This core text is a self-contained course in statistics, covering both the general linear model (including regression and analysis of variance) and the generalized linear model. The authors review the prerequisite methods and ideas in a concise and clear way, and the material is application-oriented, with the software package GENSTAT for Windows integrated into the text. The basics of GENSTAT are introduced, then used in conjunction with a review of simple linear regression, moving on to more sophisticated analyses, such as multiple linear regression, analysis of variance, logistic regression…mehr
This core text is a self-contained course in statistics, covering both the general linear model (including regression and analysis of variance) and the generalized linear model. The authors review the prerequisite methods and ideas in a concise and clear way, and the material is application-oriented, with the software package GENSTAT for Windows integrated into the text. The basics of GENSTAT are introduced, then used in conjunction with a review of simple linear regression, moving on to more sophisticated analyses, such as multiple linear regression, analysis of variance, logistic regression and loglinear modelling. The final chapter consists of four data analysis case studies using techniques drawn from the whole of the book.
K. J. McConway and M. C. Jones are the authors of Statistical Modelling Using Genstat, published by Wiley.
Inhaltsangabe
Preface ix Introduction 1 What methods will this book cover? 2 Exploring an interesting dataset 4 A brief outline of the book 11 Review of statistical concepts 13 The normal distribution 13 Basic attributes 13 Data and the normal distribution 15 Transforming to normality 19 Some distributional properties 21 Confidence intervals 21 Confidence interval for the mean of a normal distribution; Student's t distribution 22 Hypothesis testing 24 The one-sample t test 25 The two sample t test 28 Chi-squared and F distributions 30 The ¿2 distribution 30 The F distribution 31 Bernoulli, binomial and Poisson distributions 32 The Bernoulli distribution 32 The binomial distribution 33 The Poisson distribution 34 Maximum likelihood estimation 36 The central limit theorem 38 Categorical and quantitative variables 40 Introduction to GENSTAT 43 Getting started 43 Loading, storing, retrieving and manipulating data 49 Summaries and graphics 54 Using the help system 60 Searching for help on a topic 60 Genstat Language Reference 61 The help system 62 Some useful hints about GENSTAT 63 Linear regression with one explanatory variable 65 The simple linear regression model 65 Fitting lines and making inferences 71 Confidence intervals and prediction 78 Checking the assumptions 83 Transformations 87 Comparing slopes 93 A look forward 96 Correlation 97 One-way analysis of variance 103 Regression with a continuous response variable and a categorical explanatory variable 103 One-way ANOVA: data and model 110 The completely randomized experiment 110 The basic one-way analysis of variance model 113 Testing for equality of means 116 Checking the model 123 Differences between treatments 129 Planned comparisons and contrasts 129 Unplanned comparisons 133 A final example 134 Multiple linear regression 137 Using the model 138 Choosing explanatory variables 145 Parallels with the case of one explanatory variable 156 Using indicator variables I: comparing regression lines 159 Using indicator variables II: analysis of variance 163 The analysis of factorial experiments 169 Two-way factorial analysis of variance 169 The basics: main effects and interactions 169 Developing the methods 177 More than two factors 181 Using regression 186 Factorial ANOVA without replication 192 Experiments with blocking 197 ( Blocking 197 Paired data 198 More than two units per block 200 More complicated blocking 208 Latin squares 208 Incomplete block designs 211 Factorial experiments with incomplete blocks 215 Split plot designs 216 Confounding 219 Designing experiments 222 Binary regression 225 The logistic function 226 The logistic regression model 232 Using the logistic regression model 234 Exercises in logistic regression 241 What are generalized linear models? 247 Poisson regression 247 The generalized linear model 252 Inference for GLMs 254 A short history of GLMs 260 Some more GLM applications 261 Mixing insecticides 261 Toxoplasmosis and rainfall 265 Survival of leukaemia patients 266 Janka hardness revisited 268 Diagnostic checking 273 Leverage 273 The Cook statistic 278 Diagnostics for generalized linear models 282 Residuals for generalized linear models 283 Detection of observations with high leverage or influence 288 Recommended use of model diagnostics 291 Loglinear models for contingency tables 293 Two-way contingency tables 294 Sampling models 297 Loglinear models in practice 303 Logistic and loglinear models 313 Further data analyses 317 Agglomeration of alumina 317 Prostatic cancer 321 Ground cover and apple trees 324 Epileptic seizures 328 Postscript 335 Ordinal responses 335 Smoothing: generalized additive models 336 Censoring in survival data 338 Solutions to the Exercises 341 Index of datasets 497 Subject index 499
Preface ix Introduction 1 What methods will this book cover? 2 Exploring an interesting dataset 4 A brief outline of the book 11 Review of statistical concepts 13 The normal distribution 13 Basic attributes 13 Data and the normal distribution 15 Transforming to normality 19 Some distributional properties 21 Confidence intervals 21 Confidence interval for the mean of a normal distribution; Student's t distribution 22 Hypothesis testing 24 The one-sample t test 25 The two sample t test 28 Chi-squared and F distributions 30 The ¿2 distribution 30 The F distribution 31 Bernoulli, binomial and Poisson distributions 32 The Bernoulli distribution 32 The binomial distribution 33 The Poisson distribution 34 Maximum likelihood estimation 36 The central limit theorem 38 Categorical and quantitative variables 40 Introduction to GENSTAT 43 Getting started 43 Loading, storing, retrieving and manipulating data 49 Summaries and graphics 54 Using the help system 60 Searching for help on a topic 60 Genstat Language Reference 61 The help system 62 Some useful hints about GENSTAT 63 Linear regression with one explanatory variable 65 The simple linear regression model 65 Fitting lines and making inferences 71 Confidence intervals and prediction 78 Checking the assumptions 83 Transformations 87 Comparing slopes 93 A look forward 96 Correlation 97 One-way analysis of variance 103 Regression with a continuous response variable and a categorical explanatory variable 103 One-way ANOVA: data and model 110 The completely randomized experiment 110 The basic one-way analysis of variance model 113 Testing for equality of means 116 Checking the model 123 Differences between treatments 129 Planned comparisons and contrasts 129 Unplanned comparisons 133 A final example 134 Multiple linear regression 137 Using the model 138 Choosing explanatory variables 145 Parallels with the case of one explanatory variable 156 Using indicator variables I: comparing regression lines 159 Using indicator variables II: analysis of variance 163 The analysis of factorial experiments 169 Two-way factorial analysis of variance 169 The basics: main effects and interactions 169 Developing the methods 177 More than two factors 181 Using regression 186 Factorial ANOVA without replication 192 Experiments with blocking 197 ( Blocking 197 Paired data 198 More than two units per block 200 More complicated blocking 208 Latin squares 208 Incomplete block designs 211 Factorial experiments with incomplete blocks 215 Split plot designs 216 Confounding 219 Designing experiments 222 Binary regression 225 The logistic function 226 The logistic regression model 232 Using the logistic regression model 234 Exercises in logistic regression 241 What are generalized linear models? 247 Poisson regression 247 The generalized linear model 252 Inference for GLMs 254 A short history of GLMs 260 Some more GLM applications 261 Mixing insecticides 261 Toxoplasmosis and rainfall 265 Survival of leukaemia patients 266 Janka hardness revisited 268 Diagnostic checking 273 Leverage 273 The Cook statistic 278 Diagnostics for generalized linear models 282 Residuals for generalized linear models 283 Detection of observations with high leverage or influence 288 Recommended use of model diagnostics 291 Loglinear models for contingency tables 293 Two-way contingency tables 294 Sampling models 297 Loglinear models in practice 303 Logistic and loglinear models 313 Further data analyses 317 Agglomeration of alumina 317 Prostatic cancer 321 Ground cover and apple trees 324 Epileptic seizures 328 Postscript 335 Ordinal responses 335 Smoothing: generalized additive models 336 Censoring in survival data 338 Solutions to the Exercises 341 Index of datasets 497 Subject index 499
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