Analyzing the misperception of exponential growth in graphs

Trend judgment as a perceptual building block of graphicacy and mathematics, across age, education, and culture

Data plots are widely used in science, journalism and politics, since they efficiently allow to depict a large amount of information. Graphicacy, the ability to understand graphs, has thus become a fundamental cultural skill comparable to literacy or numeracy. Here, we introduce a measure of intuitive graphicacy that assesses the perceptual ability to detect a trend in noisy scatterplots ("does this graph go up or down?"). In 3943 educated participants, responses vary as a sigmoid function of the t-value that a statistician would compute to detect a significant trend. We find a minimum level of core intuitive graphicacy even in unschooled participants living in remote Namibian villages (N = 87) and 6-year-old 1st-graders who never read a graph (N = 27). The sigmoid slope that we propose as a proxy of intuitive graphicacy increases with education and tightly correlates with statistical and mathematical knowledge, showing that experience contributes to refining graphical intuitions. Our tool, publicly available online, allows to quickly evaluate and formally quantify a perceptual building block of graphicacy.

Is my visualization better than yours? Analyzing factors modulating exponential growth bias in graphs

Humans tend to systematically underestimate exponential growth and perceive it in linear terms, which can have severe consequences in a variety of fields. Recent studies attempted to examine the origins of this bias and to mitigate it by using the logarithmic vs. the linear scale in graphical representations. However, they yielded conflicting results as to which scale induces more perceptual errors. In the current study, in an experiment with a short educational intervention, we further examine the factors modulating the exponential bias in graphs and suggest a theoretical explanation for our findings. Specifically, we test the hypothesis that each of the scales can induce misperceptions in a particular context. In addition to this, we explore the effect of mathematical education by testing two groups of participants (with a background in humanities vs. formal sciences). The results of this study confirm that when used in an inadequate context, these scales can have a dramatic effect on the interpretation of visualizations representing exponential growth. In particular, while the log scale leads to more errors in graph description tasks, the linear scale misleads people when they have to make predictions on the future trajectory of exponential growth. The second part of the study revealed that the difficulties with both scales can be reduced by means of a short educational intervention. Importantly, while no difference between participants groups was observed prior to the intervention, participants with a better mathematical education showed a stronger learning effect at posttest. The findings of this study are discussed in light of a dual-process model.

The role of transdisciplinarity for mineral economics and mineral resource management: coping with fallacies related to phosphorus in science and practice

Mineral economics is a genuine multidisciplinary field dealing with economic and policy matters related to the production, distribution, and consumption of mineral commodities. We discuss why the increasing complexity, ambiguity, ambivalence, and social contestation of subjects of mineral economics promote the participation of mineral economists in transdisciplinary processes. These processes relate (a) knowledge from targeted interdisciplinary processes and (b) mitigated discourses among different stakeholders to provide (c) a shared problem definition and to attain shared basic knowledge about problem transformation science and practice. We discuss known examples of misperceptions regarding minerals (phosphorus), such as an imminent scarcity threat, the incorrectly understood causations of the 2007/2008 price peak and present the phosphorus ore-grades increased by 3.2% between 1983 and 2013 fallacies (which is based on the Simpson’s paradox), and only few countries have mineable reserves fallacy. Here, we also illuminate motivations underlying several mineral economics–related misunderstandings. We argue that societally relevant questions require an honest mineral economics knowledge brokership. The example of the Global TraPs project, which targeted sustainable phosphorus management, is presented. Honest brokership to attain a clearinghouse function of science requires trust formation in society. We argue that this calls for increasing the understandability of relationships that are not well-understood, such as “if prices rise, so do stocks.” Wellmer and Becker-Platen’s feedback control cycle may be considered an example of how complex mineral economics can become and how challenging it is to be understandable to scientists from different disciplines and faculties as well as to practitioners whose knowledge may well be used to cope with the complexity of given problems. Thus, the present paper represents a plea for mutual learning between science and practice in order to understand the complex social and economic challenges of mineral resource dynamics.