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A Ansari—Bradley test, 786 Beta functions, incomplete, 207 |
Additive model Association, causation and, 251,671 Bias-corrected and accelerated |
for ANOVA, 584-6, 589 Asymptotic normal distribution, 298, interval, 415, 417, 538 |
for linear regression analysis, 624 371, 375, 377, 671 Bimodal histogram, 18, 19 |
for multiple regression Asymptotic relative efficiency, Binomial distribution |
analysis, 682 164, 769 basics of, 128-135 |
Alternative hypothesis, 426 Autocorrelation coefficient, 674 Bayesian approach to, 777-780 |
Analysis of covariance, 699 Average multinomial distribution and, 240 |
Analysis of variance (ANOVA) definition of, 25 normal distribution and, |
additive model for, 584-586, deviation, 33 189-190, 302 |
597 pairwise, 379, 772-773, 775 Poisson distribution and, |
data transformation for, 579 rank, 785 147-149 |
definition of, 552 weighted (see Weighted average) Binomial experiment, 130-131, 134, |
expected value in, 556, 573, 147, 240, 302, 724 |
589, 597 B Binomial random variable |
fixed vs. random effects, 579 Bar graph, 9, 19 Bernoulli random variables and, |
Friedman test, 785 Bartlett’s test, 562 134, 302 |
fundamental identity of, 560, Bayesian approach to inference, 758, cdf for, 132 |
564, 587, 599, 600, 635 716-782 definition of, 130 |
interaction model for, 597-606 Bayes’ Theorem, 79-81, 777, 780 distribution of, 132 |
Kruskal-Wallis test, 784 Bemoulli distribution, 104, 122, 134, expected value of, 134, 135 |
Levene test, 562-563 302 373, 375, 377, 777 in hypergeometric experiment, |
linear regression and, 636,639, Bernoulli random variable 141 |
664, 708, 717 binomial random variable and, in hypothesis testing, 428-431, |
mean in, 553, 555, 557 134, 302 450-454 |
mixed effects model for, Cramér-Rao inequality for, 375 mean of, 134-135 |
593, 603 definition of, 98 moment generating function for, |
multiple comparisons in, expected value, 113 135 |
564-571, 578, 589-590, 603 Fisher information on, 372-373, multinomial distribution of, 240 |
noncentrality parameter for, 377 in negative binomial experiment, |
574, 582 Laplace’s rule of succession 142 |
notation for, 555, 559, 598 and, 782 normal approximation of, |
power curves for, 574-575 mean of, 113 189-190, 302 |
randomized block experiments mle for, 377 pmf for, 132 |
and, 590-593 moment generating function for, and Poisson distribution, |
regression identity of, 635-636 122, 123, 127 147-149 |
sample sizes in, 574-576 pmf of, 103 standard deviation of, 134 |
single-factor, 553-582 score function for, 372 unbiased estimation, 335, 337 |
two-factor, 582-608 in Wilcoxon’s signed-rank variance of, 134, 135 |
type I error in, 558-559 statistic, 314 Binomial theorem, 135, 142-144 |
type I error in, 574 Beta distribution, 206-208, 777 Bioequivalence tests, 551 |
835 |
--- Trang 849 --- |
836 Index |
Birth process, pure, 378 in confidence intervals, Complement of an event, 53, 60 |
Bivariate data, 3, 617, 623, 632, 389-390, 410 Compound event, 52, 62 |
691, 721 critical values for, 317, 389, Concentration parameter, 779 |
Bivariate normal distribution, 409-410, 477, 725, 727, Conceptual population, 6, 113, |
258-260, 310, 318, 477, 737-138 287, 487 |
667-671 definition of, 200 Conditional density, 253 |
Bonferroni confidence intervals, degrees of freedom for, 200,315 Conditional distribution, 253-263, |
424, 657-659, 689 exponential distribution 361, 369, 667, 735, 758, 777 |
Bootstrap procedure and, 317 Conditional mean, 255-262 |
for confidence intervals, F distribution and, 323-325 Conditional probability, 74-81, |
411-418, 532-534 gamma distribution and, 200, 315 84-85, 200, 253-255, 362, |
for paired data, 538-540 in goodness-of-fit tests, 720-751 365-366 |
for point estimates, 345-346 Rayleigh distribution and, 226 Conditional probability density |
Bound on the error of estimation, 388 standard normal distribution function, 253 |
Box-Muller transformation, 271 and, 224, 316-317, 325 Conditional probability mass |
Boxplot, 37-41 of sum of squares, 317, 557 function, 253, 255 |
comparative, 40-41 1 distribution and, 320, 325 Conditional variance, 255-262, 367 |
Branching process, 281 in transformation, 224 Confidence bound, 398-399, 403, |
Weibull distribution and, 231 440, 494, 500, 513 |
c Chi-squared random variable Confidence interval |
Categorical data in ANOVA, 557 adjustment of, 400 |
classification of, 30 cdf for, 316 in ANOVA, 565, 570-571, 578, |
graphs for, 19 expected value of, 315 589, 591, 603 |
in multiple regression analysis, in hypothesis testing, 482 based on f distribution, 401-404, |
696-699 in likelihood ratio tests, 477, 480 499-501, 505, 513-515, |
Pareto diagram, 24 mean of, 315 570-571, 643-646 |
sample proportion in, 30 moment generating function Bonferroni, 424, 657-659 |
Cauchy distribution of, 315 bootstrap procedure for, |
mean of, 322, 342 pdf of, 200, 315 411-418, 538, 540, 532-534 |
median of, 342 standard normal random for a contrast, 571 |
minimal sufficiency for, 367 variables and, 224, for a correlation coefficient, 671 |
reciprocals and, 231 316-317, 325 vs. credibility interval, 777-781 |
standard normal distribution in Tukey’s procedure, 565 definition of, 382 |
and, 271 variance of, 315 derivation of, 389 |
uniform distribution and, 226 Chi-squared test for difference of means, 493-495, |
variance of sample mean degrees of freedom in, 726, 734, 500-501, 505, 513-515, |
for, 349 736, 745, 748 532-534, 539-540, 565-569, |
Causation, association and, 251, 671 for goodness of fit, 724-730, 578, 589, 591, 603 |
cdf. See Cumulative distribution for homogeneity, 745~747 for difference of proportions, 524 |
function for independence, 747-749 distribution-free, 771-776 |
Cell counts/frequencies, 725-727, P-value for, 727-728 for exponential distribution |
729-730, 732-740, 744-750 for specified distribution, parameter, 389 |
Cell probabilities, 729, 732, 737, 739 729-730 in linear regression, 643-646, |
Censored experiments, 32, 343-344 z test and, 752 656-658 |
Census, 2 Class intervals, 15-17, 278, 293, for mean, 383~387, 392, |
Central Limit Theorem 738-739 403-404, 411-415 |
basics of, 298-303 Coefficient of determination for median, 415-417 |
Law of Large Numbers and, 305 definition of, 632-634, 686 in multiple regression, 689, 712 |
proof of, 329-330 F ratio and, 687 one-sided, 398, 500, 513 |
sample proportion distribution in multiple regression, 686 for paired data, 513-515, 539 |
and, 190 sample correlation coefficient for ratio of variances, 530-531, 537 |
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