In this thesis, we hypothesize that data visualization users are subject to systematic errors, or cognitive biases, in decision-making under uncertainty. Based on research from psychology, behavioral economics, and cognitive science, we design five experiments to measure the role of anchoring bias, confirmation bias, belief bias, and myopic loss aversion under different uncertain decision tasks like social media event detection, misinformation identification, and financial portfolio allocation. This thesis makes three major contributions. First, we find evidence of cognitive biases in data visualization through multiple behavioral trace data including user decisions, user hover and click interactions, qualitative feedback, and belief elicitation techniques. Second, we design multiple experiments with interactive data visualization systems across different design complexities (coordinated multiple views to single plot), data types (social network, linguistic, geospatial, temporal, statistical), and evaluate them on user populations that range from novice to expert (crowdsourced, undergraduate, data scientist, domain expert). Third, we evaluate the experiments using multiple statistical and probabilistic techniques to measure the effects of cognitive biases including classical statistical tests, (Bayesian) mixed effects modeling, hierarchical clustering, natural language processing, and Bayesian cognitive modeling. These experiments show the promising role data visualizations and human-computer techniques could mitigate such biases and lead to better decision-making under uncertainty.