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Biostatistical Analysis

by: Zar, Jerrold H.

Biostatistical Analysis

by: Zar, Jerrold H.

ISBN 13:
9780130815422
ISBN 10:
013081542X
Edition: 4th
Format: Hardcover
Copyright: 01/01/2010
Publisher: Pearson College Div
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Summary

The latest edition of this best-selling biostatistics book is both comprehensive and easy to read.It provides a broad and practical overview of the statistical analysis methods used by researchers to collect, summarize, analyze, and draw conclusions from biological research data. TheFourth Editioncan serve as either an introduction to the discipline for beginning studentsora comprehensive procedural reference for today's practitioners.

PREFACE

1 INTRODUCTION

(15)

1.1 Types of Biological Data

(3)

1.2 Accuracy and Significant Figures

(1)

1.3 Frequency Distributions

(7)

1.4 Cumulative Frequency Distributions

(3)

2 POPULATIONS AND SAMPLES

(4)

2.1 Populations

(1)

2.2 Samples from Populations

(1)

2.3 Random Sampling

(1)

2.4 Parameters and Statistics

(2)

3 MEASURES OF CENTRAL TENDENCY

(12)

3.1 The Arithmetic Mean

(3)

3.2 The Median

(3)

3.3 Other Quantiles

(1)

3.4 The Mode

(1)

3.5 Other Measures of Central Tendency

(1)

3.6 The Effect of Coding Data

(2)

Exercises

(1)

4 MEASURES OF DISPERSION AND VARIABILITY

(16)

4.1 The Range

(2)

4.2 Dispersion Measured with Quantiles

(1)

4.3 The Mean Deviation

(1)

4.4 The Variance

(4)

4.5 The Standard Deviation

(1)

4.6 The Coefficient of Variation

(1)

4.7 Indices of Diversity

(4)

4.8 The Effect of Coding Data

(3)

Exercises

(1)

5 PROBABILITIES

(17)

5.1 Counting Possible Outcomes

(1)

5.2 Permutations

(4)

5.3 Combinations

(2)

5.4 Sets

(2)

5.5 Probability of an Event

(1)

5.6 Adding Probabilities

(2)

5.7 Multiplying Probabilities

(2)

Exercises

(2)

6 THE NORMAL DISTRIBUTION

(26)

6.1 Symmetry and Kurtosis

(5)

6.2 Proportions of a Normal Distribution

(4)

6.3 The Distribution of Means

(3)

6.4 Introduction to Statistical Hypothesis Testing

(7)

6.5 Assessing Departures from Normality

(3)

Exercises

(2)

7 ONE-SAMPLE HYPOTHESES

(31)

7.1 Two-Tailed Hypotheses Concerning the Mean

(5)

7.2 One-Tailed Hypotheses Concerning the Mean

(2)

7.3 Confidence Limits for the Population Mean

(2)

7.4 Reporting Variability about the Mean

100

(5)

7.5 Sample Size and Estimation of the Population Mean

105

(1)

7.6 Power and Sample Size in Tests Concerning the Mean

105

(3)

7.7 Sampling Finite Populations

108

(2)

7.8 Confidence Limits for the Population Median

110

(1)

7.9 Hypotheses Concerning the Median

110

(1)

7.10 Confidence Limits for the Population Variance

110

(2)

7.11 Hypotheses Concerning the Variance

112

(1)

7.12 Power and Sample Size in Tests Concerning the Variance

113

(1)

7.13 Hypotheses Concerning the Coefficient of Variation

114

(1)

7.14 Hypotheses Concerning Symmetry and Kurtosis

115

(5)

Exercises

120

(2)

8 TWO-SAMPLE HYPOTHESES

122

(39)

8.1 Testing for Difference between Two Means

122

(7)

8.2 Confidence Limits for Population Means

129

(2)

8.3 Sample Size and Estimation of the Difference between Two Population Means

131

(1)

8.4 Power and Sample Size in Tests for Difference between Two Means

132

(4)

8.5 Testing for Difference between Two Variances

136

(3)

8.6 Confidence Interval for the Population Variance Ratio

139

(1)

8.7 Sample Size and Power in Tests for Difference between Two Variances

140

(1)

8.8 Testing for Difference between Two Coefficients of Variation

141

(4)

8.9 Nonparametric Statistical Methods

145

(1)

8.10 Two-Sample Rank Testing

146

(9)

8.11 Testing for Difference between Two Medians

155

(1)

8.12 The Effect of Coding

155

(1)

8.13 Two-Sample Testing of Nominal-Scale Data

156

(1)

8.14 Testing for Difference between Two Diversity Indices

156

(3)

Exercises

159

(2)

9 PAIRED-SAMPLE HYPOTHESES

161

(16)

9.1 Testing Mean Difference

161

(3)

9.2 Confidence Limits for the Population Mean Difference

164

(1)

9.3 Power and Sample Size in Paired-Sample Testing of Means

164

(1)

9.4 Testing for the Difference between Variances from Two Correlated Populations

164

(1)

9.5 Paired-Sample Testing by Ranks

165

(4)

9.6 Confidence Limits for the Population Median Difference

169

(1)

9.7 Paired-Sample Testing of Nominal-Scale Data

169

(6)

Exercises

175

(2)

10 MULTISAMPLE HYPOTHESES: THE ANALYSIS OF VARIANCE

177

(31)

10.1 Single-Factor Analysis of Variance

178

(11)

10.2 Confidence Limits for Population Means

189

(1)

10.3 Power and Sample Size in Analysis of Variance

189

(6)

10.4 Nonparametric Analysis of Variance

195

(5)

10.5 Testing for Difference among Several Medians

200

(2)

10.6 Homogeneity of Variances

202

(2)

10.7 Homogeneity of Coefficients of Variation

204

(2)

10.8 The Effect of Coding

206

(1)

10.9 Multisample Testing for Nominal-Scale Data

206

(1)

Exercises

206

(2)

11 MULTIPLE COMPARISONS

208

(23)

11.1 The Tukey Test

210

(4)

11.2 The Newman-Keuls Test

214

(1)

11.3 Confidence Intervals Following Multiple Comparisons

215

(2)

11.4 Comparisons of a Control Mean to Each Other Group Mean

217

(2)

11.5 Scheffe's Multiple Contrasts

219

(4)

11.6 Nonparametric Multiple Comparisons

223

(3)

11.7 Nonparametric Multiple Contrasts

226

(1)

11.8 Multiple Comparisons among Medians

226

(2)

11.9 Multiple Comparisons among Variances

228

(2)

Exercises

230

(1)

12 TWO-FACTOR ANALYSIS OF VARIANCE

231

(42)

12.1 Two-Factor Analysis of Variance with Equal Replication

232

(13)

12.2 Two-Factor Analysis of Variance with Unequal Replication

245

(3)

12.3 Two-Factor Analysis of Variance without Replication

248

(2)

12.4 The Randomized Block Experimental Design

250

(5)

12.5 Repeated-Measures Experimental Designs

255

(5)

12.6 Multiple Comparisons and Confidence Intervals in Two-Factor Analysis of Variance

260

(1)

12.7 Power and Sample Size in Two-Factor Analysis of Variance

261

(2)

12.8 Nonparametric Randomized Block or Repeated-Measures Analysis of Variance

263

(4)

12.9 Multiple Comparisons for Nonparametric Randomized Block or Repeated-Measures Analysis of Variance

267

(1)

12.10 Dichotomous Nominal-Scale Data in Randomized Blocks or from Repeated Measures

268

(2)

12.11 Multiple Comparisons with Dichotomous Randomized Block or Repeated-Measures Data

270

(1)

12.12 Introduction to Analysis of Covariance

270

(1)

Exercises

271

(2)

13 DATA TRANSFORMATIONS

273

(9)

13.1 The Logarithmic Transformation

275

(1)

13.2 The Square Root Transformation

275

(3)

13.3 The Arcsine Transformation

278

(2)

13.4 Other Transformations

280

(1)

Exercises

280

(2)

14 MULTIWAY FACTORIAL ANALYSIS OF VARIANCE

282

(21)

14.1 Three-Factor Analysis of Variance

283

(3)

14.2 The Latin Square Experimental Design

286

(1)

14.3 Higher-Order Factorial Analysis of Variance

287

(1)

14.4 Blocked and Repeated-Measures Experimental Designs

288

(10)

14.5 Factorial Analysis of Variance with Unequal Replication

298

(1)

14.6 Multiple Comparisons and Confidence Intervals in Multiway Analysis of Variance

299

(1)

14.7 Power and Sample Size in Multiway Analysis of Variance

300

(1)

Exercises

300

(3)

15 NESTED (HIERARCHICAL) ANALYSIS OF VARIANCE

303

(9)

15.1 Nesting within One Main Factor

305

(3)

15.2 Nesting in Factorial Experiments

308

(2)

15.3 Multiple Comparisons and Confidence Intervals

310

(1)

15.4 Power and Sample Size in Nested Analysis of Variance

311

(1)

Exercises

311

(1)

16 MULTIVARIATE ANALYSIS OF VARIANCE

312

(12)

16.1 The Multivariate Normal Distribution

313

(3)

16.2 Multivariate Analysis of Variance Hypothesis Testing

316

(6)

16.3 Further Analysis

322

(1)

16.4 Other Experimental Designs

322

(1)

Exercises

323

(1)

17 SIMPLE LINEAR REGRESSION

324

(36)

17.1 Regression vs. Correlation

324

(2)

17.2 The Simple Linear Regression Equation

326

(7)

17.3 Testing the Significance of a Regression

333

(4)

17.4 Confidence Intervals in Regression

337

(5)

17.5 Inverse Prediction

342

(2)

17.6 Interpretations of Regression Functions

344

(1)

17.7 Regression with Replication and Testing for Linearity

345

(5)

17.8 Power and Sample Size in Regression

350

(1)

17.9 Regression through the Origin

351

(2)

17.10 Data Transformations in Regression

353

(4)

17.11 The Effect of Coding

357

(1)

Exercises

358

(2)

18 COMPARING SIMPLE LINEAR REGRESSION EQUATIONS

360

(17)

18.1 Comparing Two Slopes

360

(4)

18.2 Comparing Two Elevations

364

(4)

18.3 Comparing Points on Two Regression Lines

368

(1)

18.4 Comparing more than Two Slopes

369

(3)

18.5 Comparing more than Two Elevations

372

(1)

18.6 Multiple Comparisons among Slopes

372

(1)

18.7 Multiple Comparisons among Elevations

373

(1)

18.8 Multiple Comparisons of Points among Regression Lines

374

(1)

18.9 An Overall Test for Coincidental Regressions

375

(1)

Exercises

375

(2)

19 SIMPLE LINEAR CORRELATION

377

(36)

19.1 The Correlation Coefficient

377

(4)

19.2 Hypotheses about the Correlation Coefficient

381

(2)

19.3 Confidence Intervals for the Population Correlation Coefficient

383

(2)

19.4 Power and Sample Size in Correlation

385

(1)

19.5 Comparing Two Correlation Coefficients

386

(2)

19.6 Power and Sample Size in Comparing Two Correlation Coefficients

388

(2)

19.7 Comparing more than Two Correlation Coefficients

390

(2)

19.8 Multiple Comparisons among Correlation Coefficients

392

(3)

19.9 Rank Correlation

395

(3)

19.10 Weighted Rank Correlation

398

(3)

19.11 Correlation for Dichotomous Nominal-Scale Data

401

(3)

19.12 Intraclass Correlation

404

(3)

19.13 Concordance Correlation

407

(3)

19.14 The Effect of Coding

410

(1)

Exercises

410

(3)

20 MULTIPLE REGRESSION AND CORRELATION

413

(39)

20.1 Intermediate Computational Steps

414

(5)

20.2 The Multiple Regression Equation

419

(3)

20.3 Analysis of Variance of Multiple Regression or Correlation

422

(2)

20.4 Hypotheses Concerning Partial Regression Coefficients

424

(2)

20.5 Standardized Partial Regression Coefficients

426

(1)

20.6 Partial Correlation

426

(2)

20.7 Round-off Error and Coding Data

428

(1)

20.8 Selection of Independent Variables

429

(4)

20.9 Predicting Y Values

433

(3)

20.10 Testing Difference between Two Partial Regression Coefficients

436

(1)

20.11 "Dummy" Variables

436

(1)

20.12 Interaction of Independent Variables

437

(1)

20.13 Comparing Multiple Regression Equations

437

(3)

20.14 Multiple Regression through the Origin

440

(1)

20.15 Nonlinear Regression

440

(2)

20.16 Descriptive vs. Predictive Models

442

(1)

20.17 Concordance: Rank Correlation among Several Variables

443

(7)

Exercises

450

(2)

21 POLYNOMIAL REGRESSION

452

(9)

21.1 Polynomial Curve Fitting

452

(5)

21.2 Round-off Error and Coding Data

457

(1)

21.3 Quadratic Regression

457

(2)

Exercises

459

(2)

22 TESTING FOR GOODNESS OF FIT

461

(25)

22.1 Chi-Square Goodness of Fit

462

(2)

22.2 Chi-Square Goodness of Fit for More than Two Categories

464

(2)

22.3 Subdividing Chi-Square Analyses

466

(2)

22.4 Chi-Square Correction for Continuity

468

(2)

22.5 Bias in Chi-Square Calculations

470

(1)

22.6 Heterogeneity Chi-Square

471

(2)

22.7 The Log-Likehood Ratio

473

(2)

22.8 Kolmogorov-Smirnov Goodness of Fit for Discrete Data

475

(3)

22.9 Kolmogorov-Smirnov Goodness of Fit for Continuous Data

478

(3)

22.10 Sample Size Required for Kolmogorov-Smirnov Goodness of Fit for Continuous Data

481

(2)

Exercises

483

(3)

23 CONTINGENCY TABLES

486

(30)

23.1 Chi-Square Analysis of Contingency Tables

488

(2)

23.2 Graphing Contingency Table Data

490

(1)

23.3 The 2 x 2 Contingency Table

491

(9)

23.4 Heterogeneity Testing of 2 x 2 Tables

500

(2)

23.5 Subdividing Contingency Tables

502

(2)

23.6 Bias in Chi-Square Contingency Table Analyses

504

(1)

23.7 The Log-Likehood Ratio for Contingency Tables

505

(1)

23.8 Three-Dimensional Contingency Tables

506

(6)

23.9 Log-Linear Models for Multidimensional Contingency Tables

512

(2)

Exercises

514

(2)

24 MORE ON DICHOTOMOUS VARIABLES

516

(55)

24.1 Binomial Probabilities

517

(6)

24.2 The Hypergeometric Distribution

523

(1)

24.3 Sampling a Binomial Population

524

(3)

24.4 Confidence Limits for Population Proportions

527

(3)

24.5 Goodness of Fit for the Binomial Distribution

530

(3)

24.6 The Binomial Test

533

(5)

24.7 The Sign Test

538

(1)

24.8 Power of the Binomial and Sign Tests

539

(3)

24.9 Confidence Interval for the Population Median

542

(1)

24.10 The Fisher Exact Test

543

(2)

24.11 Comparing Two Proportions

555

(3)

24.12 Power and Sample Size in Comparing Two Proportions

558

(4)

24.13 Comparing more than Two Proportions

562

(1)

24.14 Multiple Comparisons for Proportions

563

(2)

24.15 Trends among Proportions

565

(3)

Exercises

568

(3)

25 TESTING FOR RANDOMNESS

571

(21)

25.1 Poisson Probabilities

571

(3)

25.2 Confidence Limits for the Poisson Parameter

574

(1)

25.3 Goodness of Fit of the Poisson Distribution

575

(3)

25.4 The Binomial Test Revisited

578

(4)

25.5 Comparing Two Poisson Counts

582

(1)

25.6 Serial Randomness of Nominal-Scale Categories

583

(3)

25.7 Serial Randomness of Measurements: Parametric Testing

586

(1)

25.8 Serial Randomness of Measurements: Nonparametric Testing

587

(3)

Exercises

590

(2)

26 CIRCULAR DISTRIBUTIONS: DESCRIPTIVE STATISTICS

592

(24)

26.1 Data on a Circular Scale

592

(3)

26.2 Graphical Presentation of Circular Data

595

(2)

26.3 Sines and Cosines of Circular Data

597

(2)

26.4 The Mean Angle

599

(3)

26.5 Angular Dispersion

602

(3)

26.6 The Median and Modal Angles

605

(1)

26.7 Confidence Limits for the Population Mean and Median Angles

605

(2)

26.8 Diametrically Bimodal Distributions

607

(1)

26.9 Second-Order Analysis: The Mean of Mean Angles

608

(3)

26.10 Confidence Limits for the Second-Order Mean Angle

611

(3)

Exercises

614

(2)

27 CIRCULAR DISTRIBUTIONS: HYPOTHESIS TESTING

616

27.1 Testing Significance of the Mean Angle Unimodal Distributions

616

(5)

27.2 Testing Significance of the Median Angle: Omnibus Test

621

(3)

27.3 Testing Significance of the Median Angle: Binomial Test

624

(1)

27.4 Testing Symmetry around the Median Angle

624

(1)

27.5 Two-Sample and Multisample Testing of Mean Angles

625

(5)

27.6 Nonparametric Two-Sample and Multisample Testing of Angles

630

(5)

27.7 Two-Sample and Multisample Testing of Median Angles

635

(1)

27.8 Two-Sample and Multisample Testing of Angular Distances

635

(2)

27.9 Two-Sample and Multisample Testing of Angular Dispersion

637

(1)

27.10 Parametric One-Sample Second-Order Analysis of Angles

638

(1)

27.11 Nonparametric One-Sample Second-Order Analysis of Angles

639

(2)

27.12 Parametric Two-Sample Second-Order Analysis of Angles

641

(2)

27.13 Nonparametric Two-Sample Second-Order Analysis of Angles

643

(2)

27.14 Parametric Paired-Sample Testing with Angles

645

(2)

27.15 Nonparametric Paired-Sample Testing with Angles

647

(2)

27.16 Parametric Angular Correlation and Regression

649

(4)

27.17 Nonparametric Angular Correlation

653

(1)

27.18 Goodness of Fit Testing for Circular Distributions

654

(4)

27.19 Serial Randomness of Nominal-Scale Categories on a Circle

658

(2)

Exercises

660

APPENDIX A ANALYSIS OF VARIANCE HYPOTHESIS TESTING

App1

(10)

A.1 Determination of Appropriate F's and Degrees of Freedom

App1

(4)

A.2 Two-Factor Analysis of Variance

App5

(1)

A.3 Three-Factor Analysis of Variance

App6

(1)

A.4 Nested Analysis of Variance

App7

(1)

A.5 Split-Plot and Mixed Within-Subjects Analysis of Variance

App8

(3)

APPENDIX B STATISTICAL TABLES AND GRAPHS

App11

Table B.1 Critical Values of Chi-Square Distribution

App12

(5)

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

App17

(2)

Table B.3 Critical Values of the t Distribution

App19

(2)

Table B.4 Critical Values of the F Distribution

App21

(37)

Table B.5 Critical Values of the q Distribution

App58

(16)

Table B.6 Critical Values of q' for the One-Tailed Dunnett's Test

App74

(2)

Table B.7 Critical Values of q' for the Two-Tailed Dunnett's Test

App76

(1)

Table B.8 Critical Values of d(max) for the Kolmogorov-Smirnov Goodness of Fit Test for Discrete or Grouped Data

App77

(6)

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

App83

(4)

Table B.10 Critical Values of D(Delta) for the Delta-Corrected Kolmogorov-Smirnov Goodness of Fit Test for Continuous Distribution

App87

(2)

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

App89

(12)

Table B.12 Critical Values of the Wilcoxon T Distribution

App101

(3)

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

App104

(2)

Table B.14 Critical Values of the Friedman X(2)(r) Distribution

App106

(1)

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

App107

(1)

Table B.16 Critical Values of Q' for Nonparametric Multiple Comparison Testing with a Control

App108

(1)

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

App109

(2)

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

App111

(2)

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

App113

(3)

Table B.20 Critical Values of the Spearman Rank Correlation Coefficient, r(s)

App116

(2)

Table B.21 Critical Values of the Top-Down Correlation Coefficient, r(T)

App118

(1)

Table B.22 Critical Values of the Symmetry Measure, g(1)

App119

(2)

Table B.23 Critical Values of the Kurtosis Measure, g(2)

App121

(3)

Table B.24 The Arcsine Transformation, p'

App124

(3)

Table B.25 Proportions, p, Corresponding to Arcsine Transformations, p'

App127

(2)

Table B.26a Binomial Coefficients, (n)C(X)

App129

(3)

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

App132

(1)

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

App133

(10)

Table B.28 Critical Values for Fisher's Exact Test

App143

(28)

Table B.29 Critical Values for Runs Test

App171

(9)

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

App180

(2)

Table B.31 Critical Values for the Runs Up and Down Test

App182

(2)

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

App184

(2)

Table B.33 Circular Standard Deviation, s(0), As a Function of Vector Length, r

App186

(2)

Table B.34 Critical Values of Rayleigh's z

App188

(2)

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

App190

(1)

Table B.36 Critical Values of m for the Hodges-Ajne Test

App191

(2)

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

App193

(2)

Table B.38 Critical Values of Watson's U(2)

App195

(3)

Table B.39 Critical Values of R' for the Moore Test of Circular Uniformity

App198

(1)

Table B.40 Common Logarithms of Factorials

App199

(2)

Table B.41 Ten Thousand Random Digits

App201

(4)

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

App205

ANSWERS TO EXERCISES

Ans1

LITERATURE CITED

INDEX

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Biostatistical Analysis

Biostatistical Analysis

9780130815422

013081542X

Summary

Table of Contents

Supplemental Materials

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Amazon no longer offers textbook rentals. We do!

Biostatistical Analysis

Biostatistical Analysis

9780130815422

013081542X

Summary

Table of Contents

Supplemental Materials

Write a Review

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