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Hodges J. L., Lehmann E. L. — Basic Concepts Of Probability And Statistics
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Название: Basic Concepts Of Probability And StatisticsАвторы: Hodges J. L., Lehmann E. L. Аннотация: Basic Concepts of Probability and Statistics provides a mathematically rigorous introduction to the fundamental ideas of modern statistics for readers without a calculus background. It is the only book at this level to introduce readers to modern concepts of hypothesis testing and estimation, covering basic concepts of finite, discrete models of probability and elementary statistical methods. Although published in 1970, it maintains a modern outlook, especially in its emphasis on models and model building and also by its coverage of topics such as simple random and stratified survey sampling, experimental design, and nonparametric tests and its discussion of power.The book covers a wide range of applications in manufacturing, biology, and social science, including demographics, political science, and sociology. Each section offers extensive problem sets, with selected answers provided at the back of the book. Among the topics covered that readers may not expect in an elementary text are optimal design and a statement and proof of the fundamental (NeymanPearson) lemma for hypothesis testing.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 2-е изданиеГод издания: 2005Количество страниц: 462Добавлена в каталог: 17.11.2013Операции: Положить на полку |
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Point estimation 240 see POINTS see "Sum" Poisson approximation, table of 199 417 Poisson approximation, to binomial 195 198 Poisson approximation, to generalized binomial 200 Poisson approximation, to matching 207 Poisson binomial trials model 171 Poisson distribution 202 Poisson distribution, normal approximation to 202 Poisson distribution, table of 199 417 Poisson random variable 202 Poisson random variable, expectation of 202 Poisson random variable, sum of two 203 Poisson random variable, variance of 202 Poisson, S.D. 171 Poker 48 88 96 Poker hands 88 96 POLITICS see "Income" Poplars see "Diseased" Population covariance 225 229 280 Population mean 261 Population mean, difference of two 273 Population mean, estimation of 262 289 Population mean, stratified estimate of 300 see Population size, estimation of 249 Population variance 159 227 261 283 Population variance, coded computation of 263 Population variance, estimation of 283 Populations see "Comparison" Posterior probabilities 114 129 Power (of a test) 382 388 407 Power (of a test), binomial 382 385 Power (of a test), Hypergeometric 383 385 Power (of a test), matching 385 Power (of a test), normal approximation to 372 395 403 Power (of a test), Wilcoxon two-sample 384 Power (of a test), X 404 Power curve 383 389 404 Pre-school children 262 PRECISION 269 see Principle of insufficient reason 24 Prior probabilities 114 129 probability 13 18 Probability and long-run frequency 13 250 Probability model 13 17 18 Probability model, conditional 91 92 Probability model, goodness of fit of 320 see Probability model, uniform 23 Probability of a boy 24 Probability of a composite event 19 23 Probability of false acceptance 371 373 Probability of guilt 130 Probability ratio test 396 Probability, conditional 91 96 114 Probability, determined by frequency 14 Probability, determined by symmetry 14 Probability, empirical basis for 10 25 Probability, personal 127 see Producer's risk 375 Product model 62 64 66 98 154 156 Product model with several parts see also "Binomial trials" "Independent "Model "Multinomial "Random "Stratified Product model, realism of 68 70 Product of event sets 63 Production see "Defective" Proportion, estimation of 245 250 256 259 285 Proportion, testing of 374 379 383 see "Chi-square "Frequency" "Hypergeometric Proportional allocation 301 303 Purposive sampling 39 Quadrinomial distribution 234 Quality control 10 42 80 169 231 see Quality improvement 401 Quantal response 332 quantities see "Comparison" "Several" Quantization of data 339 357 Quiz see "Multiple-choice" "Poetry" Rain on successive days 79 Rainmaking 275 326 342 Random digit 6 9 84 167 231 Random digit generator 320 323 Random digit, generator 6 320 Random digits 6 167 231 Random experiment 4 18 265 Random experiment with several parts 55 Random numbers 43 83 see Random ordered sample 54 Random quantity 132 143 217 see Random sample 41 42 52 54 see "Sampling" Random variables 133 143 Random variables, constant 151 161 Random variables, defined on factors of a product model 139 154 163 225 Random variables, multinomial 232 see "Expectation" "Independent "Number "Variance" "The "Hypergeometric" "Indicator" "Poisson Random variables, standardized 180 Random variables, uncorrelated 226 Randomization 363 Randomization in paired comparisons 330 352 354 see Randomization, complete 329 332 341 Randomization, within blocks 329 Randomized test 400 RANGE 8 Rank (of an observation) 340 357 Rank (of an observation), inverse 348 Rank (of an observation), tied 362 Rank test 331 406 see Realism of mathematical models 11 Realism of probability models 15 24 320 Realism of product models 68 70 74 Realism of the additivity assumption 296 see Realism of the binomial model 78 Realism of the conditional probability model 93 Realism of the model for several measurements 268 Realism of the multinomial model 231 Rectangular distribution 204 see Recursion formula for binomial coefficients 47 51 Recursion formula for matching distribution 208 Recursion formula for Wilcoxon paired-comparison distribution 361 Recursion formula for Wilcoxon two-sample distribution 351 Red at roulette 79 Rejection of a null hypothesis 311 Repeated measurements 281 288 Repeated measurements model 267 281 288 401 replacement see "Sampling" Response 275 327 Response, discrete 362 Response, graded 332 339 Response, judged 362 Response, quantal 332 Results, composite 18 Results, list of simple 12 18 24 Results, simple 12 18 89 Roulette see "Red" Rounding errors 204 Saik vaccine 326 334 Sample 39 Sample size 169 254 Sample size for estimating a measurable quantity 268 Sample size for estimating a proportion 256 262 Sample size for estimating binomial probability 255 Sample size in hypothesis testing 377 404 see Sample size, pilot study for determining 263 268 283 Sample, ordered 52 Sample, purposive 39 Sample, random 41 42 52 54 Sample, stratified 300 Sampling 39 83 173 283 289 Sampling by variables 144 261 see Sampling fraction 79 176 269 278 Sampling inspection 379 Sampling with and without replacement 91 Sampling with replacement 72 79 91 176 261 269 Sampling without replacement 92 100 Sampling, purposive 39 Sampling, two-stage 104 see "Lottery "Model "Ordered "Stratified Selection bias 336 see Self-selection bias 355 see Sempling see "Defectives" "Lot-sampling" "Stratified" Sequential binomial trials 212 Sequentially stopped families 214 Series see "Worid" Several dice 163 Several measurements of the same quantity 286 Several measurements, model for 266 Sex of children in three-child families 78 Sex of twins 72 108 Sex ratio see "Changing" Shaft diameter 260 Shooting gallery 81 SIB see "Affected" Sign test 354 Sign test, ties in 365 significance 311 317 343 Significance level 311 317 370 Significance probability 191 317 364 Significance probability, normal approximation to 318 Simple event 12 18 Simple hypothesis (alternative) 396 Simple result 12 18 89 Size of an experiment 169 Smoking 302 Smoking and lung cancer 101 Special items 173 Specified item see "Inclusion" Square root law 256 270 Square roots, explanation of table of 183 Square roots, table of 415 Stability property of frequencies 9 10 208 210 see Standard deviation 161 180 250 251 267 281 see Standard units 180 Standardized test statistic 402 Standardized variable 180 States see "Choosing" Statistical control 169 231 see Statistical hypothesis 309 313 Statistics, four stages of 241 286 Statistics, history of 239 Statistics, relation to probability theory 239 Stopped see "Sequentially" Stopping rule 212 Strata 62 241 300 305 Stratified sampling 62 99 153 178 248 264 300 304 330 Strength see "Breaking" Student's t, distribution 405 Student's t, statistic 405 Student's t, test 407 Subject (experimental) 275 327 Subject (experimental), homogeneity of 328 352 Subjective probability 127 Success 77 Successive days see "Rain" Suicides 201 Sum of integers 205 207 Sum of odd integers 207 Sum of points on several dice 179 Sum of points on three dice 190 Sum of points on two dice 25 Sum of squares 205 207 Sum of squares of odd integers 207 Sun-tan lotions 353 357 Symmetry 148 150 406 Symmetry as basis for probability 14 Symmetry of binomial distribution 169 173 Symmetry of normal curve 188 Symmetry of number of samples 41 Symmetry of Wilcoxon paired-comparison distribution 361 Symmetry of Wilcoxon two-sample distribution 348 Synergistic drugs 297 systems see "Gambling" t-test see "Student's t" table see "Life" Table of binomial distribution 168 413 414 Table of chi-square approximation 322 418 Table of matching distribution 206 Table of normal approximation 187 416 Table of number of ordered samples 53 Table of number of samples (binomial coefficients, number of combinations) 42 48 412 Table of Poisson approximation 199 417 Table of random digits 84 Table of square roots 183 415 Table of Wilcoxon paired-comparison distribution 358 420 421 Table of Wilcoxon two-sample distribution 347 349 366 419 Taste tests see "Triangular" Tchuprow — Neyman allocation 304 308 Telephone traffic 201 Tennis see "Winning" Test (of a statistical hypothesis) 241 309 311 Test (of a statistical hypothesis), chi-square 321 Test (of a statistical hypothesis), choice of 393 Test (of a statistical hypothesis), equal-tails 392 Test (of a statistical hypothesis), error probabilities in 371 377 Test (of a statistical hypothesis), Fisher — Irwin 334 362 Test (of a statistical hypothesis), goodness-of-fit 321 Test (of a statistical hypothesis), Mann — Whitney 347 Test (of a statistical hypothesis), one-sided 390 Test (of a statistical hypothesis), optimum 396 Test (of a statistical hypothesis), probability ratio 396 Test (of a statistical hypothesis), randomized 400 Test (of a statistical hypothesis), sign 354 Test (of a statistical hypothesis), significance of 311 317 343 370 Test (of a statistical hypothesis), statistic 310 387 393 Test (of a statistical hypothesis), t 407 see "Test "Testing" "Wilcoxon Test (of a statistical hypothesis), two-sided 390 Test (of a statistical hypothesis), uniformly most powerful 397 Test (of a statistical hypothesis), Wilcoxon paired comparison 358 Test (of a statistical hypothesis), Wilcoxon two-sample 340 Test (of a statistical hypothesis), X 402 Test of binomial probability 310 312 390 391 394 Test of binomial probability as probability ratio test 396 Test of binomial probability as sign test 354 Test of binomial probability, false acceptance in 371 Test of binomial probability, normal approximation for 318 Test of binomial probability, power of 382 386 Test of binomial probability, sample size for 377 Test of binomial probability, two-sided 387 Testing 241 310 see Testing binomial p 396 Testing for absence of treatment effect 333 339 352 357 384 Testing for adulteration 401 403 Testing for goodness of fit 321 Testing of a proportion 374 379 383 see "Sample "Test" "Test Testing of random matching 310 313 316 385 Tests see "College" "Diagnostic" "Triangular" "Wilcoxon" Three dice see "Sum" Three throws with a die 77 Three types see "Items" Three-child families see "Sex" Three-decision problem 392 Throwing a die 4 5 13 142 143 158 Throwing a loaded die 13 Throws see "Two" Tied rank 362 Ties in sign test 365 Ties in Wilcoxon paired-comparison test 365 Ties in Wilcoxon two-sample test 363 Tossing a penny 14 Traffic see "Telephone" Training see "Effect" Treatment 275 294 327 Treatment effect see "Allocation" Treatment effects 275 Treatment effects, additivity of 296 Treatment effects, comparison of two 327 332
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