Perception of bar graphs – A biased impression?

Highlights

• Bar graphs can give a biased impression of the central tendency.

• The mean appeared lower than it actually was in bar graphs compared to point graphs.

• The height of the bars had no effect on the underestimation.

• The estimated mean was biased towards the outliers, but still underestimated.

Abstract

Computers provide ubiquitous contact to data graphs. Yet, employing the power of the human perception system bears the risk of being subject to its biases. Data graphs are used to present the means of different conditions and are supposed to convey group information, such as variability across conditions, as well as the grand average. Across three samples, we tested whether there is a bias in the central tendency perceived in bar graphs, 53 participants with a mean age of 27 years (plus replication with N = 38, mean age = 23 years). Participants were provided with bar and point graphs and had to judge their means. We found that the mean value was systematically underestimated in bar graphs (but not in point graphs) across different methods of testing for biased evaluation. In a second experiment (N = 80, mean age = 24 years) we replicated and extended this finding, by testing the effect of outliers on the bias in average estimation. For instance, outliers might trigger controlled processing. Yet, the underestimation of the average was replicated and was not affected by including outliers – despite that the estimate was torn towards the outlier. Thus, we should be cautious with relying on bar graphs when a bias free estimate of the grand average is relevant.

Introduction

Continuous and immediate access to computer includes contact to data graphs. For instance, web applications employ automated bar graphs and spread sheet software grants easy access to generate data graphs in different contexts. Ainley (1994) showed that school children, who are competent in using spreadsheets to record data, are able to produce graphs quickly and easily and even assimilate these skills by producing hand–drawn graphs if required. Abilities to produce and read data graphs are correlated (Davis, 2011), moreover Burley (2010) argues that information visualization is a valuable tool for knowledge integration. Most companies use spread sheet software in work contexts. The use of data graphs in research has increased during the 20th century (Gross, Harmon, & Reidy, 2002) in publications and on conferences (Cleveland, 1984). Data graphs enable a rapid apprehension of result patterns in terms of quantitative relations between values. In some cases, conclusions might be drawn to fast when graphs are involved. Even people with high expertise in the subject matter find articles with data graphs more plausible, attributing data graphs a potential for persuasion (Isberner et al., 2013). Note however that disciplines differ greatly in the extent to which they use data graphs (Arsenault et al., 2006, Kubina et al., 2010, Smith et al., 2000). Furthermore, there are many ways to visualize scientific results and the design of graphs can affect the interpretation of the presented results (Fischer et al., 2005, Huestegge and Philipp, 2011). Thus, while by and large data graphs are a common and efficient means to convey pattern information, there might be systematic biases in how perception extracts general aspects of a data set form a graph. Increasing our knowledge about the perception of data graphs might be most pressing for frequently used formats and features. The aim of our study was to examine whether bar graphs give a biased impression of central tendency.

There are extensive studies on various properties of different types of data graphs. For example, results shown in bar graphs can be read faster and with higher accuracy compared to pie graphs (Simkin & Hastie, 1987). The same authors specify that divided bar graphs should be avoided in favor of simple bar graphs for reducing errors. Furthermore, vertical bar graphs are reported to be more user-friendly than horizontal ones (Fischer et al., 2005). While bar graphs are recommended for discrete values, trends should be represented in line graphs (cf. Zacks & Tversky, 1999). This should, however, not suggest that bar graphs are about individual values only. The specific strength of presenting data in a graph (e.g., rather than in a table) is that the reader can gain an instant impression about overall properties of the data set. A bar graph should not only convey the values of individual bars, but instead it should also convey group information, such as the variability across conditions and the grand average. For instance, a bar graph representing % sugar per kind of convenience food should allow assessing variability across foods, but also giving an impression of the overall level. Also, a bar graph on percent climate gas emission change per industrial sector should convey the general level of change in the period assessed as well as the differences among the branches. Peebles (2008) compared line graph, bar graph, and kiviat chart and showed that if people have to judge how much larger or smaller the value of a dimension is compared to the average, the values in bar graphs were systematically underestimated. In an experimental study we investigated whether there is a bias in the central tendency perceived in bar graphs. We report two experiments. In the first experiment, we tested the ‘underestimation of the mean in bar graphs’ across different methods. In the second experiment, we tested the ‘effect of outliers on the bias in average estimation’.