Statistical methods of analysis:
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| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
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River Edge, NJ [u.a.]
World Scientific
2003
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| Beschreibung: | XXI, 631 S. graph. Darst. |
| ISBN: | 9812383107 |
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Datensatz im Suchindex
| _version_ | 1804132754743361536 |
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| adam_text | Titel: Statistical methods of analysis
Autor: Chiang, Chin Long
Jahr: 2003
Contents Preface vii Chapter 1 Descriptive Statistics 1 1.1. Introduction.......................... 1 1.2. Measures of Location..................... 3 1.2.1. Mean ......................... 3 1.2.1.1. Some properties of mean......... 5 1.2.2. Median........................ 6 1.2.3. Mode ......................... 7 1.3. Measures of Dispersion.................... 8 1.3.1. Range...........;.............. 9 1.3.2. Variance and standard deviation.......... 9 1.3.2.1. Some properties of variance and standard deviation ............ 10 1.3.2.2. Two alternative formulas for the variance................ 11 1.3.3. Covariance Cov(X, Y), or Sx,y ........... 11 1.4. Grouped Data......................... 12 1.4.1. Computational formulas for grouped data..... 13 1.5. Graphics............................ 15 1.5.1. Histogram....................... 16 xi
Statistical Methods of Analysis xii 1.5.2. Relative frequency polygon............. 16 1.5.3. Cumulative frequency polygon........... 17 1.5.4. Percentiles and quartiles and interquartile range . 18 1.6. An Example.......................... 20 1.7. Proofs of the Results in this Chapter............ 22 1.8. Exercises and Problems ................... 23 Chapter 2 Probability 25 2.1. Basic Concepts........................ 25 2.1.1. Three components of probability . . . ....... 25 2.1.2. Definition of probability............... 26 2.1.3. Values of a probability................ 29 2.1.4. Sure event and impossible event .......... 29 2.1.5. Complement of an event (or negation of an event) 29 2.2. Composite Event “ A and B” ................ 30 2.2.1. Conditional probability ............... 32 2.2.2. Multiplication theorem................ 34 2.2.3. Bayes’ theorem.................... 35 2.2.4. Independence of events ............... 37 2.2.5. A theorem of pairwise independence........ 38 2.2.6. Multiplication theorem when events are independent ................... 39 2.3. Composite Event “A or B” ................. 40 2.3.1. Addition theorem................... 40 2.3.2. Composite events of complements ......... 41 2.3.3. De Morgan’s laws .................. 43 2.3.4. Addition theorem when events are mutually exclusive.................. 44 2.4. Remarks on the Addition and Multiplication Theorems . . 44 2.4.1. Summary of the two theorems ........... 44 2.4.2. The sssociative and distributive laws........ 44 2.5. Factorials, Permutations, and Combinations........ 46 2.5.1. Permutations..................... 46 2.5.2. Combinations..................... 48 2.6. Proofs of the Results in this Chapter............ 50 2.7. Exercises and Problems ................... 51 Chapter 3 Random Variables 55
Contents xiii 3.1. Definition of a Random Variable .............. 55 3.1.1. Illustrative examples ................. 56 3.2. Joint Probability Distribution................ 57 3.2.1. Marginal probability ................. 58 3.2.2. Conditional probability ............... 59 3.2.3. Independence of random variables......... 59 3.3. Expectation of a Random Variable............. 62 3.3.1. Some properties of the expectation of a random variable ................... 65 3.3.2. Expectation of a linear function of random variables................... 66 3.3.3. Expectation of a sample mean ........... 67 3.4. Variance of a Random Variable............... 67 3.4.1. Two properties of the variance........... 69 3.4.2. Variance of a linear function of independent random variables................... 70 3.4.3. Variance of sample mean .............. 70 3.4.4. Expectation of sample variance........... 71 3.5. Covariance of a Bivariate Distribution........... 71 3.5.1. Some properties of the covariance.......... 72 3.5.2. The variance of a linear function of random variables................... 72 3.6. Continuous Random Variables................ 74 3.6.1. Joint probability distribution of two random variables................... 74 3.7. Proofs of the Results in this Chapter............ 76 3.8. Exercises and Problems ................... 78 Chapter 4 Probability Distributions 81 4.1. Introduction.......................... 81 4.2. Uniform Distribution (Discrete)............... 82 4.3. The Binomial Distribution, B(n p) ............. 83 4.4. The Hypergeometric Distribution.............. 91 4.4.1. Relation with the binomial distribution...... 93 4.4.2. Applications of the hypergeometric distribution . . 94 4.5. The Poisson Distribution................... 96 4.6. The Multinomial Distribution................ 99 4.6.1. The covariance between X l and Xj ......... 100
xiv Statistical Methods of Analysis 4.7. Continuous Uniform Distribution.............. 103 4.8. The Exponential Distribution................ 105 4.9. The Normal Distribution................... 107 4.9.1. Density function and distribution function..... 109 4.9.2. The standard normal distribution N(0, 1)..... Ill 4.10. Proofs of the Results in this Chapter............ 114 4.11. Exercises and Problems ................... 121 Chapter 5 Statistical Inference—Interval Estimation 127 5.1. Introduction.................... 127 5.1.1. The central limit theorem.............. 129 5.1.2. Normal approximation for the binomial distribution................. 133 5.2. Interval Estimation of Population Means.......... 136 5.2.1. Interval estimation of a population mean when the standard deviation is known............. 136 5.2.1.1. Length of the confidence interval..... 139 5.2.2. Interval estimation of a population mean when the standard deviation is unknown........... 141 5.2.3. Confidence interval for the difference between two population means when population variances are known....................... 143 5.2.4. Confidence interval of the difference between two population means when the population variances are unknown..................... 144 5.3. Confidence Intervals for Population Proportions...... 146 5.3.1. Confidence intervals for a single population proportion, p ..................... 146 5.3.2. Confidence interval for the difference between two population proportions................ 147 5.4. Exercises and Problems ................... 147 Chapter 6 Hypothesis Testing — Fundamental Concepts 151 6.1. Introduction.......................... 151 6.2. Basic Elements in Hypothesis Testing............ 153 6.2.1. Statistical hypothesis................. 153 6.2.1.1. Simple hypothesis versus composite hypothesis................. 154
Contents xv 6.2.2. Statistical test and two hypotheses......... 154 6.2.3. Two kinds of errors.................. 156 6.2.4. Level of significance and power of test....... 157 6.2.5. Statistic (or test statistic) and critical ratio .... 158 6.2.6. Critical region and region of acceptance...... 159 6.2.7. Computation of power, 1 — /3............ 159 6.3. Illustrative Examples of Hypothesis Testing........ 160 6.4. Power of Test......................... 168 6.4.1. Determination of sample size n ........... 169 6.5. Power of Test Concerning a Single Probability....... 171 6.6. Exercises and Problems ................... 172 Chapter 7 Testing Hypotheses Concerning Population Means and Population Proportions 175 7.1. Introduction.......................... 175 7.2. The “Student’s” t Distribution ............... 176 7.2.1. One-sample case................... 176 7.2.2. Two-sample case................... 178 7.3. Procedure for Hypothesis Testing.............. 180 7.4. Test of Hypotheses Concerning Population Means..... 181 7.4.1. Test of hypotheses concerning a single population mean................... 182 7.4.2. Test of hypotheses concerning two population means................... 183 7.4.3. Two populations — before and after treatment . . 184 7.4.4. Some remarks regarding hypothesis testing .... 188 7.5. Test of Hypotheses Concerning Probabilities........ 191 7.5.1. Hypothesis testing concerning a single probability 192 7.5.2. Hypothesis testing concerning two probabilities . . 193 7.6. Exercises and Problems ................... 196 Chapter 8 The Chi-Square Test 203 8.1. Introduction.......................... 203 8.1.1. The chi-square distribution.............204 8.2. Some Theorems Concerning the Chi-Square Distribution . 205 8.3. Chi-Square Tests....................... 207 8.3.1. One-way classification................ 207
XVI Statistical Methods of Analysis 8.3.1.1. The chi-square test versus the normal Z test I .................... 211 8.3.2. Two-way classification................ 212 8.3.2.1. Conditional distribution of Y given X . . 216 8.3.2.2. The 2x2 contingency table.......220 8.3.2.3. The chi-square test versus the normal Z test II ................... 221 8.3.2.4. Case-control studies............223 8.3.2.5. Relative risk and odds ratio....... 226 8.3.3. Goodness of fit . ............ 227 8.4. More Remarks about the Chi-Square Test.........231 8.5. Proof of the Results in this Chapter ............ 233 8.6. Exercises and Problems ................... 235 Chapter 9 Linear Regression 243 9.1. Introduction.......................... 243 9.2. Estimation of a and b ..................... 245 9.3. Underlying Assumptions................... 252 9.4. Relevant Theorems...................... 254 9.5. Statistical Inference in Linear Regression.......... 256 9.5.1. Hypothesis testing regarding b ...........256 9.5.2. Confidence interval for the expectation E(Y X 0 ) = a+bX 0 ................. 258 9.5.3. Confidence belt for the regression line E(Y X)=a + bX .................. 259 9.6. Test of the Linear Regression Assumption......... 265 9.6.1. The F distribution.................. 266 9.6.2. The F test of linear regression........... 267 9.6.3. Test of hypothesis 5 = 0............... 268 9.7. Remarks............................ 272 9.7.1. A linear model.................... 272 9.7.2. Choice of values of X ................ 273 9.7.3. Interval of prediction for an individual Y ..... 273 9.7.4. Interpolation versus extrapolation......... 274 9.8. Some Other Forms of Regression.............. 274 9.8.1. Curve-linear regression................ 274 9.8.2. Logistic regression.................. 275 9.9. Proofs of the Results in this Chapter............ 276
Contents xvii 9.10. Exercises and Problems ................... 278 Chapter 10 Correlation 281 10.1. The Correlation Coefficient, p XY ( or P) ..........281 10.1.1. The sample correlation coefficient, r XY ...... 283 10.2. Relationship Between Correlation and Regression..... 284 10.3. The Bivariate Normal Distribution............. 288 10.4. Statistical Inference About p XY ............... 291 10.4.1. Test of zero correlation ...............291 10.4.2. Confidence interval for p XY .............293 10.4.3. Spurious correlation?................. 296 10.5. Other Types of Correlation ................. 300 10.5.1. Rank correlation coefficient (Spearman’s correlation coefficient), r s ..............300 10.5.2. Point biserial correlation coefficient, r p b ......302 10.5.3. The 4 coefficient................... 304 10.6. Proofs of the Results in this Chapter............306 10.7. Exercises and Problems ................... 314 Chapter 11 Multiple Regression and Correlation 319 11.1. The Regression Equation................... 319 11.2. Estimation of a, bi, 62 .................... 320 11.3. Theorems and Inferences................... 323 11.4. Multiple Correlation Coefficient, p y . 2 329 11.4.1. Test of hypothesis concerning true correlation coefficient p y . 12 .................... 330 11.5. Partial Correlation...................... 332 11.6. A General Multiple Regression . .) ............. 335 11 . 6 . 1 . The regression equation and estimation of the constants.................... 335 11 . 6 . 2 . Some theorems for statistical inference.......338 11.6.3. Multiple correlation coefficient, p y .i 2 — s ....... 340 11.7. Multiple Logistic Regression................. 341 11.8. Proofs of the Results in this Chapter............342 11.9. Exercises and Problems ................... 345 Chapter 12 One-Way Analysis of Variance 349 12 . 1 . Introduction.......................... 349
xviii Statistical Methods of Analysis 12.2. One-Way Analysis of Variance................ 350 12.2.1. The layout and linear model ............350 12.2.2. Least-squares estimates, sums of squares (ssq), and mean squares (msq)................. 352 12.2.3. Null hypothesis and test statistic.......... 355 12.3. Examples........................... 358 12.4. Multiple Comparisons.................... 362 12.4.1. The least significant difference (LSD) .......362 12.4.2. The studentized range................ 364 12.4.3. Contrasts................—......365 12.4.3.1. Bonferroni’s inequality..........366 12.4.4. The t test....................... 368 12.5. Random-Effects Model.................... 373 12.5.1. Partition of sums of squares............. 375 12.5.2. The null hypothesis ................. 376 12.6. A Comparison of Two Models................ 378 12.7. Proofs of the Results in this Chapter............380 12.8. Exercises and Problems ................... 385 Chapter 13 Two-Way Analysis of Variance — Fixed-Effects Models 389 13.1. Introduction.......................... 389 13.2. The Linear Model....................... 391 13.3. One Observation Per Cell.................. 394 13.3.1. Least squares estimates and sums of squares (ssq) 395 13.3.2. Null hypotheses and test statistics......... 396 13.3.3. Multiple comparisons ................ 403 13.4. n Observations Per Cell................... 404 13.4.1. Linear model..................... 406 13.4.2. Least squares estimates and sums of squares (ssq) 407 13.4.3. Null hypotheses and test statistics.........408 13.4.4. Multiple comparisons ................ 414 13.5. Proofs of Results in this Chapter.............. 420 13.6. Exercises and Problems ................... 425 Chapter 14 Two-Way Analysis of Variance Random-Effects Models and Mixed Model 429 14.1. Introduction.......................... 429
Contents xix 14.2. One Observation Per Cell — Random-Effects Model . . . 430 14.2.1. Sums of squares and mean squares.........431 14.2.2. Null hypotheses and test statistics.........432 14.3. to Observations Per Cell — Random-Effects Model .... 434 14.3.1. Sums of squares and mean squares.........435 14.3.2. Null hypotheses and test statistics.........437 14.4. A Comparison of Two Models — Fixed-Effects Model versus Random-Effects Model................ 440 14.4.1. Expectations and variances............. 440 14.4.2. Statistical inference and test statistics.......442 14.5. Mixed Model......................... 446 14.5.1. Effects and interactions............... 447 14.5.2. Estimation of effects and sums of squares.....448 14.5.3. Expectations of mean squares............ 449 14.5.4. Hypotheses and test statistics............451 14.6. Proofs of the Results in this Chapter............ 456 14.7. Exercises and Problems ................... 464 Chapter 15 Design of Experiment 467 15.1. Introduction.......................... 467 15.1.1. Randomization.................... 469 15.1.2. Replication...................... 469 15.2. Completely Randomized Design............... 470 15.2.1. Table of random numbers.............. 471 15.2.2. Method of analysis.................. 472 15.3. Randomized Blocks — Single Blocking...........473 15.3.1. Some remarks..................... 473 15.3.2. An illustration.......)............. 474 15.3.3. Linear model and F ratios.............. 475 15.3.4. Efficiency of blocking................. 476 15.3.4.1. Measurement of efficiency.........477 15.3.4.2. Efficiency expressed in F ratio......479 15.4. Latin Squares — Double Blocking.............. 479 15.4.1. Examples....................... 481 15.4.2. Symmetry of the three factors............ 483 15.4.3. Replication of Latin squares............. 484 15.4.4. Observations in a Latin square........... 486 15.4.5. Linear model and hypotheses....... .... 487
xx Statistical Methods of Analysis 15.4.6. Sums of squares and test statistics.........489 15.4.7. Analysis of data — an example...........492 15.4.8. Efficiency of Latin square.............. 496 15.4.8.1. Preliminaries................ 496 15.4.8.2. Efficiency relative to randomized blocks.................... 498 15.4.8.3. Efficiency relative to complete randomization............... 499 15.5. Graeco-Latin Square — Triple Blocking.......... 503 15.6. Proofs of the Results in this Chapter............ 507 15.7. Exercises and Problems ................... 514 Chapter 16 Analysis of Covariance 519 16.1. Introduction.......................... 519 16.2. Linear Model, Hypotheses, and Regression Equations . . . 522 16.2.1. Null hypotheses.................... 522 16.2.2. Regression equations and regression lines.....524 16.3. Partition of Sum of Squares and F Statistics........ 530 16.3.1. The F statistics ................... 532 16.3.1.1. Test of hypothesis Hi : E(Yi X?) = ?? W + b w X? ....... 532 16.3.1.2. Test of hypothesis H 2 : E(Yi Xi) = a t + b t Xi ........ 533 16.3.1.3. Test of hypothesis H? : E(Ÿi Xi) = ?? b?,Xi ........533 16.3.1.4. Test of hypothesis : b w = bb ......535 16.3.1.5. Test of hypothesis H$ b w = Q ...... 536 16.4. Computation Formulas of the Sums of Squares ...... 537 16.5. An Example — Oral Contraceptives and Metabolic Rate in Women........................ 540 16.6. Proofs of the Results in this Chapter............ 544 16.7. Exercises and Problems .................. 549 Chapter 17 Non-Parametric Statistics 555 17.1. Introduction.......................... 555 17.2. Sign Test............................ 556 17.3. Wilcoxon Signed Rank Test................. 558 17.3.1. Critical values of R + ................. 558
Contents xxi 17.3.2. Normal approximation ................ 560 17.4. Wilcoxon Two-Sample Rank-Sum Test........... 560 17.4.1. Normal approximation ................ 563 17.4.2. Test for equality of two variances..........564 17.5. Mann-Whitney Test..................... 565 17.6. Kruskal-Wallis Test — One-Way Analysis of Variance . . 566 17.7. Friedman Test — Two-Way Analysis of Variance.....569 17.8. Proofs of the Results in this Chapter............574 17.9. Exercises and Problems ................... 580 Appendix: Tables 587 Bibliography 599 Hints and Answers to Selected Exercises 601 Index 617
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| spelling | Chiang, Chin L. Verfasser aut Statistical methods of analysis Chin Long Chiang River Edge, NJ [u.a.] World Scientific 2003 XXI, 631 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Estatística (textos elementares) larpcal Statistiek gtt Statistik Statistics Methodology Statistics Study and teaching Statistik (DE-588)4056995-0 gnd rswk-swf Statistik (DE-588)4056995-0 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012798729&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chiang, Chin L. Statistical methods of analysis Estatística (textos elementares) larpcal Statistiek gtt Statistik Statistics Methodology Statistics Study and teaching Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4056995-0 |
| title | Statistical methods of analysis |
| title_auth | Statistical methods of analysis |
| title_exact_search | Statistical methods of analysis |
| title_full | Statistical methods of analysis Chin Long Chiang |
| title_fullStr | Statistical methods of analysis Chin Long Chiang |
| title_full_unstemmed | Statistical methods of analysis Chin Long Chiang |
| title_short | Statistical methods of analysis |
| title_sort | statistical methods of analysis |
| topic | Estatística (textos elementares) larpcal Statistiek gtt Statistik Statistics Methodology Statistics Study and teaching Statistik (DE-588)4056995-0 gnd |
| topic_facet | Estatística (textos elementares) Statistiek Statistik Statistics Methodology Statistics Study and teaching |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012798729&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT chiangchinl statisticalmethodsofanalysis |