Abstract

This monograph provides an epistemological rational for a novel science grounded in trichotomous statistical analysis metrics. Triology is the study of the trifold nature of phenomena. It has its foundation in the mathematical “Law of Trichotomy”. Triology is measured using the Tri–Squared Statistic. Advanced post hoc measurement of Triology is conducted using Triostatistics (or more simply “Triostat”) is the application of Post Hoc measures to the statistically significant outcomes of the Trichotomous Squared Test. Triology involves a variety of concepts that are defined using robust and rigorous calculations provided in this paper. It uses its computations to provide further insight on the inner workings of the threefold aspects of nature. The topology and taxonomy of the triology are covered in detail along with Tri–Squared and Triostatistics procedures.

Keywords
Analysis, Holistic, MULTICOVA, Outcomes, Post Hoc, Research, Results, Statistics, Taxonomy, Topology, Tri–Center Analysis, Tri–Cubed Tri–Coordinate Meta–Analysis Test, The Trimetric Tri–Squared Test, TRICOM, TRICOVA, TRIMOD, TRINOVA, Trichotomous, Trichotomous Calculations, Trichotomous Categorical Variables, Trichotomous Outcome Variables, Trichotomous Progression Analysis, Triology, Triostatistics, Tri–Squared, Tri–Squared Test, Tri–Squared Mean Cross Comparative Analysis, Tri–Symmetrical
How to Cite this Article?
Osler II,J.E. (2017). Triology: A Novel, Innovative, and in–Depth Science Concerned with the Mathematical Triadic, Tripartite, and Triplex Components, Content, and Cycles of Life, Learning, Logic, and the Universal Aspects of Nature. i-manager’s Journal on Mathematics, 6(1), 1-17.
References
[1]. Apostol, T.M., (1967). Calculus, Volume one: One–variable Calculus, with an Introduction to Linear Algebra, 2nd Edition, Waltham, MA: Blaisdell.
[2]. Kant, I., (2007). Critique of Pure Reason (based on Max Müller's Translation). P. Classics a Division of Pearson PLC. New York, NY
[3]. Osler, J.E., (2010). Visualus™ © Visioneering Volumetrically: The Mathematics of the Innovative Problem–Solving Model of Inventive Instructional Design (First edition). OSI: Publishing Division. Lulu, Morrisville NC.
[4]. Osler, J.E., (2012). “Trichotomy – Squared – A novel mixed methods test and research procedure designed to analyze, transform, and compare qualitative and quantitative data for education scientists who are administrators, practitioners, teachers, and technologists”. i-manager's Journal on Mathematics, Vol.1, No.3, pp.23–31, ISSN Print: 2277-5129, ISSN Online: 2277-5137.
[5]. Osler, J.E., and Waden, C., (2012). “Using innovative technical solutions as an intervention for at risk students: A meta–cognitive statistical analysis to determine the impact of ninth grade freshman academies, centers, and center models upon minority student retention and achievement”. i-manager's Journal on School Educational Technology, Vol.7, No.3, pp.11–23, ISSN Print: 0973-2217, ISSN Online: 2230-7133.
[6]. Osler, J.E., (2013a). “Algorithmic Triangulation Metrics for Innovative Data Transformation: Defining the Application Process of the Tri–Squared Test”. i-manager's Journal on Mathematics, Vol.2, No.2, pp.10–16, ISSN Print: 2277-5129, ISSN Online: 2277-5137.
[7]. Osler, J.E., (2013b). “The Triangulation Algorithmic: A Transformative Function for Designing and Deploying Effective Educational Technology Assessment Instruments”. i-manager's Journal of Educational Technology, Vol.10, No.1, pp.46–54, , ISSN Print: 0973-0559, ISSN Online: 2230-7125.
[8]. Osler, J.E., (2013c). “Transformational Research Engineering: Research Design Metrics for In–Depth and Empowering K–12 Teacher Professional Development”. i-manager's Journal on School Educational Technology, Vol.9, No.1, pp.43–60, ISSN Print: 0973-2217, ISSN Online: 2230-7133.
[9]. Osler, J.E., (2013d). “The Psychometrics of Educational Science: Designing Trichotomous Inventive Investigative Instruments for Qualitative and Quantitative for Inquiry”. i-manager's Journal on Educational Psychology, Vol.8, No.3, pp.15–22, ISSN Print: 0973-8827, ISSN Online: 2230-7141.
[10]. Osler, J.E., (2013e). “The Psychological Efficacy of Education as a Science through Personal, Professional, and Contextual Inquiry of the Affective Learning Domain”. i-manager's Journal on Educational Psychology, Vol.6, No.4, pp.36–41, ISSN Print: 0973-8827, ISSN Online: 2230-7141.
[11]. Osler, J.E., (2013f). “Tri–Squared Mean Cross Comparative Analysis: An Advanced Post Hoc Qualitative and Quantitative Metric for a More In–Depth Examination of the Initial Research Outcomes of the Tri–Square Test”. i-manager's Journal of Educational Technology, Vol.10, No.3, pp.35–41, ISSN Print: 0973-0559, ISSN Online: 2230-7125.
[12]. Osler, J.E., (2014a). “Triostatistics: The Application of Innovative In–Depth Advanced Post Hoc Statistical Metrics for the Assessment and Analysis of Statistically Significant Tri–Squared Test Outcomes”. Kentucky Journal of Excellence in College Teaching and Learning, Vol.12, No.3, pp.27–39.
[13]. Osler, J.E., (2014b). “Introducing TRINOVA: ‘Trichotomous Nomo graphical Variance’ A Post Hoc Advanced Statistical Test of Between and within Group Variances of Trichotomous Categorical and Outcome Variables of a Significant Tri–Squared Test”. i-manager's Journal on Mathematics, Vol.3, No.4, pp.1–14, ISSN Print: 2277-5129, ISSN Online: 2277-5137.
[14]. Osler, J.E., (2014c). “Trichotomous Progression Analysis: An Advanced Comprehensive Statistical Post Hoc Measure of the Tri–Squared Test”. i-manager's Journal on Mathematics, Vol.3, No.3, pp.7–20, ISSN Print: 2277-5129, ISSN Online: 2277- 5137.
[15]. Osler, J.E., (2014d). “The Trimetric Tri–Squared Test: An Advanced Post Hoc Exact Test designed to Statistically determine Construct Validity”. i-manager's Journal on Mathematics, Vol.3, No.2, pp.27–35, ISSN Print: 2277-5129, ISSN Online: 2277- 5137.
[16]. Osler, J.E., (2014e). “Tri–Center Analysis: Determining Measures of Trichotomous Central Tendency for the Parametric Analysis of Tri–Squared Test Results”. i-manager's Journal of Educational Technology, Vol.11, No.1, pp. 23–30, ISSN Print: 0973- 0559, ISSN Online: 2230-7125.
[17]. Osler, J.E., (2014f). “Calculating Tri–Symmetrical Analytics: A Guide into the In–Depth Processes associated with the Post Hoc Advanced Statistical Metrics used to determine the Value of Significant Tri–Squared Tests”. i-manager's January– March Journal on Mathematics, Vol.3, No.1, pp.14–26, ISSN Print: 2277-5129, ISSN Online: 2277-5137
[18]. Osler, J.E., (2015a). “TRICOM: ‘Trichotomous Comparative Oneness of Measurement’ The Functional Analysis of Trichotomous Squared Single Case Research for the Application of the Tri–Squared Test to Single Subject Research Designs”. i-manager's Journal on Mathematics, Vol.4, No.2, pp.11–21, ISSN Print: 2277-5129, ISSN Online: 2277-5137.
[19]. Osler, J.E. (2015b). “Introducing MULTICOVA: ‘Multiple Trichotomous Coefficient of Variation Analysis’ The Advanced Post Hoc Test of the Tri–Squared Coefficient of Variation”. i-manager's Journal on Mathematics, Vol.4, No.1, pp.11–31, ISSN Print: 2277-5129, ISSN Online: 2277-5137 .
[20]. Rust, J., and Golombok, S., (1989). Modern Psychometrics: The Science of Psychological Assessment, (2nd ed.). Florence, KY, US: Taylor & Frances/Routledge.
[21]. Sensagent, (2012). Trichotomy (Mathematics). Retrieved: http://dictionary.sensagent.com/trichotomy%20 (mathematics)/ en–en/
[22]. Singh, S., (1997). Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem. A. Books - A Division of Random House. New York, NY.
[23]. Stevens, J.P. (2002). Applied Multivariate Statistics for the Social Sciences. Mahwah, NJ: Lawrence Erblaum.
Username / Email
Password
Don't have an account?  Sign Up
  • If you would like institutional access to this content, please recommend the title to your librarian.
    Library Recommendation Form
  • If you already have i-manager's user account: Login above and proceed to purchase the article.
  • New Users: Please register, then proceed to purchase the article.

Purchase Instant Access

PDF
10
USD

250
INR

HTML
10
USD

250
INR


We strive to bring you the best. Your feedback is of great value to us. Feel free to post your comments and suggestions.