Biometry FOURTH EDITION
3620002FM.indd i
8/5/11 1:07 PM
3620002FM.indd ii
8/5/11 1:07 PM
Biometry The Principles and Practice of Statistics in Biological Research FOURTH EDITION
Robert R. Sokal and F. James Rohlf Stony Brook University
W.H. Freeman and Company New York
3620002FM.indd iii
8/5/11 1:07 PM
Publisher: Peter Marshall Acquisitions Editor: Jerry Correa Marketing Manager: Debbie Clare Project Editor: Marni Rolfes Art Director: Diana Blume Project management, Illustrations, and Composition: MPS Limited, a Macmillan Company Production Coordinator: Lawrence Guerra Printing and Binding: RR Donnelley
Library of Congress Control Number: 2010939805
ISBN-13: 978-0-7167-8604-4 ISBN-10: 0-7167-8604-4
©2012, 1995, 1981, 1969 by W. H. Freeman and Company All rights reserved
Printed in the United States of America First printing
W.H. Freeman and Company 41 Madison Avenue New York, NY 10010 Houndmills, Basingstoke RG21 6XS, England www.whfreeman.com
3620002FM.indd iv
8/11/11 10:19 AM
To our wives Julie and Janice
3620002FM.indd v
8/5/11 1:07 PM
3620002FM.indd vi
8/5/11 1:07 PM
Contents
Preface Notes on the Fourth Edition
1 Introduction 1.1 1.2 1.3
Some Definitions The Development of Biometry The Statistical Frame of Mind
2 Data in Biology 2.1 2.2 2.3 2.4 2.5
Samples and Populations Variables in Biology Accuracy and Precision of Data Derived Variables Frequency Distributions
3 Computers and Data Analysis 3.1 3.2 3.3
Computers Software Efficiency and Economy in Data Processing
4 Descriptive Statistics 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9
The Arithmetic Mean Other Means The Median The Mode Sample Statistics and Parameters The Range The Standard Deviation Coding Data Before Computation The Coefficient of Variation
xiii xvii
1 1 3 5
9 9 11 13 16 19
33 33 35 37
39 40 44 45 47 49 49 51 54 55
vii
3620002FM.indd vii
8/5/11 1:07 PM
viii Contents
5 Introduction to Probability Distributions: Binomial and Poisson
59
5.1 5.2 5.3 5.4
60 68 78 87
Probability, Random Sampling, and Hypothesis Testing The Binomial Distribution The Poisson Distribution Other Discrete Probability Distributions
6 The Normal Probability Distribution 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8
Frequency Distributions of Continuous Variables Properties of the Normal Distribution A Model for the Normal Distribution Applications of the Normal Distribution Fitting a Normal Distribution to Observed Data Skewness and Kurtosis Graphic Methods Other Continuous Distributions
7 Hypothesis Testing and Interval Estimation 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10 7.11 7.12 7.13
Introduction to Hypothesis Testing: Randomization Approaches Distribution and Variance of Means Distribution and Variance of Other Statistics The t-Distribution More on Hypothesis Testing: Normally Distributed Data Power of a Test Tests of Simple Hypotheses Using the Normal and t-Distributions The Chi-Square Distribution Testing the Hypothesis H0: s2 5 s02 Introduction to Interval Estimation (Confidence Limits) Confidence Limits Using Sample Standard Deviations Confidence Limits for Variances The Jackknife and the Bootstrap
8 Introduction to Analysis of Variance 8.1 8.2 8.3 8.4 8.5
3620002FM.indd viii
Variances of Samples and Their Means The F-Distribution The Hypothesis H0: s12 5 s22 Heterogeneity Among Sample Means Partitioning the Total Sum of Squares and Degrees of Freedom
93 93 95 100 102 104 106 108 117
119 120 131 137 140 142 146 148 154 156 157 162 167 168
177 178 182 187 190 197
8/5/11 1:07 PM
Contents
8.6 8.7
Model I Anova Model II Anova
9 Single-Classification Analysis of Variance 9.1 9.2 9.3 9.4 9.5
Computational Formulas General Case: Unequal and Equal n Special Case: Two Groups Comparisons Among Means in a Model I Anova: Essential Background Comparisons Among Means: Special Methods
10 Nested Analysis of Variance 10.1 Nested Anova: Design 10.2 Nested Anova: Computation 10.3 Nested Anovas with Unequal Sample Sizes
11 Two-Way and Multiway Analysis of Variance 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 11.10
Two-Way Anova: Design Two-Way Anova with Equal Replication: Computation Two-Way Anova: Hypothesis Testing Two-Way Anova Without Replication Paired Comparisons The Factorial Design A Three-Way Factorial Design Higher-Order Factorial Anovas Other Designs Anova by Computer
ix
200 203
207 208 208 220 228 246
277 277 280 301
319 319 321 331 340 349 354 355 365 370 372
12 Statistical Power and Sample Size in the Analysis of Variance 12.1 Effect Size 12.2 Noncentral t- and F-Distributions and Confidence Limits for Effect Sizes 12.3 Power in an Anova 12.4 Sample Size in an Anova 12.5 Minimum Detectable Difference 12.6 Post Hoc Power Analysis 12.7 Optimal Allocation of Resources in a Nested Design 12.8 Randomized Blocks and Other Two-Way and Multiway Designs
3620002FM.indd ix
379 379 382 390 391 395 396 397 406
8/5/11 1:07 PM
x Contents
13 Assumptions of Analysis of Variance 13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9 13.10
A Fundamental Assumption Independence Homogeneity of Variances Normality Transformations The Logarithmic Transformation The Square Root Transformation The Box–Cox Transformation The Arcsine Transformation Nonparametric Methods in Lieu of Single-Classification Anova 13.11 Nonparametric Methods in Lieu of Two-Way Anova
14 Linear Regression 14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 14.9 14.10 14.11 14.12 14.13
Introduction to Regression Models in Regression The Linear Regression Equation Hypothesis Testing in Regression More Than One Value of Y for Each Value of X The Uses of Regression Estimating X From Y Comparing Two Regression Lines Linear Comparisons in Anovas Examining Residuals and Transformations in Regression Nonparametric Tests for Regression Model II Regression Effect Size, Power, and Sample Size in Regression
15 Correlation 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9
3620002FM.indd x
Correlation Versus Regression The Product–Moment Correlation Coefficient Computing the Product–Moment Correlation Coefficient The Variance of Sums and Differences Hypothesis Tests for Correlations Applications of Correlation Nonparametric Tests for Association Major Axes and Confidence Regions Effect Size, Power, and Sample Size
409 410 410 413 422 426 427 433 435 438 440 460
471 472 475 477 485 495 506 511 513 515 524 532 535 544
551 551 554 562 565 567 577 580 588 592
8/12/11 6:49 PM
Contents
16 Multiple and Curvilinear Regression 16.1 16.2 16.3 16.4 16.5 16.6 16.7 16.8 16.9 16.10 16.11
Multiple Regression: Computation Multiple Regression: Hypothesis Tests Path Analysis and Structural Equation Modeling Partial and Multiple Correlation Selection of Independent Variables Computation of Multiple Regression by Matrix Methods Solving Anovas as Regression Problems: General Linear Models Analysis of Covariance (Ancova) Curvilinear Regression Effect Size, Power, and Sample Size in Multiple Regression Advanced Topics in Regression and Correlation
17 Analysis of Frequencies 17.1 17.2 17.3 17.4 17.5 17.6 17.7 17.8
Introduction to Tests for Goodness of Fit Single-Classification Tests for Goodness of Fit Replicated Tests of Goodness of Fit Tests of Independence: Two-Way Tables Analysis of Three-Way Tables Analysis of Proportions Randomized Blocks for Frequency Data Effect Sizes, Power, and Sample Sizes
18 Meta-Analysis and Miscellaneous Methods 18.1 18.2 18.3 18.4 18.5 18.6
Synthesis of Prior Research Results: Meta-Analysis Tests for Randomness of Nominal Data: Runs Tests Isotonic Regression Application of Randomization Tests to Unconventional Statistics The Mantel Test of Association Between Two Distance Matrices The Future of Biometry: Data Analysis
xi
603 604 614 625 644 649 656 659 665 671 685 694
703 704 714 730 739 758 773 793 801
817 817 841 847 850 852 859
Appendices A. Mathematical Proofs B. Introduction to Matrices
Bibliography Author Index Subject Index
3620002FM.indd xi
869 885
891 909 915
8/5/11 1:07 PM
3620002FM.indd i
8/5/11 1:07 PM
3620002FM.indd ii
8/5/11 1:07 PM
Biometry The Principles and Practice of Statistics in Biological Research FOURTH EDITION
Robert R. Sokal and F. James Rohlf Stony Brook University
W.H. Freeman and Company New York
3620002FM.indd iii
8/5/11 1:07 PM
Publisher: Peter Marshall Acquisitions Editor: Jerry Correa Marketing Manager: Debbie Clare Project Editor: Marni Rolfes Art Director: Diana Blume Project management, Illustrations, and Composition: MPS Limited, a Macmillan Company Production Coordinator: Lawrence Guerra Printing and Binding: RR Donnelley
Library of Congress Control Number: 2010939805
ISBN-13: 978-0-7167-8604-4 ISBN-10: 0-7167-8604-4
©2012, 1995, 1981, 1969 by W. H. Freeman and Company All rights reserved
Printed in the United States of America First printing
W.H. Freeman and Company 41 Madison Avenue New York, NY 10010 Houndmills, Basingstoke RG21 6XS, England www.whfreeman.com
3620002FM.indd iv
8/11/11 10:19 AM
To our wives Julie and Janice
3620002FM.indd v
8/5/11 1:07 PM
3620002FM.indd vi
8/5/11 1:07 PM
Contents
Preface Notes on the Fourth Edition
1 Introduction 1.1 1.2 1.3
Some Definitions The Development of Biometry The Statistical Frame of Mind
2 Data in Biology 2.1 2.2 2.3 2.4 2.5
Samples and Populations Variables in Biology Accuracy and Precision of Data Derived Variables Frequency Distributions
3 Computers and Data Analysis 3.1 3.2 3.3
Computers Software Efficiency and Economy in Data Processing
4 Descriptive Statistics 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9
The Arithmetic Mean Other Means The Median The Mode Sample Statistics and Parameters The Range The Standard Deviation Coding Data Before Computation The Coefficient of Variation
xiii xvii
1 1 3 5
9 9 11 13 16 19
33 33 35 37
39 40 44 45 47 49 49 51 54 55
vii
3620002FM.indd vii
8/5/11 1:07 PM
viii Contents
5 Introduction to Probability Distributions: Binomial and Poisson
59
5.1 5.2 5.3 5.4
60 68 78 87
Probability, Random Sampling, and Hypothesis Testing The Binomial Distribution The Poisson Distribution Other Discrete Probability Distributions
6 The Normal Probability Distribution 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8
Frequency Distributions of Continuous Variables Properties of the Normal Distribution A Model for the Normal Distribution Applications of the Normal Distribution Fitting a Normal Distribution to Observed Data Skewness and Kurtosis Graphic Methods Other Continuous Distributions
7 Hypothesis Testing and Interval Estimation 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10 7.11 7.12 7.13
Introduction to Hypothesis Testing: Randomization Approaches Distribution and Variance of Means Distribution and Variance of Other Statistics The t-Distribution More on Hypothesis Testing: Normally Distributed Data Power of a Test Tests of Simple Hypotheses Using the Normal and t-Distributions The Chi-Square Distribution Testing the Hypothesis H0: s2 5 s02 Introduction to Interval Estimation (Confidence Limits) Confidence Limits Using Sample Standard Deviations Confidence Limits for Variances The Jackknife and the Bootstrap
8 Introduction to Analysis of Variance 8.1 8.2 8.3 8.4 8.5
3620002FM.indd viii
Variances of Samples and Their Means The F-Distribution The Hypothesis H0: s12 5 s22 Heterogeneity Among Sample Means Partitioning the Total Sum of Squares and Degrees of Freedom
93 93 95 100 102 104 106 108 117
119 120 131 137 140 142 146 148 154 156 157 162 167 168
177 178 182 187 190 197
8/5/11 1:07 PM
Contents
8.6 8.7
Model I Anova Model II Anova
9 Single-Classification Analysis of Variance 9.1 9.2 9.3 9.4 9.5
Computational Formulas General Case: Unequal and Equal n Special Case: Two Groups Comparisons Among Means in a Model I Anova: Essential Background Comparisons Among Means: Special Methods
10 Nested Analysis of Variance 10.1 Nested Anova: Design 10.2 Nested Anova: Computation 10.3 Nested Anovas with Unequal Sample Sizes
11 Two-Way and Multiway Analysis of Variance 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 11.10
Two-Way Anova: Design Two-Way Anova with Equal Replication: Computation Two-Way Anova: Hypothesis Testing Two-Way Anova Without Replication Paired Comparisons The Factorial Design A Three-Way Factorial Design Higher-Order Factorial Anovas Other Designs Anova by Computer
ix
200 203
207 208 208 220 228 246
277 277 280 301
319 319 321 331 340 349 354 355 365 370 372
12 Statistical Power and Sample Size in the Analysis of Variance 12.1 Effect Size 12.2 Noncentral t- and F-Distributions and Confidence Limits for Effect Sizes 12.3 Power in an Anova 12.4 Sample Size in an Anova 12.5 Minimum Detectable Difference 12.6 Post Hoc Power Analysis 12.7 Optimal Allocation of Resources in a Nested Design 12.8 Randomized Blocks and Other Two-Way and Multiway Designs
3620002FM.indd ix
379 379 382 390 391 395 396 397 406
8/5/11 1:07 PM
x Contents
13 Assumptions of Analysis of Variance 13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9 13.10
A Fundamental Assumption Independence Homogeneity of Variances Normality Transformations The Logarithmic Transformation The Square Root Transformation The Box–Cox Transformation The Arcsine Transformation Nonparametric Methods in Lieu of Single-Classification Anova 13.11 Nonparametric Methods in Lieu of Two-Way Anova
14 Linear Regression 14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 14.9 14.10 14.11 14.12 14.13
Introduction to Regression Models in Regression The Linear Regression Equation Hypothesis Testing in Regression More Than One Value of Y for Each Value of X The Uses of Regression Estimating X From Y Comparing Two Regression Lines Linear Comparisons in Anovas Examining Residuals and Transformations in Regression Nonparametric Tests for Regression Model II Regression Effect Size, Power, and Sample Size in Regression
15 Correlation 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9
3620002FM.indd x
Correlation Versus Regression The Product–Moment Correlation Coefficient Computing the Product–Moment Correlation Coefficient The Variance of Sums and Differences Hypothesis Tests for Correlations Applications of Correlation Nonparametric Tests for Association Major Axes and Confidence Regions Effect Size, Power, and Sample Size
409 410 410 413 422 426 427 433 435 438 440 460
471 472 475 477 485 495 506 511 513 515 524 532 535 544
551 551 554 562 565 567 577 580 588 592
8/12/11 6:49 PM
Contents
16 Multiple and Curvilinear Regression 16.1 16.2 16.3 16.4 16.5 16.6 16.7 16.8 16.9 16.10 16.11
Multiple Regression: Computation Multiple Regression: Hypothesis Tests Path Analysis and Structural Equation Modeling Partial and Multiple Correlation Selection of Independent Variables Computation of Multiple Regression by Matrix Methods Solving Anovas as Regression Problems: General Linear Models Analysis of Covariance (Ancova) Curvilinear Regression Effect Size, Power, and Sample Size in Multiple Regression Advanced Topics in Regression and Correlation
17 Analysis of Frequencies 17.1 17.2 17.3 17.4 17.5 17.6 17.7 17.8
Introduction to Tests for Goodness of Fit Single-Classification Tests for Goodness of Fit Replicated Tests of Goodness of Fit Tests of Independence: Two-Way Tables Analysis of Three-Way Tables Analysis of Proportions Randomized Blocks for Frequency Data Effect Sizes, Power, and Sample Sizes
18 Meta-Analysis and Miscellaneous Methods 18.1 18.2 18.3 18.4 18.5 18.6
Synthesis of Prior Research Results: Meta-Analysis Tests for Randomness of Nominal Data: Runs Tests Isotonic Regression Application of Randomization Tests to Unconventional Statistics The Mantel Test of Association Between Two Distance Matrices The Future of Biometry: Data Analysis
xi
603 604 614 625 644 649 656 659 665 671 685 694
703 704 714 730 739 758 773 793 801
817 817 841 847 850 852 859
Appendices A. Mathematical Proofs B. Introduction to Matrices
Bibliography Author Index Subject Index
3620002FM.indd xi
869 885
891 909 915
8/5/11 1:07 PM
![Sokal biometry download torrent Sokal biometry download torrent](/uploads/1/2/6/2/126289117/642706842.jpg)
Biometry by Robert R. James Rohlf, 1995, W.H. Freeman edition, in English - 3rd ed.