Error Bars Considered Harmful: Exploring Alternate Encodings for Mean and Error

Michael Correll, Michael Gleicher
2014 IEEE Transactions on Visualization and Computer Graphics  
0 20 40 60 80 100 Snow Expected (mm) City A City B Margin of Error +/-15 (a) Bar chart with error bars: the height of the bars encodes the sample mean, and the whiskers encode a 95% tconfidence interval. 0 20 40 60 80 100 Snow Expected (mm) City A City B Margin of Error +/-15 (b) Modified box plot: The whiskers are the 95% t-confidence interval, the box is a 50% t-confidence interval. 0 20 40 60 80 100 Snow Expected (mm) City A City B Margin of Error +/-15 (c) Gradient plot: the transparency of
more » ... the colored region corresponds to the cumulative density function of a tdistribution. 0 20 40 60 80 100 Snow Expected (mm) City A City B Margin of Error +/-15 (d) Violin plot: the width of the colored region corresponds to the probability density function of a t-distribution. Fig. 1. Four encodings for mean and error evaluated in this work. Each prioritizes a different aspect of mean and uncertainty, and results in different patterns of judgment and comprehension for tasks requiring statistical inferences. 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.
doi:10.1109/tvcg.2014.2346298 pmid:26356928 pmcid:PMC6214189 fatcat:qertnjopvfbbxpazogtpymb6ke