Statistical Modelling Using Genstat

by K. J. McConway; M. C. Jones; P. C. Taylor

• ISBN13: 9780340759851
• ISBN10: 0340759852
• Format: Paperback
• Copyright: 1999-10-01
• Publisher: Wiley

Summary

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.

Table of Contents

Preface	ix
Introduction	1	(12)
What methods will this book cover?	2	(2)
Exploring an interesting dataset	4	(7)
A brief outline of the book	11	(2)
Review of statistical concepts	13	(30)
The normal distribution	13	(8)
Basic attributes	13	(2)
Data and the normal distribution	15	(4)
Transforming to normality	19	(2)
Some distributional properties	21	(1)
Confidence intervals	21	(3)
Confidence interval for the mean of a normal distribution; Student's t distribution	22	(2)
Hypothesis testing	24	(6)
The one-sample t test	25	(3)
The two sample t test	28	(2)
Chi-squared and F distributions	30	(2)
The χ2 distribution	30	(1)
The F distribution	31	(1)
Bernoulli, binomial and Poisson distributions	32	(4)
The Bernoulli distribution	32	(1)
The binomial distribution	33	(1)
The Poisson distribution	34	(2)
Maximum likelihood estimation	36	(2)
The central limit theorem	38	(2)
Categorical and quantitative variables	40	(3)
Introduction to GENSTAT	43	(22)
Getting started	43	(6)
Loading, storing, retrieving and manipulating data	49	(5)
Summaries and graphics	54	(6)
Using the help system	60	(3)
Searching for help on a topic	60	(1)
Genstat Language Reference	61	(1)
The help system	62	(1)
Some useful hints about GENSTAT	63	(2)
Linear regression with one explanatory variable	65	(38)
The simple linear regression model	65	(6)
Fitting lines and making inferences	71	(7)
Confidence intervals and prediction	78	(5)
Checking the assumptions	83	(4)
Transformations	87	(6)
Comparing slopes	93	(3)
A look forward	96	(1)
Correlation	97	(6)
One-way analysis of variance	103	(34)
Regression with a continuous response variable and a categorical explanatory variable	103	(7)
One-way ANOVA: data and model	110	(6)
The completely randomized experiment	110	(3)
The basic one-way analysis of variance model	113	(3)
Testing for equality of means	116	(7)
Checking the model	123	(6)
Differences between treatments	129	(5)
Planned comparisons and contrasts	129	(4)
Unplanned comparisons	133	(1)
A final example	134	(3)
Multiple linear regression	137	(32)
Using the model	138	(7)
Choosing explanatory variables	145	(11)
Parallels with the case of one explanatory variable	156	(3)
Using indicator variables I: comparing regression lines	159	(4)
Using indicator variables II: analysis of variance	163	(6)
The analysis of factorial experiments	169	(28)
Two-way factorial analysis of variance	169	(12)
The basics: main effects and interactions	169	(8)
Developing the methods	177	(4)
More than two factors	181	(5)
Using regression	186	(6)
Factorial ANOVA without replication	192	(5)
Experiments with blocking	197	(28)
Blocking	197	(11)
Paired data	198	(2)
More than two units per block	200	(8)
More complicated blocking	208	(7)
Latin squares	208	(3)
Incomplete block designs	211	(4)
Factorial experiments with incomplete blocks	215	(7)
Split plot designs	216	(3)
Confounding	219	(3)
Designing experiments	222	(3)
Binary regression	225	(22)
The logistic function	226	(6)
The logistic regression model	232	(2)
Using the logistic regression model	234	(7)
Exercises in logistic regression	241	(6)
What are generalized linear models?	247	(26)
Poisson regression	247	(5)
The generalized linear model	252	(2)
Inference for GLMs	254	(6)
A short history of GLMs	260	(1)
Some more GLM applications	261	(12)
Mixing insecticides	261	(4)
Toxoplasmosis and rainfall	265	(1)
Survival of leukaemia patients	266	(2)
Janka hardness revisited	268	(5)
Diagnostic checking	273	(20)
Leverage	273	(5)
The Cook statistic	278	(4)
Diagnostics for generalized linear models	282	(9)
Residuals for generalized linear models	283	(5)
Detection of observations with high leverage or influence	288	(3)
Recommended use of model diagnostics	291	(2)
Loglinear models for contingency tables	293	(24)
Two-way contingency tables	294	(3)
Sampling models	297	(6)
Loglinear models in practice	303	(10)
Logistic and loglinear models	313	(4)
Further data analyses	317	(18)
Agglomeration of alumina	317	(4)
Prostatic cancer	321	(3)
Ground cover and apple trees	324	(4)
Epileptic seizures	328	(7)
Postscript	335	(6)
Ordinal responses	335	(1)
Smoothing: generalized additive models	336	(2)
Censoring in survival data	338	(3)
Solutions to the Exercises	341	(156)
Chapter 1	343	(2)
Chapter 2	345	(6)
Chapter 3	351	(8)
Chapter 4	359	(20)
Chapter 5	379	(12)
Chapter 6	391	(16)
Chapter 7	407	(14)
Chapter 8	421	(16)
Chapter 9	437	(12)
Chapter 10	449	(14)
Chapter 11	463	(12)
Chapter 12	475	(10)
Chapter 13	485	(12)
Index of datasets	497	(2)
Subject index	499