Bar graphs depicting averages are perceptually misinterpreted: the within-the-bar bias

Perhaps the most common method of depicting data, in both scientific communication and popular media, is the bar graph. Bar graphs often depict measures of central tendency, but they do so asymmetrically: A mean, for example, is depicted not by a point, but by the edge of a bar that originates from a single axis. Here we show that this graphical asymmetry gives rise to a corresponding cognitive asymmetry. When viewers are shown a bar depicting a mean value and are then asked to judge the likelihood of a particular data point being part of its underlying distribution, viewers judge points that fall within the bar as being more likely than points equidistant from the mean, but outside the bar--as if the bar somehow "contained" the relevant data. This "within-the-bar bias" occurred (a) for graphs with and without error bars, (b) for bars that originated from both lower and upper axes, (c) for test points with equally extreme numeric labels, (d) both from memory (when the bar was no longer visible) and in online perception (while the bar was visible during the judgment), (e) both within and between subjects, and (f) in populations including college students, adults from the broader community, and online samples. We posit that this bias may arise due to principles of object perception, and we show how it has downstream implications for decision making.