Mathematics and Statistics in Anesthesiology

Abstract

Mathematics is the language of quantitative science, and probability and statistics are the extension of classical logic to real world data analysis and experimental design. The basics of mathematical functions and probability theory are summarized here, providing the tools for statistical modeling and assessment of experimental results. There is a focus on the Bayesian approach to such problems (ie, Bayesian data analysis); therefore, the basic laws of probability are stated, along with several standard probability distributions (eg, binomial, Poisson, Gaussian). A number of standard classical tests (eg, p values, the t-test) are also defined and, to the degree possible, linked to the underlying principles of probability theory. This review contains 5 figures, 1 table, and 15 references. Keywords: Bayesian data analysis, mathematical models, power analysis, probability, p values, statistical tests, statistics, survey design