Statistical Principles and Techniques in Scientific and Social Research

by Krzanowski, Wojtek J.

• ISBN13: 9780199213108
• ISBN10: 0199213100
• Format: Hardcover
• Copyright: 2007-08-07
• Publisher: Oxford University Press

Summary

This graduate-level text provides a survey of the logic and reasoning underpinning statistical analysis, as well as giving a broad-brush overview of the various statistical techniques that play a major roll in scientific and social investigations. Arranged in rough historical order, the text starts with the ideas of provability that underpin statistical methods and progresses through the developments of the nineteenth and twentieth centuries to modern concerns and solutions. Assuming only a basic level of Mathematics and with numerous examples and illustrations, this text presents a valuable resource not only to the experienced researcher but also to the student, by complementing courses in a wide range of substantive areas and enabling the reader to rise above the details in order to see the overall structure of the subject.

Author Biography

Professor Krzanowski completed his PhD in Applied Statistics at Reading University in 1974. Between 1974 and 1990 he was successively Lecturer, Senior Lecturer and Reader in Applied Statistics at Reading University, and was Professor of Statistics at Exeter University from 1990 to 2005. Taking early retirement in 2005, he is now Emeritus Professor, while continuing to carry out research and to do some part-time teaching. His professional interests are in Multivariate Analysis, Statistical Modelling, Classification and Computational Methods. Publications include 5 books, over 30 contributions to books, and over 90 articles in scientific journals. He is a former Joint Editor of the Journal of the Royal Statistical Society, Series C, and has been on the Editorial Board of the Journal of Classification since its first issue in 1984.

Table of Contents

Preface	p. xi
Probability	p. 1
Introduction	p. 1
Foundations of probability theory	p. 3
Sample space; definition of probability of an event	p. 4
Conditional probability, independence and the multiplication rule	p. 7
The addition rule and mutually exclusive events	p. 10
The total probability theorem	p. 13
Bayes' theorem	p. 15
Relative frequency, subjective probability, and axiomatic structure	p. 19
Populations, Samples and Data Summary	p. 23
Introduction	p. 23
Populations	p. 23
Samples and sampling	p. 27
Random samples and some variants	p. 29
Categorical measurements: cross-tabulations	p. 31
Numerical measurements: summary statistics	p. 33
Summary distributions	p. 37
Population Models	p. 41
Introduction	p. 41
Probability distributions	p. 42
Type of measurement	p. 44
Shape of distribution	p. 46
Some common probability models	p. 47
Choosing a model	p. 52
Estimating parameter values	p. 53
Statistical Inference-the Frequentist Approach	p. 61
Introduction	p. 61
Sampling and sampling distributions	p. 62
Statistical inference	p. 69
Confidence intervals	p. 70
Interpretation of confidence intervals	p. 76
Hypothesis testing	p. 77
Nonparametric tests	p. 89
Statistical Inference-Bayesian and Other Approaches	p. 95
Introduction	p. 95
Bayesian inference	p. 97
Fiducial inference and likelihood methods	p. 107
Decision theory	p. 109
Linear Models and Least Squares	p. 113
Introduction	p. 113
Correlation	p. 115
Explanation and prediction	p. 118
Simple linear regression	p. 119
Testing significance of regression	p. 122
Multiple regression	p. 125
Model building	p. 127
Analysis of variance	p. 131
Observational data versus experimental data	p. 134
Designed experiments	p. 136
The general linear model	p. 139
Generalising the Linear Model	p. 143
Introduction	p. 143
Checking the linear model assumptions	p. 144
Non-constant variance: weighted regression	p. 151
Non-linear models	p. 153
Non-normality: generalised linear models	p. 156
Non-independence	p. 160
Tailpiece	p. 162
Association between Variables	p. 165
Introduction	p. 165
Measuring and testing association	p. 166
Explaining associations: partial correlations	p. 172
Explaining associations: latent variable models	p. 175
Factor analysis methodology	p. 177
Other latent variable models	p. 183
Exploring Complex Data Sets	p. 187
Introduction	p. 187
Dimensionality and simplification	p. 189
No a-priori structure: principal component analysis	p. 191
Grouping of the individuals: canonical variate analysis	p. 195
Grouping of the variables: canonical correlation analysis	p. 199
Scaling methods	p. 200
Unsupervised classification; cluster analysis	p. 203
Supervised classification; discriminant analysis	p. 207
Inferential techniques	p. 211
Missing values	p. 213
Special Topics	p. 215
Introduction	p. 215
Repeated observations	p. 216
Time series	p. 218
Analysis of extremes	p. 221
Survival data	p. 223
Conclusion	p. 225
Sources and Further Reading	p. 227
References	p. 229
Index	p. 231
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