INDEX

• Alternative hypothesis. See Hypothesis, alternative
• Analysis of variance (ANOVA)
  • one-way, 712, Chapter 14
  • regression, 520–521, 524, 555–557
  • two-way, 712, Chapter 15
  • verifying the conditions for, 723
• Analysis of variance table
  • one-way, 722, 724–726
  • regression, 521–522, 524, 555, 561
  • two-way, 15-13–15-14
• Anecdotal data, 124, 127
• Anonymity, 162
• Applet
  • central limit theorem, 296–297
  • confidence intervals, 305–306, 352
  • correlation and regression, 79, 88, 94, 97
  • law of large numbers, 178, 223
  • mean and median, 26, 37
  • Normal curve, 47
  • One-Variable Statistical Calculator, 13
  • One-Way ANOVA, 727, 729, 757
  • probability, 175, 178
  • simple random sample, 133, 141, 153, 158
  • statistical power, 351
  • statistical significance, 335–336
  • Statistic, 372
• Assignable cause, 598
• Association, 68, 72, 76
• Autocorrelation, 653, 678
• Autocorrelation function, 651–655, 657
• Autoregressive behavior, 647, 657
• Autoregressive model, 681–690
• Available data, 124–125, 127
• Bar graph, 8, 2, 108
• Bayes, Thomas, 203
• Bayes’s rule, 203–205, 206
• Benford’s law, 184–187, 284
• Bias. See also Unbiased estimator
  • in a sample, 131, 140, 276–280, 281
  • in an experiment, 145, 281
  • of a statistic, 276–280, 281
• Binomial coefficient, 251–252, 263
• Binomial distribution. See Distribution, binomial
• Binomial setting, 245, 263, 418, 17-1
• Block, 155
• Block design. See Experiment, block design
• Bonferroni method, 342, 741–744
• Bootstrap, 372–373, 406, 411
• Boxplot, 29, 34
  • modified, 30
  • side-by-side, 30
• Buffon, Count, 175, 187
• Capability, 619–622
• Capability indices, 622–625, 626
• Capture-recapture sampling, 139
• Case, 2, 6, 534–535, 545
• Categorical variable. See Variable, categorical
• Causation, 101–102, 103
• Cause-and-effect diagrams, 596, 599
• Cell, 457, 15-3
• Census, 26
• Center of a distribution, 24–27
• Centered moving average, 695
• Central limit theorem, 294–299
• Chi-square distribution. See Distribution, chi-square
• Chi-square statistic, 463
  • and the statistic, 465–466
• Classes, 12
• Clinical trial, 163, 167
• Coefficient, 84
• Coin tossing, 174–176, 178, 179–181, 187–188, 209–210, 220, 224, 237, 240
• Collinearity, 570, 583
• Column variable. See Variable, row and column
• Common cause, 598, 599
• Comparative experiment. See Experiment, comparative
• Complement of an event. See Event, complement of
• Conditional distribution. See Distribution, conditional
• Conditional probability. See Probability, conditional
• Confidence interval, 302–314
  • and two-sided tests, 329
  • behavior, 309–310
  • bootstrap, 372–373, 411
  • simultaneous, 744
  • for contrast, 737
  • for difference of means, 381–382, 392
    • pooled, 389, 393
  • for matched pairs, 370
  • for mean response in regression, 511, 516, 554
  • for multiple regression coefficients, 551, 561
  • for one mean, 360–362, 374
  • for regression slope, 496, 503
  • for difference of proportions, 437, 448
  • for one mean, 306–309, 313
  • for one proportion, 420, 421–422, 431

• I-2

• Confidence level, 304, 313
• Confidentiality, 162–163, 167
• Confounding, 143, 157
• Consumer Expenditure Survey, 375
• Continuity correction, 260–261, 264
• Contrasts, 717, 733–739
• Control, statistical, 597
• Control chart,
  • chart, 636–637, 638
  • chart, 616–618, 626
  • chart, 616–618, 626
  • chart, 631–635, 638
  • chart, 603–612, 626
  • chart, 613–614, 626
  • three-sigma, 602
  • chart, 602–614, 626
• Control chart constant, 603
• Control group, 145, 157
• Control limits, 602–604, 613, 616, 631, 636
• Convenience sample, 131
• Correlation, 74–78
  • and regression, 87–88, 95
  • between random variables, 230–231
  • cautions about, 98–103
  • inference for, 500–502, 503
  • population, 500, 503
  • squared, 87–88, 520–522
  • squared multiple, 558, 562
• Count, 417
  • distribution of, 245–247, 263, 268–271, 273
• Countably infinite, 210
• Critical value,
  • of chi-square distribution, 464, Table F
  • of distribution, 556, Table E
  • of standard Normal distribution, 306, Table A
  • of distribution, 360, Table D
• Cumulative probability. See Probability, cumulative
• Cumulative proportion, 11, 46
• Current Population Survey, 135, 137
• Curved relationships, 515, 569–571
• Cyclic component, 647, 657
• Data mining, 102
• Deciles, 59
• Decision, relation to inference, 346–349
• Degrees of freedom, 31
  • approximation for, 380, 392
  • for one-way ANOVA, 726–727
  • for two-way ANOVA, 15-13
  • of chi-square distribution, 464
  • of chi-square test, 464
  • of distribution, 556–557
  • of noncentral distribution, 745–746
  • of noncentral distribution, 404
  • of distribution, 359, 374
  • of regression ANOVA, 522, 524
  • of regression , 496, 503
  • of regression , 491, 496, 503, 544
  • of two-sample , 380
• Deming, W. Edwards, 592, 628
• Density curve, 38–39, 213–215, 216
  • skewed, 40
  • symmetric, 40
• Density estimation, 54–55
• Design of an experiment, 142–156
• Direction, of a relationship, 67, 72. See also Correlation
• Disjoint events. See Event, disjoint
• Distribution, 18, 21
  • binomial, 245–250, 263
    • and logistic regression, Chapter 17
    • formula, 250–252, 263
    • Normal approximation, 256–260, 264, 418, 431
    • Poisson approximation, 271
    • use in the sign test, 407–408
  • categorical variable, 3, 7
  • chi-square, 464
  • conditional, 107, 113, 458
  • , 556–558, 726, 15-14
  • joint, 458
  • jointly Normal, 502
  • marginal, 105, 113
  • noncentral , 745
  • noncentral , 404, 409
  • Normal, 42, 56, 215–216
  • standard, 45–46, 57
  • Poisson, 268–270, 273
    • Normal approximation, 270
  • probability. See Probability
  • quantitative variable, 3, 12
  • sampling. See Sampling distribution
  • skewed, 18
  • symmetric, 18
  • , 358–360, 374
  • trimodal, 55
  • uniform, 213–214, 218, 221
• Distribution-free procedure. See nonparametric procedure
• Environmental Protection Agency (EPA), 375
• Equivalence testing, 370–371
• Estimator, 255–256, 277, 279, 281, 292–293, 299, 302
• Ethics, 160–167

• I-3

• Excel, 2, 85, 134, 148, 177–180, 237, 268–271, 274, 282, 367, 387, 492, 499, 507, 521, 535, 539, 552, 665–667, 670, 676, 695–697, 700, 702, 709, 730, 15-19
• Expected cell count, 462, 470
• Expected value, 220. See also Mean, of a random variable
• Experiment, 127, 142–157, 713
  • behavioral and social science, 165–166
  • block design, 155–156, 157
  • cautions about, 153
  • comparative, 145, 157
  • completely randomized, 147
  • design of, 142–157
  • matched pairs design, 154–155, 157
  • principles, 151, 157
  • randomized comparative, 146
• Experimental units, 142, 157
• Explanatory variable. See Variable, explanatory
• Exploratory data analysis, 7, 20
• Exponential smoothing model, 699–705, 706
• Extrapolation, 98–99, 103
• Event, 181, 191
  • complement of, 182, 191, 205–206
  • disjoint, 182, 191, 195, 206
  • empty, 196
  • independent, 188–189, 191, 205, 206
  • intersection, 200, 205
  • union, 195, 205
• distribution. See Distribution,
• tests. See Significance test
• Factor, experimental, 143, 157, 712, 15-2
• Factorial, 251–252, 263
• False-positive, 340
• Fisher, R. A., 337, 350, 556
• First difference, 659
• Five-number summary, 29, 34
• Flowchart, 594–595, 599
• Forecast, 656, 657, 686
• Form, of a relationship, 67, 72
• Frequency. See Count
• Friedman, Milton, 500
• Galton, Sir Francis, 500
• General Social Survey, 137
• Goodness of fit, 470–475
• Gosset, William S., 359
• Histogram, 12, 21
• Hot hand, 224
• Hypothesis, 319–320, 332
  • alternative, 319, 332
  • one-sided, 320, 332
  • two-sided, 320, 332
  • null, 319, 332
• Hypothesis testing. See Significance test
• Independence
  • in two-way tables, 467–468
  • of events, 188–189, 191, 205, 206
  • of observations, 176, 646, 657
  • of random variables, 230, 236
• Inference, statistical. See Statistical inference
• Influential observations, 92–94, 95
• Informed consent, 161–162, 167
• Institutional Review Boards (IRB), 160–161, 167
• Instrument, 5
• Interaction, 15-5, 15-7–15-12, 15-13
  • terms in multiple regression, 577–580
• Intercept of a line, 83, 94
• Interquartile range, 35
• Intervention, 127
• Irregular component, 647, 657
• JMP, 84, 110, 177–178, 237, 262–263, 272–273, 275, 282, 301, 353, 355, 366, 367, 387, 406, 422, 425, 430, 439, 443, 446, 447, 459, 493, 540, 553, 607, 653–654, 673, 700, 702, 704–705, 724, 732, 747, Chapter 16
• Kerrich, John, 175, 187, 284
• Kruskal-Wallis test, Chapter 16
• Label, 2, 6
• Lag variable, 652, 681
• Lagging, 651
• Large numbers, law of, 222–224
• Leaf, in a stemplot, 16
• Least-significant difference (LSD) method, 741
• Least squares, 486–488, 538–539
• Least-squares line, 81–82, 483
• Level of a factor, 143, 157, Chapter 14
• Linear relationship, 67, 72
• Log transformation, 68, 72, 486, 536, 662–663, 674–678, 679, 683–686, 689–690
• Logistic regression. See Regression, logistic
• Lurking variable. See Variable, lurking
• Main effects, 15-5, 15-7–15-12, 15-13
• Margin of error, 279
  • for a difference in two means, 381, 392–393
  • for a difference in two proportions, 437, 448
  • for regression response, 511

  • I-4

  • for regression slope, 496
  • for a single mean, 304–312, 313, 360, 374, 398–399
  • for a single proportion, 420, 431
• Marginal means, Chapter 15
• Matched pairs design. See Experiments, matched pairs
  • inference for, 368–371, 374
• Mean, 24, 34
  • of binomial distribution, 254, 263
  • of density curve, 39, 56
  • of difference of sample means, 379
  • of difference of sample proportions, 436
  • of Normal distribution, 43
  • of Poisson distribution, 268, 273
  • of a random variable, 219–220, 235
  • population, 222
  • rules for, 224–226, 236
  • sample mean, 292–293, 299
  • sample proportion, 256, 418, 431
• Mean absolute deviation, 694
• Mean absolute percentage error, 694
• Mean response, estimated, 510–515
• Mean square, 522
  • in forecasting, 694
  • in multiple linear regression, 555
  • in one-way ANOVA, 725–726
  • in simple linear regression, 522, 524
  • in two-way ANOVA, Chapter 15
• Median, 24, 34
  • inference for, 407–408, Chapter 16
  • of density curve, 39, 56
• Meta-analysis, 468–469
• Minimum variance portfolio, 234
• Minitab, 85, 177–178, 237, 248, 274, 282, 301, 346, 353, 355, 366, 387, 400, 403, 422, 425, 430, 439, 443, 446, 459, 473, 493, 511, 514, 517, 524, 527, 536, 537, 541, 552, 607, 653–655, 666, 669, 676, 678, 683–686, 688–689, 700, 702, 704–705, 731, 747, 752, Chapter 15, Chapter 16, Chapter 17
• Model, mathematical, 38, 54
• Model building, 566
• Mosaic plot, 109–110, 461
• Moving average model, 691–693, 706
• Moving range, 615
• Multiple comparisons, 717, 740–743
• Multiple regression. See Regression, multiple
• Naive forecast, 660
• National Longitudinal Survey of Youth (NLSY), 485
• National Science Foundation (NSF), 493–494
• Natural Resources Canada, 510
• Neyman, Jerzy, 350
• Noncentrality parameter, 404–405, 409, 745–746
• Nonlinear regression. See Regression, nonlinear
• Nonparametric procedure, 406, Chapter 16
• Nonresponse, 137
• Nonsense correlation, 101
• Normal distribution. See Distribution, Normal
• Normal probability plot. See Normal quantile plot
• Normal quantile plot, 51
• Normal score, 51
• Null hypothesis. See Hypothesis, null
• Observational study, 127
• Odds, 581, Chapter 17
• Office of the Superintendent of Bankruptcy Canada (OSB), 375
• Out-of-control signal, 602, 607, 610–611, 626, 627
• Outliers, 21, 67, 71, 94, 95, 494
  • rule, 36
• Overdispersion, 262
• Parameter, 276, 281
• Pareto chart, 10, 21, 596, 599
• Partial autocorrelation function, 683, 690
• Pattern of a distribution, 18, 21
• Pearson, Egon, 350
• Pearson, Karl, 175, 187
• Percent, 8, 417
• Percentile, 28
• Pie chart, 9, 21
• Placebo, 145
• Placebo effect, 145
• Poisson setting, 267, 273
• Pooled estimator
  • of population proportion, 441
  • of variance in ANOVA, 721, Chapter 15
  • of variance in two samples, 386–387, 393, 714
• Population, 126, 127, 129, 418, 276
• Population regression equation, 485, 492, 502, 548–549
• Power, 343–345, 350
  • and sample size, 345–346
  • and Type II error, 349
  • for one-way ANOVA, 745–748
  • increasing, 345
  • of test
    • one-sample, 402–403, 409
    • two-sample, 404–406, 409
  • of test, 343–345
• Power curve, 403, 747
• Prediction, 81, 83, 94
• Prediction interval, 510–511, 516, 554
• Probability, 175, 176
  • conditional, 197–199, 205

  • I-5

  • cumulative, 269
  • equally likely outcomes, 186–187
  • finite sample space, 184
• Probability distribution, 210, 215, 216
  • mean of, 219–220, 235
  • standard deviation of, 229, 231, 236
  • variance of, 229–231, 236
• Probability histogram, 211, 216
• Probability model, 179, 191
• Probability rules, 182, 191, 206
  • addition, 182, 191, 195, 196, 206
  • complement, 182, 191, 206
  • multiplication, 187–188, 191, 198, 206
• Probability sample. See Sample, probability
• Process, 592–593, 599
• Proportion
  • population, 256
  • sample, 244
• -value, 322, 332
• Quartiles, 27–28, 34
  • of a density curve, 39, 41
• Quantitative variable. See Variable, quantitative
• Random digits, 132, 140
• Random digit dialing, 138
• Random phenomenon, 175, 176
• Random process, 646
• Random sample. See Sample
• Random variable, 209–210, 216
  • continuous, 213, 216
  • discrete, 210, 216
  • mean of, 219–220, 235–236
  • standard deviation of, 229, 235–236
  • variance of, 229, 236
• Random walk, 657–659, 663
• Randomness, 174–176
• Randomize, how to, 132–134, 147–149
• Randomized comparative experiment. See Experiment, randomized comparative
• Range statistic, 602
• Rate, 5, 6
• Rational subgroup, 600–601
• Regression, 80–95
  • and correlation, 87–88, 95
  • cautions about, 98–103
  • conditions for, 494–495
  • equation, 83, 95, 485
  • interaction terms, 577–580, 582
  • least-squares, 81–82, 94
  • line, 80–81
  • logistic, 580–581, Chapter 17
  • multiple, Chapter 11
  • multicollinearity, 570
  • model building, 566
  • nonlinear, 515
  • polynomial, 570
  • simple linear, Chapter 10
  • standardized coefficients, 585
  • quadratic, 569, 582
  • variable selection methods, 577–580
  • variance inflation factor (VIF), 570, 583
  • with categorical explanatory variables, 571–574
• Regression fallacy, 500
• Relative risk, 447–448
• Replication, in experiments, 151, 157
• Residual, 88–89, 491, 503, 539, 541–543, 720
  • distribution, 92
  • plots, 90–91, 494, 503, 542–543, 667, 678, 685
• Resistant measure, 25, 26, 32, 35
• Response bias, 138
• Response rate, 130
• Response variable. See Variable, response
• Risk, investment, 33, 225
• Risk pooling, 233
• Robustness, 371–372, 374, 384, 391, 496
• Rounding, 24
• Row variable. See Variable, row
• Run, in coin tossing, 224
• Run chart, 595
• Runs rules for control charts, 627
• Runs test for randomness, 648–650, 657
• Sample, 126, 127, 129, 140, 418
  • cautions about, 136–138
  • convenience, 131
  • design of, 129–140
  • frame, 129
  • multistage, 135, 140
  • probability, 134, 140
  • simple random, 132, 140
  • stratified, 135, 140
  • survey, 126, 127, 129
  • systematic, 141
• Sample size, choosing
  • confidence interval for a difference in proportions, 444–445, 448
  • confidence interval for a mean, 311, 313, 398–402
  • confidence interval for a proportion, 426–427, 431
  • for a desired power, 345–346
  • for one-way ANOVA, 745–748
  • significance test for a difference in proportions, 445–446, 448
  • significance test for a proportion, 429–430, 432

• I-6

• Sample space, 179, 191
  • finite, 184
• Sampling, 129–140
• Sampling distribution, 277, 288
  • of difference of means, 379–380
  • of difference of two proportions, 436
  • of one sample statistic, 372
  • of regression estimators, 496
  • of sample mean, 294, 299
  • of sample proportion, 277
• Sampling frame, 129
• Sampling variability, 276–277
• SAS, 388, 525, 540, 568, 570, 572, 574, 575, 576, 577, 579, 730, 745, 15-20, 17-11, 17-16
• Satterthwaite approximation, 380, 392, 398
• Scatterplot, 65–71
• Scatterplot smoothing, 69, 486–487, 537–538
• Seasonal ratio, 697, 706
• Seasonality, 647, 671–676, 679, 693–699
• Seasonally adjusted, 698–699
• Secrist, Horace, 500
• Shape of a distribution, 18, 19
• Shewhart, Walter, 592, 600
• Sign test. See Significance test, sign test
• Significance level, 324, 337–338
• Significance, statistical, 151–152, 316–332
  • and practical significance, 337–338, 341
  • and Type I error, 349
• Significance test, 316–333
  • chi-square for goodness of fit, 472
  • chi-square for two-way table, 463–464, 470
  • common practice, 349–350
  • test for a collection of regression coefficients, 559, 562
  • test for one-way ANOVA, 726–727
  • test in multiple regression, 556–558, 561–562
  • test in regression, 522, 524
  • test for two-way ANOVA, 15-14, 15-21
  • runs test for randomness, 648–650
  • sign test, 407–408, 409
  • test for contrast, 737
  • test for correlation, 501, 503
  • test for matched pairs, 368–370
  • test for multiple regression coefficients, 551, 561
  • test for one mean, 362–363, 373–374
  • test for regression slope, 496, 503
  • test for two means, 383, 392
    • pooled, 389, 714
  • using, 336–341
  • test for one mean, 327, 333
  • test for one proportion, 423–424, 431
  • test for two means, 380, 392
  • test for two proportions, 441–442, 448
• Simple linear regression. See Regression, simple linear
• Simple random sample. See Sample, simple random
• Simpson’s paradox, 111–112, 113, 121
• Simulation, 277
• Six-sigma quality, 630
  • 68–95–99.7 rule, 43, 57
• Skewed distribution. See Distribution, skewed
• Slope, 83, 94
• Small numbers, law of, 224
• Smoothing. See Scatterplot smoothing
• Special cause, 598, 599
• Spread of a distribution, 18, 27–28, 31
• Spreadsheet, 3. See also Excel
• SPSS, 366, 388, 460, 473, 734, 735, 739, 742, 15-17, 15-20
• Standard deviation, 31, 34
  • of binomial distribution, 254, 263
  • of density curve, 41
  • of difference of sample means, 380
  • of difference of sample proportions, 441, 448
  • of Normal distribution, 42
  • of Poisson distribution, 268, 273
  • of random variable, 229, 236
  • of sample mean, 293, 299
  • of sample proportion, 256, 263
  • pooling, 386–387, 393, 441, 448, 721, 15-6, 15-13
  • rules for pooling, 720
• Standard error, 358
  • for regression prediction, 519
  • of a contrast, 737
  • of a difference of sample proportions, 436, 448
  • of a sample mean, 358, 373
  • of a sample proportion, 419, 431
  • of mean regression response, 518
  • of regression intercept and slope, 518
  • pooled, 389, 393, 721, 15-6, 15-13
  • regression, 492, 503, 544, 546, 551, 561
• Standard Normal distribution. See Distribution, Normal
• Standardized observation, 45, 56, 75
• Statistic, 276, 281
• Statistical inference, 275–281, 288
• Statistical process control, 597–599
• Statistical significance. See Significance, statistical
• Stem-and-leaf plot. See Stemplot
• Stemplot, 15–16, 21
  • back-to-back, 17
  • rounding, 17
  • splitting stems, 17
• Strata, 135, 140

• I-7

• Strength, of a relationship, 67, 72. See also correlation
• Subgroup, 600
• Subjects, experimental, 142, 157
• Subpopulation, 484, 549
• Sums of squares, 521
  • in multiple linear regression, 555
  • in one-way ANOVA, 725
  • in simple linear regression, 521
  • in two-way ANOVA, 15-7, 15-13
• Survey, 126, 129
• Symmetric distribution. See Distribution, symmetric
  • distribution. See Distribution,
  • confidence intervals. See Confidence interval,
  • significance tests. See Significance test,
• Table
  • Table A Standard Normal Probabilities, 48–50
  • Table B Random digits, 132, 149
  • Table C Binomial probabilities, 248
  • Table D distribution critical values, 360
  • Table E critical values, 556–557
  • Table F distribution critical values, 464
  • Table G Critical values of the correlation, 501
• Test of significance. See Significance test
• Test statistic, 321. See also Significance test
• Testing hypotheses. See Significance test
• Time plot, 19–20, 21, 645
• Time series, Chapter 13
• Transformation, 72
  • log, 68, 72
• Treatment, experimental, 127, 142–143, 157
• Tree diagram, 201–202
• Trend, 647, 664–670
  • exponential, 669–670
  • linear, 665–666
  • quadratic, 668–669
• Tuskegee Study, 164
• Two-sample problems, 379
• Two-way table
  • data analysis for, 104–113
  • hypothesis, 462
  • inference for, 455– 470
  • models for, 466–467
• Type I and II error, 346–347
• Unbiased estimator, 279–280, 281
• Uncountably infinite, 213
• Undercoverage, 137
• Unit, of measurement, 3, 75
• United States Department of Agriculture (USDA), 377, 384
• Value, 2
• Variability of a statistic, 279
• Variable, 2, 6
  • categorical, 3, 6, 7, 70, 104–113
  • dependent, 63
  • explanatory, 63, 71
  • independent, 63
  • indicator, 572–574
  • lurking, 100, 103
  • quantitative, 3, 6, 12, 15–16
  • response, 63, 71
  • row and column, 105, 112
• Variable selection methods, 577–580
• Variance, 31, 34. See also Standard deviation
  • of random variable, 229, 236
  • rules for, 231, 236
• Variation
  • between-group, 724, 733
  • within-group, 724, 726, 733
• Venn diagram, 182
• Voluntary response, 130–131, 140
• Wilcoxon rank sum test, Chapter 16
• Wilson estimate, 422, 440
• Wording questions, 138
• confidence interval. See Confidence interval,
• -score, 45
• significance test. See Significance test,
• Zero inflation, 272

• I-8