# Biometry The Principles and Practice of Statistics in Biological Research

 Author: Robert R. Sokal & F. James Rohlf Release at: 1995 Pages: 899 Edition: Third Edition File Size: 26 MB File Type: DjVu Language: English

### Content of Biometry The Principles and Practice of Statistics in Biological Research

INTRODUCTION 1
1.1 Some Definitions 1
1.2 The Development of Biometry 3
1.3 The Statistical Frame of Mind 5
DATA IN BIOLOGY
2.5 Samples and Populations
Variables in Biology
Accuracy and Precision of Data
Derived Variables
Frequency Distributions
THE HANDLING OF DATA
3.3 Computers
Software
Efficiency and Economy in Data Processing
DESCRIPTIVE STATISTICS
4.6 The Arithmetic Mean
Other Means
The Median
The Mode
The Range
The Standard Deviation 8
4.7 Sample Statistics and Parameters 52
4.8 Coding Data Before Computation 53
4.9 Computing Means and Standard Deviations 54
4.10 The Coefficient of Variation 57
5 INTRODUCTION TO PROBABILITY DISTRIBUTIONS:
BINOMIAL AND POISSON 61
5.1 Probability, Random Sampling, and Hypothesis Testing 62
5.2 The Binomial Distribution 71
5.3 The Poisson Distribution 81
5.4 Other Discrete Probability Distributions 93
6 THE NORMAL PROBABILITY DISTRIBUTION 98
6.1 Frequency Distributions of Continuous Variables 98
6.2 Properties of the Normal Distribution 101
6.3 A Model for the Normal Distribution 106
6.4 Applications of the Normal Distribution 109
6.5 Fitting a Normal Distribution to Observed Data 111
6.6 Skewness and Kurtosis 111
6.7 Graphic Methods 116
6.8 Other Continuous Distributions 123
7 ESTIMATION AND HYPOTHESIS TESTING 127
7.1 Distribution and Variance of Means 128
7.2 Distribution and Variance of Other Statistics 136
7.3 Introduction to Confidence Limits 139
7.4 The /-Distribution 143
7.5 Confidence Limits Based on Sample Statistics 146
7.6 The Chi-Square Distribution 152
7.7 Confidence Limits for Variances 154
7.8 Introduction to Hypothesis Testing 157
7.9 Tests of Simple Hypotheses Using the Normal and
/-Distributions 169
7.10 Testing the Hypothesis H0: a2 = <j\ 175
8 INTRODUCTION TO THE ANALYSIS
OF VARIANCE 179
8.1 Variances of Samples and Their Means 180
8.2 The F-Distribution 184
8.3 The Hypothesis H0: <r2= <r\ 189
8.7 Heterogeneity Among Sample Means Partitioning the Total Sum of Squares and Degrees of Freedom
Model 1 Anova
Model 11 Anova 190
9 SINGLE-CLASSIFICATION ANALYSIS
OF VARIANCE 207
9.1 Computational Formulas 208
9.2 General Case: Unequal n 208
9.3 Special Case: Equal n 217
9.4 Special Case: Two Groups 219
9.5 Special Case: A Single Specimen Compared With a Sample 227
9.6 Comparisons Among Means: Planned Comparisons 229
9.7 Comparisons Among Means: Unplanned Comparisons 240
9.8 Finding the Sample Size Required for a Test 260
10 NESTED ANALYSIS OF VARIANCE 272
10.1 Nested Anova: Design 272
10.2 Nested Anova: Computation 275
10.3 Nested Anovas With Unequal Sample Sizes 292
10.4 The Optimal Allocation of Resources 309
11 TWO-WAY ANALYSIS OF VARIANCE 321
11.1 Two-Way Anova: Design 321
11.2 Two-Way Anova With Equal Replication: Computation 323
11.3 Two-Way Anova: Significance Testing 331
11.4 Two-Way Anova Without Replication 342
11.5 Paired Comparisons 352
11.6 Unequal Subclass Sizes 357
11.7 Missing Values in a Randomized-Blocks Design 363
12 MULTIWAY ANALYSIS OF VARIANCE 369
12.1 The Factorial Design 369
12.2 A Three-Way Factorial Anova 370
12.3 Higher-Order Factorial Anovas 381
12.4 Other Designs 385
12.5 Anovas by Computer 3#7
1} ASSUMPTIONS OF ANALYSIS OF VARIANCE 392
13.1 A Fundamental Assumption 393
13.2 Independence 393
13.3 Homogeneity of Variances 2%
13.4 Normality 495
13.6 Transformations 499
13.7 The Logarithmic Transformation 413
13.8 The Square-Root Transformation 415
13.9 The Box-Cox Transformation 417
13.10 The Arcsine Transformation 419
13.11 Nonparametric Methods in Lieu of Single-
Classification Anovas 423
13.12 Nonparametric Methods in Lieu of Two-Way Anova 440
ft LINEAR REGRESSION 451
14.1 Introduction to Regression 452
14.2 Models in Regression 455
14.3 The Linear Regression Equation 457
14.4 Tests of Significance in Regression 466
14.5 More Than One Value of Y for Each Value of X 476
14.6 The Uses of Regression 486
14.7 Estimating X from Y 491
14.8 Comparing Regression Lines 493
14.9 Analysis of Covariance 499
14.10 Linear Comparisons in Anovas 521
14.11 Examining Residuals and Transformations
in Regression 531
14.12 Nonparametric Tests for Regression 539
14.13 Model II Regression 541
1\$ CORRELATION 555
15.1 Correlation and Regression 556
15.2 The Product-Moment Correlation Coefficient 559
15.3 The Variance of Sums and Differences 567
15.4 Computing the Product-Moment Correlation
Coefficient 569
15.5 Significance Tests in Correlation 574
15.6 Applications of Correlation 583
15.7 Principal Axes and Confidence Regions 586
15.K Nonparametric Tests for Association 593
16 MULTIPLE AND CURVILINEAR REGRESSION 609
16.1 Multiple Regression: Computation 610
16.2 Multiple Regression: Significance Tests 623
16.3 Path Analysis 634
16.4 Partial and Multiple Correlation 649
16.5 Choosing Predictor Variables 654
16.6 Curvilinear Regression 665
16.7 Advanced Topics in Regression and Correlation 678
17 ANALYSIS OF FREQUENCIES 685
17.1 Introduction to Tests for Goodness of Fit 686
17.2 Single-Classification Tests for Goodness of Fit 697
17.3 Replicated Tests of Goodness of Fit 715
17.4 Tests of Independence: Two-Way Tables 724
17.5 Analysis of Three-Way and Multiway Tables 743
17.6 Analysis of Proportions 760
17.7 Randomized Blocks for Frequency Data 778
18 MISCELLANEOUS METHODS 794
18.1 Combining Probabilities From Tests of Significance 794
18.2 Tests for Randomness of Nominal Data: Runs Tests 797
18.3 Randomization Tests 803
18.4 The Jackknife and the Bootstrap 820
18.5 The Future of Biometry: Data Analysis 825
APPENDIX: MATHEMATICAL PROOFS 833
BIBLIOGRAPHY 850
AUTHOR INDEX 865
SUBJECT INDEX 871

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