Biometry

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

• ISBN13: 9780716724117
• ISBN10: 0716724111
• Edition: 3rd
• Format: Hardcover
• Copyright: 1994-09-15
• 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	xiii	(4)
NOTES ON THE THIRD EDITION	xvii
1 INTRODUCTION	1	(7)
1.1 Some Definitions	1	(2)
1.2 The Development of Biometry	3	(2)
1.3 The Statistical Frame of Mind	5	(3)
2 DATA IN BIOLOGY	8	(25)
2.1 Samples and Populations	8	(2)
2.2 Variables in Biology	10	(3)
2.3 Accuracy and Precision of Data	13	(3)
2.4 Derived Variables	16	(3)
2.5 Frequency Distributions	19	(14)
3 THE HANDLING OF DATA	33	(6)
3.1 Computers	34	(1)
3.2 Software	35	(2)
3.3 Efficiency and Economy in Data Processing	37	(2)
4 DESCRIPTIVE STATISTICS	39	(22)
4.1 The Arithmetic Mean	40	(3)
4.2 Other Means	43	(1)
4.3 The Median	44	(3)
4.4 The Mode	47	(1)
4.5 The Range	48	(1)
4.6 The Standard Deviation	49	(3)
4.7 Sample Statistics and Parameters	52	(1)
4.8 Coding Data Before Computation	53	(1)
4.9 Computing Means and Standard Deviations	54	(3)
4.10 The Coefficient of Variation	57	(4)
5 INTRODUCTION TO PROBABILITY DISTRIBUTION: BINOMIAL AND POISSON	61	(37)
5.1 Probability, Random Sampling, and Hypothesis Testing	62	(9)
5.2 The Binomial Distribution	71	(10)
5.3 The Poisson Distribution	81	(12)
5.4 Other Discrete Probability Distributions	93	(5)
6 THE NORMAL PROBABILITY DISTRIBUTION	98	(29)
6.1 Frequency Distributions of Continuous Variables	98	(3)
6.2 Properties of the Normal Distribution	101	(5)
6.3 A Model for the Normal Distribution	106	(3)
6.4 Applications of the Normal Distribution	109	(2)
6.5 Fitting a Normal Distribution to Observed Data	111	(1)
6.6 Skewness and Kurtosis	111	(5)
6.7 Graphic Methods	116	(7)
6.8 Other Continuous Distributions	123	(4)
7 ESTIMATION AND HYPOTHESIS TESTING	127	(52)
7.1 Distribution and Variance of Means	128	(8)
7.2 Distribution and Variance of Other Statistics	136	(3)
7.3 Introduction to Confidence Limits	139	(4)
7.4 The t-Distribution	143	(3)
7.5 Confidence Limits Based on Sample Statistics	146	(6)
7.6 The Chi-Square Distribution	152	(2)
7.7 Confidence Limits for Variances	154	(3)
7.8 Introduction to Hypothesis Testing	157	(12)
7.9 Tests of Simple Hypotheses Using the Normal and t-Distributions	169	(6)
7.10 Testing the Hypothesis H(0): Sigma^2 = Sigma^2(0)	175	(4)
8 INTRODUCTION TO THE ANALYSIS OF VARIANCE	179	(28)
8.1 Variances of Samples and Their Means	180	(4)
8.2 The F-Distribution	184	(5)
8.3 The Hypothesis H(0): Sigma^2(1) = Sigma^2(2)	189	(1)
8.4 Heterogeneity Among Sample Means	190	(7)
8.5 Partitioning the Total Sum of Squares and Degrees of Freedom	197	(4)
8.6 Model I Anova	201	(2)
8.7 Model II Anova	203	(4)
9 SINGLE-CLASSIFICATION ANALYSIS OF VARIANCE	207	(65)
9.1 Computational Formulas	208	(1)
9.2 General Case: Unequal n	208	(9)
9.3 Special Case: Equal n	217	(2)
9.4 Special Case: Two Groups	219	(8)
9.5 Special Case: A Single Specimen Compared With a Sample	227	(2)
9.6 Comparisons Among Means: Planned Comparisons	229	(11)
9.7 Comparisons Among Means: Unplanned Comparisons	240	(20)
9.8 Finding the Sample Size Required for a Test	260	(12)
10 NESTED ANALYSIS OF VARIANCE	272	(49)
10.1 Nested Anova: Design	272	(3)
10.2 Nested Anova: Computation	275	(17)
10.3 Nested Anovas With Unequal Sample Sizes	292	(17)
10.4 The Optimal Allocation of Resources	309	(12)
11 TWO-WAY ANALYSIS OF VARIANCE	321	(48)
11.1 Two-Way Anova: Design	321	(2)
11.2 Two-Way Anova With Equal Replication: Computation	323	(8)
11.3 Two-Way Anova: Significance Testing	331	(11)
11.4 Two-Way Anova Without Replication	342	(10)
11.5 Paired Comparisons	352	(5)
11.6 Unequal Subclass Sizes	357	(6)
11.7 Missing Values in a Randomized-Blocks Design	363	(6)
12 MULTIWAY ANALYSIS OF VARIANCE	369	(23)
12.1 The Factorial Design	369	(1)
12.2 A Three-Way Factorial Anova	370	(11)
12.3 Higher-Order Factorial Anovas	381	(4)
12.4 Other Designs	385	(2)
12.5 Anovas by Computer	387	(5)
13 ASSUMPTIONS OF ANALYSIS OF VARIANCE	392	(59)
13.1 A Fundamental Assumption	393	(1)
13.2 Independence	393	(3)
13.3 Homogeneity of Variances	396	(10)
13.4 Normality	406	(1)
13.5 Additivity	407	(2)
13.6 Transformations	409	(4)
13.7 The Logarithmic Transformation	413	(2)
13.8 The Square-Root Transformation	415	(2)
13.9 The Box-Cox Transformation	417	(2)
13.10 The Arcsine Transformation	419	(4)
13.11 Nonparametric Methods in Lieu of Single-Classification Anovas	423	(17)
13.12 Nonparametric Methods in Lieu of Two-Way Anova	440	(11)
14 LINEAR REGRESSION	451	(104)
14.1 Introduction to Regression	452	(3)
14.2 Models in Regression	455	(2)
14.3 The Linear Regression Equation	457	(9)
14.4 Tests of Significance in Regression	466	(10)
14.5 More Than One Value of Y for Each Value of X	476	(10)
14.6 The Uses of Regression	486	(5)
14.7 Estimating X from Y	491	(2)
14.8 Comparing Regression Lines	493	(6)
14.9 Analysis of Covariance	499	(22)
14.10 Linear Comparisons in Anovas	521	(10)
14.11 Examining Residuals and Transformations in Regression	531	(8)
14.12 Nonparametric Tests for Regression	539	(2)
14.13 Model II Regression	541	(14)
15 CORRELATION	555	(54)
15.1 Correlation and Regression	556	(3)
15.2 The Product-Moment Correlation Coefficient	559	(8)
15.3 The Variance of Sums and Differences	567	(2)
15.4 Computing the Product-Moment Correlation Coefficient	569	(5)
15.5 Significance Tests in Correlation	574	(9)
15.6 Applications of Correlation	583	(3)
15.7 Principal Axes and Confidence Regions	586	(7)
15.8 Nonparametric Tests for Association	593	(16)
16 MULTIPLE AND CURVILINEAR REGRESSION	609	(76)
16.1 Multiple Regression: Computation	610	(13)
16.2 Multiple Regression: Significance Tests	623	(11)
16.3 Path Analysis	634	(15)
16.4 Partial and Multiple Correlation	649	(5)
16.5 Choosing Predictor Variables	654	(11)
16.6 Curvilinear Regression	665	(13)
16.7 Advanced Topics in Regression and Correlation	678	(7)
17 ANALYSIS OF FREQUENCIES	685	(109)
17.1 Introduction to Tests for Goodness of Fit	686	(11)
17.2 Single-Classification Tests for Goodness of Fit	697	(18)
17.3 Replicated Tests of Goodness of Fit	715	(9)
17.4 Tests of Independence: Two-Way Tables	724	(19)
17.5 Analysis of Three-Way and Multiway Tables	743	(17)
17.6 Analysis of Proportions	760	(18)
17.7 Randomized Blocks for Frequency Data	778	(16)
18 MISCELLANEOUS METHODS	794	(39)
18.1 Combining Probabilities From Tests of Significance	794	(3)
18.2 Tests for Randomness of Nominal Data: Runs Tests	797	(6)
18.3 Randomization Tests	803	(17)
18.4 The Jackknife and the Bootstrap	820	(5)
18.5 The Future of Biometry: Data Analysis	825	(8)
APPENDIX: MATHEMATICAL PROOFS	833	(17)
BIBLIOGRAPHY	850	(15)
AUTHOR INDEX	865	(6)
SUBJECT INDEX	871