This monograph provides an epistemological rational for novel “Trichotomous Covariance” statistic represented by the acronym [“TRICOVA”]. This new statistic is an innovative in depth way of investigating a Post Hoc Tri–Squared Test as an advanced data analytical methodology. TRICOVA is a detailed statistical procedure for the internal testing of the outcomes of a significant transformation of qualitative data into quantitative outcomes through the Tri–Squared Test (first introduced in the i-manager’s Journal on Mathematics, and detailed further in the Journal on Educational Technology, Journal on School Educational Technology, and in the Journal on Educational Psychology). TRICOVA as an advanced statistical procedure; is designed to measure the overall size of the movement (or change) between inputted and outputted Tri–Squared variables. It is also designed to identify the magnitude and type of covariant relationship in existence between Tri–Squared Test qualitative and quantitative variables. This new innovative approach to the advanced statistical post hoc metrics of the Tri–Squared Test adds an additional layer of richness and insight into the inner workings of the Tri–Squared Test. It also adds considerable value to the mixed methods approach of research design that involves the holistic combination and comparison of qualitative and quantitative data outcomes. Two TRICOVA equations are presented as well as the entire process of advanced statistical Tri–Covariance analytics that display how to conduct Trichotomous Covariance inquiry.