Statistics - An Introduction Using R

Informationen zum Autor Michael J. Crawley, FRS, Department of Biological Sciences, Imperial College of Science, Technology and Medicine. Author of three bestselling Wiley statistics titles and five life science books. Klappentext "...I know of no better book of its kind..." (Journal of the Royal Statistical Society, Vol 169 (1), January 2006) A revised and updated edition of this bestselling introductory textbook to statistical analysis using the leading free software package R This new edition of a bestselling title offers a concise introduction to a broad array of statistical methods, at a level that is elementary enough to appeal to a wide range of disciplines. Step-by-step instructions help the non-statistician to fully understand the methodology.  The book covers the full range of statistical techniques likely to be needed 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. Zusammenfassung ". I know of no better book of its kind. Inhaltsverzeichnis Preface xi Chapter 1 Fundamentals 1 Everything Varies 2 Significance 3 Good and Bad Hypotheses 3 Null Hypotheses 3 p Values 3 Interpretation 4 Model Choice 4 Statistical Modelling 5 Maximum Likelihood 6 Experimental Design 7 The Principle of Parsimony (Occam's Razor) 8 Observation, Theory and Experiment 8 Controls 8 Replication: It's the ns that Justify the Means 8 How Many Replicates? 9 Power 9 Randomization 10 Strong Inference 14 Weak Inference 14 How Long to Go On? 14 Pseudoreplication 15 Initial Conditions 16 Orthogonal Designs and Non-Orthogonal Observational Data 16 Aliasing 16 Multiple Comparisons 17 Summary of Statistical Models in R 18 Organizing Your Work 19 Housekeeping within R 20 References 22 Further Reading 22 Chapter 2 Dataframes 23 Selecting Parts of a Dataframe: Subscripts 26 Sorting 27 Summarizing the Content of Dataframes 29 Summarizing by Explanatory Variables 30 First Things First: Get to Know Your Data 31 Relationships 34 Looking for Interactions between Continuous Variables 36 Graphics to Help with Multiple Regression 39 Interactions Involving Categorical Variables 39 Further Reading 41 Chapter 3 Central Tendency 42 Further Reading 49 Chapter 4 Variance 50 Degrees of Freedom 53 Variance 53 Variance: A Worked Example 55 Variance and Sample Size 58 Using Variance 59 A Measure of Unreliability 60 Confidence Intervals 61 Bootstrap 62 Non-constant Variance: Heteroscedasticity 65 Further Reading 65 Chapter 5 Single Samples 66 Data Summary in the One-Sample Case 66 The Normal Distribution 70 Calculations Using z of the Normal Distribution 76 Plots for Testing Normality of Single Samples 79 Inference in the One-Sample Case 81 Bootstrap in Hypothesis Testing with Single Samples 81 Student's t Distribution 82 Higher-Order Moments of a Distribution 83 Skew 84 Kurtosis 86 Reference 87 Further Reading 87 Chapter 6 Two Samples 88 Comparing Two Variances 88 Comparing Two Means 90 Student's t Test 91 Wilcoxon Rank-Sum Test 95 Tests on Paired Samples 97 The Binomial Test 98 Binomial Tests to Compare Two Proportions 100 Chi-Squared Contingency Tables 100 Fi...

List of contents

Preface xi
 
Chapter 1 Fundamentals 1
 
Everything Varies 2
 
Significance 3
 
Good and Bad Hypotheses 3
 
Null Hypotheses 3
 
p Values 3
 
Interpretation 4
 
Model Choice 4
 
Statistical Modelling 5
 
Maximum Likelihood 6
 
Experimental Design 7
 
The Principle of Parsimony (Occam's Razor) 8
 
Observation, Theory and Experiment 8
 
Controls 8
 
Replication: It's the ns that Justify the Means 8
 
How Many Replicates? 9
 
Power 9
 
Randomization 10
 
Strong Inference 14
 
Weak Inference 14
 
How Long to Go On? 14
 
Pseudoreplication 15
 
Initial Conditions 16
 
Orthogonal Designs and Non-Orthogonal Observational Data 16
 
Aliasing 16
 
Multiple Comparisons 17
 
Summary of Statistical Models in R 18
 
Organizing Your Work 19
 
Housekeeping within R 20
 
References 22
 
Further Reading 22
 
Chapter 2 Dataframes 23
 
Selecting Parts of a Dataframe: Subscripts 26
 
Sorting 27
 
Summarizing the Content of Dataframes 29
 
Summarizing by Explanatory Variables 30
 
First Things First: Get to Know Your Data 31
 
Relationships 34
 
Looking for Interactions between Continuous Variables 36
 
Graphics to Help with Multiple Regression 39
 
Interactions Involving Categorical Variables 39
 
Further Reading 41
 
Chapter 3 Central Tendency 42
 
Further Reading 49
 
Chapter 4 Variance 50
 
Degrees of Freedom 53
 
Variance 53
 
Variance: A Worked Example 55
 
Variance and Sample Size 58
 
Using Variance 59
 
A Measure of Unreliability 60
 
Confidence Intervals 61
 
Bootstrap 62
 
Non-constant Variance: Heteroscedasticity 65
 
Further Reading 65
 
Chapter 5 Single Samples 66
 
Data Summary in the One-Sample Case 66
 
The Normal Distribution 70
 
Calculations Using z of the Normal Distribution 76
 
Plots for Testing Normality of Single Samples 79
 
Inference in the One-Sample Case 81
 
Bootstrap in Hypothesis Testing with Single Samples 81
 
Student's t Distribution 82
 
Higher-Order Moments of a Distribution 83
 
Skew 84
 
Kurtosis 86
 
Reference 87
 
Further Reading 87
 
Chapter 6 Two Samples 88
 
Comparing Two Variances 88
 
Comparing Two Means 90
 
Student's t Test 91
 
Wilcoxon Rank-Sum Test 95
 
Tests on Paired Samples 97
 
The Binomial Test 98
 
Binomial Tests to Compare Two Proportions 100
 
Chi-Squared Contingency Tables 100
 
Fisher's Exact Test 105
 
Correlation and Covariance 108
 
Correlation and the Variance of Differences between Variables 110
 
Scale-Dependent Correlations 112
 
Reference 113
 
Further Reading 113
 
Chapter 7 Regression 114
 
Linear Regression 116
 
Linear Regression in R 117
 
Calculations Involved in Linear Regression 122
 
Partitioning Sums of Squares in Regression: SSY = SSR + SSE 125
 
Measuring the Degree of Fit, r2 133
 
Model Checking 134
 
Transformation 135
 
Polynomial Regression 140
 
Non-Linear Regression 142
 
Generalized Additive Models 146
 
Influence 148
 
Further Reading 149
 
Chapter 8 Analysis of Variance 150
 
One-Way ANOVA 150
 

About the author

Michael J. Crawley, FRS, Department of Biological Sciences, Imperial College of Science, Technology and Medicine. Author of three bestselling Wiley statistics titles and five life science books.

Product details

• Authors: Michael J Crawley, Michael J. Crawley, Michael J. (Imperial College of Science Crawley, Mj Crawley, Crawley Michael J.
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Paperback / Softback
• Released: 14.11.2014
• EAN: 9781118941096
• ISBN: 978-1-118-94109-6
• No. of pages: 368
• Dimensions: 174 mm x 245 mm x 20 mm
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; Statistik, Statistics, Angewandte Wahrscheinlichkeitsrechnung u. Statistik, Applied Probability & Statistics, R (Programm), Statistiksoftware / R, Statistical Software / R, Statistics - Text & Reference, Statistik / Lehr- u. Nachschlagewerke, Computational Statistics