Mathematics that Clarify Slope & Scale, Help Set Standards, and Improve Interrater Agreement on Time-Series Graphs
Date of Award
Doctor of Philosophy (PhD)
This paper introduces new mathematic equations that clarify slope and scale and help overcome difficulties with visually interpreting slopes (or trends)--a significant culprit of poor interrater agreement (IRA) of graphed data. Three experiments tested applications of the equations and demonstrated the following results: (a) Graphic Variability Quotient (GVQ) manipulation strongly predicts viewer ratings (and accuracy) of behavior change, β = .895, R2 = .801, (b) mathematical standards that control the inherent variability in non-standard graphs can be empirically based (to facilitate reliable visual comparison), and (c) visual aids posted on graphs, such as angles of inclination and a simple slope change guide, can produce very high IRA (α = .956)--significantly higher than in a group with only pre-drawn trend lines, F(1, 52) = 3.11, p = .002. The discussion explores how these results could become a basis for setting future standards in visual analysis, improve measures of effect size, and facilitate between-study comparison of graphed single-subject data in systematic reviews and meta-analyses.
Kinney, Chad Erick Liming, "Mathematics that Clarify Slope & Scale, Help Set Standards, and Improve Interrater Agreement on Time-Series Graphs" (2020). Theses and Dissertations. 176.
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