Aug 5, 2011 - 3620002FM.indd ii ... Project management, Illustrations, and Composition: MPS Limited, ... Notes on the Fourth Edition ... 7.6 Power of a Test.
Biometry FOURTH EDITION
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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
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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
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
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viii Contents
5 Introduction to Probability Distributions: Binomial and Poisson
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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
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
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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
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
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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
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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
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
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
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
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
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
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Appendices A. Mathematical Proofs B. Introduction to Matrices
