Sections :
- Cover formula 1, 2 p. 1
- authors p. 5
- contents p. 7
- preface p. 15
- note to the student p. 23
- 1 What Is Statistics? 1.1 Introduction p. 25 (p. 1)
- 1.2 Characterizing a Set of Measurements: Graphical Methods p. 27 (p. 3)
- 1.3 Characterizing a Set of Measurements: Numerical Methods p. 32 (p. 8)
- 1.4 How Inferences Are Made p. 37 (p. 13)
- 1.5 Theory and Reality p. 38 (p. 14)
- 1.6 Summary p. 39 (p. 15)
- 2 Probability 2.1 Introduction p. 44 (p. 20)
- 2.2 Probability and Inference p. 45 (p. 21)
- 2.3 A Review of Set Notation p. 47 (p. 23)
- 2.4 A Probabilistic Model for an Experiment: The Discrete Case p. 50 (p. 26)
- 2.5 Calculating the Probability of an Event: The Sample-Point Method p. 59 (p. 35)
- 2.6 Tools for Counting Sample Points p. 64 (p. 40)
- 2.7 Conditional Probability and the Independence of Events p. 75 (p. 51)
- 2.8 Two Laws of Probability p. 81 (p. 57)
- 2.9 Calculating the Probability of an Event: The Event-Composition Method p. 86 (p. 62)
- 2.10 The Law of Total Probability and Bayes’ Rule p. 94 (p. 70)
- 2.11 Numerical Events and Random Variables p. 99 (p. 75)
- 2.12 Random Sampling p. 101 (p. 77)
- 2.13 Summary p. 103 (p. 79)
- 3 Discrete Random Variables and Their Probability Distributions 3.1 Basic Definition p. 110 (p. 86)
- 3.2 The Probability Distribution for a Discrete Random Variable p. 111 (p. 87)
- 3.3 The Expected Value of a Random Variable or a Function of a Random Variable p. 115 (p. 91)
- 3.4 The Binomial Probability Distribution p. 131 (p. 107)
- 3.5 The Geometric Probability Distribution p. 138 (p. 114)
- 3.6 The Negative Binomial Probability Distribution (Optional) p. 145 (p. 121)
- 3.7 The Hypergeometric Probability Distribution p. 149 (p. 125)
- 3.8 The Poisson Probability Distribution p. 155 (p. 131)
- 3.9 Moments and Moment-Generating Functions p. 162 (p. 138)
- 3.10 Probability-Generating Functions (Optional) p. 167 (p. 143)
- 3.11 Tchebysheff’s Theorem p. 170 (p. 146)
- 3.12 Summary p. 173 (p. 149)
- 4 Continuous Variables and Their Probability Distributions 4.1 Introduction p. 181 (p. 157)
- 4.2 The Probability Distribution for a Continuous Random Variable p. 182 (p. 158)
- 4.3 Expected Values for Continuous Random Variables p. 194 (p. 170)
- 4.4 The Uniform Probability Distribution p. 198 (p. 174)
- 4.5 The Normal Probability Distribution p. 202 (p. 178)
- 4.6 The Gamma Probability Distribution p. 209 (p. 185)
- 4.7 The Beta Probability Distribution p. 218 (p. 194)
- 4.9 Other Expected Values p. 226 (p. 202)
- 4.10 Tchebysheff’s Theorem p. 231 (p. 207)
- 4.11 Expectations of Discontinuous Functions and Mixed Probability Distributions (Optional) p. 234 (p. 210)
- 4.12 Summary p. 238 (p. 214)
- 5 Multivariate Probability Distributions 5.1 Introduction p. 247 (p. 223)
- 5.2 Bivariate and Multivariate Probability Distributions p. 248 (p. 224)
- 5.3 Marginal and Conditional Probability Distributions p. 259 (p. 235)
- 5.4 Independent Random Variables p. 271 (p. 247)
- 5.5 The Expected Value of a Function of Random Variables p. 279 (p. 255)
- 5.6 Special Theorems p. 282 (p. 258)
- 5.7 The Covariance of Two Random Variables p. 288 (p. 264)
- 5.8 The Expected Value and Variance of Linear Functions of Random Variables p. 294 (p. 270)
- 5.9 The Multinomial Probability Distribution p. 303 (p. 279)
- 5.10 The Bivariate Normal Distribution (Optional) p. 307 (p. 283)
- 5.11 Conditional Expectations p. 309 (p. 285)
- 5.12 Summary p. 314 (p. 290)
- 6 Functions of Random Variables 6.1 Introduction p. 320 (p. 296)
- 6.2 Finding the Probability Distribution of a Function of Random Variables p. 321 (p. 297)
- 6.3 The Method of Distribution Functions p. 322 (p. 298)
- 6.4 The Method of Transformations p. 334 (p. 310)
- 6.5 The Method of Moment-Generating Functions p. 342 (p. 318)
- 6.6 Multivariable Transformations Using Jacobians (Optional) p. 349 (p. 325)
- 6.7 Order Statistics p. 357 (p. 333)
- 6.8 Summary p. 365 (p. 341)
- 7 Sampling Distributions and the Central Limit Theorem 7.1 Introduction p. 370 (p. 346)
- 7.2 Sampling Distributions Related to the Normal Distribution p. 377 (p. 353)
- 7.3 The Central Limit Theorem p. 394 (p. 370)
- 7.4 A Proof of the Central Limit Theorem (Optional) p. 401 (p. 377)
- 7.5 The Normal Approximation to the Binomial Distribution p. 402 (p. 378)
- 7.6 Summary p. 409 (p. 385)
- 8 Estimation 8.1 Introduction p. 414 (p. 390)
- 8.2 The Bias and Mean Square Error of Point Estimators p. 416 (p. 392)
- 8.3 Some Common Unbiased Point Estimators p. 420 (p. 396)
- 8.4 Evaluating the Goodness of a Point Estimator p. 423 (p. 399)
- 8.5 Confidence Intervals p. 430 (p. 406)
- 8.6 Large-Sample Confidence Intervals p. 435 (p. 411)
- 8.7 Selecting the Sample Size p. 445 (p. 421)
- 8.8 Small-Sample Confidence Intervals for μ and μ1 − μ2 p. 449 (p. 425)
- 8.9 Confidence Intervals for σ2 p. 458 (p. 434)
- 8.10 Summary p. 461 (p. 437)
- 9 Properties of Point Estimators and Methods of Estimation 9.1 Introduction p. 468 (p. 444)
- 9.2 Relative Efficiency p. 469 (p. 445)
- 9.3 Consistency p. 472 (p. 448)
- 9.4 Sufficiency p. 483 (p. 459)
- 9.5 The Rao–Blackwell Theorem and Minimum-Variance Unbiased Estimation p. 488 (p. 464)
- 9.6 The Method of Moments p. 496 (p. 472)
- 9.7 The Method of Maximum Likelihood p. 500 (p. 476)
- 9.8 Some Large-Sample Properties of Maximum-Likelihood Estimators (Optional) p. 507 (p. 483)
- 9.9 Summary p. 509 (p. 485)
- 10.1 Introduction p. 512 (p. 488)
- 10.2 Elements of a Statistical Test p. 513 (p. 489)
- 10.3 Common Large-Sample Tests p. 520 (p. 496)
- 10.4 Calculating Type II Error Probabilities and Finding the Sample Size for Z Tests p. 531 (p. 507)
- 10.5 Relationships Between Hypothesis-Testing Procedures and Confidence Intervals p. 535 (p. 511)
- 10.6 Another Way to Report the Results of a Statistical Test: Attained Significance Levels, or p-Values p. 537 (p. 513)
- 10.7 Some Comments on the Theory of Hypothesis Testing p. 542 (p. 518)
- 10.8 Small-Sample Hypothesis Testing for μ and μ1 − μ2 p. 544 (p. 520)
- 10.9 Testing Hypotheses Concerning Variances p. 554 (p. 530)
- 10.10 Power of Tests and the Neyman–Pearson Lemma p. 564 (p. 540)
- 10.11 Likelihood Ratio Tests p. 573 (p. 549)
- 10.12 Summary p. 580 (p. 556)
- 11 Linear Models and Estimation by Least Squares p. 587 (p. 563)
- 11.1 Introduction p. 588 (p. 564)
- 11.2 Linear Statistical Models p. 590 (p. 566)
- 11.3 The Method of Least Squares p. 593 (p. 569)
- 11.4 Properties of the Least-Squares Estimators: Simple Linear Regression p. 601 (p. 577)
- 11.5 Inferences Concerning the Parameters βi p. 608 (p. 584)
- 11.6 Inferences Concerning Linear Functions of the Model Parameters: Simple Linear Regression p. 613 (p. 589)
- 11.7 Predicting a Particular Value of Y by Using Simple Linear Regression p. 617 (p. 593)
- 11.8 Correlation p. 622 (p. 598)
- 11.9 Some Practical Examples p. 628 (p. 604)
- 11.10 Fitting the Linear Model by Using Matrices p. 633 (p. 609)
- 11.11 Linear Functions of the Model Parameters: Multiple Linear Regression p. 639 (p. 615)
- 11.12 Inferences Concerning Linear Functions of the Model Parameters: Multiple Linear Regression p. 640 (p. 616)
- 11.14 A Test for H0 : βg+1 = βg+2 = · · · = βk = 0 p. 648 (p. 624)
- 11.15 Summary and Concluding Remarks p. 657 (p. 633)
- 12 Considerations in Designing Experiments 12.1 The Elements Affecting the Information in a Sample p. 664 (p. 640)
- 12.2 Designing Experiments to Increase Accuracy p. 665 (p. 641)
- 12.3 The Matched-Pairs Experiment p. 668 (p. 644)
- 12.4 Some Elementary Experimental Designs p. 675 (p. 651)
- 12.5 Summary p. 681 (p. 657)
- 13 The Analysis of Variance 13.1 Introduction p. 685 (p. 661)
- 13.2 The Analysis of Variance Procedure p. 686 (p. 662)
- 13.3 Comparison of More Than Two Means: Analysis of Variance for a One-Way Layout p. 691 (p. 667)
- 13.4 An Analysis of Variance Table for a One-Way Layout p. 695 (p. 671)
- 13.5 A Statistical Model for the One-Way Layout p. 701 (p. 677)
- 13.6 Proof of Additivity of the Sums of Squares and E(MST) for a One-Way Layout (Optional) p. 703 (p. 679)
- 13.7 Estimation in the One-Way Layout p. 705 (p. 681)
- 13.8 A Statistical Model for the Randomized Block Design p. 710 (p. 686)
- 13.9 The Analysis of Variance for a Randomized Block Design p. 712 (p. 688)
- 13.10 Estimation in the Randomized Block Design p. 719 (p. 695)
- 13.11 Selecting the Sample Size p. 720 (p. 696)
- 13.12 Simultaneous Confidence Intervals for More Than One Parameter p. 722 (p. 698)
- 13.13 Analysis of Variance Using Linear Models p. 725 (p. 701)
- 13.14 Summary p. 729 (p. 705)
- 14 Analysis of Categorical Data 14.1 A Description of the Experiment p. 737 (p. 713)
- 14.2 The Chi-Square Test p. 738 (p. 714)
- 14.3 A Test of a Hypothesis Concerning Specified Cell Probabilities: A Goodness-of-Fit Test p. 740 (p. 716)
- 14.5 r × c Tables with Fixed Row or Column Totals p. 753 (p. 729)
- 14.6 Other Applications p. 758 (p. 734)
- 14.7 Summary and Concluding Remarks p. 760 (p. 736)
- 15 Nonparametric Statistics 15.1 Introduction p. 765 (p. 741)
- 15.2 A General Two-Sample Shift Model p. 766 (p. 742)
- 15.3 The Sign Test for a Matched-Pairs Experiment p. 768 (p. 744)
- 15.4 The Wilcoxon Signed-Rank Test for a Matched-Pairs Experiment p. 774 (p. 750)
- 15.5 Using Ranks for Comparing Two Population Distributions: Independent Random Samples p. 779 (p. 755)
- 15.6 The Mann–Whitney U Test: Independent Random Samples p. 782 (p. 758)
- 15.7 The Kruskal–Wallis Test for the One-Way Layout p. 789 (p. 765)
- 15.8 The Friedman Test for Randomized Block Designs p. 795 (p. 771)
- 15.9 The Runs Test: A Test for Randomness p. 801 (p. 777)
- 15.10 Rank Correlation Coefficient p. 807 (p. 783)
- 15.11 Some General Comments on Nonparametric Statistical Tests p. 813 (p. 789)
- 16 Introduction to Bayesian Methods for Inference 16.1 Introduction p. 820 (p. 796)
- 16.2 Bayesian Priors, Posteriors, and Estimators p. 821 (p. 797)
- 16.3 Bayesian Credible Intervals p. 832 (p. 808)
- 16.4 Bayesian Tests of Hypotheses p. 837 (p. 813)
- 16.5 Summary and Additional Comments p. 840 (p. 816)
- Appendix 1 Matrices and Other Useful Mathematical Results A1.1 Matrices and Matrix Algebra p. 845 (p. 821)
- A1.2 Addition of Matrices p. 846 (p. 822)
- A1.3 Multiplication of a Matrix by a Real Number A1.4 Matrix Multiplication p. 847 (p. 823)
- A1.5 Identity Elements p. 849 (p. 825)
- A1.6 The Inverse of a Matrix p. 851 (p. 827)
- A1.7 The Transpose of a Matrix A1.8 A Matrix Expression for a System of Simultaneous Linear Equations p. 852 (p. 828)
- A1.9 Inverting a Matrix p. 854 (p. 830)
- A1.10 Solving a System of Simultaneous Linear Equations p. 858 (p. 834)
- A1.11 Other Useful Mathematical Results p. 859 (p. 835)
- Appendix 2 Common Probability Distributions, Means,Variances, and Moment-Generating Functions Table 1 Discrete Distributions p. 861 (p. 837)
- Table 2 Continuous Distributions p. 862 (p. 838)
- Table 1 Binomial Probabilities p. 863 (p. 839)
- Table 2 Table of e−x p. 866 (p. 842)
- Table 3 Poisson Probabilities p. 867 (p. 843)
- Table 4 Normal Curve Areas p. 872 (p. 848)
- Table 5 Percentage Points of the t Distributions p. 873 (p. 849)
- Table 6 Percentage Points of the χ2 Distributions p. 874 (p. 850)
- Table 7 Percentage Points of the F Distributions p. 876 (p. 852)
- Table 8 Distribution Function of U p. 886 (p. 862)
- Table 9 Critical Values of T in the Wilcoxon Matched-Pairs, Signed-Ranks Test; n = 5(1)50 p. 892 (p. 868)
- Table 10 Distribution of the Total Number of Runs R in Samples of Size(n1, n2); P(R ≤ a) p. 893 (p. 869)
- Table 11 Critical Values of Spearman’s Rank Correlation Coefficient p. 896 (p. 872)
- Table 12 Random Numbers p. 897 (p. 873)
- Answers to Exercises p. 901 (p. 877)
- Index p. 920 (p. 896)
Mathematical Statistics (W,M,S 2008)