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Understanding correlation judgement is important to designing effectivevisualizations of bivariate data. Prior work on correlation perception has notconsidered how factors including prior beliefs and uncertainty representationimpact such judgements. The present work focuses on the impact of uncertaintycommunication when judging bivariate visualizations. Specifically, we model howusers update their beliefs about variable relationships after seeing ascatterplot with and without uncertainty representation. To model and evaluatethe belief updating, we present three studies. Study 1 focuses on a proposed''Line + Cone'' visual elicitation method for capturing users' beliefs in anaccurate and intuitive fashion. The findings reveal that our proposed method ofbelief solicitation reduces complexity and accurately captures the users'uncertainty about a range of bivariate relationships. Study 2 leverages the``Line + Cone'' elicitation method to measure belief updating on therelationship between different sets of variables when seeing correlationvisualization with and without uncertainty representation. We compare changesin users beliefs to the predictions of Bayesian cognitive models which providenormative benchmarks for how users should update their prior beliefs about arelationship in light of observed data. The findings from Study 2 revealed thatone of the visualization conditions with uncertainty communication led to usersbeing slightly more confident about their judgement compared to visualizationwithout uncertainty information. Study 3 builds on findings from Study 2 andexplores differences in belief update when the bivariate visualization iscongruent or incongruent with users' prior belief. Our results highlight theeffects of incorporating uncertainty representation, and the potential ofmeasuring belief updating on correlation judgement with Bayesian cognitivemodels.

A Bayesian cognition approach for belief updating of correlation judgement through uncertainty visualizations