Visualizing data with bounded uncertainty

Visualization is a powerful way to facilitate data analysis, but it is crucial that visualization systems explicitly convey the presence, nature, and degree of uncertainty to users. Otherwise, there is a danger that data will be falsely interpreted, potentially leading to inaccurate conclusions. A common method for denoting uncertainty is to use error bars or similar techniques designed to convey the degree of statistical uncertainty. While uncertainty can often be modeled statistically, a second form of uncertainty, bounded uncertainty, can also arise that has very different properties than statistical uncertainty. Error bars should not be used for bounded uncertainty because they do not convey the correct properties, so a different technique should be used instead. We describe a technique for conveying bounded uncertainty in visualizations and show how it can be applied systematically to common displays of abstract charts and graphs. Interestingly, it is not always possible to show the exact degree of uncertainty, and in some cases it can only be displayed approximately.