Biometry

by Sokal, Robert R.; Rohlf, F. James

• ISBN13: 9780716786047
• ISBN10: 0716786044
• Edition: 4th
• Format: Hardcover
• Copyright: 2011-09-16
• Publisher: W. H. Freeman

Summary

Sokal and Rohlf's classic text deals with statistics from numerous areas of biological research, focusing on practical applications and incorporates computer calculations.

Table of Contents

Preface	p. xiii
Notes on the Fourth Edition	p. xvii
Introduction	p. 1
Some Definitions	p. 1
The Development of Biometry	p. 3
The Statistical Frame of Mind	p. 5
Data in Biology	p. 9
Samples and Populations	p. 9
Variables in Biology	p. 11
Accuracy and Precision of Data	p. 13
Derived Variables	p. 16
Frequency Distributions	p. 19
Computers and Data Analysis	p. 33
Computers	p. 33
Software	p. 35
Efficiency and Economy in Data Processing	p. 37
Descriptive Statistics	p. 39
The Arithmetic Mean	p. 40
Other Means	p. 44
The Median	p. 45
The Mode	p. 47
Sample Statistics and Parameters	p. 49
The Range	p. 49
The Standard Deviation	p. 51
Coding Data Before Computation	p. 54
The Coefficient of Variation	p. 55
Introduction to Probability Distributions: Binomial and Poisson	p. 59
Probability, Random Sampling, and Hypothesis Testing	p. 60
The Binomial Distribution	p. 68
The Poisson Distribution	p. 78
Other Discrete Probability Distributions	p. 87
The Normal Probability Distribution	p. 93
Frequency Distributions of Continuous Variables	p. 93
Properties of the Normal Distribution	p. 95
A Model for the Normal Distribution	p. 100
Applications of the Normal Distribution	p. 102
Fitting a Normal Distribution to Observed Data	p. 104
Skewness and Kurtosis	p. 106
Graphic Methods	p. 108
Other Continuous Distributions	p. 117
Hypothesis Testing and Interval Estimation	p. 119
Introduction to Hypothesis Testing: Randomization Approaches	p. 120
Distribution and Variance of Means	p. 131
Distribution and Variance of Other Statistics	p. 137
The t-Distribution	p. 140
More on Hypothesis Testing: Normally Distributed Data	p. 142
Power of a Test	p. 146
Tests of Simple Hypotheses Using the Normal and f-Distributions	p. 148
The Chi-Square Distribution	p. 154
Testing the Hypothesis H0: ¿2 = ¿20	p. 156
Introduction to Interval Estimation (Confidence Limits)	p. 157
Confidence Limits Using Sample Standard Deviations	p. 162
Confidence Limits for Variances	p. 167
The Jackknife and the Bootstrap	p. 168
Introduction to Analysis of Variance	p. 177
Variances of Samples and Their Means	p. 178
TheF-Distribution	p. 182
The Hypothesis H0: ¿21 = ¿22	p. 187
Heterogeneity Among Sample Means	p. 190
Partitioning the Total Sum of Squares and Degrees of Freedom	p. 197
Model I Anova	p. 200
Model II Anova	p. 203
Single-Classification Analysis of Variance	p. 207
Computational Formulas	p. 208
General Case: Unequal and Equal n	p. 208
Special Case: Two Groups	p. 220
Comparisons Among Means in a Model I Anova: Essential Background	p. 228
Comparisons Among Means: Special Methods	p. 246
Nested Analysis of Variance	p. 277
Nested Anova: Design	p. 277
Nested Anova: Computation	p. 280
Nested Anovas with Unequal Sample Sizes	p. 301
Two-Way and Multiway Analysis of Variance	p. 319
Two-Way Anova: Design	p. 319
Two-Way Anova with Equal Replication: Computation	p. 321
Two-Way Anova: Hypothesis Testing	p. 331
Two-Way Anova Without Replication	p. 340
Paired Comparisons	p. 349
The Factorial Design	p. 354
A Three-Way Factorial Design	p. 355
Higher-Order Factorial Anovas	p. 365
Other Designs	p. 370
Anova by Computer	p. 372
Statistical Power and Sample Size in the Analysis of Variance	p. 379
Effect Size	p. 379
Noncentral t- and F-Distributions and Confidence Limits for Effect Sizes	p. 382
Power in an Anova	p. 390
Sample Size in an Anova	p. 391
Minimum Detectable Difference	p. 395
Post Hoc Power Analysis	p. 396
Optimal Allocation of Resources in a Nested Design	p. 397
Randomized Blocks and Other Two-Way and Multiway Designs	p. 406
Assumptions of Analysis of Variance	p. 409
A Fundamental Assumption	p. 410
Independence	p. 410
Homogeneity of Variances	p. 413
Normality	p. 422
Transformations	p. 426
The Logarithmic Transformation	p. 427
The Square Root Transformation	p. 433
The Box-Cox Transformation	p. 435
The Arcsine Transformation	p. 438
Nonparametric Methods in Lieu of Single-Classification Anova	p. 440
Nonparametric Methods in Lieu of Two-Way Anova	p. 460
Linear Regression	p. 471
Introduction to Regression	p. 472
Models in Regression	p. 475
The Linear Regression Equation	p. 477
Hypothesis Testing in Regression	p. 485
More Than One Value of Y for Each Value of X	p. 495
The Uses of Regression	p. 506
Estimating X From Y	p. 511
Comparing Two Regression Lines	p. 513
Linear Comparisons in Anovas	p. 515
Examining Residuals and Transformations in Regression	p. 524
Nonparametric Tests for Regression	p. 532
Model II Regression	p. 535
Effect Size, Power, and Sample Size in Regression	p. 544
Correlation	p. 551
Correlation Versus Regression	p. 551
The Product-Moment Correlation Coefficient	p. 554
Computing the Product-Moment Correlation Coefficient	p. 562
The Variance of Sums and Differences	p. 565
Hypothesis Tests for Correlations	p. 567
Applications of Correlation	p. 577
Nonparametric Tests for Association	p. 580
Major Axes and Confidence Regions	p. 588
Effect Size, Power, and Sample Size	p. 592
Multiple and Curvilinear Regression	p. 603
Multiple Regression: Computation	p. 604
Multiple Regression: Hypothesis Tests	p. 614
Path Analysis and Structural Equation Modeling	p. 625
Partial and Multiple Correlation	p. 644
Selection of Independent Variables	p. 649
Computation of Multiple Regression by Matrix Methods	p. 656
Solving Anovas as Regression Problems: General Linear Models	p. 659
Analysis of Covariance (Ancova)	p. 665
Curvilinear Regression	p. 671
Effect Size, Power, and Sample Size in Multiple Regression	p. 685
Advanced Topics in Regression and Correlation	p. 694
Analysis of Frequencies	p. 703
Introduction to Tests for Goodness of Fit	p. 704
Single-Classification Tests for Goodness of Fit	p. 714
Replicated Tests of Goodness of Fit	p. 730
Tests of Independence: Two-Way Tables	p. 739
Analysis of Three-Way Tables	p. 758
Analysis of Proportions	p. 773
Randomized Blocks for Frequency Data	p. 793
Effect Sizes, Power, and Sample Sizes	p. 801
Meta-Analysis and Miscellaneous Methods	p. 817
Synthesis of Prior Research Results: Meta-Analysis	p. 817
Tests for Randomness of Nominal Data: Runs Tests	p. 841
Isotonic Regression	p. 847
Application of Randomization Tests to Unconventional Statistics	p. 850
The Mantel Test of Association Between Two Distance Matrices	p. 852
The Future of Biometry: Data Analysis	p. 859
Appendices
Mathematical Proofs	p. 869
Introduction to Matrices	p. 885
Bibliography	p. 891
Author Index	p. 909
Subject Index	p. 915
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