The Measurement of Association

This research monograph utilizes exact and Monte Carlo permutation statistical methods to generate probability values and measures of effect size for a variety of measures of association. Association is broadly defined to include measures of correlation for two interval-level variables, measures of association for two nominal-level variables or two ordinal-level variables, and measures of agreement for two nominal-level or two ordinal-level variables. Additionally, measures of association for mixtures of the three levels of measurement are considered: nominal-ordinal, nominal-interval, and ordinal-interval measures. Numerous comparisons of permutation and classical statistical methods are presented.

Unlike classical statistical methods, permutation statistical methods do not rely on theoretical distributions, avoid the usual assumptions of normality and homogeneity of variance, and depend only on the data at hand. This book takes a unique approach to explaining statistics by integrating a large variety of statistical methods, and establishing the rigor of a topic that to many may seem to be a nascent field. This topic is relatively new in that it took modern computing power to make permutation methods available to those working in mainstream research.

Written for a statistically informed audience, it is particularly useful for teachers of statistics, practicing statisticians, applied statisticians, and quantitative graduate students in fields such as psychology, medical research, epidemiology, public health, and biology. It can also serve as a textbook in graduate courses in subjects like statistics, psychology, and biology.

Paul W. Mielke, Jr. is Emeritus Professor at Colorado State University and a fellow of the American Statistical Association. He received a B.A. in mathematics from the University of Minnesota before training in meteorology at the University of Chicago for the U.S. Air Force. He earned an M.A. in mathematics from the University of Arizona and a Ph.D. in biostatistics from the University of Minnesota. In 1963 he joined the Department of Mathematics and Statistics at Colorado State University, retiring in 2002. His research interests are in permutation methods, meteorology, and environmental issues.

Janis E. Johnston works for the U.S. Government as a data analyst. She received B.S. degrees in mathematics and natural science from the University of Wyoming, her M.A. in sociology from the University of Wyoming, and her Ph.D. from Colorado State University. From 2007 to 2009 she was an American Association for the Advancement of Science, Science & Technology fellow and began government service after the fellowship. Her research interests are in permutation methods, statistical inference, and policy analysis.