Table Of Contents:
Preface v
1. Basic Definitions and Concepts 1(30)

1.1 Variables and Variation 1(3)

1.2 Frequency Distributions and Cumulative Frequency Distributions 4(5)

1.3 Sample and Population 9(3)

1.4 Measures Describing the Center of Data Distributions 12(4)

1.5 Measurement of the Spread of Data 16(6)

1.6 Coding 22(2)

1.7 Precision, Accuracy, and Bias 24(3)

1.8 The Question of Significant Figures 27(1)

Key Terms 28(1)

Exercises 28(2)

References 30(1)
2. Data Graphics 31(18)

2.1 Introduction 31(1)

2.2 The Histogram 32(1)

2.3 Construction and Labeling of Graphs 33(7)

2.4 Scatter Plots (Correlation Diagrams) 40(2)

2.5 Semilogarithmic Plots 42(1)

2.6 Other Descriptive Figures 43(3)

Key Terms 46(1)

Exercises 46(2)

References 48(1)
3. Introduction to Probability: The Binomial and Normal Probability Distributions 49(33)

3.1 Introduction 49(1)

3.2 Some Basic Probability 50(4)

3.3 Probability Distributions-The Binomial Distribution 54(9)

3.4 Continuous Data Distributions 63(13)

3.5 Other Common Probability Distributions 76(3)

Key Terms 79(1)

Exercises 80(1)

References 81(1)
4. Choosing Samples 82(14)

4.1 Introduction 82(1)

4.2 Random Sampling 83(5)

4.3 Other Sampling Procedures: Stratified, Systematic, and Cluster Sampling 88(2)

4.4 Sampling in Quality Control 90(2)

Key Terms 92(1)

Exercises 92(3)

References 95(1)
5. Statistical Inference: Estimation and Hypothesis Testing 96(55)

5.1 Statistical Estimation (Confidence Intervals) 96(8)

5.2 Statistical Hypothesis Testing 104(35)

5.3 Comparison of Variances in Independent Samples 139(2)

5.4 Test of Equality of More than Two Variances 141(1)

5.5 Confidence Limits for a Variance 142(2)

5.6 Tolerance Intervals 144(2)

Key Terms 146(1)

Exercises 146(3)

References 149(2)
6. Sample Size and Power 151(22)

6.1 Introduction 151(2)

6.2 Determination of Sample Size for Simple Comparative Experiments for Normally Distributed Variables 153(6)

6.3 Determination of Sample Size for Binomial Tests 159(2)

6.4 Determination of Sample Size to Obtain a Confidence Interval of Specified Width 161(1)

6.5 Power 162(4)

6.6 Sample Size and Power for More than Two Treatments 166(2)

6.7 Sample Size for Bioequivalence Studies 168(2)

Key Terms 170(1)

Exercises 170(2)

References 172(1)
7. Linear Regression and Correlation 173(42)

7.1 Introduction 174(4)

7.2 Analysis of Standard Curves in Drug Analysis: Application of Linear Regression 178(1)

7.3 Assumptions in Tests of Hypotheses in Linear Regression 179(2)

7.4 Estimate of the Variance: Variance of Sample Estimates of the Parameters 181(2)

7.5 A Drug Stability Study: A Second Example of the Application of Linear Regression 183(6)

7.6 Confidence Intervals in Regression Analysis 189(4)

7.7 Weighted Regression 193(2)

7.8 Analysis of Residuals 195(2)

7.9 Nonlinear Regression 197(3)

7.10 Correlation 200(8)

7.11 Comparison of Variances in Related Samples 208(2)

Key Terms 210(1)

Exercises 210(4)

References 214(1)
8. Analysis of Variance 215(50)

8.1 One-Way Analysis of Variance 215(7)

8.2 Planned Versus a Posteriori (Unplanned) Comparisons in ANOVA 222(10)

8.3 Another Example of One-Way Analysis of Variance: Unequal Sample Sizes and the Fixed and Random Models 232(2)

8.4 Two-Way Analysis of Variance (Randomized Blocks) 234(15)

8.5 Statistical Models 249(1)

8.6 Analysis of Covariance 250(6)

8.7 ANOVA for Pooling Regression Lines as Related to Stability Data 256(4)

Key Terms 260(1)

Exercises 261(3)

References 264(1)
9. Factorial Designs 265(24)

9.1 Definitions (Vocabulary) 265(5)

9.2 Two Simple Hypothetical Experiments to Illustrate the Advantages of Factorial Designs 270(3)

9.3 Performing Factorial Experiments: Recommendations and Notation 273(2)

9.4 A Worked Example of a Factorial Experiment 275(6)

9.5 Fractional Factorial Designs 281(4)

9.6 Some General Comments 285(1)

Key Terms 285(1)

Exercises 285(3)

References 288(1)
10. Transformations and Outliers 289(22)

10.1 Transformations 290(10)

10.2 Outliers 300(9)

Key Terms 309(1)

Exercises 309(1)

References 310(1)
11. Experimental Design in Clinical Trials 311(62)

11.1 Introduction 311(1)

11.2 Some Principles of Experimental Design and Analysis 312(5)

11.3 Parallel Design 317(4)

11.4 Crossover Designs and Bioavailability/Bioequivalence Studies 321(39)

11.5 Repeated Measures (Split-Plot) Designs 360(5)

11.6 Multiclinic Studies 365(2)

11.7 Interim Analyses 367(2)

Key Terms 369(1)

Exercises 369(2)

References 371(2)
12. Quality Control 373(43)

12.1 Introduction 373(1)

12.2 Control Charts 374(14)

12.3 Acceptance Sampling and Operating Characteristic Curves 388(3)

12.4 Statistical Procedures in Assay Development 391(10)

12.5 Establishing In-House Limits 401(3)

12.6 Some Statistical Aspects of Quality and the "Barr Decision" 404(4)

12.7 Important QC Tests for Finished Solid Dosage Forms (Tablets and Capsules) 408(4)

12.8 Out of Specification (005) Results

Key Terms 412(1)

Exercises 413(2)

References 415(1)
13. Validation 416(21)

13.1 Process Validation 416(12)

13.2 Assay Validation 428(7)

13.3 Concluding Remarks 435(1)

Key Terms 435(1)

Exercises 435(1)

References 436(1)
14. Computer Intensive Methods 437(27)

14.1 Monte Carlo Simulation 438(20)

14.2 Bootstrapping 458(5)

References 463(1)
15. Nonparametric Methods 464(42)

15.1 Data Characteristics and an Introduction to Nonparametric Procedures 464(3)

15.2 Sign Test 467(2)

15.3 Wilcoxon Signed Rank Test 469(4)

15.4 Wilcoxon Rank Sum Test (Test for Differences Between Two Independent Groups) 473(6)

15.5 Kroskal-Wallis Test (One-Way ANOVA) 479(2)

15.6 Friedman Test (Two-Way Analysis of Variance) 481(4)

15.7 Nonparametric Analysis of Covariance 485(1)

15.8 Runs Test for Randomness 486(3)

15.9 Contingency Tables 489(11)

15.10 Non Parametric Tolerance Interval 500(1)

Key Terms 501(1)

Exercises 501(4)

References 505(1)
16. Optimization Techniques and Screening Designs 506(34)

16.1 Introduction 506(2)

16.2 Optimization Using Factorial Designs 508(10)

16.3 Composite Designs to Estimate Curvature 518(5)

16.4 The Simplex Lattice 523(8)

16.5 Sequential Optimization 531(6)

Key Terms 537(1)

Exercises 537(1)

References 538(2)
Glossary 540(2)
Appendix I: Some Properties of the Variance 542(3)

I.1 Pooling Variances 542(1)

I.2 Components of Variance 543(1)

I.3 Variance of Linear Combinations of Independent Variables 543(1)

Reference 544(1)
Appendix II: Comparison of Slopes and Testing of Linearity: Determination of Relative Potency 545(6)

Reference 550(1)
Appendix III: Multiple Regression 551(6)

References 556(1)
Appendix IV: Tables 557(21)

IV. 1 Random Numbers 557(1)

IV.2 Cumulative Normal Distribution Cumulative Area Under the Normal Distribution (Less Than or Equal to Z) 558(1)

IV.3 Individual Terms of the Binomial Distribution for N = 2 to 10 and P = 0.2, 0.5, and 0.7 559(2)

IV.4 t Distributions 561(1)

IV.5 Short Table of Chi-Square Distributions 561(1)

IV.6A Upper 5% Values of the F Distribution 562(1)

IV.6B Short Table of Upper 1 % Values of the F Distribution 563(1)

IV.7A Upper 5% Points in the Studentized Range 564(1)

IV.7B Values of t' for Dunnett' s Comparison of Several Treatments and a Control (α = 0.05) 564(1)

IV.8 Dixon's Criteria for Rejecting Outliers 565(1)

IV.9 Critical Values of T for a Two-Sided Test at the 5% Level of Significance (Test for Outliers) 566(1)

IV.10 Factors for Determining Upper and Lower 3σ Limits for Mean (X) and Range (R) Charts, and for Estimating σ from R 567(1)

IV.11 Number of Correct Guesses Needed for Significance in the Triangle Test 568(1)

IV.12 Number of Positive or Negative Signs Needed for Significance for the Sign Test 568(1)

IV.13 Values Leading to Significance for the Wilcoxon Signed Rank Test (Two-Sided Test) 569(1)

IV.14 Critical Values for Number of Runs at the 5% Level of Significance 569(1)

IV.15 Probability of Getting at Least One Run of Given Size for N Samples 570(1)

IV.16 Critical Values for Wilcoxon Rank Sum Test (α = 0.05) 570(1)

IV.17 Critical Differences for Significance (α = 0.05) Comparing All Possible Pairs of Treatments for Nonparametric One-Way ANOVA 571(1)

IV.18 Critical Differences for Significance (α = 0.05) Comparing All Possible Pairs of Treatments for Nonparametric Two-Way ANOVA 572(1)

IV. 19 Factors for Two-Sided Tolerance Limits for Normal Distributions 573(3)

IV.20 Test for Outliers 576(2)
Appendix V: Outlier Tests and Chemical Assays 518.

V.1 Introduction 578(1)

V.2 Can Outlier Tests Be Justified? 579(1)

V.3 Why Is There Not a USP Test for Outliers for Chemical Assays? 580(1)

V.4 Some Comments on the Nature of Outliers and Outlier Tests, and Other Inconsistencies in the Decision That Outlier Tests Be Used for Biological Assays but Not for Chemical Assays 581(1)

V.5 What Is the Purpose of Performing Replicate Assays and When is Averaging Appropriate? 582(1)

V.6 In What Situations Might Outlier Tests Be Applicable? 582(2)

References 584(1)
Appendix VI: Should a Single Unexplained Failing Assay Be Reason to Reject a Batch? 585(9)

References 593(1)
Appendix VII: When it is Appropriate to Average and its Relationship to the Barr Decision 594(5)
Appendix VIII: Excel Workbooks and SAS Programs 599(112)

Excel Workbooks 599(54)

SAS Programs 653(58)
Appendix IX: An Alternative Solution to the Distribution of the Individual Bioequivalence Metric 711(11)
Answers to Exercises 722(21)
Index 743