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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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Acceptance of a null hypothesis 311 Acceptance of a null hypothesis, false 370 373 Accuracy (of an unbiased estimate) 250 252 269 283 see "Precision" "Sample "Standard "Variance" Acreage see "Wheat" Addition law for exclusive events 34 35 Addition law for general events 35 38 Addition law of covariance 225 Addition law of expectation 151 Addition law of variance 162 163 227 Additives see "Engine-oil" Additivity (of treatment effects) 296 Admissions see "College" Adulterations see "Testing" Affected sib 119 Affected uncle 120 Agricultural field trials 352 Algebra of events 28 31 Allocation (of observations) in estimating a difference 293 307 Allocation (of observations) in estimating a treatment effect 294 Allocation (of observations) in estimating the effects of two treatments 294 Allocation (of observations) in stratified sampling 301 303 308 Allocation (of observations), equal 293 Allocation (of observations), optimum 293 298 303 307 Allocation (of observations), proportional 301 303 Allocation in estimating difference 293 Allocation in estimating treatment effect 294 Alternative (to the null hypothesis) 372 381 Arithmetic mean 145 164 261 Arithmetic mean, coded computation of 263 see "Population Assessment bias 336 355 see Assignment bias 353 363 see authorship see "Disputed" Average of n random variables as best weighted average 288 Average of n random variables as estimate 261 267 Average of n random variables as test statistic 401 see Average of n random variables, expectation of 155 Average of n random variables, law of large numbers for 211 Average of n random variables, variance of 164 Average treatment effect 276 294 Baby pictures 206 balance see "Weighing" Bayes' law for composite events 116 Bayes' law for simple events 114 Bayes' law in subjective approach 129 Bernoulli, J. 210 Bias 328 329 335 Bias in assessing a treatment effect 279 327 Bias in measuring 269 Bias in using random numbers 86 Bias of estimates 245 284 Bias of purposive sampling 40 Bias, assessment 336 355 Bias, assignment 329 353 363 Bias, correction for 250 Bias, selection 336 Bias, self-selection 355 see Binomial (trials) model 77 Binomial (trials) model as basis for sign test 354 Binomial (trials) model as basis for Wilcoxon paired-comparison test 357 Binomial (trials) model as measurement model 269 Binomial (trials) model for defectives in mass production 80 169 Binomial (trials) model, combination of two 397 see "Test Binomial (trials) model, estimation of n in 248 Binomial (trials) model, estimation of p in 243 245 250 Binomial (trials) model, estimation of p(1 — p) in 283 284 Binomial (trials) model, estimation of p/q in 247 Binomial (trials) model, generalization to unequal probabilities 81 200 211 Binomial (trials) model, probabilities in 80 Binomial (trials) model, realism of 78 Binomial (trials) model, relation to sampling model of 78 176 Binomial (trials) model, sample size in 255 257 Binomial (trials) model, sequential 212 Binomial coefficients 47 see Binomial distribution 167 Binomial distribution as approximation to generalized binomial 200 Binomial distribution as approximation to hypergeometric 176 Binomial distribution as multinomial marginal 232 Binomial distribution in sign test 354 365 see "Quality "Statistical "Test Binomial distribution, expectation of 170 Binomial distribution, generalized 200 211 Binomial distribution, normal approximation to 191 210 Binomial distribution, normal tendency of 186 187 Binomial distribution, Poisson approximation to 195 198 Binomial distribution, standardized 181 Binomial distribution, symmetry in 169 173 Binomial distribution, tables of 167 413 414 Binomial distribution, use of Tables B and C for 168 Binomial distribution, variance of 171 Binomial distributions 187 Binomial model 243 245 247 250 255 283 Binomial probabilities, comparing two 246 251 see Binomial probabilities, estimation of 243 245 247 250 255 Binomial random variable 167 Binomial random variable and law of large numbers 209 Binomial random variable as sum of indicators 170 Binomial random variable, expectation of 170 Binomial random variable, variance of 171 Binomial theorem 60 167 173 Binomial trials 77 80 166 Binomials see "Combination" "Difference" "Testing" Bioassay 265 Birthdays 60 Births see "Male" Blind (clinical) trial 337 362 Blocking 330 see Bonus see "Bridge" Boosters see "Vaccine" Boxes see "Two" "Two Boy or girl? 14 Boys see "Distribution" "Number" "Probability" Breakdown law 115 Breaking strength 366 Bridge 23 48 143 Bridge bonus 143 Brother-sister marriage 123 125 Cancer see "Smoking" Card see "Drawing" "Heart" Carrier 118 121 123 126 Causality 100 Center of a distribution 148 245 see "Median" Center of gravity 148 Central limit theorem 187 192 402 Changing the sex ratio 310 312 370 371 377 387 Chebyshev inequality 209 268 Chemical balance see "Weighing" Chemotherapy 371 Chi-square test (of goodness of fit) 321 Chi-square test (of goodness of fit), table of 322 418 Children see "Pre-school" "Sex" Choosing one of an arbitrary number of items 85 Choosing one of one hundred items 85 Choosing one of ten items 85 Choosing ten of the fifty American states 86 Choosing two of ten items 86 Clinical trials 352 Clinical trials, blind 337 362 Clinical trials, double blind 337 Clinical trials, paired comparisons in 352 Coding of observations 263 Coins 14 70 95 224 College admissions 113 374 College entrance tests 359 Combination of two binomials 397 Combinations 47 see Comparative experiments 80 326 Comparative experiments for two binomial probabilities 246 Comparative experiments for two hypergeometric models 253 Comparative experiments for two measured quantities 272 Comparative experiments for two populations 273 Comparative experiments for two treatments 276 332 339 351 357 Comparative experiments, stratification in 304 see "Fisher "Paired "Randomization" "Sign "Wilcoxon "Wilcoxon Comparing two drugs 80 Comparison of populations 273 Comparison of two measured quantities 272 Complement 28 31 34 Complementation 31 Complementation law 34 Composite event 18 Composite result 18 Computation of null distribution of Q 321 322 Conditional distribution 221 235 Conditional expectation 221 223 Conditional frequency 69 89 91 97 Conditional probability 91 96 114 see Conditional probability model 91 92 Conditional probability model, realism of 93 Consistency of notation for product models 66 Consistent estimate 268 Constant effect model 276 278 280 Constant random variable 151 161 Consumer's risk 375 Control see "Quality" Controls 278 313 327 see "Comparative Correction factor for sampling without replacement 177 228 257 262 Correlation coefficient 226 228 230 Counter see "Lunch" Covariance 162 223 Covariance in double lottery model 225 230 280 Covariance in multinomial distribution 232 Covariance in multiple hypergeometric distribution 235 see Covariance of two indicators 164 Covariance, addition law of 225 Covariance, population 225 229 280 Critical value (of a test statistic) 311 372 374 days see "Rain" De Morgan's laws 33 Defective items in mass production 80 Defectives in lot sampling 78 219 374 379 Defectives in mass production 80 169 231 see Degrees of freedom 322 Delegation 40 41 137 143 Dependence of events 100 Dependence of random variables 225 Dependence, indirect 72 100 126 Design 241 276 293 303 Design, factorial 296 Design, two-stage sequential 104 263 Design, use of binomial trials in 80 336 Design, weighing 271 299 see "Blocking" "Stratified Deterministic experiments 3 Diabetes see "Insulin" Diagnostic tests 113 114 116 see Diameter see "Shaft" Dice 5 25 152 190 see "Several" "Sum" "Three" "Throwing" "Two" "Two "Two Dice, loaded 13 64 90 233 Dice, testing 383 398 Die see "Fair" Difference see "Allocation" Difference of two binomial probabilities 246 251 Difference of two binomials 246 251 Difference of two measurements 272 Difference of two population averages 273 Difference of two proportions 253 Difference of two random variables 155 Differential selection 93 DIGITS see "Random" DiME see "Penny" Discrete response 362 Diseased poplars 43 Dispersion of a random variable 157 209 Dispersion of a random variable, Laplace's measure of 158 see "Standard "Variance" Disputed authorship 129 Distance see "Measuring" Distribution (of a random variable) 137 Distribution (of a random variable) of a measurement 265 see "Normal "Random "Symmetry" "Variance" "Binomial" "Hypergeometric" "Matching" "Multinomial" "Uniform" "Poisson" "Wilcoxon "Wilcoxon Distribution (of a random variable) of an estimate 244 Distribution (of a random variable) of indicator 138 Distribution (of a random variable) of maximum 208 Distribution (of a random variable) of standardized variable 180 Distribution (of a random variable), center of 148 245 Distribution (of a random variable), conditional 221 Distribution (of a random variable), dispersion of 157 Distribution (of a random variable), histogram of 138 180 Distribution (of a random variable), joint 218 Distribution (of a random variable), marginal 220 222 Distribution (of a random variable), multiple hyper-geometrlc 219 234 235 Distribution (of a random variable), normal approximation to 190 Distribution (of a random variable), quadrinomial 234 Distribution (of a random variable), rectangular 183 Distribution (of a random variable), symmetry of 148 Distribution (of a random variable), trinomial 232 Distribution of boys and girls 219 Distributions see "Binomial" "Computation" "Variance" Dominance 119 Double blind (clinical) trial 337 Double lottery 218 224 Double lottery model 218 224 230 280 Double lottery model as basis for estimating treatment effect 276 280 Double lottery model as basis for power of Wilcoxon two-sample test 384 see Double lottery model, allocation in comparison of two 294 Drawing a card 23 Draws see "Two" drugs see "Comparing" e 196 202 Effect see "Treatment effect" Effect of a growth hormone 406 Effect of training 200 effects see "Allocation" "Estimating" Election forecasting 231 256 Empirical basis of probability 10 25 Empirical histogram 192 Empty set 29 30 Engine-oil additives 275 Entrance tests see "College" Equal allocation 293 Equal-tails test 392 Equally likely cases 24 105 Equivalence law of ordered sampling 55 59 Equivalence law of ordered sampling, generalized 55 59 277 Error probabilities 371 373 377 Estimate, consistent 268 Estimating difference see "Allocation" Estimating the effects of two treatments 294 Estimating treatment effect see "Allocation" Estimation 240 Estimation of a measured quantity 267 286 307 Estimation of a population average 261 299 303 Estimation of a proportion 245 250 256 Estimation of average treatment effect 276 294 304 Estimation of binomial p 243 250 255 Estimation of difference of two binomial p's 246 251 Estimation of population size 249 Estimation of the difference of two measured quantities 272 293 307 Estimation of the difference of two population averages 273 Estimation of two treatment effects 294 see "Bias" "Design" "Estimation "Sample Estimation of variance 281 Estimation of variance in binomial model 283 Estimation of variance in lottery model 283 Estimation of variance in repeated measurements model 281 Estimation of variance, accuracy of 283 Estimation of variance, bias corrections for 284 Estimation, interval 240 243 Estimation, point 240 Estimation, unbiased 245 Euler, L. 196 Event set 15 18 Event set, product of two 63 Events, complement of 28 31 34 Events, composite 18 Events, exclusive 30 33 35 102
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