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


Models of human perception – including perceptual “laws” – will be valuable tools for deriving visualization design recommendations. But, it's important to assess the explanatory power of such models when using them to tell style. We present a secondary analysis of information previously used to rank the effectiveness of bivariate visualizations for assessing correlation (measured with Pearson's r) in step with the well-known Weber-Fechner Law. Beginning with the model of Harrison et al. [1], we present a sequence of refinements as well as incorporation of individual variations, log transformation, censored regression, and adoption of Bayesian statistics. Our model incorporates all observations dropped from the original analysis, together with data near ceilings caused by the info collection method and whole visualizations dropped thanks to giant numbers of observations worse than probability. This model deviates from Weber's Law, but provides improved predictive accuracy and generalization. Using Bayesian credibility intervals, we tend to derive a partial ranking that teams visualizations with similar performance, and we offer precise estimates of the difference in performance between these groups. We tend to notice that compared to different visualizations, scatterplots are distinctive in combining low variance between people and high precision on each positively- and negatively-correlated information. We conclude with a discussion of the worth of data sharing and replication, and share implications for modeling similar experimental data.

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