Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Behavioral Analysis

First Advisor

Nicholas Weatherly

Second Advisor

Gary Burns

Third Advisor

Mark Harvey

Fourth Advisor

Catherine Nicholson


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.


Copyright held by author.