THE PRINCIPLES AND PRACTICE OF STATISTICS IN BIOLOGICAL RESEARCH. Robert R. SOKAL and F. James ROHLF. State University of New York at Stony Brook
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1 BIOMETRY THE PRINCIPLES AND PRACTICE OF STATISTICS IN BIOLOGICAL RESEARCH THIRD E D I T I O N Robert R. SOKAL and F. James ROHLF State University of New York at Stony Brook W. H. FREEMAN AND COMPANY New York
2 PREFACE NOTES ON THE THIRD EDITION xiii xvii I INTRODUCTION 1.1 Some Definitions The Development of Biometry The Statistical Frame of Mind 5 2 DATA IN BIOLOGY Samples and Populations Variables in Biology Accuracy and Precision of Data Derived Variables Frequency Distributions 19 3 THE HANDLING OF DATA Computers Software Efficiency and Economy in Data Processing 37 4 DESCRIPTIVE STATISTICS The Arithmetic Mean Other Means The Median The Mode The Range The Standard Deviation Vii
3 VIM 4.7 Sample Statistics and Parameters Coding Data Before Computation Computing Means and Standard Deviations The Coefficient of Variation 57 5 INTRODUCTION TO PROBABILITY DISTRIBUTION: BINOMIAL AND POISSON Probability, Random Sampling, and Hypothesis Testing The Binomial Distribution The Poisson Distribution Other Discrete Probability Distributions 93 6 THE NORMAL PROBABILITY DISTRIBUTION 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 ESTIMATION AND HYPOTHESIS TESTING Distribution and Variance of Means Distribution and Variance of Other Statistics Introduction to Confidence Limits The i-distribution Confidence Limits Based on Sample Statistics The Chi-Square Distribution Confidence Limits for Variances Introduction to Hypothesis Testing Tests of Simple Hypotheses Using the Normal and f-distributions Testing the Hypothesis H o \ σ 2 = ag INTRODUCTION TO THE ANALYSIS OF VARIANCE Variances of Samples and Their Means The F-Distribution The Hypothesis H Q : σ\= σ\ 189
4 IX 8.4 Heterogeneity Among Sample Means Partitioning the Total Sum of Squares and Degrees of Freedom Model I Anova Model II Anova SINGLE-CLASSIFICATION ANALYSIS OF VARIANCE Computational Formulas General Case: Unequal η Special Case: Equal η Special Case: Two Groups Special Case: A Single Specimen Compared With a Sample Comparisons Among Means: Planned Comparisons Comparisons Among Means: Unplanned Comparisons Finding the Sample Size Required for a Test NESTED ANALYSIS OF VARIANCE Nested Anova: Design Nested Anova: Computation Nested Anovas With Unequal Sample Sizes The Optimal Allocation of Resources TWO-WAY ANALYSIS OF VARIANCE Two-Way Anova: Design Two-Way Anova With Equal Replication: Computation Two-Way Anova: Significance Testing Two-Way Anova Without Replication Paired Comparisons Unequal Subclass Sizes Missing Values in a Randomized-B locks Design MULTIWAY ANALYSIS OF VARIANCE The Factorial Design A Three-Way Factorial Anova Higher-Order Factorial Anovas Other Designs Anovas by Computer 387
5 13 ASSUMPTIONS OF ANALYSIS OF VARIANCE A Fundamental Assumption Independence Homogeneity of Variances Normality Additivity Transformations The Logarithmic Transformation The Square-Root Transformation The Box-Cox Transformation The Arcsine Transformation Nonparametric Methods in Lieu of Single- Classification Anovas Nonparametric Methods in Lieu of Two-Way Anova LINEAR REGRESSION Introduction to Regression Models in Regression The Linear Regression Equation Tests of Significance in Regression More Than One Value of Y for Each Value of X The Uses of Regression Estimating X from Y Comparing Regression Lines Analysis of Covariance Linear Comparisons in Anovas Examining Residuals and Transformations in Regression Nonparametric Tests for Regression Model II Regression 541 IS CORRELATION Correlation and Regression The Product-Moment Correlation Coefficient The Variance of Sums and Differences Computing the Product-Moment Correlation Coefficient Significance Tests in Correlation Applications of Correlation Principal Axes and Confidence Regions Nonparametric Tests for Association 593
6 Xi 16 MULTIPLE AND CURVILINEAR REGRESSION Multiple Regression: Computation Multiple Regression: Significance Tests Path Analysis Partial and Multiple Correlation Choosing Predictor Variables Curvilinear Regression Advanced Topics in Regression and Correlation ANALYSIS OF FREQUENCIES 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 and Multiway Tables Analysis of Proportions Randomized Blocks for Frequency Data MISCELLANEOUS METHODS Combining Probabilities From Tests of Significance Tests for Randomness of Nominal Data: Runs Tests Randomization Tests The Jackknife and the Bootstrap The Future of Biometry: Data Analysis 825 APPENDIX: MATHEMATICAL PROOFS 833 BIBLIOGRAPHY 850 AUTHOR INDEX 865 SUBJECT INDEX 871
Contents. Acknowledgments. xix
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