The effects of x‐axis time compression on the visual analysis of single‐case data

Abstract

Single‐case design is a research methodology that entails repeated measurement to assess the influence of an independent variable on a dependent variable over time. Data collected in this manner are regularly analyzed using visual analysis of data displayed in a linear graph. Although there is agreement regarding critical elements of visual analysis, research has highlighted poor reliability between raters. One potential contributor to this poor reliability are variations in visual presentation of the data during construction of the linear graph. The current study sought to determine the potential effect of one common variation, scaling of the x‐axis by intervention session or by calendar date. Results of the study indicated a significant effect of x‐axis scaling, with data presented by session, rather than by calendar day, judged as reflecting larger intervention effects, Z = 1981, p < .001. This effect was consistent across graphs displaying treatment effects of various magnitudes. Results of the study are discussed with the respect to the standardization of visual representation of single case data.

Effects of portable interventions on school psychologists’ graph-rating inconsistency.

“…Characteristics of the graphical displays of time-series data can meaningfully affect individuals’ interpretation of the data themselves (Dart & Radley, 2023; Radley et al, 2018). However, few studies on this topic have been conducted with practicing school psychologists.…”

“…A series of studies conducted by Radley, Dart, and colleagues provided strong evidence that aspects of the graphs in which SCD data are presented can influence raters’ decision making. For example, variations in the scaling of the Y -axis (Dart & Radley, 2017), the scaling of the X -axis (Dart & Radley, 2023), and the number of data points per X - to Y -axis ratio (DPPXYR; Radley et al, 2018), all influenced visual analysts’ identification of treatment effects and ratings regarding the magnitude of treatment effects. In fact, the manner in which graphs were assembled (e.g., Y -axis range, DPPXYR) had an impact on visual analysts’ judgements of the magnitude of effects even when the graphs were accompanied by a disclaimer that identified that graph manipulation was used to magnify intervention effects (Radley & Dart, 2023).…”

The effect of the level of data presentation on visual analysts’ decisions.

“…The findings of Dart and Radley (2017), Radley et al (2018), and Dart and Radley (2023) provide initial evidence for two analysis-altering elements of graphs (Dart & Radley, 2018)—or graph construction features that influence visual analyst decisions. Subsequently, the identification of these elements may be used to inform the development of empirically derived guidelines for the graphic presentation of SCD data.…”

“…Data were consistently rated by visual analysts as displaying a greater intervention effect when plotted on a graph with lower DPPXYR values than those with higher DPPXYR values. Dart and Radley (2023) subsequently found DPPXYR manipulation by way of x -axis time compression, or plotting data either by session (all data points plotted consecutively despite temporal gaps in data collection) or by calendar date (data plotted to represent temporal gaps in data collection), to impact visual analyst decisions. Findings indicated that when data were presented as session data (i.e., graphs with a lower DPPXYR value due to no visual gaps in data collection), visual analysts reported larger effects; when those same data were plotted by calendar date (i.e., graphs with a higher DPPXYR value due to gaps in data collection being accurately represented), visual analysts reported smaller intervention effects.…”

“…Extant research provides no guidance as to how altering the level of data presentation may impact decisions reached through visual analysts. As it is known that graph construction elements impact the appearance and visual analysis of data (Dart & Radley, 2017, 2023; Radley et al, 2018), the present study sought to determine whether changes in graph appearance associated with different levels of data presentation would impact decisions made by visual analysts regarding intervention effects. It was hypothesized that visual analysts would be more likely to identify intervention effects when data were presented in more macroscopic levels (i.e., day, week) than when data were presented in more microscopic levels (i.e., probe, session).…”