STATISTICS FOR THE LIFE SCIENCES

Fourth Edition

MYRA L. SAMUELS

Purdue University

JEFFREY A. WITMER

Oberlin College

ANDREW A. SCHAFFNER

California Polytechnic State University,San Luis Obispo

PEARSON-----Boston Columbus Indianapolis New York San Francisco Upper Saddle River

Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montreal Toronto

Delhi Mexico City Sao Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo

CONTENTS

Preface vii

1 INTRODUCTION

1.1 Statistics and the Life Sciences

1.2 Types of Evidence 7

1.3 Random Sampling 15

2 DESCRIPTION OF SAMPLES AND POPULATIONS 26

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

Introduction 26

Frequency Distributions 28

Descriptive Statistics: Measures.of Center 40p ' . !,-:,..::: .. ." .

Boxplots 45 ., : " .. "

Relationships between Variables 52

Measures of Dispersion 59

Effect of Transformation of Variables (Optional) 68

Statistical Inference 73

Perspective 79

3 PROBABILITY AND THE BINOMIAL DISTRIBUTION 84

3.1 Probability and the Life Sciences 84

3.2 Introduction to Probability 84

3.3 Probability Rules (Optional) 94

3,4 Density Curves 99

3.5 Random Variables 102

3.6 The Binomial Distribution 107

3.7 Fitting a Binomial Distribution to Data (Optional) 116

4 THE NORMAL DISTRIBUTION 121

4.1 Introduction 121

4.2 The Normal Curves 123

4.3 Areas Under a Normal Curve 125

4.4 Assessing Normality 132

4.5 Perspective 142

iii

iv Contents

5 SAMPLING DISTRIBUTIONS 145

5.1 Basic Ideas 145

5.2 The Sample Mean 149

5.3 Illustration of the Central Limit Theorem (Optional) 159

5.4 The Normal Approximation to the Binomial Distribution(Optional) 162

5.5 Perspective 167

6 CONFIDENCE INTERVALS 170

6.1 Statistical Estimation 170

6.2 Standard Error of the Mean 171

6.3 Confidence Interval for J.1 177

6.4 Planninga Study to Estimate J.1 187

6.5 Conditions for Val idity of Estimation Methods 190

6.6 ComparingTwo Means 199

6.7 Confidence Interval for (ILL - IL2) 206

6.8 Perspective and Summary 212

7 COMPARISON OF Two INDEPENDENT SAMPLES 218

7.1 Hypothesis Testing: The Randomization Test 218

7.2 Hypothesis Testing: The t Test 223

7.3 Further Discussion of the t Test 234

7.4 Association and Causation 242

7.5 One-Tailed t Tests 250

7.6 More on Interpretation of Statistical Sign ificance 260

7.7 Planningfor Adequate Power (Optional) 267

7.8 Student's t: Conditions and Summary 273

7.9 More on Principles of Testing Hypotheses 277

7.10 The Wilcoxon-Mann-Whitney Test 282

7.1 1 Perspective 291

8 COMPARISON OF PAIRED SAMPLES 299

8.1 Introduction 299

8.2 The Paired-Sample t Test and Confidence Interval 300

8.3 The Paired Design 310

Contents v

8.4 The Sign Test 315

8.5 The Wilcoxon Signed-Rank Test 321

8.6 Perspective 326

9 CATEGORICAL DATA: ONE-SAMPLE DISTRIBUTIONS 336

9.1 Dichotomous Observations 336

9.2 Confidence Interval for a Population Proportion 341

9.3 Other Confidence levels (Optional) 347

9.4 Inference for Proportions: The Chi-Square Goodness-of-Fit Test 348

9.5 Perspective and Summary 359

10 CATEGORICAL DATA: RELATIONSHIPS 363

10.1 Introduction 363

10.2 The Chi-Square Test for the 2 X 2 Contingency Table 365

10.3 Independence and Association in the 2 X 2 ContingencyTable 373

10.4 Fisher's ExactTest (Optional) 381

10.5 The r X k Contingency Table 385

10.6 Applicability of Methods 391

10.7 Confidence Interval for Difference between Probabilities 395

10.8 Paired Data and 2 X 2 Tables (Optional) 398

10.9 Relative Risk and the Odds Ratio (Optional) 401

10.10 Summary of Chi-Square Test 409

11 COMPARING THE MEANS OF MANY INDEPENDENTSAMPLES 414

I 1.1 Introduction 414

11.2 The Basic One-Way Analysis of Variance 418

11.3 The Analysis of Variance Model 427

11.4 The Global FTest 429

11.5 Applicability of Methods 433

11.6 One-Way Randomized Blocks Design 437

11.7 Two-Way ANOVA 449

11.8 linear Combinations of Means (Optional) 456

11.9 Multiple Comparisons (Optional) 464

I 1.10 Perspective 475

vi Contents

12 LINEAR REGRESSION AND CORRELATION 480

12.1 Introduction 480

12.2 The Correlation Coefficient 482

12.3 The Fitted Regression Line 492

12.4 Parametric Interpretation of Regression: The Linear Model 505

12.5 Statistical Inference Concerning {31 511

12.6 Guidelines for Interpreting Regression and Correlation 516

12.7 Precision in Prediction (Optional) 527

12.8 Perspective 531

12.9 Summary of Formulas 542

13 A SUMMARY OF INFERENCE METHODS 550

13.1 Introduction 550

13.2 Data Analysis Examples 552

Appendices 566

Chapter Notes 583

Statistical Tables 610

Answers to Selected Exercises 639

Index 647

Index of Examples 655