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Wilcoxon rank-sum test and, 770 and, 664 sample size and, 388
Wilcoxon signed-rank test Coefficient of skewness, 121, Scheffé method for, 610
and, 765 128, 178 sign, 784
Central ¢ distribution, 320-323, 423. Coefficient of variation, 45, 229, 357 for slope coefficient, 643
Chebyshev’s inequality, 120, 138, Cohort, 281 for standard deviation, 409-410
156, 194, 303, 345 Combination, 70-72 for variance, 409-410
Chi-squared distribution Comparative boxplot, 40-41, 502, width of, 385, 387-388, 394, 397,
censored experiment and, 421 503, 554 404, 417, 495
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Index 837
Wilcoxon rank-sum, 774-776 paired data and, 515-516 for Studentized range
Wilcoxon signed-rank, 772-774 sample (see Sample correlation distribution, 565
Confidence level coefficient) for f distribution, 320, 390,
definition of, 382, 385-388 Covariance 500, 504
simultaneous, 565-570, 578, correlation coefficient and, 249 type Il error and, 574
589, 591, 658 Cramér-Rao inequality and, Delta method, 174
in Tukey’s procedure, 565-570, 374-375 De Morgan’s laws, 56
578, 589, 591 definition of, 247 Density
Confidence set, 772 of independent random conditional, 253-257
Consistency, 304, 357, 375-377 variables, 250-251 curve, 160
Consistent estimator, 304, 357, of linear functions, 249 function (pdf), 160
375-377 matrix format for, 711 joint, 235
Contingency tables, two-way, Covariate, 699 marginal, 236
744-751 Cramér-Rao inequality, 374-375 scale, 17
Continuity correction, 189-190 Credibility interval, 777-782 Dependence, 84-88, 238-242, 250,
Continuous random variable(s) Critical values 257, 747
conditional pdf for, 254, 789 chi-squared, 317 Dependent events, 84-88
cumulative distribution function F324 Dependent variable, 614
of, 163-168 standard normal (z), 184 Descriptive statistics, 1-41
definition of, 99, 159 studentized range, 565 Deviation
vs. discrete random variable, 162 1, 322, 409 definition of, 33
expected value of, 171-172 tolerance, 406 minimize absolute deviations
joint pdf of (see Joint probability Cumulative distribution function principle, 33, 679
density functions) for a continuous random Dichotomous trials, 128
marginal pdf of, 236-238 variable, 163-168 Difference statistic, 347
mean of, 171, 172 for a discrete random variable, _ Discrete random variable(s)
moment generating of, 175-177 104-108 conditional pmf for, 253
pdf of (see Probability density inverse function of, 223-224 cumulative distribution function
function) joint, 282 of, 104-108
percentiles of, 166-168 of order statistics, 272-273 definition of, 99
standard deviation of, 173-175 pdf and, 163 expected value of, 112
transformation of, 220-225, percentiles and, 167 joint pmf of (see Joint probability
265-270 pmf and, 105-108 mass function)
variance of, 173-175 transformation and, 220-225 marginal pmf of, 234
Contrast of means, 570-571 Cumulative frequency, 24 mean of, 112
Convenience samples, 7 Cumulative relative frequency, 24 moment generating of, 122
Convergence pmf of (see Probability mass
in distribution, 153, 329 D function)
in mean square, 303 Data standard deviation of, 117
in probability, 304 bivariate, 3, 617, 632, 691 transformation of, 225
Convex function, 231 categorical (see Categorical data) variance of, 117
Correction factor, 141, 560, 568, censoring of, 32, 343-344 Disjoint events, 54
577, 582 characteristics of, 3 Dotplots, 12
Correction for the mean, 560 collection of, 7-8 Dummy variable, 696
Correlation coefficient definition of, 2 Dunnett’s method, 571
autocorrelation coefficient and, 674 multivariate, 3, 220
in bivariate normal distribution, qualitative, 19 E
258-260, 310, 667 univariate, 3 Efficiency, asymptotic relative,
confidence interval for, 671 Deductive reasoning, 6 764, 769
covariance and, 249 Degrees of freedom (df) Empirical rule, 187
Cramér-Rao inequality and, in ANOVA, 557-559, Erlang distribution, 202, 229
374-375 587, 599 Error(s)
definition of, 249, 663 for chi-squared distribution, estimated standard, 344, 646, 713
estimator for, 666 200, 315-320 estimation, 334
Fisher transformation, 669 in chi-squared tests, 726, 734, family vs. individual, 570
for independent random 737, 746 measurement, 179, 211, 337,477
variables, 250 for F distribution, 323 prediction, 405, 658, 683
in linear regression, 664, 667, 669 in regression, 631, 685 rounding, 36
measurement error and, 328 sample variance and, 35 standard, 344, 713
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838 Index
Error(s) (cont.) observational studies in, 488 Fisher—Irwin test, 525
type I, 429 paired data, 515 Fisher transformation, 669
type II, 429 paired vs. independent samples, Fitted values, 588, 629, 674
Estimated regression function, 520-521 Fixed effects model, 579, 592, 597
676, 685 randomized block, 590-593 Fourth spread, 37, 41, 285
Estimated regression line, 625 randomized controlled, 489 Frequency, 13
Estimated standard error, 344, repeated measures designs in, 591 Frequency distribution, 13
646, 713 with replacement, 69, 141,287 Friedman’s test, 785
Estimator, 332 retrospective, 488 F test
Event(s) simulation, 291-294 in ANOVA, 558, 580, 587,
complement of, 53 Explanatory variable, 614 593, 600
compound, 52, 62 Exponential distribution Bartlett's test and, 562
definition of, 52 censored experiments and, 343 coefficient of determination
dependent, 84-88 chi-squared distribution and, 687
disjoint, 54 and, 317 critical values for, 324, 528, 558
exhaustive, 79 confidence interval for distribution and, 323, 527, 558
independent, 84-88 parameter, 389 for equality of variances, 527, 537
indicator function for, 364 double, 477 expected mean squares and, 573,
intersection of, 53 estimators for parameter, 343, 351 589, 593, 600, 604
mutually exclusive, 54 goodness-of-fit test for, 739 Levene test and, 562
mutually independent, 87 mixed, 229 power curves and, 574-575
simple, 52 in pure birth process, 378 P-value for, 529, 537, 559
union of, 53 shifted, 360, 479 in regression, 687, 709
Venn diagrams for, 55 skew in, 277 sample sizes for, 574
Expected mean squares standard gamma distribution single-factor, 558, 580