A Word from our 2009 Section Chairs

Displaying both relative quantities and the differences between those quantities in an illustration remains a challenge. The fan plot, a variation on the pie chart, is presented as an alternative way of illustrating relative magnitude and differences. Using real data, the bar plot, pie chart and fan plot are compared and a test of the ability of the fan plot to convey the required information is suggested. Summary illustrations of quantitative data continue to challenge the researcher who presents to an audience that does not share the researcher's expertise. The concepts may not be especially complex, but the difficulty of conveying them is well recognized (Tufte, 2001). Ideally, an illustration should explain the concept with little or no supplementary explanation by the presenter. The observation that many illustrations do not achieve this suggests that there is room for development in this area. Beginning with the principle that no single illustrative technique can suit all data sets, the first task is to define the characteristics of the data to be presented. In what follows, it will be assumed that a small number, say a maximum of ten, quantities are to be displayed. Each quantity will have a label that links it to its source. The principal aim is to display the relative magnitudes and differences between the quantities. As an example, the numbers of threatened species in various areas of the world, as estimated by the IUCN, will be used. The success of the illustration may be judged by having a previously uninformed member of the intended audience correctly explain those relationships upon viewing the illustration. A final restriction is that the sensory modality be visual. The successful comparison of quantities depends to some extent upon how they are portrayed. Relative comparisons are most easily made if the representations of quantities are adjacent, have the same origin and numeric scale. This suggests a bar plot. Figure 1 shows the example data as a bar plot, using the "barplot" function of the R statistical language. Figure 1. Bar chart of threatened species by geographical area. Because the numbers have been placed in decreasing order, it is easy to see that Asia is home to the most endangered species, while Europe is home to the fewest. It is also easy to see that Asia is home to considerably more endangered species than Africa, and that Oceania has a smaller excess compared to Europe. Could the hypothetical member of the audience correctly state the relative proportion of Oceania to Africa or the relation of the differences between the Americas and Europe and Oceania? Clearly the farther apart any two rectangles are, the more difficult it will be to make such a comparison. The STATISTICAL COMPUTING AND GRAPHICS NEWSLETTER VOLUME 20, No 1, JUNE 2009 PAGE 9 same objection holds for any comparison of length. If the bars were to be made very narrow in order to facilitate such comparisons, the labels would be commensurately crowded and it would be more difficult to identify which bar represented which area. If the plot area began just below the smallest quantity to be displayed, the adjacent differences would be magnified, but the proportional comparisons would be difficult or impossible. The ever popular pie chart (Playfair, 1801), useful for displaying large differences between very small numbers of quantities, appears less successful than the barplot in this instance. Comparisons of adjacent and opposite sectors are equally difficult. Does South America have more threatened species than North and Central? If the actual numbers were appended to the sector labels, the audience could do the comparisons with simple arithmetic, but a table would then be satisfactory and the illustration would become a mere decoration. Figure 2. Pie chart of threatened species by geographical area. Yet the attraction of the pie chart is that the audience typically understands it, or appears to. The technique to be described is a modification of the pie chart intended to address the shortcomings while preserving the intelligibility. The sectors of the pie chart are first rotated so that they are concentric and overlapping, with a common radial alignment. In decreasing order of angular extent, each sector but the largest is reduced in radius so that the outer arc of each sector is visible. An illustration somewhat reminiscent of a folding fan is produced, as in Figure 3. Differences between adjacent sectors are apparent as thinner sectors, allowing the relative differences between non-adjacent sectors to be visually compared. To estimate the difference between the number of endangered species in Oceania and Europe with the same difference between the Americas is now at least possible, and the success of the audience in estimating that ratio is a proposed test of the effectiveness of the fan plot. Figure 3. Fan plot of threatened species by area. The inspiration for the fan plot, as for the pie chart, derives from the latter’s reference to food. Many items of food apart from pies are roughly circular and their division may be of considerable importance to the consumers. The popularity of the pie chart may in part derive from this analogy, in that most people are practiced in the estimation of equality or difference of circular sectors. Anyone who doubts this is encouraged to slice a pie into fairly equal sectors and then ask a hungry child to take the largest. While the average person can make a fairly accurate determination of the relative size of a circular sector, estimating the differences between sectors is a much more difficult task. However, if those differences can be converted into sectors, they should be easier to compare. The superimposition of the sectors means that the visible radial slice of each sector but the smallest represents the difference between it and the adjacent sector. In the original implementation of the fan plot, the sum of the sectors was restricted to a complete circle. This is not strictly necessary, as the overlapping sectors can be stretched until the largest is a complete circle STATISTICAL COMPUTING AND GRAPHICS NEWSLETTER VOLUME 20, No 1, JUNE 2009 PAGE 10 while still allowing the complete extent of every sector to be visible. This manipulation expands the differences as well, perhaps making those differences more easily compared. Figure 3 illustrates the data with the largest sector expanded to a semicircle. The fan plot has been programmed in the R statistical language (R Core Team, 2006) and is available in the plotrix package (Lemon, 2003). The options of the fan plot function allow circumferential labels to be displayed, so that the sectors can be identified without the inclusion of a legend. Circumferential tick marks can also be included if this improves the intelligibility of the plot. The fan plot is intended primarily for use in illustrations where both relative quantities and the differences between those quantities are to be conveyed to the reader or audience. It maintains the simplicity and comprehensibility of the pie chart, but deals more effectively with relative quantities and differences. The aim is to produce understandable and memorable images that require minimal explanation. REFERENCES Lemon, J. (2006) plotrix: A package in the red light district of R. R News, 6(4),8-12. Playfair, W. (1801) Commercial and Political Atlas and Statistical Breviary. Cambridge: Cambridge University Press. R Development Core Team (2003) R: a language and environment for statistical computing. (ISBN 3-90005100-3), Vienna: R Foundation for Statistical Computing. Tufte, E.R. (2001) The visual display of quantitative information. Cheshire: Graphics Press. SOFTWARE INSTALLATION From within R, select from the menu “Packages” the item “Install Packages”. Select from the list a location close to you, select from the next menu the item plotrix, click OK. If you prefer the R command line, enter utils:::menuInstallPkgs() and then proceed as described above. After successful installation of the library, enter > library(plotrix) Enter