Moving beyond the Ordinal Methodological Controversy: A Systematic Review (Manuscript 1). Cubic Spline Interpolation for the Treatment of Ordinal Outcome Data in Education: A Model Fit Comparison of Parallel Approaches (Manuscript 2). Cubic Spline Interpolation for the Treatment of Ordinal Outcome Data in Education: An Empirical Examination of Select Approaches (Manuscript 3)

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Data; Educational Research; Statistical Analysis; Social Sciences; Behavioral Sciences; Validity

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Moving Beyond the Ordinal Methodological Controversy: A Systematic Review (Manuscript 1): Ordinal outcome data is a common byproduct of education research. Yet more than seventy-five years after the development of Stevens' original measurement framework, the permissibility of select analytic techniques to ordinal outcome data remains a topic of debate. Accordingly, the purpose of this paper was to provide the necessary background from which to begin considering alternative means for examining such data. Peer-reviewed and published journal articles concerned with the ordinal controversy were obtained from Web of Science via systematic review techniques. Additional sources covering statistical analysis were also referenced in order to provide an encompassing description of the intellectual landscape that is ordinal methodology. While by no means meant to inspire consensus, this paper is designed as a concise resource for both beginner and advanced researchers alike to be apprised of their data analysis options. Cubic Spline Interpolation for the Treatment of Ordinal Outcome Data in Education: A Model Fit Comparison of Parallel Approaches (Manuscript 2): Cubic spline interpolation is used extensively in science, technology, engineering, and mathematics disciplines, but has yet to find application within the realm of education. Accordingly, the purpose of this comparative methodological exploration was to juxtapose this novel approach with three procedures common to the social and behavioral sciences. Using simulated data combined with adapted computer code, this study aimed to determine the theoretical and utilitarian significance of cubic spline interpolation for the treatment of ordinal outcome data in education. Results ultimately showed that cubic spline interpolation outperformed linear regression, logistic regression, and ordinal logistic regression when working with leptokurtotic and platykurtotic ordinal outcome data. Furthermore, cubic spline interpolation performed the same or better than linear regression regardless of ordinal distribution and better than ordinal logistic regression when working with negatively skewed, leptokurtotic, and platykurtotic ordinal outcome data. Such a result not only highlights the problem-solving potential of cubic spline interpolation but more importantly opens the door for investigation into other statistical models largely unconsidered by social and behavioral science researchers. Cubic Spline Interpolation for the Treatment of Ordinal Outcome Data in Education: An Empirical Examination of Select Approaches (Manuscript 3): Cubic spline interpolation is a promising method of nonparametric regression in the social and behavioral sciences, but currently lacks empirical testing. Therefore, the purpose of this comparative methodological exploration was to replicate and extend earlier work rooted in simulation. Using cross-sectional data from the Education Longitudinal Study of 2002 together with adapted computer code, this study sought to validate the problem-solving potential of cubic spline interpolation for the treatment of ordinal outcome data in education. Replication results demonstrated that cubic spline interpolation outperformed linear regression on markers of model fit. In contrast, extension results revealed that linear regression outperformed cubic spline interpolation on markers of coefficient precision. Such results both corroborate the applicability of cubic spline interpolation while also highlighting an urgent need for continued research into its information value. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

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2023

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