Elements of Statistics - Fergus Daly, Et Al

Data........................................... ................................................ ........................ Chapter 1 Data................... ...................... 13 1.1 Data and questions............ questions.................................... ...................................... .............. ........................... ...................... ..... 14 1.2 Graphical displays................ displays......................................... .................................. ......... ........................... ...................... ..... 20 1.3 Numerical summaries............... summaries........................................ .................................. ......... ........................... ...................... ..... 32 1.4 Graphical displays and numerical summaries.......................... ........................... ...................... ..... 43 1.5 A look ahead........................................................ ahead........................................................ ........................... ...................... ..... 48 Summary....................................... Summary............... ................................................. .......................... . ........................... ...................... ..... 53 Chapter 2 Models for Data................. Data......................................... ...................................... .............. ....................... ...................... . 55 2.1 Random variables and probability.......... probability................................... .......................... . ........................... ...................... ..... 58 2.2 Probability distributions and describing them....................... ........................... ...................... ..... 66 2.3 The Bernoulli and binomial probability models....................... models....................... ........................... ...................... ..... 83 2.4 The normal distribution............................................. distribution............................................. ........................... ...................... ..... 94 2.5 Some further exercises.............................................. exercises.............................................. ...........................101 Summary....................................... Summary............... ................................................. .......................... . ...........................105 Chapter 3 Models for Data................. Data......................................... ...................................... .............. .......................106 3.1 Population means and variances............ variances..................................... .......................... . ...........................107 3.2 Independence of random variables.............. variables.................................... ...................... ...........................123 3.3 The geometric probability model..................................... model..................................... ...........................126 3.4 Two models for uniformity............. uniformity...................................... .............................. ..... ...........................135 3.5 Population quantiles.............. quantiles....................................... .................................. ......... ...........................143 Summary....................................... Summary............... ................................................. .......................... . ...........................149 Chapter 4 Models' for Data.................... Data............................................. .................................. ......... .......................152 4.1 Rare events................... events........................................... ...................................... .............. ...........................153 4.2 Drawing random samples.............................................. samples.............................................. ...........................164 4.3 Moments of linear functions............... functions........................................ .......................... . ...........................169 4.4 The exponential distribution........................................ distribution........................................ ...........................178 4.5 On simulation............. simulation..................................... .......................................... .................. ...........................187 Summary....................................... Summary............... ................................................. .......................... . ...........................192 Chapter 5 The normal distribution......... distribution................................. ...................................... .............. .......................194 5.1 Some history.................. history.......................................... ...................................... .............. ...........................195

5.2 The standard normal distribution.................................... ...........................202 5.3 The central limit theorem........................................... ...........................216 5.4 Normal approximations to continuous distributions................... ...........................221 5.5 The normal approximation to discrete distributions.................. ...........................225 Summary................................................................. ...........................232 Chapter 6 Point estimation...................................................... .......................234 6.1 Principles of point estimation...................................... ...........................236 6.2 Methods of estimation............................................... ...........................246 6.3 The method of maximum likelihood.................................... ...........................253 6.4 More about maximum likelihood estimation............................ ...........................260 6.5 Estimating a normal variance........................................ ...........................267 Summary................................................................. ...........................273 Chapter 7 Estimation with confidence............................................ .......................275 7.1 Samples of size one................................................. ...........................277 7.2 Small samples....................................................... ...........................286 7.3 Confidence intervals for the parameters of a normal distribution.... ...........................290 7.4 Larger samples...................................................... ...........................300 7.5 Inference without a model........................................... ...........................308 Summary................................................................. ...........................310 Chapter 8 Testing hypotheses.................................................... .......................312 8.1 An approach using confidence intervals.............................. ...........................316 8.2 Fixed-level testing................................................. ...........................322 8.3 Significance testing................................................ ...........................334 8.4 Comparing the means of two normal populations....................... ...........................341 8.5 Other comparisons................................................... ...........................348 Summary................................................................. ...........................352 Chapter 9 Examining the assumptions............................................. .......................355 9.1 Are the distributional assumptions plausible........................ ...........................357 9.2 Can we quantify discrepancy between the data and the model.......... ...........................363 9.3 If the distributional assumptions are not plausible, what can we do. ...........................370

9.4 Is a modelling distribution necessary for answering the questions we  are asking of the data....376 9.5 Are the data typical or do they contain some 'unlucky' values....... ...........................383 Summary................................................................. ...........................385 Chapter 10 Explanatory relations................................................ .......................387 10.1 Some examples and a brief history.................................. ...........................392 10.2 Fitting the chosen regression model................................ ...........................401 10.3 Sampling properties of the model................................... ...........................414 10.4 The prediction problein............................................ ...........................420 10.5 The assumptions of the regression model............................ ...........................424 Summary................................................................. ...........................429 Chapter 11 Related variables.................................................... .......................432 11.1 Bivariate data..................................................... ...........................433 11.2 Measures of association............................................ ...........................440 11.3 Exact tests for association in 2 X 2 contingency tables............ ...........................454 11.4 The chi-squared test for contingency tables........................ ...........................458 11.5 The bivariate normal distribution.................................. ...........................463 Summary................................................................. ...........................467 Chapter 12 Random processes..................................................... .......................469 12.1 Examples of random processes....................................... ...........................471 12.2 The Bernoulli process as an inadequate model....................... ...........................485 12.3 Markov chains...................................................... ...........................489 12.4 The Poisson process................................................ ...........................495 12.5 Variations......................................................... ...........................503 Summary................................................................. ...........................505 Chapter 13 A Look Back.......................................................... .......................507 13.1 Exploiting statistical graphics.................................... ...........................508 13.2 Model fitting and testing.......................................... ...........................512 13.3 Comparing two populations.......................................... ...........................517 13.4 Contingency tables................................................. ...........................525 13.5 Correlation........................................................ ...........................529

13.6 Regression analysis................................................ ...........................531 Conclusion.............................................................. ...........................535 Chapter 14 A Look Forward....................................................... .......................536 14.1 Analysis of variance............................................... ...........................537 14.2 Cluster analysis................................................... ...........................543 14.3 Principal components analysis...................................... ...........................549 14.4 Discriminant analysis.............................................. ...........................554 14.5 Log-linear modelling............................................... ...........................559 14.6 Multiple regression analysis....................................... ...........................561 14.7 And beyond......................................................... ...........................564 Conclusion.............................................................. ...........................565 Solutions to the exercises...................................................... .......................567 Appendix........................................................................ .......................672 Index of data sets.............................................................. .......................678 Index of examples............................................................... .......................679 General index................................................................... .......................681