JMAT_V5_N3_RP1 James Edward Osler II Journal on Mathematics 2277-5137 5 3 8 26 Algorithmic Model, Algorithmics, Cartesian Coordinates, Geometric Vectors, Models, Research Engineering, Triangulation, Trichotomy, Tri–Squared, Vector This work provides a mathematical and an epistemological rational for the transformative process of qualitative data into quantitative outcomes through the Tri–Squared Test. The design of fixed-parameter algorithms for research engineering can prove to be beneficial to a variety of fields of learning. This novel methodology provides statistical power and mathematical elegance to research outcomes. It is a comprehensive approach that has a wide range of applicability as it practically addresses important and relevant problems with sample sizes that are small and research arenas that are rather complex. This research is the continuation of a dynamic mixed methods approach that is a transformative process which changes qualitative data into quantitative outcomes through the Tri–Squared statistical measure first introduced in i-manager's Journal of Mathematics. July - September 2016 Copyright © 2016 i-manager publications. All rights reserved. i-manager Publications http://www.imanagerpublications.com/Article.aspx?ArticleId=8224