On the Commonly-Used Incorrect Visual Representation of Accuracy and Precision

Abstract

We performed a Google image search using the search phrase “accuracy and precision” and, after removing unresponsive and duplicate web pages from the search results, found that 78 of the top 100 results use the bullseye chart to visually explain this concept. Unfortunately, we also found that 52 of those 78 results, i.e., an incredible two thirds, use a visual similar to what is shown in Fig. 1(i) or Fig. 1(ii), both of which are at best highly misleading and factually incorrect according to relevant standards and guidelines. In this figure, the black dots represent the values obtained by replicated measurements of the same measurand (the quantity intended to be measured), and the visual aims to present how close the measured values are to each other and to an agreed-upon reference value, represented by the red bullseye. In the search results, visuals similar to Fig. 1(i) and Fig. 1(ii) appeared 25 and 27 times, respectively. In the top 20 search results, which is where the great majority of users look for answers, the earliest correct visual appeared only at position 11, followed by 13, 15, and 19 in the rankings. The great majority of the 52 incorrect visuals were in non-peer-reviewed documents, reinforcing the notion that one should not believe everything one sees on the internet, although shockingly, a few were in papers published in peer-reviewed scientific venues, including one in Elsevier's Journal of Clinical Epidemiology and another one in the SCMR's Journal of Cardiovascular Magnetic Resonance, both well-cited journals. The actual numbers are probably higher, as many scientific articles are behind pay-walls and inaccessible to Google search.