Quantitative Research Methods in Chaos and Complexity: From Probability to Post Hoc Regression Analyses

Abstract

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.

When Time Makes a Difference: Addressing Ergodicity and Complexity in Education

“…particularly good case in point to study complexity processes. The field of education has shown high responsiveness to the substantive aspects of dynamical thinking, such as the use of a complexity paradigm to analyze educational politics and policy (Osberg & Biesta, 2010), but there are also important methodological implications that come with the study of stability and change in educational systems that have not yet been fully appreciated, in spite of comprehensive discussions of the implications of complexity for qualitative research (Bloom, 2011;Bloom & Volk, 2007) as well as quantitative research (Gilstrap, 2013). This paper focuses on the latter perspective, which invites us to consider one implication which has not received its due recognition in the educational research literature, namely the study of how behavioral outcomes fluctuate in the course of time.…”

Moral approval of xenotransplantation in Egypt: associations with religion, attitudes towards animals and demographic factors

“…The purpose of the post-hoc regression models was to use exclusively the predictors that turned out to be significant in the first place, and therefore make the estimates more precise in the absence of non-significant predictors. This is a procedure that is recommended by some statisticians [ 37 ]. For the presentation of results in the post-hoc regression models, any associations that turned out to be statistically significant were obtained while controlling for the effect of other predictors.…”

Graph theoretic methods for the analysis of data in developing systems

“…In a similar vein, Koopmans (2014b) questioned the use of randomized controlled trials as a gold standard for education, and examined how a more dynamic systems approach to studies in education may produce a deeper understanding of what works in education. Gilstrap (2013) examines the issue of quantitative analyses directly, focusing on the need for more post hoc analyses when dealing with complex systems.…”