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The Tri–Sigma Test: The Triple–Sigma Trichotomous Summation Triostatistic for the Viability, Verifiability, and Validityof Multiple Tri–Squared Test Outcomes

James Edward Osler II*

Associate Professor, Department of Curriculum and Instruction, North Carolina Central University, USA.

Periodicity:January - March'2018
DOI : https://doi.org/10.26634/jmat.7.1.14026

Abstract

This paper provides a novel statistical methodology called “Triple or Tri–Sigma” (“Tri-Σ”) that is designed to conceptually add to the research that has been conducted on and with the Tri–Squared Test (Osler, 2012a). The Tri–Sigma Test is an advanced statistical procedure that is used to analyze multiple Tri–Squared Tests that have been delivered at different times. Tripleseries summation provides an innovative way of investigating the data derived from a series of researchbased investigative instruments that are known as “Trichotomous Tri-Squared Test Triple-I's” (Osler and Mansaray, 2013b). The Triple–I is directly derived from specific research questions as an in-depth associated instrument [first introduced in the i-manager's Journal on Mathematics as a part of the “Tri-Squared Test” (Osler, 2012a)]. This new approach to research inquiry lends additional strength to trichotomous research designs. Trichotomous tests can now be offered at multiple stages, multiple times, and in multiple ways with multiple research questions.

Keywords

Mid-Test, Multiple Tests, Pre-Test, Post-Test, Research, Summation, Tri–Sigma Test, Tri-Squared Test, Triple Summation, Trichotomy, Triple-I, Trichotomous Categorical Variables, Trichotomous Outcome Variables, Trichotomous Test Procedures, Triostatistics

How to Cite this Article?

Osler, J. E., II. (2018). The Tri-Sigma Test: The Triple-Sigma Trichotomous Summation Triostatistic for the Viability, Verifiability, and Validity of Multiple Tri-Squared Test Outcomes. i-manager’s Journal on Mathematics, 7(1), 1-12. https://doi.org/10.26634/jmat.7.1.14026

References

[1]. Apostol, T. M. (1967). Calculus, second edition, Volume one: One-variable calculus, with an introduction to linear algebra. 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. (2012a). 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, 1(3), 23-32.

[4]. Osler, J. E. & Waden, C. (2012b). 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, 7(3), 11-23.

[5]. Osler, J. E. (2013a). The Psychometrics of Educational Science: Designing Trichotomous Inventive Investigative Instruments for Qualitative and Quantitative for Inquiry. i-manager's Journal on Educational Psychology, 8(3), 15-22.

[6]. Osler, J. E. & Mansaray M. A. (2013b). Technology Engineering Online Learner Metrics to Analyze Instructional Efficacy. i-manager's Journal of Educational Technology, 10 (2), 43-59.

[7]. Osler, J. E. (2014). 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, 12(3), 27-39.

[8]. Osler, J. E. (2015). 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, 4(1), 11-31.

[9]. Osler, J. E. (2016). MULTRICOR [“Multiple Trichotomous Correlation” Analysis]: The Post Hoc Examination and Measurement of Statistically Significant Tri-Squared Tests to Determine the Total and Internal Strength of Relationships between Trichotomous Variables used for Dynamic Psychometric Circuit Assessment. i-manager's Journal on Circuits and Systems, 4(1), 1-11.

[10]. Osler, J. E., (2017). Triangular Equation Modeling [TEM]: The Base Operation, Basic Rationale, and Foundational Logic that is the Basis for “Research Architectural Metrics” that are Essential to the Planning, Scope, and Schema of Trichotomous Research Designs. i-manager's Journal on Mathematics, 6(3), 1-11.

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