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The Trimetric Tri–Squared Test: An Advanced Post Hoc Exact Test Designed to Statistically Determine Construct Validity

James Edward Osler II*

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

Periodicity:April - June'2014
DOI : https://doi.org/10.26634/jmat.3.2.3001

Abstract

This monograph provides a logical and epistemological rational for the Post Hoc testing of the instrumentation used in the transformative process of qualitative data into quantitative outcomes through the Tri–Squared Test introduced in the Journal on Mathematics and expounded upon in the Journal on Educational Psychology. An advanced Post Hoc statistical measure using the Del Differential Operator and Matrix Algebra is used to determine the Construct Validity of researcher designed instruments using the Tri–Squared research design parameters. This additional novel approach to advanced data analysis adds additional value to Tri–Squared as an innovative mixed methods approach to investigative inquiry.

Keywords

Algebra, Categorical, Construct Validity, Del Operator, Exact Test, Instrument, Investigation, Mathematical Model, Nabla, Outcomes, Post Hoc, Research, Statistics, Trichotomy, Trimetric Test, Validity, and Variables.

How to Cite this Article?

Osler, J. E., II. (2014). The Trimetric Tri–Squared Test: An Advanced Post Hoc Exact Test Designed to Statistically Determine Construct Validity. i-manager’s Journal on Mathematics, 3(2), 13-21. https://doi.org/10.26634/jmat.3.2.3001

References

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[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]. James Edward Osler (2012). Introducing: 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), Jul - Sep 2012 Print ISSN 2277-5129, E-ISSN 2277-5137, pp. 23-32.

[4]. James Edward Osler and Carl Waden(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, 8(2), Sep-Nov 2012, Print ISSN: 0973-2217, E-ISSN: 2230-7133, pp. 11-23.

[5]. James Edward Osler (2013). The Psychometrics Of Educational Science: Designing Trichotomous Inventive Investigative Instruments For Qualitative And Quantitative Inquiry. i-manager's Journal on School Educational Technology, 8(3), Dec-Feb 2013, Print ISSN: 0973-2217, E-ISSN: 2230-7133, pp. 15-22.

[6]. James Edward Osler (2013). 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. 6(4) Feb-April 2013 Print ISSN 0973-8827, E-ISSN 2230-7141, pp. 36-41.

[7]. James Edward Osler II (2013). Algorithmic Triangulation Metrics for Innovative Data Transformation: Defining The Application Process of The Tri–Squared Test. i-manager's Journal on Mathematics, 2(2) Apr - Jun 2013 Print ISSN 2277-5129, EISSN 2277-5137, pp. 10-16.

[8]. Rust, J. & Golombok, S. (1989). Modern psychometrics: The science of psychological assessment(2nd ed.). Florence, KY, US: Taylor & Frances/Routledge.

[9]. Sensagent: Retrieved, May 9, 2012: http://dictionary.sensagent.com/trichotomy+(mathematics)/en-en/

[10]. 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.

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