PART Ⅰ: Data 1
CHAPTER1Looking at Data-Distributions 2
Introduction 4
Variables 4
1.1 Displaying Distributions with Graphs 5
Graphs for categorical variables 6
Measuring the speed of light 7
Measurement 8
Variation 9
Stemplots 10
Examining distributions 13
Histograms 14
Looking at data 17
Time plots 18
Beyond the basics: decomposing time series 21
Section 1.1 Exercises 23
1.2 Describing Distributions with Numbers 40
Measuring center: the mean 41
Measuring center: the median 42
Mean versus median 43
Measuring spread: the quartiles 44
Measuring spread: the interquartile range 46
The five-number summary and boxplots 47
Comparing distributions 50
Measuring spread: the standard deviation 51
Properties of the standard deviation 53
Choosing measures of center and spread 54
Changing the unit of measurement 55
Section 1.2 Exercises 58
1.3 The Normal Distributions 64
Density curves 66
Measuring center and spread for density curves 68
Normal distributions 70
The 68-95-99.7 rule 72
Standardizing observations 73
The standard normal distribution 74
Normal distribution calculations 76
Normal quantile plots 79
Beyond the basics: density estimation 84
Section 1.3 Exercises 85
Chapter 1 Exercises 93
CHAPTER 2Looking at Data-Relationships 102
Introduction 104
Getting started 104
2.1 Scatterplots 106
Interpreting scatterplots 107
Adding categorical variables to scatterplots 108
More examples of scatterplots 109
Beyond the basics: scatterplot smoothers 112
Categorical explanatory variables 115
Section 2.1 Exercises 117
2.2 Correlation 126
The correlation r 126
Properties of correlation 128
Section 2.2 Exercises 131
2.3 Least-Squares Regression 135
Fitting a line to data 137
Prediction 137
Least-squares regression 139
Interpreting the regression line 142
Correlation and regression 142
Understanding r 2 145
Section 2.3 Exercises 148
2.4 Cautions about Regression and Correlation 153
Residuals 154
Lurking variables 156
Outliers and inuential observations 160
Beyond the basics: regression diagnostics 163
Beware the lurking variable 166
Beware correlations based on averaged data 167
The restricted-range problem 168
Section 2.4 Exercises 169
2.5 An Application: Exponential Growth and WorldOil Production 181
The nature of exponential growth 181
The logarithm transformation 184
Residuals again 185
Prediction in the exponential growth model 188
Section 2.5 Exercises 189
2.6 Relations in Categorical Data 193
Marginal distributions 194
Describing relationships 196
Conditional distributions 196
Simpson's paradox 199
The perils of aggregation 200
Section 2.6 Exercises 201
2.7 The Question of Causation 207
Explaining association: causation 208
Explaining association: common response 209
Explaining association: confounding 209
Establishing causation 210
Section 2.7 Exercises 212
Chapter 2 Exercises 214
CHAPTER 3Producing Data 228
Introduction 230
3.1 First Steps 230
Where to find data: the libraryand the Internet 231
Sampling 233
Experiments 234
Section 3.1 Exercises 235
3.2 Design of Experiments 237
Comparative experiments 239
Randomization 241
Randomized comparative experiments 242
How to randomize 243
Cautions about experimentation 246
Matched pairs design 246
Block designs 247
Section 3.2 Exercises 250
3.3 Sampling Design 256
Simple random samples 257
Stratified samples 258
Multistage samples 259
Cautions about sample surveys 260
Section 3.3 Exercises 262
3.4 Toward Statistical Inference 267
Sampling variability 268
Sampling distributions 269
The bias of a statistic 272
The variability of a statistic 272
Bias and variability 274
Why randomize? 275
Beyond the basics: capture-recapture sampling 275
Section 3.4 Exercises 277
Chapter 3 Exercises 281
PART Ⅱ: Probability and Inference 287
CHAPTER 4Probability: The Study of Randomness 288
4.1 Randomness 290
The language of probability 290
Thinking about randomness 291
The uses of probability 292
Section 4.1 Exercises 293
4.2 Probability Models 295
Sample spaces 295
Intuitive probability 297
Probability rules 298
Assigning probabilities:nite number of outcomes 299
Assigning probabilities: equally likely outcomes 300
Independence and the multiplication rule 301
Applying the probability rules 304
Section 4.2 Exercises 306
4.3 Random Variables 312
Discrete random variables 313
Continuous random variables 317
Normal distributions as probability distributions 320
Section 4.3 Exercises 322
4.4 Means and Variances of Random Variables 326
The mean of a random variable 326
Statistical estimation and the law of large numbers 328
Thinking about the law of large numbers 331
Beyond the basics: more laws of large numbers 333
Rules for means 333
The variance of a random variable 335
Rules for variances 337
Section 4.4 Exercises 340
4.5 General Probability Rules 346
General addition rules 347
Conditional probability 350
General multiplication rules 353
Tree diagrams 354
Bayes's rule 355
Independence again 356
Decision analysis 357
Section 4.5 Exercises 359
Chapter 4 Exercises 365
CHAPTER 5From Probability to Inference 373
Introduction 374
5.1 Sampling Distributions for Counts and Proportions 375
The binomial distributions for sample counts 375
Binomial distributions in statistical sampling 377
Finding binomial probabilities: tables 378
Binomial mean and standard deviation 380
Sample proportions 381
Normal approximation for counts and proportions 382
The continuity correction 386
Binomial formulas 387
Section 5.1 Exercises 390
5.2 The Sampling Distribution of a Sample Mean 397
The mean and standard deviation of x 398
The sampling distribution of x 400
The central limit theorem 401
Beyond the basics: Weibull distributions 406
Section 5.2 Exercises 408
5.3 Control Charts 415
x control charts 415
Statistical process control 418
Using control charts 419
Section 5.3 Exercises 422
Chapter 5 Exercises 428
CHAPTER 6Introduction to Inference 432
Introduction 434
6.1 Estimating with Confidence 435
Statistical confidence 435
Confidence intervals 437
Confidence interval for a population mean 439
How confidence intervals behave 441
Choosing the sample size 443
Some cautions 444
Beyond the basics: the bootstrap 445
Section 6.1 Exercises 447
6.2 Tests of Significance 453
The reasoning of signicance tests 453
Stating hypotheses 454
Test statistics 456
P -values 457
Statistical significance 458
Tests for a population mean 460
Two-sided significance tests and confidence intervals 463
P -values versus fixed a 466
Section 6.2 Exercises 468
6.3 Use and Abuse of Tests 475
Choosing a level of significance 476
What statistical significance doesn't mean 477
Don't ignore lack of significance 478
Statistical inference is not valid for all sets of data 479
Beware of searching for significance 479
Section 6.3 Exercises 481
6.4 Power and Inference as a Decision 483
Power 483
Increasing the power 486
Inference as decision 488
Two types of error 488
Error probabilities 490
The common practice of testing hypotheses 492
Section 6.4 Exercises 493
Chapter 6 Exercises 496
CHAPTER 7Inference for Distributions 502
7.1 Inference for the Mean of a Population 504
The t distributions 504
The one-sample t condence interval 505
The one-sample t test 507
Matched pairs t procedures 513
Robustness of the t procedures 515
The power of the t test 517
Inference for nonnormal populations 518
The sign test 519
Section 7.1 Exercises 523
7.2 Comparing Two Means 537
The two-sample z statistic 538
The two-sample t procedures 540
The two-sample t signicance test 541
The two-sample t condence interval 544
Robustness of the two-sample procedures 545
Inference for small samples 546
Software approximation for the degrees of freedom 549
The pooled two-sample t procedures 550
Section 7.2 Exercises 556
7.3 Optional Topics in Comparing Distributions 566
Inference for population spread 566
The F test for equality of spread 567
Robustness of normal inference procedures 570
The power of the two-sample t -test 570
Section 7.3 Exercises 573
Chapter 7 Exercises 575
CHAPTER 8Inference for Proportions 584
8.1 Inference for a Single Proportion 586
Condence interval for a single proportion 586
Significance test for a single proportion 588
Confidence intervals provide additional information 591
Choosing a sample size 592
Section 8.1 Exercises 596
8.2 Comparing Two Proportions 601
Confidence intervals 602
Significance tests 604
Beyond the basics: relative risk 607
Section 8.2 Exercises 609
Chapter 8 Exercises 615
PART Ⅲ: Topics in Inference 621
CHAPTER 9Inference for Two-Way Tables 622
9.1 Inference for Two-Way Tables 624
The two-way table 624
Describing relations in two-way tables 626
The hypothesis: no association 628
Expected cell counts 629
The chi-square test 629
The chi-square test and the z test 632
Beyond the basics: meta-analysis 632
9.2 Formulas and Models for Two-Way Tables 634
Computations 634
Computing conditional distributions 635
Computing expected cell counts 637
Computing the chi-square statistic 638
Models for two-way tables 639
Comparing several populations: the first model 640
Testing independence: the second model 641
Concluding remarks 642
chapter9 Exercses 643
CHAPTER 10Inference for Regression 660
10.1 Simple Linear Regression 662
Statistical model for linear regression 662
Data for simple linear regression 663
Estimating the regression parameters 666
Confidence intervals and signicance tests 671
Confidence intervals for mean response 673
Prediction intervals 676
Beyond the basics: nonlinear regression 678
10.2 More Detail about Simple Linear Regression 681
Analysis of variance for regression 681
The ANOVA F 684
Calculations for regression inference 686
Preliminary calculations 687
Inference for slope and intercept 688
Confidence intervals for the mean response and predictionintervals for a future observation 690
Inference for correlation 691
chapter10Exercises 695
CHAPTER 11Multiple Regression 710
Population multiple regression equation 712
Data for multiple regression 713
Multiple linear regression model 713
Estimation of the multiple regression parameters 714
Confidence intervals and significance tests for regressioncoeficients 715
ANOVA table for multiple regression 717
Squared multiple correlation R 2 718
A case study: preliminary analysis 719
Relationships between pairs of variables 721
Regression on high school grades 722
Interpretation of results 723
Residuals 724
Refining the model 724
Regression on SAT scores 726
Regression using all variables 726
Test for a collection of regression coefficients 728
Beyond the basics: multiple logistic regression 730
Chapter 11 Exercises 732
CHAPTER 12One-Way Analysis of Variance 742
Data for a one-way ANOVA 744
Comparing means 745
The two-sample t statistic 747
ANOVA hypotheses 747
The ANOVA model 750
Estimates of population parameters 751
Testing hypotheses in one-way ANOVA 753
The ANOVA table 757
The F test 759
Contrasts 762
Multiple comparisons 769
Software 773
Power 775
Chapter 12 Exercises 779
CHAPTER 13Two-Way Analysis of Variance 798
Advantages of two-way ANOVA 800
The two-way ANOVA model 803
Main effects and interactions 804
The ANOVA table for two-way ANOVA 809
Chapter 13 Exercises 815