Quantitative research methods in chaos and complexity: from probability to post hoc regression analyses

© Copyright 2013. The author, DONALD GILSTRAP, assigns to the University of Alberta and other educational and non-profit institutions a non-exclusive license to use this document for personal use and in courses of instruction provided that the article is used in full and this copyright statement is reproduced. The author also grant a non-exclusive license to the University of Alberta to publish this document in full on the World Wide Web, and for the document to be published on mirrors on the World Wide Web. Any other usage is prohibited without the express permission of the authors.In addition to qualitative methods presented in chaos and complexity theories in educational research, this article addresses quantitative methods that may show potential for future research studies. Although much in the social and behavioral sciences literature has focused on computer simulations, this article explores current chaos and complexity methods that have the potential to bridge the divide between qualitative and quantitative, as well as theoretical and applied, human research studies. These methods include multiple linear regression, nonlinear regression, stochastics, Monte Carlo methods, Markov Chains, and Lyapunov exponents. A postulate for post hoc regression analysis is then presented as an example of an emergent, recursive, and iterative quantitative method when dealing with interaction effects and collinearity among variables. This postulate also highlights the power of both qualitative and quantitative chaos and complexity theories in order to observe and describe both the micro and macro levels of systemic emergence