Krzanowski W.J. Statistical Principles and Techniques in Scientific and Social Research

Oxford University Press, 2007. — 256 p. — ISBN: 0199213097, 978-0199213092.
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 probability 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.Probability.
Foundations of probability theory.
Sample space; definition of probability of an event.
Conditional probability, independence and the multiplication rule.
The addition rule and mutually exclusive events.
The total probability theorem.
Bayes’ theorem.
Relative frequency, subjective probability, and an axiomatic structure.
Populations, Samples and Data Summary.
Populations.
Samples and sampling.
Random samples and some variants.
Categorical measurements: cross-tabulations.
Numerical measurements: summary statistics.
Summary distributions.
Population Models.
Probability distributions.
Type of measurement.
Shape of distribution.
Some common probability models.
Choosing a model.
Estimating parameter values.
Statistical Inference — the Frequentist Approach.
Sampling and sampling distributions.
Statistical inference.
Confidence intervals.
Interpretation of confidence intervals.
Hypothesis testing.
Nonparametric tests.
Statistical Inference — Bayesian and Other Approaches.
Bayesian inference.
Fiducial inference and likelihood methods.
Decision theory.
Linear Models and Least Squares.
Correlation.
Explanation and prediction.
Simple linear regression.
Testing significance of regression.
Multiple regression.
Model building.
Analysis of variance.
Observational data versus experimental data.
Designed experiments.
The general linear model.
Generalising the Linear Model.
Checking the linear model assumptions.
Non-constant variance: weighted regression.
Non-linear models.
Non-normality: generalised linear models.
Non-independence.
Tailpiece.
Association between Variables.
Measuring and testing association.
Explaining associations: partial correlations.
Explaining associations: latent variable models.
Factor analysis methodology.
Other latent variable models.
Exploring Complex Data Sets.
Dimensionality and simplification.
No a-priori structure: principal component analysis.
Grouping of the individuals: canonical variate analysis.
Grouping of the variables: canonical correlation analysis.
Scaling methods.
Unsupervised classification; cluster analysis.
Supervised classification; discriminant analysis.
Inferential techniques.
Missing values.
Special Topics.
Repeated observations.
Time series.
Analysis of extremes.
Survival data.Sources and Further Reading.