This monograph provides an epistemological rational for the design of a novel post hoc statistical measure called "Tri-Center Analysis". This new statistic is designed to analyze the post hoc outcomes of the Tri-Squared Test. In Tri-Center Analysis trichotomous parametric inferential parametric statistical measures are calculated from statistically significant Tri-Squared Test data. The Tri-Squared Test was first introduced in i-manager's "Journal on Mathematics" as a qualitative to quantitative transformative mixed methods data analysis procedure. Tri-Center Analysis is an advanced statistical post hoc holomorphic that rigorously examines trichotomous investigative inquiry outcomes as in-depth parametric relations.