Statistical Modelling Using Genstat

K. J. McConway and M. C. Jones are the authors of Statistical Modelling Using Genstat, published by Wiley.

• Preface ix Introduction 1What methods will this book cover? 2Exploring an interesting dataset 4A brief outline of the book 11Review of statistical concepts 13The normal distribution 13Basic attributes 13Data and the normal distribution 15Transforming to normality 19Some distributional properties 21Confidence intervals 21Confidence interval for the mean of a normal distribution; Student's t distribution 22Hypothesis testing 24The one-sample t test 25The two sample t test 28Chi-squared and F distributions 30The χ2 distribution 30The F distribution 31Bernoulli, binomial and Poisson distributions 32The Bernoulli distribution 32The binomial distribution 33The Poisson distribution 34Maximum likelihood estimation 36The central limit theorem 38Categorical and quantitative variables 40Introduction to GENSTAT 43Getting started 43Loading, storing, retrieving and manipulating data 49Summaries and graphics 54Using the help system 60Searching for help on a topic 60Genstat Language Reference 61The help system 62Some useful hints about GENSTAT 63Linear regression with one explanatory variable 65The simple linear regression model 65Fitting lines and making inferences 71Confidence intervals and prediction 78Checking the assumptions 83Transformations 87Comparing slopes 93A look forward 96Correlation 97One-way analysis of variance 103Regression with a continuous response variable and a categorical explanatory variable 103One-way ANOVA: data and model 110The completely randomized experiment 110The basic one-way analysis of variance model 113Testing for equality of means 116Checking the model 123Differences between treatments 129Planned comparisons and contrasts 129Unplanned comparisons 133A final example 134Multiple linear regression 137Using the model 138Choosing explanatory variables 145Parallels with the case of one explanatory variable 156Using indicator variables I: comparing regression lines 159Using indicator variables II: analysis of variance 163The analysis of factorial experiments 169Two-way factorial analysis of variance 169The basics: main effects and interactions 169Developing the methods 177More than two factors 181Using regression 186Factorial ANOVA without replication 192Experiments with blocking 197 (Blocking 197Paired data 198More than two units per block 200More complicated blocking 208Latin squares 208Incomplete block designs 211Factorial experiments with incomplete blocks 215Split plot designs 216Confounding 219Designing experiments 222Binary regression 225The logistic function 226The logistic regression model 232Using the logistic regression model 234Exercises in logistic regression 241What are generalized linear models? 247Poisson regression 247The generalized linear model 252Inference for GLMs 254A short history of GLMs 260Some more GLM applications 261Mixing insecticides 261Toxoplasmosis and rainfall 265Survival of leukaemia patients 266Janka hardness revisited 268Diagnostic checking 273Leverage 273The Cook statistic 278Diagnostics for generalized linear models 282Residuals for generalized linear models 283Detection of observations with high leverage or influence 288Recommended use of model diagnostics 291Loglinear models for contingency tables 293Two-way contingency tables 294Sampling models 297Loglinear models in practice 303Logistic and loglinear models 313Further data analyses 317Agglomeration of alumina 317Prostatic cancer 321Ground cover and apple trees 324Epileptic seizures 328Postscript 335Ordinal responses 335Smoothing: generalized additive models 336Censoring in survival data 338Solutions to the Exercises 341Index of datasets 497Subject index 499