Abstract
When making an inference or comparison with uncertain, noisy, or incomplete data, measurement error and confidence intervals can be as important for judgment as the actual mean values of different groups. These often misunderstood statistical quantities are frequently represented by bar charts with error bars. This paper investigates drawbacks with this standard encoding, and considers a set of alternatives designed to more effectively communicate the implications of mean and error data to a general audience, drawing from lessons learned from the use of visual statistics in the information visualization community. We present a series of crowd-sourced experiments that confirm that the encoding of mean and error significantly changes how viewers make decisions about uncertain data. Careful consideration of design tradeoffs in the visual presentation of data results in human reasoning that is more consistently aligned with statistical inferences. We suggest the use of gradient plots (which use transparency to encode uncertainty) and violin plots (which use width) as better alternatives for inferential tasks than bar charts with error bars.