JMAT_V5_N4_RP4 Advanced Tri–Analytic Trichotomous Post Hoc Repeated Measures for Tri–Squared Test Inventive Investigative Instrument Items Using Trichotomous Variation Analysis [Trivariant Analysis] James Edward Osler II Journal on Mathematics 2277-5137 5 4 30 46 Analytics, Instrument, Investigation, Mathematical Model, Outcomes, Post Hoc, Research, Static Test, Statistics, Trichotomy, Tri–Analytic, Tri–Squared, Tri–Squared Tests, Trivariant, Variables, Variation This monograph provides an epistemological rational for the Post Hoc testing of the transformative process of qualitative data into quantitative outcomes through the Tri–Squared Test introduced in the Journal on Mathematics, and further detailed in the Journal on Educational Technology, Journal on School Educational Technology, and in Journal on Educational Psychology articles. Advanced statistical measures of internal research instrument Trichotomous Repeated Measures and Trichotomous Variation of significant Transformative Trichotomy–Squared [Tri–Squared] research variables are analyzed. This additional novel approach to advanced Tri–Squared data analysis adds additional value to the mixed methods approach of research design that involves the holistic combination and comparison of qualitative and quantitative data outcomes. Multiple sequential mathematical models are provided that illustrate the entire process of advanced Tri–Analytic inquiry. October - December 2016 Copyright © 2016 i-manager publications. All rights reserved. i-manager Publications http://www.imanagerpublications.com/Article.aspx?ArticleId=8308