Back Matter

INDEX

Page I-1

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
- $t$ 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 $z$ 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
- $t$ for contrast, 737
- $t$ for difference of means, 381–382, 392
  - pooled, 389, 393
- $t$ for matched pairs, 370
- $t$ for mean response in regression, 511, 516, 554
- $t$ for multiple regression coefficients, 551, 561
- $t$ for one mean, 360–362, 374
- $t$ for regression slope, 496, 503
- $z$ for difference of proportions, 437, 448
- $z$ for one mean, 306–309, 313
- $z$ for one proportion, 420, 421–422, 431
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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,
- $c$ chart, 636–637, 638
- $I$ chart, 616–618, 626
- $M R$ chart, 616–618, 626
- $p$ chart, 631–635, 638
- $R$ chart, 603–612, 626
- $s$ chart, 613–614, 626
- three-sigma, 602
- $\bar{x}$ 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 $F$ distribution, 556, Table E
- of standard Normal distribution, 306, Table A
- of $t$ 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 $F$ distribution, 556–557
- of noncentral $F$ distribution, 745–746
- of noncentral $t$ distribution, 404
- of $t$ distribution, 359, 374
- of regression ANOVA, 522, 524
- of regression $t$ , 496, 503
- of regression $s$ , 491, 496, 503, 544
- of two-sample $t$ , 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
- $F$ , 556–558, 726, 15-14
- joint, 458
- jointly Normal, 502
- marginal, 105, 113
- noncentral $F$ , 745
- noncentral $t$ , 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
- $t$ , 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
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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
$F$ distribution. See Distribution, $F$
$F$ 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
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- 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
- $1.5 \times I Q R$ 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 $t$ test
  - one-sample, 402–403, 409
  - two-sample, 404–406, 409
- of $z$ test, 343–345
Power curve, 403, 747
Prediction, 81, 83, 94
Prediction interval, 510–511, 516, 554
Probability, 175, 176
- conditional, 197–199, 205
- Page 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
$P$ -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
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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 $t$ 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
- $F$ test for a collection of regression coefficients, 559, 562
- $F$ test for one-way ANOVA, 726–727
- $F$ test in multiple regression, 556–558, 561–562
- $F$ test in regression, 522, 524
- $F$ test for two-way ANOVA, 15-14, 15-21
- runs test for randomness, 648–650
- sign test, 407–408, 409
- $t$ test for contrast, 737
- $t$ test for correlation, 501, 503
- $t$ test for matched pairs, 368–370
- $t$ test for multiple regression coefficients, 551, 561
- $t$ test for one mean, 362–363, 373–374
- $t$ test for regression slope, 496, 503
- $t$ test for two means, 383, 392
  - pooled, 389, 714
- using, 336–341
- $z$ test for one mean, 327, 333
- $z$ test for one proportion, 423–424, 431
- $z$ test for two means, 380, 392
- $z$ 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
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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
- $t$ distribution. See Distribution, $t$
- $t$ confidence intervals. See Confidence interval, $t$
- $t$ significance tests. See Significance test, $t$
Table
- Table A Standard Normal Probabilities, 48–50
- Table B Random digits, 132, 149
- Table C Binomial probabilities, 248
- Table D $t$ distribution critical values, 360
- Table E $F$ critical values, 556–557
- Table F $χ^{2}$ 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
$z$ confidence interval. See Confidence interval, $z$
$z$ -score, 45
$z$ significance test. See Significance test, $z$
Zero inflation, 272
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