To Teachers: About This Book p. ix
To Students: What Is Statistics? p. xxi
About the Authors p. xxv
Data p. 1
Looking at Data--Distributions p. 3
Introduction p. 4
Variables p. 4
Displaying Distributions with Graphs p. 5
Graphs for categorical variables p. 6
Measuring the speed of light p. 7
Measurement p. 8
Variation p. 9
Stemplots p. 10
Examining distributions p. 12
Histograms p. 14
Dealing with outliers p. 17
Time plots p. 18
Beyond the basics: Decomposing time series p. 20
Summary p. 21
Section 1.1 Exercises p. 22
Describing Distributions with Numbers p. 38
Measuring center: the mean p. 39
Measuring center: the median p. 40
Mean versus median p. 41
Measuring spread: the quartiles p. 42
The five-number summary and boxplots p. 43
The 1.5 X IQR criterion for suspected outliers p. 46
Measuring spread: the standard deviation p. 48
Properties of the standard deviation p. 50
Choosing measures of center and spread p. 50
Changing the unit of measurement p. 51
Summary p. 54
Section 1.2 Exercises p. 55
The Normal Distributions p. 63
Density curves p. 64
Measuring center and spread for density curves p. 67
Normal distributions p. 68
The 68-95-99.7 rule p. 70
Standardizing observations p. 71
The standard normal distribution p. 73
Normal distribution calculations p. 74
Normal quantile plots p. 78
Beyond the basics: Density estimation p. 82
Summary p. 83
Section 1.3 Exercises p. 84
Chapter 1 Exercises p. 93
Looking at Data--Relationships p. 103
Introduction p. 104
Examining relationships p. 104
Scatterplots p. 106
Interpreting scatterplots p. 107
Adding categorical variables to scatterplots p. 108
More examples of scatterplots p. 109
Beyond the basics: Scatterplot smoothers p. 112
Categorical explanatory variables p. 113
Summary p. 115
Section 2.1 Exercises p. 116
Correlation p. 126
The correlation r p. 127
Properties of correlation p. 128
Summary p. 130
Section 2.2 Exercises p. 131
Least-Squares Regression p. 135
Fitting a line to data p. 136
Prediction p. 138
Least-squares regression p. 139
Interpreting the regression line p. 141
Correlation and regression p. 143
Understanding r[superscript 2] p. 146
Summary p. 147
Section 2.3 Exercises p. 147
Cautions about Regression and Correlation p. 154
Residuals p. 154
Lurking variables p. 158
Outliers and influential observations p. 160
Beware the lurking variable p. 164
Beware correlations based on averaged data p. 165
The restricted-range problem p. 166
Beyond the basics: Data mining p. 167
Summary p. 168
Section 2.4 Exercises p. 168
The Question of Causation p. 179
Explaining association: causation p. 180
Explaining association: common response p. 181
Explaining association: confounding p. 181
Establishing causation p. 182
Summary p. 184
Section 2.5 Exercises p. 185
Transforming Relationships p. 187
First steps in transforming p. 189
The ladder of power transformations p. 191
Exponential growth p. 195
The logarithm transformation p. 197
Prediction in the exponential growth model p. 200
Power law models p. 201
Prediction in power law models p. 202
Summary p. 203
Section 2.6 Exercises p. 203
Chapter 2 Exercises p. 211
Producing Data p. 221
Introduction p. 222
First Steps p. 222
Where to find data: the library and the Internet p. 223
Sampling p. 225
Experiments p. 225
Summary p. 226
Section 3.1 Exercises p. 227
Design of Experiments p. 229
Comparative experiments p. 230
Randomization p. 232
Randomized comparative experiments p. 233
How to randomize p. 235
Cautions about experimentation p. 237
Matched pairs designs p. 238
Block designs p. 239
Summary p. 240
Section 3.2 Exercises p. 241
Sampling Design p. 248
Simple random samples p. 249
Stratified samples p. 250
Multistage samples p. 251
Cautions about sample surveys p. 252
Summary p. 254
Section 3.3 Exercises p. 255
Toward Statistical Inference p. 260
Sampling variability p. 261
Sampling distributions p. 262
Bias and variability p. 265
Sampling from large populations p. 267
Why randomize? p. 267
Beyond the basics: Capture-recapture sampling p. 268
Summary p. 269
Section 3.4 Exercises p. 269
Chapter 3 Exercises p. 274
Probability and Inference p. 279
Probability--The Study of Randomness p. 281
Introduction p. 282
Randomness p. 282
The language of probability p. 283
Thinking about randomness p. 284
The uses of probability p. 284
Summary p. 285
Section 4.1 Exercises p. 285
Probability Models p. 287
Sample spaces p. 288
Intuitive probability p. 289
Probability rules p. 290
Assigning probabilities: finite number of outcomes p. 292
Assigning probabilities: equally likely outcomes p. 293
Independence and the multiplication rule p. 294
Applying the probability rules p. 296
Summary p. 298
Section 4.2 Exercises p. 298
Random Variables p. 305
Discrete random variables p. 305
Continuous random variables p. 309
Normal distributions as probability distributions p. 312
Summary p. 313
Section 4.3 Exercises p. 314
Means and Variances of Random Variables p. 318
The mean of a random variable p. 318
Statistical estimation and the law of large numbers p. 321
Thinking about the law of large numbers p. 323
Beyond the basics: More laws of large numbers p. 325
Rules for means p. 326
The variance of a random variable p. 328
Rules for variances p. 329
Summary p. 332
Section 4.4 Exercises p. 333
General Probability Rules p. 340
General addition rules p. 340
Conditional probability p. 343
General multiplication rules p. 347
Tree diagrams p. 348
Bayes's rule p. 349
Independence again p. 350
Decision analysis p. 350
Summary p. 352
Section 4.5 Exercises p. 353
Chapter 4 Exercises p. 359
Sampling Distributions p. 365
Introduction p. 366
Sampling Distributions for Counts and Proportions p. 367
The binomial distributions for sample counts p. 367
Binomial distributions in statistical sampling p. 369
Finding binomial probabilities: tables p. 370
Binomial mean and standard deviation p. 371
Sample proportions p. 373
Normal approximation for counts and proportions p. 375
The continuity correction p. 379
Binomial formulas p. 380
Summary p. 382
Section 5.1 Exercises p. 383
The Sampling Distribution of a Sample Mean p. 391
The mean and standard deviation of x p. 393
The sampling distribution of x p. 395
The central limit theorem p. 397
Beyond the basics: Weibull distributions p. 400
Summary p. 402
Section 5.2 Exercises p. 402
Chapter 5 Exercises p. 409
Introduction to Inference p. 415
Introduction p. 416
Estimating with Confidence p. 417
Statistical confidence p. 417
Confidence intervals p. 419
Confidence interval for a population mean p. 420
How confidence intervals behave p. 423
Choosing the sample size p. 425
Some cautions p. 426
Beyond the basics: The bootstrap p. 427
Summary p. 428
Section 6.1 Exercises p. 429
Tests of Significance p. 435
The reasoning of significance tests p. 436
Stating hypotheses p. 437
Test statistics p. 439
P-values p. 440
Statistical significance p. 441
Tests for a population mean p. 444
Two-sided significance tests and confidence intervals p. 447
P-values versus fixed [alpha] p. 449
Summary p. 451
Section 6.2 Exercises p. 452
Use and Abuse of Tests p. 461
Choosing a level of significance p. 461
What statistical significance doesn't mean p. 463
Don't ignore lack of significance p. 463
Statistical inference is not valid for all sets of data p. 464
Beware of searching for significance p. 465
Summary p. 466
Section 6.3 Exercises p. 466
Power and Inference as a Decision p. 469
Power p. 470
Increasing the power p. 472
Inference as decision p. 474
Two types of error p. 475
Error probabilities p. 476
The common practice of testing hypotheses p. 478
Summary p. 479
Section 6.4 Exercises p. 479
Chapter 6 Exercises p. 483
Inference for Distributions p. 491
Introduction p. 492
Inference for the Mean of a Population p. 492
The t distributions p. 492
The one-sample t confidence interval p. 494
The one-sample t test p. 496
Matched pairs t procedures p. 501
Robustness of the t procedures p. 504
The power of the t test p. 505
Inference for nonnormal populations p. 506
Summary p. 511
Section 7.1 Exercises p. 512
Comparing Two Means p. 525
The two-sample z statistic p. 526
The two-sample t procedures p. 528
The two-sample t significance test p. 529
The two-sample t confidence interval p. 532
Robustness of the two-sample procedures p. 533
Inference for small samples p. 534
Software approximation for the degrees of freedom p. 536
The pooled two-sample t procedures p. 537
Summary p. 542
Section 7.2 Exercises p. 543
Optional Topics in Comparing Distributions p. 553
Inference for population spread p. 553
The F test for equality of spread p. 554
Robustness of normal inference procedures p. 556
The power of the two-sample t test p. 557
Summary p. 559
Section 7.3 Exercises p. 559
Chapter 7 Exercises p. 561
Inference for Proportions p. 571
Introduction p. 572
Inference for a Single Proportion p. 572
Confidence interval for a single proportion p. 572
Significance test for a single proportion p. 575
Confidence intervals provide additional information p. 577
Choosing a sample size p. 578
Summary p. 581
Section 8.1 Exercises p. 582
Comparing Two Proportions p. 587
Confidence intervals p. 588
Significance tests p. 591
Beyond the basics: Relative risk p. 593
Summary p. 595
Section 8.2 Exercises p. 595
Chapter 8 Exercises p. 601
Topics in Inference p. 609
Analysis of Two-Way Tables p. 611
Introduction p. 612
Data Analysis for Two-Way Tables p. 612
The two-way table p. 612
Marginal distributions p. 614
Describing relations in two-way tables p. 615
Conditional distributions p. 615
Simpson's paradox p. 617
The perils of aggregation p. 619
Summary p. 619
Inference for Two-Way Tables p. 620
The hypothesis: no association p. 623
Expected cell counts p. 623
The chi-square test p. 624
The chi-square test and the z test p. 626
Beyond the basics: Meta-analysis p. 626
Summary p. 628
Formulas and Models for Two-Way Tables p. 629
Computations p. 629
Computing conditional distributions p. 630
Computing expected cell counts p. 632
Computing the chi-square statistic p. 632
Models for two-way tables p. 634
Concluding remarks p. 636
Summary p. 637
Chapter 9 Exercises p. 637
Inference for Regression p. 657
Introduction p. 658
Simple Linear Regression p. 658
Statistical model for linear regression p. 658
Data for simple linear regression p. 660
Estimating the regression parameters p. 662
Confidence intervals and significance tests p. 668
Confidence intervals for mean response p. 671
Prediction intervals p. 673
Beyond the basics: Nonlinear regression p. 675
Summary p. 676
More Detail about Simple Linear Regression p. 678
Analysis of variance for regression p. 678
The ANOVA F test p. 680
Calculations for regression inference p. 682
Inference for correlation p. 688
Summary p. 690
Chapter 10 Exercises p. 691
Multiple Regression p. 709
Introduction p. 710
Inference for Multiple Regression p. 710
Population multiple regression equation p. 710
Data for multiple regression p. 711
Multiple linear regression model p. 711
Estimation of the multiple regression parameters p. 712
Confidence intervals and significance tests for regression coefficients p. 713
ANOVA table for multiple regression p. 715
Squared multiple correlation R[superscript 2] p. 716
A Case Study p. 717
Preliminary analysis p. 717
Relationships between pairs of variables p. 719
Regression on high school grades p. 720
Interpretation of results p. 722
Residuals p. 722
Refining the model p. 723
Regression on SAT scores p. 724
Regression using all variables p. 725
Test for a collection of regression coefficients p. 728
Beyond the basics: Multiple logistic regression p. 728
Summary p. 729
Chapter 11 Exercises p. 731
One-Way Analysis of Variance p. 745
Introduction p. 746
Inference for One-Way Analysis of Variance p. 746
Data for a one-way ANOVA p. 746
Comparing means p. 747
The two-sample t statistic p. 749
ANOVA hypotheses p. 750
The ANOVA model p. 752
Estimates of population parameters p. 754
Testing hypotheses in one-way ANOVA p. 756
The ANOVA table p. 760
The F test p. 762
Comparing the Means p. 765
Contrasts p. 765
Multiple comparisons p. 771
Software p. 775
Power p. 778
Summary p. 780
Chapter 12 Exercises p. 781
Two-Way Analysis of Variance p. 801
Introduction p. 802
The Two-Way ANOVA Model p. 802
Advantages of two-way ANOVA p. 802
The two-way ANOVA model p. 805
Main effects and interactions p. 806
Inference for Two-Way ANOVA p. 811
The ANOVA table for two-way ANOVA p. 812
Summary p. 816
Chapter 13 Exercises p. 817
Data Appendix p. 1
Tables p. 1
Solutions to Selected Exercises p. 1
Notes p. 1
Index p. 1
Nonparametric Tests
Introduction
The Wilcoxon Rank Sum Test
The rank transformation
The Wilcoxon rank sum test
The normal approximation
What hypotheses does Wilcoxon test?
Ties
Limitations of nonparametric tests
Summary
Section 14.1 Exercises
The Wilcoxon Signed Rank Test
The normal approximation
Ties
Summary
Section 14.2 Exercises
The Kruskal-Wallis Test
Hypotheses and assumptions
The Kruskal-Wallis test
Summary
Section 14.3 Exercises
Chapter 14 Exercises
Notes
Logistic Regression
Introduction
The Logistic Regression Model
Binomial distributions and odds
Model for logistic regression
Fitting and interpreting the logistic regression model
Inference for Logistic Regression
Confidence intervals and significance tests
Multiple logistic regression
Summary
Chapter 15 Exercises
Notes