Beyond Weber's Law: A Second Look at Ranking Visualizations of Correlation

Matthew Kay, Jeffrey Heer

Research output: Contribution to journalArticlepeer-review

79 Scopus citations


Models of human perception - including perceptual "laws" - can be valuable tools for deriving visualization design recommendations. However, it is important to assess the explanatory power of such models when using them to inform design. We present a secondary analysis of data previously used to rank the effectiveness of bivariate visualizations for assessing correlation (measured with Pearson's r) according to the well-known Weber-Fechner Law. Beginning with the model of Harrison et al. [1], we present a sequence of refinements including incorporation of individual differences, log transformation, censored regression, and adoption of Bayesian statistics. Our model incorporates all observations dropped from the original analysis, including data near ceilings caused by the data collection process and entire visualizations dropped due to large numbers of observations worse than chance. This model deviates from Weber's Law, but provides improved predictive accuracy and generalization. Using Bayesian credibility intervals, we derive a partial ranking that groups visualizations with similar performance, and we give precise estimates of the difference in performance between these groups. We find that compared to other visualizations, scatterplots are unique in combining low variance between individuals and high precision on both positively- and negatively-correlated data. We conclude with a discussion of the value of data sharing and replication, and share implications for modeling similar experimental data.

Original languageEnglish (US)
Article number7192661
Pages (from-to)469-478
Number of pages10
JournalIEEE Transactions on Visualization and Computer Graphics
Issue number1
StatePublished - Jan 31 2016
Externally publishedYes


  • Analytical models
  • Correlation
  • Data models
  • Data visualization
  • Gaussian distribution
  • Predictive models
  • Visualization

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Computer Graphics and Computer-Aided Design


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