Visual statistical decisions

Abstract

To identify variables that underlie intuitive judgments about the sizes of groups of similar objects, we asked people to judge the relative heights of vertical bars briefly shown, two groups at a time, on a computer display. Randomly selected normal deviates determined individual bar height. Average differences in height and group sizes were also randomly varied. Twenty-eight participants judged 250 differences each, which were then submitted to multiple regression analysis and psychophysical inspection. The total number of bars sharpened discrimination, whereas variance dulled it. Critical ratio (CR), the forerunner to the modern t test, emerged as the most important predictor; little additional variance was explained by other factors. The difference in the number of bars was a reliable factor, favoring the greater number of bars. Confidence limits around thresholds, defined as CRs needed to say "possibly greater," surrounded 1.65; as a z value, this corresponded to a one-tailed probability of .05. Judgments about noisy stimuli thus seem to be based on a statistical process and to employ a probability criterion similar to that used in the formal statistical evaluation of experimental findings-namely, p .05.

The capacity limitations of orientation summary statistics

“…Consistent with this, accurate summaries are found to occur over space and time for both low-level stimuli and more complex objects, including mean brightness (Bauer, 2009), motion speed and direction (e.g., Watamaniuk, Sekular, & Williams, 1989), spatial position (e.g., Alvarez & Oliva, 2008), orientation (e.g., Dakin, 2001), height (Fouriezos, Rubenfeld, & Capstick, 2008), size over space (Ariely, 2001), size over time (Albrecht & Scholl, 2010), length (Weiss & Anderson, 1969), color (Demeyere et al, 2008), inclination (Miller & Sheldon, 1969), biological motion (Sweeny, Haroz, & Whitney, 2013), facial identity (e.g., de Fockert & Wolfenstein, 2009), facial attractiveness (Walker & Vul, 2014), and facial emotion and gender (e.g., Haberman & Whitney, 2007). Thus, it is clear that SSRs can be formed for a wide range of visual attributes, consistent with the suggestion that establishing SSRs is a fundamental early step in visual processing.…”

Perception of Average Value in Multiclass Scatterplots

“…The proposed experimental task (comparison of mean values) and its connection with a relatively high-level aggregate statistical comparison of mean has been used by Foureizos et al to analyze statistical decision-making in bar charts [21], where as Doherty et al [17] and Rensink & Baldridge [45] have both looked at correlation coefficients in scatterplots. Two recent papers by Correll et al have examined the visual perception, aggregation, and comparison of mean values, in both time series data and in paragraphs of tagged text [14, 15].…”

Effects of ensemble complexity and perceptual similarity on rapid averaging of hue

“…As such, the pattern of results is similar to that expected from models representing ensembles (holistically and their elements individually) as a probability distribution or set of probability distributions, each subject to internal noise (e.g., Alvarez, 2011;Haberman & Whitney, 2012). Similarly, it has been shown that visual judgments of which of two groups of bars has the greater mean height involves assessment of the relative variance in each set as well as the mean difference, the process of which appears to follow that of Student's t test (Fouriezos, Rubenfeld, & Capstick, 2008).…”