Advanced Level Statistics: An Integrated Course

A. Francis

За особеностите на екземпляра

Advanced Level Statistics: An Integrated Course

Advanced Level Statistics: An Integrated Course - снимка 1

Състояние:: Много добро
Забележка:: Здрава, чиста и стегната книга, поовехтял външен вид.
Език:: Английски
Наличност:: 1 бр.

За изданието

Издателство:: Stanley Thornes
Град на издаване:: Cheltenham, England
Година:: 1990 г.
Език:: Английски
Страници:: 711
Корици:: Меки
Категория:: Математика
Тегло (гр.):: 951
Ширина (мм):: 165
Височина (мм):: 240
Дебелина (мм):: 30
ISBN:: 9780859508131

Second Edition This very popular book for students of statistics at advanced level is now in its second edition. A number of new topics, mainly concerned with practical statistics,, have been added, along with useful statistical tables. ■ The book provides a logical and ordered presentation of topics through definitions and fundamental results. ■ Fully worked examples follow each section of theory. ■ End of chapter exercises provide plenty of questions grouped by topic, ending with miscellaneous questions. All questions are of A level standard. * CONTENTS PREFACE TO SECOND EDITION v PREFACE TO FIRST EDITION vii ACKNOWLEDGEMENTS xi LIST OF DEFINITIONS xix LIST OF STATEMENTS xxi CHAPTER 1 PRESENTATION OF DATA 1 1.1 INTRODUCTION 1 1.2 TYPES OF DATA 3 1.2.1 Quantitative data 3 1.2.2 Qualitative data 5 1.3 TABULATION OF DATA 5 1.3.1 Frequency distributions 5 1.3.2 Intervals, limits and boundaries 8 1.3.3 Relative frequency 11 1.4 GRAPHICAL PRESENTATION 11 1.4.1 Bar charts and histograms 11 1.4.2 Frequency polygons and curves 17 1.4.3 Pie diagrams 21 1.5 CUMULATIVE FREQUENCY 24 1.6 EXERCISES 26 CHAPTER 2 STATISTICAL MEASURES 35 2.1 INTRODUCTION AND NOTATION 35 2.1.1 Introduction 35 2.1.2 Variable and summation notation 36 2.2 THE ARITHMETIC MEAN 39 2.2.1 For a set 39 2.2.2 For a frequency distribution 40 2.2.3 The method of coding 44 2.3 THE MEDIAN 50 2.3.1 For a set 50 2.3.2 For a frequency distribution 51 2.4 OTHER AVERAGES 57 2.4.1 The mode 57 2.4.2 The geometric mean 60 2.4.3 The harmonic mean 62 2.4.4 Quantiles 63 2.5 ELEMENTARY MEASURES OF DISPERSION 68 2.5.1 The range 68 2.5.2 The mean deviation 68 2.5.3 Measures associated with quantiles 71 2.6 THE STANDARD DEVIATION AND VARIANCE 72 2.6.1 For a set 73 2.6.2 For a frequency distribution 75 2.6.3 The method of coding 77 2.6.4 The variance 80 2.7 MOMENTS AND FURTHER MEASURES 81 2.7.1 Moments of a frequency distribution 81 2.7.2 Skewness and kurtosis 87 2.8 EXERCISES 89 CHAPTER 3 REGRESSION AND CORRELATION 106 3.1 INTRODUCTION TO BIVARIATE DATA 106 3.1.1 Scatter diagrams and correlation 107 3.1.2 Bivariate frequency distributions 112 3.2 RELATED MATHEMATICS 113 3.2.1 The equation of a straight line 113 3.2.2 The solution of linear, simultaneous equations 119 3.2.3 Differentiation 1: The differential operator 123 3.2.4 Differentiation 2: Partial differentiation 127 3.2.5 Differentiation 3: Maxima and minima 129 3.3 REGRESSION LINES 133 3.3.1 Fitting regression lines 133 3.3.2 The least squares technique 141 3.3.3 The method of coding 150 3.4 PRODUCT MOMENT CORRELATION 157 3.4.1 The covariance 157 3.4.2 The correlation coefficient 163 3.4.3 The method of coding 165 3.5 BIVARIATE FREQUENCY DISTRIBUTIONS 168 3.6 RANK CORRELATION 174 3.7 LOGARITHMIC TRANSFORMATIONS 176 3.7.1 Confirming the relationship 177 3.7.2 Identifying the relationship 181 3.8 EXERCISES 183 CHAPTER 4 PROBABILITY 198 4.1 INTRODUCTION 198 4.2 RELATED MATHEMATICS 199 4.2.1 Elementary set theory 199 4.2.2 Arithmetic and geometric progressions 204 4.2.3 Inequalities 209 4.3 BASIC PROBABILITY CONCEPTS 212 4.3.1 Experiments and events 212 4.3.2 Elementary probability 218 4.4 CONDITIONAL PROBABILITY 228 4.4.1 Conditional probability and independence 228 4.4.2 Bayes theorem 243 4.5 PERMUTATIONS AND COMBINATIONS 248 4.6 EXERCISES 257 CHAPTER 5 RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS 269 5.1 INTRODUCTION 269 5.2 RELATED MATHEMATICS 273 5.2.1 Differentiation 4: Products and quotients 273 5.2.2 Differentiation 5: Function of a function 274 5.2.3 Integration 1: The integral operator 276 5.2.4 Integration 2: Definite integration/Area under curve 279 5.2.5 The exponential function 283 5.3 RANDOM VARIABLES AND DISTRIBUTIONS 285 5.3.1 Discrete and continuous random variables 285 5.3.2 Density and distribution functions 289 5.3.3 A probability distribution 297 5.4 EXPECTATION 301 5.4.1 The expectation of A 302 5.4.2 The expectation of g(X) 307 5.4.3 Properties of operator E 308 5.4.4 The variance of A 312 5.4.5 The calculation of quantiles 317 5.5 MOMENTS AND GENERATING FUNCTIONS 319 5.5.1 Moments of a probability distribution 319 5.5.2 The moment generating function 321 5.5.3 The probability generating function 324 5.6 EXERCISES 326 CHAPTER 6 SOME SPECIAL PROBABILITY DISTRIBUTIONS 336 6.1 INTRODUCTION 336 6.2 RELATED MATHEMATICS 336 6.2.1 The binomial theorem 336 6.2.2 Integration 3: By parts 341 6.3 THE BINOMIAL DISTRIBUTION 344 6.3.1 Definition and notation 344 6.3.2 Derivation 347 6.3.3 The mean and variance 351 6.3.4 Recurrence formula 355 6.3.5 Binomial tables 358 6.3.6 Fitting a theoretical distribution 360 6.4 THE POISSON DISTRIBUTION 364 6.4.1 Definition and notation 364 6.4.2 The mean and variance 367 6.4.3 Uses of the Poisson distribution 368 6.4.4 Recurrence formula and Poisson tables 372 6.4.5 Fitting a theoretical distribution 374 6.4.6 Poisson probability paper 376 6.5 THE NORMAL DISTRIBUTION 378 6.5.1 Definition, notation and characteristics 379 6.5.2 The standard normal distribution 381 6.5.3 Fitting a theoretical distribution 390 6.5.4 Normal approximation to binomial and Poisson 395 6.5.5 Normal probability paper 398 6.6 SOME OTHER DISTRIBUTIONS 400 6.6.1 The Bernoulli distribution 400 6.6.2 The geometric distribution 402 6.6.3 The rectangular distribution 403 6.6.4 The exponential distribution 407 6.7 GENERATING FUNCTION TECHNIQUES 408 6.7.1 The binomial distribution 408 6.7.2 The Poisson distribution 409 6.7.3 The geometric distribution 409 6.7.4 The normal distribution 410 6.7.5 The rectangular distribution 411 6.7.6 The exponential distribution 411 6.8 EXERCISES 412 CHAPTER 7 RANDOM SAMPLES AND THEIR STATISTICS 428 7.1 INTRODUCTION 428 7.2 SUMS AND DIFFERENCES OF RANDOM VARIABLES 430 7.2.1 Two random variables 430 7.2.2 An extension 433 7.2.3 Multiples of normal random variables 435 7.3 THE SAMPLE MEAN 436 7.3.1 From any infinite population 436 7.3.2 From a normal population 437 7.3.3 From a finite population 438 7.3.4 The Central Limit Theorem 440 7.4 THE X2 DISTRIBUTION 443 7.4.1 Probability density function 444 7.4.2 Some special characteristics 444 7.4.3 Use of tables 445 7.5 SOME OTHER SAMPLE STATISTICS 447 7.5.1 The sample variance 447 7.5.2 A sample proportion 449 7.5.3 The correlation coefficient 452 7.6 SIMULATED RANDOM SAMPLING 455 7.6.1 Random number tables 455 7.6.2 Sampling from given distributions 457 7.7 ACCEPTANCE SAMPLING 462 7.7.1 Introduction 462 7.7.2 Single and double sampling plans 463 7.7.3 Operating characteristic 467 7.8 EXERCISES 472 CHAPTER 8 ESTIMATION 484 8.1 INTRODUCTION 484 8.2 POINT ESTIMATION 485 8.2.1 Unbiasedness. The mean and variance 485 8.2.2 Efficiency and consistency 488 8.2.3 Some other estimators 493 8.2.4 Pooled estimates 496 8.3 DEGREES OF FREEDOM 503 8.4 THE T DISTRIBUTION 505 8.4.1 Probability density function 505 8.4.2 Some special characteristics 505 8.4.3 Use of tables 507 8.5 THE F DISTRIBUTION 509 8.5.1 Probability density function 509 8.5.2 Some special characteristics 509 8.5.3 Use of tables 510 8.6 INTERVAL ESTIMATION 512 8.6.1 The mean (known variance) 513 8.6.2 The mean (unknown variance — small samples) 517 8.6.3 The mean (unknown variance — large sample approximation) 520 8.6.4 A proportion 522 8.6.5 The variance 525 8.6.6 The correlation coefficient 527 8.7 CONTROL CHARTS 529 8.7.1 Introduction 529 8.7.2 Control charts for means and ranges 531 8.7.3 Control charts for number or proportion defective 535 8.8 EXERCISES 539 CHAPTER 9 STATISTICAL TESTS 1 551 9.1 INTRODUCTION 551 9.2 FORMULATION OF THE CONCEPTS 551 9.2.1 A statistical test 551 9.2.2 Some notation and definitions 555 9.2.3 Further considerations: errors and power 560 9.3 TEST FOR A SAMPLE MEAN 570 9.3.1 With known variance (z test) 570 9.3.2 With unknown variance: small samples (t test) 572 9.3.3 With unknown variance: large sample approximation (z test) 574 9.4 TEST FOR THE DIFFERENCE BETWEEN TWO MEANS 577 9.4.1 Test for paired samples 578 9.4.2 Test for unpaired samples 581 9.5 TESTS INVOLVING SAMPLE PROPORTIONS 586 9.5.1 Test for a sample proportion (z test) 586 9.5.2 Test for the difference between two sample proportions (z test) 590 9.6 TESTS INVOLVING SAMPLE VARIANCES 592 9.6.1 Test for a sample variance (x2 test) 593 9.6.2 Test for the ratio of two sample variances (F test) 595 9.7 TESTS INVOLVING THE CORRELATION COEFFICIENT 600 9.7.1 Test for a correlation coefficient (z and t tests) 601 9.7.2 Test for the difference between two correlation coefficients (z test) 604 9.8 EXERCISES 606 CHAPTER 10 STATISTICAL TESTS 2 619 10.1 INTRODUCTION 619 10.2 X2 TEST: GOODNESS OF FIT 620 10.2.1 For any distribution 620 10.2.2 For a binomial 624 10.2.3 For a Poisson 628 10.2.4 For a normal 630 10.3 X2 TEST: CONTINGENCY TABLES 632 10.3.1 A 2 x 2 table 633 10.3.2 An m x n table 637 10.4 EXPERIMENTAL DESIGN AND ANALYSIS OF VARIANCE 640 10.4.1 Introduction to experimental design 640 10.4.2 One-way analysis 645 10.4.3 Two-way analysis 653 10.5 THE SIGN TEST 657 10.5.1 For a single sample 657 10.5.2 For the difference between two samples 660 10.6 EXERCISES 664 ANSWERS 681 APPENDIX 694 INDEX 708