When faced with a large collection of objects, our visual system can extract statistical properties of the collection. Most studies of this ability focus on judgments of mean value, and typically focus on a constrained set of dimensions (e.g., size, location, or facial properties). We tested a variety of judgments in addition to means - deviation, range, and extrema -- across two dimensions that have real-world application to encodings of visual information -- color (as in the color gradients used in heatmaps) and line height (as used in line graphs). People were asked to find the window within a range (with a cover story of months within a year of data on daily sales for a company) that had the largest mean, deviation, etc. We found that while the visual system can effectively extract statistics from both dimensions, there was a salient double dissociation between the two. For ensemble processing of color gradients, performance was best for statistics requiring the combination of information across values, such as recovering mean and deviation. In contrast, for ensemble processing of line height, performance was best for statistics requiring isolation of unique elements across values, such as recovering extrema and range. We replicated these results using modified versions of each representation in typical data analysis tasks: a line graph that included explicit information about judged properties and a color gradient that was randomized within 'months' to facilitate ensemble processing of each month. Overall, these findings suggest divisions in the type of ensemble processing that is possible for different types of stimuli. We speculate that color facilitates mean and variability information via summation of values at low spatial frequencies into a representation similar to a color histogram, while line height facilitates range and extrema judgments via existing biases toward shape boundary properties

@Article{ACGF14,
  author       = "Albers, Danielle and Correll, Michael and Gleicher, Michael and Franconeri, Steve",
  title        = "Ensemble Processing of Color and Shape: Beyond Mean Judgments",
  journal      = "Journal of Vision",
  number       = "11",
  volume       = "14",
  month        = "May",
  year         = "2014",
  note         = "Vision Sciences Society Meeting",
  ee           = "http://www.journalofvision.org/content/14/10/1056.abstract",
  url          = "http://graphics.cs.wisc.edu/Papers/2014/ACGF14"
}