Statistics in Scientific Investigation: Its Basis, Application, and Interpretation

688 Pages·1990·14.68 MB·English

by  Glen McPherson (auth.)

Springer Texts in Statistics
Advisors:
Stephen Fienberg Ingram Olkin
Springer Texts in Statistics
Alfred Elements of Statistics
for the Life and Social Sciences
Blom Probability and Statistics:
Theory and Applications
Chow and Teicher Probability Theory: Independence,
Interchangeability, Martingales.
Second Edition
Christensen Plane Answers to Complex Questions:
The Theory of Linear Models
du Toit, Steyn and Graphical Exploratory Data Analysis
Strumpf
Kalbfleisch Probability and Statistical Inference:
Volume 1: Probability.
Second Edition
Kalbfleisch Probability and Statistical Inference:
Volume 2: Statistical Inference.
Second Edition
Keyfitz Applied Mathematical Demography.
Second Edition
Kiefer Introduction to Statistical Inference
Kokoska and Nevison Statistical Tables and Formulae
Madansky Prescriptions for Working Statisticians
McPherson Statistics in Scientific Investigation:
Basis, Application, and Interpretation
Nguyen and Rogers Fundamentals of Mathematical Statistics:
Volume I: Probability for Statistics
Nguyen and Rogers Fundamentals of Mathematical Statistics:
Volume II: Statistical Inference
Peters Counting for Something:
Statistical Principles and Personalities
(continued after index)
Glen McPherson
Statistics in
Scientific Investigation
Its Basis, Application,
and Interpretation
With 58 Illustrations
Springer Science+Business Media, LLC
Glen McPherson
Department of Mathematics
The University of Tasmania
Hobart, Tasmania 7001
Australia
E-Mail Address: [email protected]
Editorial Board
Stephen Fienberg Ingram Olkin
Department of Statistics Department of Statistics
Carnegie-Mellon University Stanford University
Pittsburgh, PA 15213 Stanford, CA 94305
USA USA
Mathematics Subject Classification (1980): 62-01, 62-07, 62PIO, 62P15, 62P25
McPherson, Glen.
Statistics in scientific investigation : its basis, application,
and interpretation I Glen McPherson.
p. em. - (Springer texts in statistics)
I. Research-Statistical methods. 2. Science-Statistical
methods. 3. Statistics. I. Title. II. Series.
Q180.55.S7M36 1990
507.2-{!c20 89-21711
Printed on acid-free paper.
© 1990 Springer Science+ Business Media New York
Originally published by Springer-Verlag New York, Inc. in 1990
Softcover reprint of the hardcover 1st edition 1990
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Camera-ready copy prepared using LaTEX·
9 8 7 6 5 4 3 2 I
ISBN 978-1-4757-4292-3 ISBN 978-1-4757-4290-9 (eBook)
DOI 10.1007/978-l-4757-4290-9
Affectionately dedicated to my family,
Wendy, Ewen, and Meegan
Contents
Preface
Xlll
Plan of the Book
XVll
Using the Book
XXl
Commonly Used Symbols
XXV
1 The Role of Statistics in Scientific Investigation 1
1.1 Scientific Investigation 1
1.2 Statistics in the Experimental Process 2
1.3 Descriptive Statistics 10
1.4 Analytic Statistics 27
Problems 29
2 Data: The Factual Information 34
2.1 Data Collection 34
2.2 Types of Data 40
Problems 43
3 Statistical Models: The Experimenter's View 46
3.1 Components of a Model 46
3.2 Hypotheses 47
3.3 Sampling Assumptions 54
3.4 Statistical Assumptions 56
Problems 57
4 Comparing Model and Data 60
4.1 Intuitive Ideas 60
4.2 The Role of Statistics 64
4.3 Measuring Agreement Between Model and Data 65
viii Contents
5 Probability: A Fundamental Tool of Statistics 73
5.1 Probability and Statistics 73
5.2 Sampling Distributions 75
5.3 Probability: Definitions and Rules 82
5.4 Random Variables 84
Appendix: Combinatorial Formulae 94
Problems 95
6 Some Widely Used Statistical Models 100
6.1 The Binomial Model 100
6.2 The Two-State Population Model 101
6.3 A Model for Occurrences of Events 103
6.4 The Multinomial Model 105
6.5 The Normal Distribution Model 107
6.6 The Logistic Model 114
Problems 119
7 Some Important Statistics and Their
Sampling Distributions 122
7.1 The Binomial Distribution 122
7.2 The Poisson Distribution 127
7.3 The Normal Distribution 128
7.4 The t-Distribution 133
7.5 The Chi-Squared Distribution 137
7.6 The F-Distribution 138
7.7 Statistics Based on Signs and Ranks 140
7.8 Statistics Based on Permutations 145
Problems 149
8 Statistical Analysis: The Statisticians' View 154
8.1 The Range in Models and Approaches 154
8.2 Hypothesis Testing 156
8.3 Estimation 162
8.4 Likelihood 169
8.5 The Bayesian Approach 170
8.6 Choosing the Best Method 175
Problems 177
9 Examining Proportions and Success Rates 181
9.1 Experimental Aims 181
Contents
lX
9.2 Statistical Analysis 185
Problems 195
10 Model and Data Checking 199
10.1 Sources of Error in Models and Data 199
10.2 Detecting Errors in Statistical Models 201
10.3 Analyzing Residuals 206
10.4 Checking Data 218
10.5 Data Modification or Method Modification? 221
Problems 223
11 Questions About the "Average" Value 227
11.1 Experimental Considerations 227
11.2 Choosing and Applying Statistical Methods 230
Problems 240
12 Comparing Two Groups, Treatments
or Processes 242
12.1 Forms of Comparison 242
12.2 Comparisons Based on Success Rates and
Proportions 248
12.3 Comparisons of Means 260
12.4 Comparisons of Medians 274
12.5 A Consideration of Rare Events 283
Problems 289
13 Observational Studies, Surveys and
Designed Experiments 297
13.1 Observational Study or Designed Experiment? 297
13.2 Experimental and Treatment Designs 301
13.3 Paired Comparisons 309
13.4 Surveys 318
Appendix 1: Steps in Randomly Selecting a Sample
from a Population 328
Appendix 2: Steps in Random Allocation of
Units Between Treatments 329
Problems 330
14 Comparing More Than Two Treatments or Groups 332
14.1 Approaches to Analysis 332
X Contents
14.2 Statistical Models 345
14.3 Statistical Methods 352
14.4 Practical Considerations 360
14.5 Comparisons Based on Medians 363
Problems 368
15 Comparing Mean Response When There Are
Three or More Treatments 371
15.1 Experimental and Statistical Aims 371
15.2 Defining and Choosing Designs 371
15.3 Model and Data Checking 394
15.4 Analysis of Variance and One-Stratum Designs 403
15.5 Tw<rStrata Designs 408
15.6 More Complex Designs 417
15.7 Factorial Arrangement of Treatments 423
15.8 More Detailed Comparison of Treatment Differences 434
Problems 442
16 Comparing Patterns of Response: Frequency Tables 446
16.1 The Scope of Applications 446
16.2 Statistical Models and Methodology 451
Problems 473
17 Studying Association and Correlation 475
17.1 Relations Between Two Categorical Variables 475
17.2 Relations Between Two Scaled Variables 481
17.3 Relations Between Three or More Categorical Variables 497
17.4 Relations Between Three or More Scaled Variables 501
Problems 506
18 Prediction and Estimation: The Role of
Explanatory Variables 509
18.1 Regression Analysis 509
18.2 Statistical Models 516
18.3 Statistical Methods 519
18.4 Practical Considerations 528
18.5 Statistical Analysis 532
18.6 Applications of Regression Analysis 537
18.7 Experimental Design and Regression Analysis 554
Problems 562
Contents xi
19 Questions About Variability 568
19.1 Variability-Its Measurement and Application 568
19.2 Variance Components 575
Problems 587
20 Cause and Effect: Statistical Perspectives 589
20.1 The Allocation of Causality: Scientific Aims
and Statistical Approaches 589
20.2 Statistical Methods in Use 592
21 Studying Change in Response over Time 596
21.1 Applications 596
21.2 Time Series 599
21.3 Time Series: Statistical Models and Methods 606
22 Computers and Statistics 613
22.1 The Role of Computers in Statistics 613
22.2 Using Computers-Practical Considerations 615
22.3 Statistical Packages 616
22.4 Choosing a Computer 621
Appendix A: Tables for Some Common Probability
Distributions 622
References 645
Figure, Table, and Example Index 647
Index 653