  Analysts often make visual causal inferences about possible data-generating
models. However, visual analytics (VA) software tends to leave these models
implicit in the mind of the analyst, which casts doubt on the statistical
validity of informal visual "insights". We formally evaluate the quality of
causal inferences from visualizations by adopting causal support -- a Bayesian
cognition model that learns the probability of alternative causal explanations
given some data -- as a normative benchmark for causal inferences. We
contribute two experiments assessing how well crowdworkers can detect (1) a
treatment effect and (2) a confounding relationship. We find that chart users'
causal inferences tend to be insensitive to sample size such that they deviate
from our normative benchmark. While interactively cross-filtering data in
visualizations can improve sensitivity, on average users do not perform
reliably better with common visualizations than they do with textual
contingency tables. These experiments demonstrate the utility of causal support
as an evaluation framework for inferences in VA and point to opportunities to
make analysts' mental models more explicit in VA software.
