text
stringlengths
0
6.73k
Retrospective study, 488 type Il error and, 433, 440-441, likelihood ratio and, 475
Ryan-Joiner test, 741 445, 452-454, 489, 505, 523 observed, 458
variance and, 303 Sign interval, 784
s z test and, 440-441, 452-453 Sign test, 784
Sample Sample space Simple events, 52, 62, 66
convenience, 7 definition of, 51 Simple hypothesis, 469, 732
definition of, 2 probability of, 56-63 Simple random sample
outliers in, 38-40 Venn diagrams for, 54-55 definition of, 7, 287
simple random, 7, 287 Sample standard deviation independence in, 287
size of (see Sample size) in bootstrap procedure, 413, 537 sample size in, 287
stratified, 7 confidence bounds and, 398 Simulation experiment, 288,
Sample coefficient of variation, 45 confidence intervals and, 392, 291-294, 417, 463
Sample correlation coefficient 403 Skewed data
in linear regression, 662-664, definition of, 33 coefficient of skewness, 121, 178
669, 719 as estimator, 340, 379 definition of, 19
vs. population correlation expected value of, 340, 379 in histograms, 19, 413
coefficient, 666, 669-671 independence of, 318-319 mean vs. median in, 28
properties of, 664-665 mle and, 357 measure of, 121
strength of relationship, 665 population standard deviation probability plot of, 216, 411-413
Sample mean and, 286, 340, 379 Slope, 617-618, 622, 626, 642, 644
definition of, 25 sample mean and, 34, 318-319 Slope coefficient
population mean and, 296-304 sampling distribution of, confidence interval for, 644
sampling distribution of, 296-304 288-289, 320, 340, 379, 482 definition of, 617-618
Sample median variance of, 482 hypothesis tests for, 648
definition of, 27 Sample total, 296, 306, 560 least squares estimate of, 626
in order statistics, 271-272 Sample variance in logistic regression model, 622
vs. population median, 417 in ANOVA, 555-556 Standard deviation
Sample moments, 350-351 calculation of, 35 normal distribution and, 179
Sample percentiles, 210-211 definition of, 33 of point estimator, 344-346
Sample proportion, 30, 335-336, distribution of, 287-289, 320 population, 117, 173
338, 391-400, 450-455, expected value of, 339 of a random variable, 117, 173
519-526 population variance and, 35, 317, sample, 33
Sample size 322-323, 339 z table and, 186
in ANOVA, 574-576 Sampling distribution Standard error, 344-346
asymptotic relative efficiency bootstrap procedure and, 413, Standardized variable, 185
and, 764, 769 532, 758 Standard normal distribution
bound on the error of estimation definition of, 284, 287 Cauchy distribution and, 271
and, 388 derivation of, 288-291 chi-squared distribution and,
Central Limit Theorem and, 302 of intercept coefficient, 719 316, 325
confidence intervals and, of mean, 288-290, 297-299 critical values of, 184
387-388, 394, 396, 403, 495 permutation tests and, 758 definition of, 181
definition of, 9 simulation experiments for, density curve properties for,
in finite population correction 291-294 181-184
factor, 140 of slope coefficient, 640-649 F distribution and, 323, 325
for F test, 574-576 Scale parameter, 195, 203-204, percentiles of, 182-184
for Levene test, 562-563 217-218, 365 1 distribution and, 320, 325
mle and, 357-358, 375 Scatter plot, 615-617 Standard normal random variable,
noncentrality parameter and, Scheffé method, 610 181, 325
574-576, 582 Score function, 373-377 Statistic, 286
--- Trang 857 ---
844 index
Statistical hypothesis, 426 Trimming proportion, 29, 343 U
Stem-and-leaf display, 10-12 True regression function, 615 Unbiased estimator, 337-344
Step function, 106 True regression line, 618-620, 625, minimum variance, 340-343
Stratified samples, 7 640-641 Uncorrelated random variables,
Studentized range distribution, 565 test 251, 307
Student r distribution, 320-323 vs. F test, 576 Uniform distribution
Summary statistics, 627, 630, heavy tails and, 764, 769, 774 beta distribution and, 778
645, 671 likelihood ratio and, 475, 476 Box-Muller transformation
Sum of squares in linear regression, 648 and, 271
error, 557, 631, 708 in multiple regression, definition of, 161
interaction, 599 688-690, 712 discrete, 120
lack of fit, 681 one-sample, 443-445, 461, transformation and, 223-224
pure error, 681 474-476, 511, 769 Uniformly most powerful test,
regression, 636, 699, 708 paired, 511 4T3-AT4
total, 559-560, 587, 591, 645, pooled, 504-505, 576 Unimodal histogram, 18-19
686 P-value for, 461-462 Union-intersection test, 551
treatment, 557-560 two-sample, 499-504, 576,515 Union of events, 53
Symmetric distribution, 19, type I error and, 443-445, 501 Univariate data, 3
121, 168 type Il error and, 445~447, 505
vs. Wilcoxon rank-sum v
T test, 769 Variable(s)
Taylor series, 174, 579 vs. Wilcoxon signed-rank test, covariate, 699
t confidence interval 763-764 in a data set, 10
heavy tails and, 764, 769,774 Tukey's procedure, 565-570, 578, definition of, 3
in linear regression, 643, 656 589-590, 603 dependent, 614
in multiple regression, 689,712 Two one-sided tests, 551 dummy, 696-699
one-sample, 403-404 Type I error explanatory, 614
paired, 513-515 definition of, 429 independent, 614
pooled, 505 Neyman-Pearson theorem indicator, 696-699
two-sample, 500, 515 and, 470 predictor, 614
1 distribution power function of the test random, 96-231
central, 423 and, 473 response, 614
chi-squared distribution and, P-value and, 457-458 Variance
320, 325, 500, 504 sample size and, 441 conditional, 255-257
critical values of, 322, 402, significance level and, 433 of a function, 118-119,
444, 461 vs. type IT error, 433 174-175, 328
definition of, 320 Type I error ofa linear function, 118-120, 307
degrees of freedom in, definition of, 429 population, 34-35, 117, 173
320-321, 401-402 vs. type I error, 433 precision and, 781
density curve properties for, Type II error probability of a random variable, 117, 173
322, 402 in ANOVA, 574-576, 596 sample, 33-37
F distribution and, 325, 576 degrees of freedom and, 516 Venn diagram, 54-55, 62, 75, 76
noncentral, 423 for F test, 574-576, 596
standard normal distribution in linear regression, 653 w
and, 320, 322, 403 Neyman-Pearson theorem Weibull distribution
Student, 320-323 and, 469-472 basics of, 202-205
Test statistic, 428 power of the test and, 446, 473 chi-squared distribution and, 231