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Biostatistical Analysis, Fifth Edition

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Biostatistical Analysis, Fifth Edition

by Jerrold H. Zar

Publisher: Pearson

Copyright Year: 2010

Publishing Date: 2009/02/15

eText ISBN-10: 0-13-502471-4

eText ISBN-13: 978-0-13-502471-3

Print ISBN-10: 0-13-100846-3

Print ISBN-13: 978-0-13-100846-5

Course: Genetics, Operations Research / Management Sciences

Pages: 960

eTextbook $67.33

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Table of Contents | Description

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ABOUT THIS TITLE - TABLE OF CONTENTS

Acknowledgments, xiii

1. Data: Types and Presentation, 1

1.1. Types of Biological Data, 2

1.2. Accuracy and Significant Figures, 5

1.3. Frequency Distributions, 6

1.4. Cumulative Frequency Distributions, 14

2. Populations and Samples, 16

2.1. Populations, 16

2.2. Samples from Populations, 16

2.3. Random Sampling, 17

2.4. Parameters and Statistics, 18

2.5. Outliers, 19

3. Measures of Central Tendency, 21

3.1. The Arithmetic Mean, 21

3.2. The Median, 24

3.3. The Mode, 27

3.4. Other Measures of Central Tendency, 28

3.5. Coding Data, 30

4. Measures of Variability and Dispersion, 33

4.1. The Range, 33

4.2. Dispersion Measured with Quantiles, 35

4.3. The Mean Deviation, 37

4.4. The Variance, 37

4.5. The Standard Deviation, 41

4.6. The Coefficient of Variation, 42

4.7. Indices of Diversity, 42

4.8. Coding Data, 46

5. Probabilities, 49

5.1. Counting Possible Outcomes, 49

5.2. Permutations, 51

5.3. Combinations, 55

5.5. Probability of an Event, 59

5.6. Adding Probabilities, 60

5.7. Multiplying Probabilities, 63

5.8. Conditional Probabilities, 63

6. The Normal Distribution, 66

6.1. Proportions of a Normal Distribution, 68

6.2. The Distribution of Means, 72

6.3. Introduction to Statistical Hypothesis Testing, 74

6.4. Confidence Limits, 85

6.5. Symmetry and Kurtosis, 87

6.6. Assessing Departures from Normality, 91

7. One-Sample Hypotheses, 97

7.1. Two-Tailed Hypotheses Concerning the Mean, 97

7.2. One-Tailed Hypotheses Concerning the Mean, 103

7.3. Confidence Limits for the Population Mean, 105

7.4. Reporting Variability Around the Mean, 108

7.5. Reporting Variability Around the Median, 112

7.6. Sample Size and Estimation of the Population Mean, 114

7.7. Sample Size, Detectable Difference, and Power in Tests Concerning the Mean, 115

7.8. Sampling Finite Populations, 118

7.9. Hypotheses Concerning the Median, 120

7.10. Confidence Limits for the Population Median, 120

7.11. Hypotheses Concerning the Variance, 121

7.12. Confidence Limits for the Population Variance, 122

7.13. Power and Sample Size in Tests Concerning the Variance, 124

7.14. Hypotheses Concerning the Coefficient of Variation, 125

7.15. Confidence Limits for the Population Coefficient of Variation, 126

7.16. Hypotheses Concerning Symmetry and Kurtosis, 126

8. Two-Sample Hypotheses, 130

8.1. Testing for Difference Between Two Means, 130

8.2. Confidence Limits for Population Means, 142

8.3. Sample Size and Estimation of the Difference Between Two Population Means, 146

8.4. Sample Size, Detectable Difference, and Power in Tests for Difference between Two Means, 147

8.5. Testing for Difference Between Two Variances, 151

8.6. Confidence Limits for Population Variances and the Population Variance Ratio, 157

8.7. Sample Size and Power in Tests for Difference Between Two Variances, 158

8.8. Testing for Difference Between Two Coefficients of Variation, 159

8.9. Confidence Limits for the Difference Between Two Coefficients of Variation, 162

8.10. Nonparametric Statistical Methods, 162

8.11. Two-Sample Rank Testing, 163

8.12. Testing for Difference Between Two Medians, 172

8.13. Two-Sample Testing of Nominal-Scale Data, 174

8.14. Testing for Difference Between Two Diversity Indices, 174

8.15. Coding Data, 176

9. Paired-Sample Hypotheses, 179

9.1. Testing Mean Difference Between Paired Samples, 179

9.2. Confidence Limits for the Population Mean Difference, 182

9.3. Power, Detectable Difference and Sample Size in Paired-Sample Testing of Means, 182

9.4. Testing for Difference Between Variances from Two Correlated Populations, 182

9.5. Paired-Sample Testing by Ranks, 183

9.6. Confidence Limits for the Population Median Difference, 188

10. Multisample Hypotheses and the Analysis of Variance, 189

10.1. Single-Factor Analysis of Variance, 190

10.2. Confidence Limits for Population Means, 206

10.3. Sample Size, Detectable Difference, and Power in Analysis of Variance, 207

10.4. Nonparametric Analysis of Variance, 214

10.5. Testing for Difference Among Several Medians, 219

10.6. Homogeneity of Variances, 220

10.7. Homogeneity of Coefficients of Variation, 221

10.8. Coding Data, 224

10.9. Multisample Testing for Nominal-Scale Data, 224

11. Multiple Comparisons, 226

11.1. Testing All Pairs of Means, 227

11.2. Confidence Intervals for Multiple Comparisons, 232

11.3. Testing a Control Mean Against Each Other Mean, 234

11.4. Multiple Contrasts, 237

11.5. Nonparametric Multiple Comparisons, 239

11.6. Nonparametric Multiple Contrasts, 243

11.7. Multiple Comparisons Among Medians, 244

11.8. Multiple Comparisons Among Variances, 244

12. Two-Factor Analysis of Variance, 249

12.1. Two-Factor Analysis of Variance with Equal Replication, 250

12.2. Two-Factor Analysis of Variance with Unequal Replication, 265

12.3. Two-Factor Analysis of Variance Without Replication, 267

12.4. Two-Factor Analysis of Variance with Randomized Blocks or Repeated Measures, 270

12.5. Multiple Comparisons and Confidence Intervals in Two-Factor Analysis of Variance, 274

12.6. Sample Size, Detectable Difference, and Power in Two-Factor Analysis of Variance, 275

12.7. Nonparametric Randomized-Block or Repeated-Measures Analysis of Variance, 277

12.8. Dichotomous Nominal-Scale Data in Randomized Blocks or from Repeated Measures, 281

12.9. Multiple Comparisons with Dichotomous Randomized-Block or Repeated-Measures Data, 283

12.10. Introduction to Analysis of Covariance, 284

13. Data Transformations, 286

13.1. The Logarithmic Transformation, 287

13.2. The Square-Root Transformation, 291

13.3. The Arcsine Transformation, 291

13.4. Other Transformations, 295

14. Multiway Factorial Analysis of Variance, 296

14.1. Three-Factor Analysis of Variance, 296

14.2. The Latin-Square Experimental Design, 299

14.3. Higher-Order Factorial Analysis of Variance, 303

14.4. Multiway Analysis of Variance with Blocks or Repeated Measures, 304

14.5. Factorial Analysis of Variance with Unequal Replication, 304

14.6. Multiple Comparisons and Confidence Intervals in Multiway Analysis of Variance, 305

14.7. Power, Detectable Difference, and Sample Size in Multiway Analysis of Variance, 305

15. Nested (Hierarchical) Analysis of Variance, 307

15.1. Nesting Within One Factor, 307

15.2. Nesting in Factorial Experimental Designs, 313

15.3. Multiple Comparisons and Confidence Intervals, 314

15.4. Power, Detectable Difference, and Sample Size in Nested Analysis of Variance, 315

16. Multivariate Analysis of Variance, 316

16.1. The Multivariate Normal Distribution, 316

16.2. Multivariate Analysis of Variance Hypothesis Testing, 319

16.3. Further Analysis, 326

16.4. Other Experimental Designs, 326

17. Simple Linear Regression, 328

17.1. Regression versus Correlation, 328

17.2. The Simple Linear Regression Equation, 330

17.3. Testing the Significance of a Regression, 337

17.4. Interpretations of Regression Functions, 341

17.5. Confidence Intervals in Regression, 342

17.6. Inverse Prediction, 347

17.7. Regression with Replication and Testing for Linearity, 349

17.8. Power and Sample Size in Regression, 355

17.9. Regression Through the Origin, 355

17.10. Data Transformations in Regression, 357

17.11. The Effect of Coding Data, 361

18. Comparing Simple Linear Regression Equations, 363

18.1. Comparing Two Slopes, 363

18.2. Comparing Two Elevations, 367

18.3. Comparing Points on Two Regression Lines, 371

18.4. Comparing More Than Two Slopes, 372

18.5. Comparing More Than Two Elevations, 375

18.6. Multiple Comparisons Among Slopes, 375

18.7. Multiple Comparisons Among Elevations, 376

18.8. Multiple Comparisons of Points Among Regression Lines, 377

18.9. An Overall Test for Coincidental Regressions, 378

19. Simple Linear Correlation, 379

19.1. The Correlation Coefficient, 379

19.2. Hypotheses About the Correlation Coefficient, 383

19.3. Confidence Intervals for the Population Correlation Coefficient, 386

19.4. Power and Sample Size in Correlation, 386

19.5. Comparing Two Correlation Coefficients, 390

19.6. Power and Sample Size in Comparing Two Correlation Coefficients, 392

19.7. Comparing More Than Two Correlation Coefficients, 393

19.8. Multiple Comparisons Among Correlation Coefficients, 396

19.9. Rank Correlation, 398

19.10. Weighted Rank Correlation, 402

19.11. Correlation with Nominal-Scale Data, 405

19.12. Intraclass Correlation, 411

19.13. Concordance Correlation, 414

19.14. The Effect of Coding, 417

20. Multiple Regression and Correlation, 419

20.1. Intermediate Computational Steps, 420

20.2. The Multiple-Regression Equation, 423

20.3. Analysis of Variance of Multiple Regression or Correlation, 426

20.4. Hypotheses Concerning Partial Regression Coefficients, 430

20.5. Standardized Partial Regression Coefficients, 433

20.6. Selecting Independent Variables, 433

20.7. Partial Correlation, 438

20.8. Predicting Y Values, 440

20.9. Testing Difference Between Two Partial Regression Coefficients, 442

20.10. “Dummy” Variables, 443

20.11. Interaction of Independent Variables, 444

20.12. Comparing Multiple Regression Equations, 444

20.13. Multiple Regression Through the Origin, 446

20.14. Nonlinear Regression, 447

20.15. Descriptive Versus Predictive Models, 448

20.16. Concordance: Rank Correlation Among Several Variables, 449

21. Polynomial Regression, 458

21.1. Polynomial Curve Fitting, 458

21.2. Quadratic Regression, 463

22. Testing for Goodness of Fit, 466

22.1. Chi-Square Goodness of Fit for Two Categories, 467

22.2. Chi-Square Correction for Continuity, 469

22.3. Chi-Square Goodness of Fit for More Than Two Categories, 470

22.4. Subdividing Chi-Square Goodness of Fit, 472

22.5. Chi-Square Goodness of Fit with Small Frequencies, 473

22.6. Heterogeneity Chi-Square Testing for Goodness of Fit, 474

22.7. The Log-Likelihood Ratio for Goodness of Fit, 478

22.8. Kolmogorov-Smirnov Goodness of Fit, 481

23. Contingency Tables, 490

23.1. Chi-Square Analysis of Contingency Tables, 492

23.2. Visualizing Contingency-Table Data, 494

23.3. 2 × 2 Contingency Tables, 497

23.4. Contingency Tables with Small Frequencies, 503

23.5. Heterogeneity Testing of 2 × 2 Tables, 504

23.6. Subdividing Contingency Tables, 506

23.7. The Log-Likelihood Ratio for Contingency Tables, 508

23.8. Multidimensional Contingency Tables, 510

24. Dichotomous Variables, 518

24.1. Binomial Probabilities, 519

24.2. The Hypergeometric Distribution, 524

24.3. Sampling a Binomial Population, 526

24.4. Goodness of Fit for the Binomial Distribution, 529

24.5. The Binomial Test and One-Sample Test of a Proportion, 532

24.6. The Sign Test, 537

24.7. Power, Detectable Difference, and Sample Size for the Binomial and Sign Tests, 539

24.8. Confidence Limits for a Population Proportion, 543

24.9. Confidence Interval for a Population Median, 548

24.10. Testing for Difference Between Two Proportions, 549

24.11. Confidence Limits for the Difference Between Proportions, 551

24.12. Power, Detectable Difference, and Sample Size in Testing Difference Between Two Proportions, 552

24.13. Comparing More Than Two Proportions, 555

24.14. Multiple Comparisons for Proportions, 557

24.15. Trends Among Proportions, 559

24.16. The Fisher Exact Test, 561

24.17. Paired-Sample Testing of Nominal-Scale Data, 569

24.18. Logistic Regression, 577

25. Testing for Randomness, 585

25.1. Poisson Probabilities, 585

25.2. Confidence Limits for the Poisson Parameter, 587

25.3. Goodness of Fit for the Poisson Distribution, 589

25.4. The Poisson Distribution for the Binomial Test, 592

25.5. Comparing Two Poisson Counts, 595

25.6. Serial Randomness of Nominal-Scale Categories, 597

25.7. Serial Randomness of Measurements: Parametric Testing, 599

25.8. Serial Randomness of Measurements: Nonparametric Testing, 601

26. Circular Distributions: Descriptive Statistics, 605

26.1. Data on a Circular Scale, 605

26.2. Graphical Presentation of Circular Data, 607

26.3. Trigonometric Functions, 610

26.4. The Mean Angle, 612

26.5. Angular Dispersion, 615

26.6. The Median and Modal Angles, 617

26.7. Confidence Limits for the Population Mean and Median Angles, 618

26.8. Axial Data, 619

26.9. The Mean of Mean Angles, 621

27. Circular Distributions: Hypothesis Testing, 624

27.1. Testing Significance of the Mean Angle, 624

27.2. Testing Significance of the Median Angle, 629

27.3. Testing Symmetry Around the Median Angle, 631

27.4. Two-Sample and Multisample Testing of Mean Angles, 632

27.5. Nonparametric Two-Sample and Multisample Testing of Angles, 637

27.6. Two-Sample and Multisample Testing of Median Angles, 642

27.7. Two-Sample and Multisample Testing of Angular Distances, 642

27.8. Two-Sample and Multisample Testing of Angular Dispersion, 644

27.9. Parametric Analysis of the Mean of Mean Angles, 645

27.10. Nonparametric Analysis of the Mean of Mean Angles, 646

27.11. Parametric Two-Sample Analysis of the Mean of Mean Angles, 647

27.12. Nonparametric Two-Sample Analysis of the Mean of Mean Angles, 649

27.13. Parametric Paired-Sample Testing with Angles, 652

27.14. Nonparametric Paired-Sample Testing with Angles, 654

27.15. Parametric Angular Correlation and Regression, 654

27.16. Nonparametric Angular Correlation, 660

27.17. Goodness-of-Fit Testing for Circular Distributions, 662

27.18. Serial Randomness of Nominal-Scale Categories on a Circle, 665

Appendices, 669

A. The Greek Alphabet, 669

B. Statistical Tables and Graphs, 671

Table B.1. Critical Values of the Chi-Square (x²) Distribution, 672

Table B.2. Proportions of the Normal Curve (One-Tailed), 676

Table B.3. Critical Values of the t Distribution, 678

Table B.4. Critical Values of the F Distribution, 680

Table B.5. Critical Values of the q Distribution, for the Tukey Test, 717

Table B.6. Critical Values of q′ for the One-Tailed Dunnett’s Test, 733

Table B.7. Critical Values of q′ for the Two-Tailed Dunnett’s Test, 735

Table B.8. Critical Values of d_max for the Kolmogorov-Smirnov Goodness-of-Fit for Discrete or Grouped Data, 736

Table B.9. Critical Values of D for the Kolmogorov-Smirnov Goodness-of-Fit Test for Continuous Distributions, 741

Table B.10. Critical Values of D_δ for the δ-Corrected Kolmogorov-Smirnov Goodness-of-Fit Test for Continuous Distributions, 745

Table B.11. Critical Values of the Mann-Whitney U Distribution, 747

Table B.12. Critical Values of the Wilcoxon T Distribution, 758

Table B.13. Critical Values of the Kruskal-Wallis H Distribution, 761

Table B.14. Critical Values of the Friedman x²_r Distribution, 763

Table B.15. Critical Values of Q for Nonparametric Multiple-Comparison Testing, 764

Table B.16. Critical Values of Q′ for Nonparametric Multiple-Comparison Testing with a Control, 765

Table B.17. Critical Values of the Correlation Coefficient, r, 766

Table B.18. Fisher’s z Transformation for Correlation Coefficients, r, 768

Table B.19. Correlation Coefficients, r, Corresponding to Fisher’s z Transformation, 770

Table B.20. Critical Values of the Spearman Rank-Correlation Coefficient, r_s, 773

Table B.21. Critical Values of the Top-Down Correlation Coefficient, r_T, 775

Table B.22. Critical Values of the Symmetry Measure, √b₁, 776

Table B.23. Critical Values of the Kurtosis Measure, b₂, 777

Table B.24. The Arcsine Transformation, p′, 778

Table B.25. Proportions, p, Corresponding to Arcsine Transformations, p′, 780

Table B.26a. Binomial Coefficients, _nC_X, 782

Table B.26b. Proportions of the Binomial Distribution for p = q = 0.5, 785

Table B.27. Critical Values of C for the Sign Test or the Binomial Test with p = 0.5, 786

Table B.28. Critical Values for Fisher’s Exact Test, 795

Table B.29. Critical Values of u for the Runs Test, 826

Table B.30. Critical Values of C for the Mean Square Successive Difference Test, 835

Table B.31. Critical Values, u, for the Runs-Up-and-Down Test, 837

Table B.32. Angular Deviation, s, As a Function of Vector Length, r, 838

Table B.33. Circular Standard Deviation, s₀, as a Function of Vector Length, r, 840

Table B.34. Circular Values of z for Rayleigh’s Test for Circular Uniformity, 842

Table B.35. Critical Values of u for the V Test of Circular Uniformity, 844

Table B.36. Critical Values of m for the Hodges-Ajne Test for Circular Uniformity, 845

Table B.37. Correction Factor, K, for the Watson and Williams Test, 847

Table B.38a. Critical Values of Watson’s Two-Sample U², 849

Table B.38b. Critical Values of Watson’s One-Sample U², 853

Table B.39. Critical Values of R′ for the Moore Test for Circular Uniformity, 853

Table B.40. Common Logarithms of Factorials, 854

Table B.41. Ten Thousand Random Digits, 856

Figure B.1. Power and Sample Size in Analysis of Variance, 859

C. The Effects of Coding Data, 867

D. Analysis-of-Variance Hypothesis Testing, 869

D.1. Determination of Appropriate Fs and Degrees of Freedom, 869

D.2. Two-Factor Analysis of Variance, 872

D.3. Three-Factor Analysis of Variance, 872

D.4. Nested Analysis of Variance, 873

Answers to Exercises, 875

Literature Cited, 886

Author Index, 923

Subject Index, 931

Statistical Tables and Graphs, IBC-1

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ABOUT THIS TITLE - DESCRIPTION

Introduces all biostatistical methods while assuming no statiscal background. Enormously comprehensive, topical coverage that covers all areas of the biology curriculum that benefit from that benefit from statistical analysis.

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