summary
210(1)
11.9 Extensions and Bibliographic Notes
211(1)
11.10 R Functions and Packages
212(1)
11.11 Notes
212(2)
11.12 Problems
214(1)
12 Clustering and Stratification 215(20)
12.1 Overview
215(1)
12.2 Clustering
215(6)
12.3 Stratification
221(9)
12.4 Summary
230(2)
12.5 Extensions and Bibliographic Notes
232(1)
12.6 R Functions and Packages
232(1)
12.7 Notes
232(1)
12.8 Problems
233(2)
13 Multiplicity in Testing 235(18)
13.1 Overview
235(1)
13.2 Defining the Family of Hypothesis Tests
236(3)
13.3 Properties of Multiple Testing Procedures
239(1)
13.4 Procedures Using p-Values Only
240(1)
13.5 Max-t-Type (Generalized Studentized Range) Inferences
241(3)
13.6 Permutation- or Bootstrap-Based Methods
244(2)
13.7 Sequential Testing of Different Hypotheses
246(1)
13.8 Logical Constraints
247(1)
13.9 Closure Method
248(1)
13.10 Summary
248(2)
13.11 Extensions and Bibliographic Notes
250(1)
13.12 R Functions and Packages
250(1)
13.13 Notes
250(1)
13.14 Problems
251(2)
14 Testing from models 253(24)
14.1 Overview
253(1)
14.2 Linear Models
253(2)
14.3 Generalized Linear Models
255(4)
14.4 Ordinal Responses or Ranked Responses
259(2)
14.5 Clustered Data
261(5)
14.6 Covariate Selection
266(2)
14.7 Some Problems When Testing from Models
268(3)
14.8 Inference after Model Building
271(1)
14.9 Summary
271(2)
14.10 Extensions and Bibliographic Notes
273(1)
14.11 R Functions and Packages
273(1)
14.12 Notes
274(1)
14.13 Problems
275(2)
15 Causality 277(25)
15.1 Overview
277(1)
15.2 Causal Estimands
278(3)
15.3 Why Causal Inference Is Difficult for Observational Studies
281(2)
15.4 Causality and Experimental Studies
283(6)
15.5 Causality and Interference
289(1)
15.6 Causality and Observational Studies: Overview
290(1)
15.7 Observational Studies: Adjustments When Confounders Are Measured
290(7)
15.8 Observational Studies: Analysis with Unmeasured Confounders Using Instrumental Variables
297(1)
15.9 Summary
298(2)
15.10 Extensions and Bibliographic Notes
300(1)
15.11 Notes
300(1)
15.12 Problems
301(1)
16 Censoring 302(25)
16.1 Overview: Types of Censoring
302(1)
16.2 One Sample with Right Censoring
303(5)
16.3 Hazard Function
308(1)
16.4 Two Samples with Right Censoring
309(9)
16.5 Interval Censoring
318(3)
16.6 Truncation
321(1)
16.7 Summary
322(1)
16.8 Extensions and Bibliographic Notes
323(1)
16.9 R Functions and Packages
324(1)
16.10 Notes
324(1)
16.11 Problems
325(2)
17 Missing Data 327(15)
17.1 Overview
327(1)
17.2 Missing Data Terminology
328(1)
17.3 Sensitivity Analyses for Data Missing Not at Random
329(4)
17.4 Methods for Missing at Random Data
333(5)
17.5 Multiple Imputation
338(1)
17.6 Summary
339(1)
17.7 Extensions and Bibliographic Notes
340(1)
17.8 R Functions and Packages
340(1)
17.9 Problems
340(2)
18 Group Sequential and Related Adaptive Methods 342(17)
18.1 Overview
342(1)
18.2 k Preplanned Interim Analyses
343(3)
18.3 Arbitrary Number of Interim Analyses
346(2)
18.4 When the Brownian Motion Approximation Does Not Hold
348(1)
18.5 Estimates and Confidence Intervals after Interim Analyses
349(3)
18.6 Two-Stage Adaptive Designs
352(2)
18.7 Summary
354(2)
18.8 Extensions and Bibliographic Notes
356(1)
18.9 R Functions and Packages
356(1)
18.10 Notes
356(1)
18.11 Problems
357(2)
19 Testing Fit, Equivalence, and Noninferiority 359(18)
19.1 Overview
359(2)
19.2 Testing Distributions and Lack of Fit
361(4)
19.3 Equivalence Tests
365(1)
19.4 Noninferiority Tests
366(6)
19.5 Summary
372(1)
19.6 Extensions and Bibliographic Notes
373(1)
19.7 R Functions and Packages
373(1)
19.8 Notes
373(2)
19.9 Problems
375(2)
20 Power and Sample Size 377(12)
20.1 Overview
377(1)
20.2 Power Calculations by Simulation
378(2)
20.3 Power Calculations by Normal Approximations
380(2)
20.4 Simulating the Sample Size
382(1)
20.5 Nonadherence and Other Issues
383(2)
20.6 Summary
385(1)
20.7 Extensions and Bibliographic Notes
386(1)
20.8 R Functions and Packages
386(1)
20.9 Notes
386(2)
20.10 Problems
388(1)
21 Bayesian Hypothesis Testing 389(15)
21.1 Introduction
389(1)
21.2 Brief Overview of Bayesian Statistics
389(4)
21.3 Bayesian Hypothesis Testing Using Bayes Factors
393(1)
21.4 Bayesian Hypothesis Testing Using Decision Theory
394(2)
21.5 When Can p-Values Be Interpreted in a Bayesian Manner?
396(5)
21.6 Bibliographic Notes
401(1)
21.7 Problems
402(2)
References 404(16)
Notation Index 420
Concept Index 42
Michael P. Fay is a Mathematical Statistician at the National Institute of Allergy and Infectious Diseases, and previously worked at the National Cancer Institute. He has served as associate editor for Biometrics, and is currently an associate editor for Clinical Trials and a Fellow of the American Statistical Association. He is a co-author on over 100 papers in statistical and medical journals and has written and maintains over a dozen R packages on CRAN. Erica H. Brittain is Deputy Branch Chief of Biostatistics Research at the National Institute of Allergy and Infectious Diseases and has well over three decades of experience as a statistician, with previous positions at FDA, National Heart, Lung, and Blood Institute, and a statistical consulting company. Her applied work at NIH and her methodological publications in statistical journals focus on innovation in clinical trial design. She frequently serves on advisory panels for FDA and NIH, and has served as Statistical Consultant for Nature journals and Associate Editor for Controlled Clinical Trials.