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Impacts of aspect ratio on task accuracy in parallel coordinates

Hugh Garner, Sara Johansson Fernstad

TL;DR

This study investigates how axis aspect ratio ($AR$) in static parallel coordinates plots (PCPs) affects task accuracy for two common tasks: correlation estimation and value tracing. Using a within-subject design across multiple $AR$ values and dataset sizes, it employs Fisher-$z$-scaled correlations and GLMM analyses to quantify effects, finding that $AR$ significantly modulates performance and interacts with sample size and correlation strength. Key findings include asymmetric perception for correlations (negative correlations are often clearer, with $AR>1$ improving estimation of positive correlations) and substantial drops in value-tracing accuracy at extreme $AR$ values ($AR=0.25$ or $AR=4$). The results yield practical design recommendations: favor $AR>1$ for correlation-focused tasks with small samples, and prefer $AR$ between $0.5$ and $1$ for value-tracing, with caveats for cross-task use and interactions, guiding PCP layout decisions in exploratory data analysis.

Abstract

Parallel coordinates plots (PCPs) are a widely used visualization method, particularly for exploratory analysis. Previous studies show that PCPs perform much more poorly for estimating positive correlation than for estimating negative correlation, but it is not clear if this is affected by the aspect ratio (AR) of the axes pairs. In this paper, we present the results from an evaluation of the effect of the aspect ratio of axes in static (non-interactive) PCPs for two tasks: a) linear correlation estimation and b) value tracing. For both tasks we find strong evidence that AR influences accuracy, including ARs greater than 1:1 being much more performant for estimation of positive correlations. We provide a set of recommendations for visualization designers using PCPs for correlation or value-tracing tasks, based on the data characteristics and expected use cases.

Impacts of aspect ratio on task accuracy in parallel coordinates

TL;DR

This study investigates how axis aspect ratio () in static parallel coordinates plots (PCPs) affects task accuracy for two common tasks: correlation estimation and value tracing. Using a within-subject design across multiple values and dataset sizes, it employs Fisher--scaled correlations and GLMM analyses to quantify effects, finding that significantly modulates performance and interacts with sample size and correlation strength. Key findings include asymmetric perception for correlations (negative correlations are often clearer, with improving estimation of positive correlations) and substantial drops in value-tracing accuracy at extreme values ( or ). The results yield practical design recommendations: favor for correlation-focused tasks with small samples, and prefer between and for value-tracing, with caveats for cross-task use and interactions, guiding PCP layout decisions in exploratory data analysis.

Abstract

Parallel coordinates plots (PCPs) are a widely used visualization method, particularly for exploratory analysis. Previous studies show that PCPs perform much more poorly for estimating positive correlation than for estimating negative correlation, but it is not clear if this is affected by the aspect ratio (AR) of the axes pairs. In this paper, we present the results from an evaluation of the effect of the aspect ratio of axes in static (non-interactive) PCPs for two tasks: a) linear correlation estimation and b) value tracing. For both tasks we find strong evidence that AR influences accuracy, including ARs greater than 1:1 being much more performant for estimation of positive correlations. We provide a set of recommendations for visualization designers using PCPs for correlation or value-tracing tasks, based on the data characteristics and expected use cases.
Paper Structure (26 sections, 5 figures, 3 tables)

This paper contains 26 sections, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Prior work
  3. Hypotheses
  4. Correlation estimation
  5. Tracing values
  6. Methods
  7. Procedures
  8. Task A: Correlation estimation
  9. Task B: Value tracing
  10. Task structure & training
  11. Data quality
  12. Participants
  13. Analysis methodology
  14. Response measures
  15. Statistical tests
  16. ...and 11 more sections

Figures (5)

  • Figure 1: Correlation in a PCP: (a) patterns formed with increasing correlation strength; (b) patterns in a PCP by aspect ratio (central axes - top: positive correlation; bottom: negative correlation)
  • Figure 2: Example task screens (a) Task A: Correlation estimation. (b) Task B: Value tracing.
  • Figure 3: Task A: Real (true) and estimated Fisher-z scores by aspect ratio (facet rows and colour) and sample size (40 and 160, facet columns). Each facet shows a combination of aspect ratio and sample size, and a facet then includes the true Fisher-z (x-axis) and participant estimated Fisher-z (y-axis). Bubble area indicates proportion of responses at each estimated Fisher-z value for the specific true Fisher-z value.
  • Figure 4: Task A: Marginal (population-level) model predictions of signed error (y-axis, Fisher-z) by true Fisher-z (x-axis) across aspect ratios (colour) and sample sizes (top facet sample size 40, bottom 160), with 95% CIs, plotted together with the corresponding observed (unadjusted) mean errors. For any given true Fisher-z value (x-axis), the distance of the error (y-axis) indicates the magnitude of the mean error in estimated value by participants. A positive value indicates over-estimation, a negative under-estimation.
  • Figure 5: Task B: Marginal effects - model-based marginal predictions and 'real' (observed, unadjusted) probability correct by aspect ratio and sample size (number of polylines)