Statistical Principles and Techniques in Scientific and Social Research

Contents......Page 8
Preface......Page 12
Introduction......Page 16
Foundations of probability theory......Page 18
Sample space; definition of probability of an event......Page 19
Conditional probability, independence and the multiplication rule......Page 22
The addition rule and mutually exclusive events......Page 25
The total probability theorem......Page 28
Bayes' theorem......Page 30
Relative frequency, subjective probability, and an axiomatic structure......Page 34
Populations......Page 38
Samples and sampling......Page 42
Random samples and some variants......Page 44
Categorical measurements: cross-tabulations......Page 46
Numerical measurements: summary statistics......Page 48
Summary distributions......Page 52
Introduction......Page 56
Probability distributions......Page 57
Type of measurement......Page 59
Shape of distribution......Page 61
Some common probability models......Page 62
Choosing a model......Page 67
Estimating parameter values......Page 68
Introduction......Page 76
Sampling and sampling distributions......Page 77
Statistical inference......Page 84
Confidence intervals......Page 85
Interpretation of confidence intervals......Page 91
Hypothesis testing......Page 92
Nonparametric tests......Page 104
Introduction......Page 110
Bayesian inference......Page 112
Fiducial inference and likelihood methods......Page 122
Decision theory......Page 124
Introduction......Page 128
Correlation......Page 130
Explanation and prediction......Page 133
Simple linear regression......Page 134
Testing significance of regression......Page 137
Multiple regression......Page 140
Model building......Page 142
Analysis of variance......Page 146
Observational data versus experimental data......Page 149
Designed experiments......Page 151
The general linear model......Page 154
Introduction......Page 158
Checking the linear model assumptions......Page 159
Non-constant variance: weighted regression......Page 166
Non-linear models......Page 168
Non-normality: generalised linear models......Page 171
Non-independence......Page 175
Tailpiece......Page 177
Introduction......Page 180
Measuring and testing association......Page 181
Explaining associations: partial correlations......Page 187
Explaining associations: latent variable models......Page 190
Factor analysis methodology......Page 192
Other latent variable models......Page 198
Introduction......Page 202
Dimensionality and simplification......Page 204
No a-priori structure: principal component analysis......Page 206
Grouping of the individuals: canonical variate analysis......Page 210
Grouping of the variables: canonical correlation analysis......Page 214
Scaling methods......Page 215
Unsupervised classification; cluster analysis......Page 218
Supervised classification; discriminant analysis......Page 222
Inferential techniques......Page 226
Missing values......Page 228
Introduction......Page 230
Repeated observations......Page 231
Time series......Page 233
Analysis of extremes......Page 236
Survival data......Page 238
Conclusion......Page 240
Sources and Further Reading......Page 242
References......Page 244
B......Page 246
C......Page 247
E......Page 248
H......Page 249
L......Page 250
M......Page 251
P......Page 252
R......Page 253
S......Page 254
V......Page 255
Z......Page 256