Slope Identification and Decision Making: A Comparison of Linear and Ratio Graphs

Abstract

Applied behavior analysts have traditionally relied on visual analysis of graphic data displays to determine the extent of functional relations between variables and guide treatment implementation. The present study assessed the influence of graph type on behavior analysts’ ( n = 51) ratings of trend magnitude, treatment decisions based on changes in trend, and their confidence in decision making. Participants examined simulated data presented on linear graphs featuring equal-interval scales as well as graphs with ratio scales (i.e., multiply/divide or logarithmic vertical axis) and numeric indicators of celeration. Standard rules for interpreting trends using each display accompanied the assessment items. Results suggested participants maintained significantly higher levels of agreement on evaluations of trend magnitude and treatment decisions and reported higher levels of confidence in making decisions when using ratio graphs. Furthermore, decision making occurred most efficiently with ratio charts and a celeration value. The findings have implications for research and practice.

Reclaiming the Horizon: Novel Visualization Designs for Time-Series Data with Large Value Ranges

“…Visualization of Large Value Ranges A common way to display time-series with order of magnitude variations is to use a line graph with logarithmic scaling [32,38,40]. However, most of the previous research on large value ranges has been done for time-independent data.…”

“…The "default" way to visualize large value ranges, is to use a logarithmic scale. However, reading values from a logarithmic scale is not intuitive [32]. This is evidenced by the focus of previous techniques for large value ranges on perceptually linear scaling for both the mantissa 𝑚 and the exponent 𝑒 of a value 𝑣 = 𝑚 • 10 𝑒 [9,26,27].…”

Examining the impact of design-comparable effect size on the analysis of single-case design in special education.

“…Clear, replicated patterns across phases in SCDs reveal intervention effects, with stability in responses across consistent conditions indicating a functional relation between variables. Establishing this functional relation requires evaluating data traits like level, trend, and response immediacy (Kubina et al, 2023), which SCD researchers have suggested group design-related statistical analysis overlook (e.g., Maggin et al, 2022; Wolery et al, 2010). Nonetheless, the push for quantitative alternatives grows due to the limitations of visual analysis.…”

“…Nonetheless, the push for quantitative alternatives grows due to the limitations of visual analysis. Critics note that visual analysis does not provide a practical, universal metric of treatment magnitude (Browder et al, 1989; Riley-Tillman et al, 2020) and is applied inconsistently by observers (Kubina et al, 2023; Ninci et al, 2015).…”