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Extending the Johnson-Neyman Procedure to Categorical Independent Variables: Mathematical Derivations and Computational Tools

Montoya, Amanda Kay
http://rave.ohiolink.edu/etdc/view?acc_num=osu1469104326

Abstract Details

2016, Master of Arts, Ohio State University, Psychology.
Moderation analysis is used throughout many scientific fields, including psychology and other social sciences, to model contingencies in the relationship between some independent variable (X) and some outcome variable (Y) as a function of some other variable, typically called a moderator (M). Inferential methods for testing moderation provide only a simple yes/no decision about whether the relationship is contingent. These contingencies can often be complicated. Researcher often need to look closer. Probing the relationship between X and Y at different values of the moderator provides the researcher with a better understanding of how the relationship changes across the moderator. There are two popular methods for probing an interaction: simple slopes analysis and the Johnson-Neyman procedure. The Johnson-Neyman procedure is used to identify the point(s) along a continuous moderator where the relationship between the independent variable and the outcome variable transition(s) between being statistically significant to nonsignificant or vice versa. Implementation of the Johnson-Neyman procedure when X is either dichotomous of continuous is well described in the literature; however, when X is a multicategorical variable it is not clear how to implement this method. I begin with a review of moderation and popular probing techniques for dichotomous and continuous X. Next, I derive the Johnson-Neyman solutions for three groups and continue with a partial derivation for four groups. Solutions for the four-group derivation rely on finding the roots of an eighth-degree polynomial for which there is no algebraic solution. I provide an iterative computer program for SPSS and SAS that solves for the Johnson-Neyman boundaries for any number of groups. I describe the performance of this program, relative to known solutions, and typical run-times under a variety of circumstances. Using a real dataset, I show how to analyze data using the tool and how to interpret the results. I conclude with some consideration about when to use and when not to use this tool, future directions, and general conclusions.
Andrew Hayes (Advisor)
Michael Edwards (Committee Member)
Duane Wegener (Committee Member)
106 p.
Applied Mathematics; Behavioral Sciences; Biostatistics; Experimental Psychology; Psychology; Quantitative Psychology; Statistics
Johnson-Neyman; moderation; regression analysis; probing; interactions; ANCOVA

Recommended Citations

Citations

  • Montoya, A. K. (2016). Extending the Johnson-Neyman Procedure to Categorical Independent Variables: Mathematical Derivations and Computational Tools [Master's thesis, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1469104326

    APA Style (7th edition)

  • Montoya, Amanda. Extending the Johnson-Neyman Procedure to Categorical Independent Variables: Mathematical Derivations and Computational Tools. 2016. Ohio State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1469104326.

    MLA Style (8th edition)

  • Montoya, Amanda. "Extending the Johnson-Neyman Procedure to Categorical Independent Variables: Mathematical Derivations and Computational Tools." Master's thesis, Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1469104326

    Chicago Manual of Style (17th edition)

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This open access ETD is published by The Ohio State University and OhioLINK.