Statistics : An Introduction Using R

by Crawley, Michael J.

• ISBN13: 9780470022986
• ISBN10: 0470022981
• Edition: 1st
• Format: Paperback
• Copyright: 2005-04-22
• Publisher: WILEY

Summary

Computer software is an essential tool for many statistical modelling and data analysis techniques, aiding in the implementation of large data sets in order to obtain useful results. R is one of the most powerful and flexible statistical software packages available, and enables the user to apply a wide variety of statistical methods ranging from simple regression to generalized linear modelling. Statistics: An Introduction using R is a clear and concise introductory textbook to statistical analysis using this powerful and free software, and follows on from the success of the author's previous best-selling title Statistical Computing. * Features step-by-step instructions that assume no mathematics, statistics or programming background, helping the non-statistician to fully understand the methodology. * Uses a series of realistic examples, developing step-wise from the simplest cases, with the emphasis on checking the assumptions (e.g. constancy of variance and normality of errors) and the adequacy of the model chosen to fit the data. * The emphasis throughout is on estimation of effect sizes and confidence intervals, rather than on hypothesis testing. * Covers the full range of statistical techniques likely to be need to analyse the data from research projects, including elementary material like t-tests and chi-squared tests, intermediate methods like regression and analysis of variance, and more advanced techniques like generalized linear modelling. * Includes numerous worked examples and exercises within each chapter. * Accompanied by a website featuring worked examples, data sets, exercises and solutions: http://www.imperial.ac.uk/bio/research/crawley/statistics Statistics: An Introduction using R is the first text to offer such a concise introduction to a broad array of statistical methods, at a level that is elementary enough to appeal to a broad range of disciplines. It is primarily aimed at undergraduate students in medicine, engineering, economics and biology - but will also appeal to postgraduates who have not previously covered this area, or wish to switch to using R.

Table of Contents

Preface	xi
Chapter 1 Fundamentals	1	(14)
Everything Varies	2	(1)
Significance	3	(1)
Good and Bad Hypotheses	3	(1)
Null Hypotheses	3	(1)
p Values	3	(1)
Interpretation	4	(1)
Statistical Modelling	4	(1)
Maximum Likelihood	5	(2)
Experimental Design	7	(1)
The Principle of Parsimony (Occam's Razor)	7	(1)
Observation, Theory and Experiment	8	(1)
Controls	8	(1)
Replication: It's the n's that Justify the Means	8	(1)
How Many Replicates?	9	(1)
Power	9	(1)
Randomization	10	(2)
Strong Inference	12	(1)
Weak Inference	12	(1)
How Long to Go On?	13	(1)
Pseudoreplication	13	(1)
Initial Conditions	14	(1)
Orthogonal Designs and Non-orthogonal Observational Data	14	(1)
Chapter 2 Dataframes	15	(8)
Selecting Parts of a Dataframe: Subscripts	19	(1)
Sorting	20	(2)
Saving Your Work	22	(1)
Tidying Up	22	(1)
Chapter 3 Central Tendency	23	(10)
Getting Help in R	31	(2)
Chapter 4 Variance	33	(18)
Degrees of Freedom	36	(1)
Variance	37	(2)
A Worked Example	39	(3)
Variance and Sample Size	42	(1)
Using Variance	43	(1)
A Measure of Unreliability	44	(1)
Confidence Intervals	45	(1)
Bootstrap	46	(5)
Chapter 5 Single Samples	51	(22)
Data Summary in the One Sample Case	51	(4)
The Normal Distribution	55	(5)
Calculations using z of the Normal Distribution	60	(4)
Plots for Testing Normality of Single Samples	64	(1)
Inference in the One-sample Case	65	(1)
Bootstrap in Hypothesis Testing with Single Samples	66	(1)
Student's t-distribution	67	(2)
Higher-order Moments of a Distribution	69	(1)
Skew	69	(2)
Kurtosis	71	(2)
Chapter 6 Two Samples	73	(30)
Comparing Two Variances	73	(2)
Comparing Two Means	75	(1)
Student's t-test	76	(3)
Wilcoxon Rank Sum Test	79	(2)
Tests on Paired Samples	81	(2)
The Sign Test	83	(1)
Binomial Tests to Compare Two Proportions	84	(1)
Chi-square Contingency Tables	85	(5)
Fisher's Exact Test	90	(3)
Correlation and Covariance	93	(2)
Data Dredging	95	(1)
Partial Correlation	96	(1)
Correlation and the Variance of Differences Between Variables	97	(1)
Scale-dependent Correlations	98	(2)
Kolmogorov-Smirnov Test	100	(3)
Chapter 7 Statistical Modelling	103	(22)
The Steps Involved in Model Simplification	105	(1)
Caveats	106	(1)
Order of Deletion	106	(1)
Model Formulae in R	106	(2)
Interactions Between Explanatory Variables	108	(1)
Multiple Error Terms	109	(1)
The Intercept as Parameter 1	109	(1)
Update in Model Simplification	110	(1)
Examples of R Model Formulae	110	(1)
Model Formulae for Regression	111	(2)
GLMs: Generalized Linear Models	113	(1)
The Error Structure	114	(1)
The Linear Predictor	115	(1)
Fitted Values	116	(1)
The Link Function	116	(1)
Canonical Link Functions	117	(1)
Proportion Data and Binomial Errors	117	(1)
Count Data and Poisson Errors	118	(1)
GAMs: Generalized Additive Models	119	(1)
Model Criticism	119	(1)
Summary of Statistical Models in R	120	(1)
Model Checking	121	(1)
Non-constant Variance: Heteroscedasticity	122	(1)
Non-Normality of Errors	122	(1)
Influence	123	(1)
Leverage	123	(1)
Mis-specified Model	124	(1)
Chapter 8 Regression	125	(30)
Linear Regression	128	(1)
Linear Regression in R	129	(7)
Error Variance in Regression: SSY = SSR + SSE	136	(6)
Measuring the Degree of Fit, r²	142	(1)
Model Checking	143	(2)
Polynomial Regression	145	(4)
Non-linear Regression	149	(3)
Testing for Humped Relationships	152	(1)
Generalized Additive Models (gams)	152	(3)
Chapter 9 Analysis of Variance	155	(32)
One-way Anova	155	(6)
Shortcut Formula	161	(2)
Effect Sizes	163	(4)
Plots for Interpreting One-way Anova	167	(4)
Factorial Experiments	171	(4)
Pseudoreplication: Nested Designs and Split Plots	175	(1)
Split-plot Experiments	176	(2)
Random Effects and Nested Designs	178	(1)
Fixed or Random Effects?	179	(1)
Removing the Pseudoreplication	180	(1)
Analysis of Longitudinal Data	180	(1)
Derived Variable Analysis	181	(1)
Variance Components Analysis (VCA)	181	(4)
What is the Difference Between Split-plot and Hierarchical Samples?	185	(2)
Chapter 10 Analysis of Covariance	187	(8)
Chapter 11 Multiple Regression	195	(14)
A Simple Example	195	(7)
A More Complex Example	202	(6)
Automating the Process of Model Simplification Using step	208	(1)
AIC (Akaike's Information Criterion)	208	(1)
Chapter 12 Contrasts	209	(18)
Contrast Coefficients	210	(1)
An Example of Contrasts in R	211	(1)
A Priori Contrasts	212	(2)
Model Simplification by Step-wise Deletion	214	(3)
Contrast Sums of Squares by Hand	217	(1)
Comparison of the Three Kinds of Contrasts	218	(4)
Aliasing	222	(1)
Contrasts and the Parameters of Ancova Models	223	(3)
Multiple Comparisons	226	(1)
Chapter 13 Count Data	227	(20)
A Regression with Poisson Errors	227	(2)
Analysis of Deviance with Count Data	229	(5)
The Danger of Contingency Tables	234	(3)
Analysis of Covariance with Count Data	237	(3)
Frequency Distributions	240	(7)
Chapter 14 Proportion Data	247	(16)
Analyses of Data on One and Two Proportions	249	(1)
Count Data on Proportions	249	(1)
Odds	250	(1)
Overdispersion and Hypothesis Testing	251	(2)
Applications	253	(1)
Logistic Regression with Binomial Errors	253	(2)
Proportion Data with Categorical Explanatory Variables	255	(5)
Analysis of Covariance with Binomial Data	260	(3)
Chapter 15 Death and Failure Data	263	(6)
Survival Analysis with Censoring	265	(4)
Chapter 16 Binary Response Variable	269	(12)
Incidence Functions	271	(4)
Ancova with a Binary Response Variable	275	(6)
Appendix 1: Fundamentals of the R Language	281	(24)
R as a Calculator	281	(1)
Assigning Values to Variables	282	(1)
Generating Repeats	283	(1)
Generating Factor Levels	283	(1)
Changing the Look of Graphics	284	(2)
Reading Data from a File	286	(1)
Vector Functions in R	287	(1)
Subscripts: Obtaining Parts of Vectors	288	(1)
Subscripts as Logical Variables	289	(1)
Subscripts with Arrays	289	(2)
Subscripts with Lists	291	(1)
Writing Functions in R	292	(1)
Sorting and Ordering	292	(2)
Counting Elements within Arrays	294	(1)
Tables of Summary Statistics	294	(1)
Converting Continuous Variables into Categorical Variables Using cut	295	(1)
The split Function	295	(2)
Trellis Plots	297	(2)
The xyplot Function	299	(1)
Three-dimensional (3-D) Plots	300	(1)
Matrix Arithmetic	301	(3)
Solving Systems of Linear Equations	304	(1)
References and Further Reading	305	(4)
Index	309