JPSY_V9_N3_RP5 Neuromathematical Trichotomous Mixed Methods Analysis: Using the Neuroscientific Tri–Squared Test Statistical Metric as a Post Hoc Analytic To Determine North Carolina School of Science and Mathematics Leadership Efficacy James Edward Osler II Letita R. Mason Journal on Educational Psychology 2230–7141 9 3 44 61 Analysis, Education Science, Inventive Investigative Instrument, Investigation, LEQ [Leadership Efficacy Questionnaire], Leadership Efficacy, Mathematical Model, Mind Garden, Neuromathematics, Neuroscience, North Carolina School of Science and Mathematics, Outcomes, Post Hoc, Research, STEM, Self-Efficacy, Static Test, Statistics, Trichotomy, Tri–Squared Test, Variables, Variance This study examines the leadership efficacy amongst graduates of The North Carolina School of Science and Mathematics (NCSSM) for the classes of 2000 through 2007 from a neuroscientific and neuromathematic perspective. NCSSM alumni (as the primary unit of analysis) were examined using a novel neuromathematic post hoc method of analysis. This study is grounded in the theoretical construct that non-cognitive psychological (also called motivational) factors are core components of leadership efficacy (self-efficacy), indicative of NCSSM graduates (who had high academic performance and attained STEM [Science, Engineering, Technology, and Mathematics] degrees). In this neuroscientific mixed–methods analysis, a quantitative phase was conducted to collect the data captured by the Mind Garden Leadership Efficacy Questionnaire. A Post Hoc qualitative analysis was conducted in the second phase of the data analysis, using the applied neuromathematic Trichotomous–Squared Test methodology (that has an associated qualitative researcher–designed Inventive Investigative Instrument (Osler, 2012a) embedded within the statistical methodology). An additional outcome of the research investigation was the development of a new assessment methodology called the “Mason Leadership Efficacy Model”. November 2015 – January 2016 Copyright © 2016 i-manager publications. All rights reserved. i-manager Publications http://www.imanagerpublications.com/Article.aspx?ArticleId=3772