What Makes Variables Random: Probability for the Applied Researcher
provides an introduction to the foundations of probability that
underlie the statistical analyses used in applied research. By
explaining probability in terms of measure theory, it gives the
applied researchers a conceptual framework to guide statistical
modeling and analysis, and to better understand and interpret
results. The book provides a conceptual understanding of
probability and its structure. It is intended to augment existing
calculus-based textbooks on probability and statistics and is
specifically targeted to researchers and advanced undergraduate and
graduate students in the applied research fields of the social
sciences, psychology, and health and healthcare sciences. Materials
are presented in three sections. The first section provides an
overall introduction and presents some mathematical concepts used
throughout the rest of the text. The second section presents the
basic structure of measure theory and its special case of
probability theory. The third section provides the connection
between a conceptual understanding of measure-theoretic probability
and applied research. This section starts with a chapter on its use
in understanding basic models and finishes with a chapter that
focuses on more complicated problems, particularly those related to
various types and definitions of analyses related to hierarchical
modeling.
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