January 9, 2008, 4:06 pm
By Henry Woodbury
Two ways of reading the word area — its general vs. its mathematical meaning — leads to confusion in this otherwise superb article on Charts in the Economist. The chart in question is Florence Nightingale’s “Diagram of the Causes of Mortality in the Army of the East.” The data is plotted by month in 30-degree wedges. In each month, red represents deaths by injury, blue death by disease, and black death by other causes:
The Economist explains how to interpret the diagram:
As with today’s pie charts, the area of each wedge is proportional to the figure it stands for, but it is the radius of each slice (the distance from the common centre to the outer edge) rather than the angle that is altered to achieve this.
Herein lies the confusion. In fact, the areas of the wedges are not proportional. The data actually maps to the radius of each wedge. It appears that in her annotation, Nightingale used the word area in the generic sense of section or range. The great sweep of blue around the center of each chart is an artifact of the unusual radial plot. Perhaps unintentionally, Nightingale overdramatized the facts that made her case.
Our Creative Director, Piotr Kaczmarek, recalibrated Nightingale’s chart to correct this error. The diagram below uses all the elements of the original, but makes the data proportional to area:
Nightingale’s diagram, often referred to as Nightingale’s Rose or Nightingale’s Coxcomb, represents one of the inherent risks in visual explanation. An image may be so visually interesting — so iconic (a rose, a coxcomb) — that we assume its conclusions without examining its data.
This is better: a stacked bar chart that introduces a scale (!), more readable labels, and a single chart for the entire 1854-1856 period. These changes provide context and continuity, and make clear the two campaigns of the war:
UPDATE (January 14, 2008): In the comments, hstern recommends separating the three data types to allow better comparison. As it happens, Piotr created that chart as one of his alternatives to the radial plot. I’ve uploaded it below.
UPDATE (November 22, 2010): In a BBC News Magazine article titled “Diagrams that changed the world” Marcus du Sautoy includes a link to this post. Welcome BBC readers!
Thanks for the clarification. I came upon your critique while surfing for sites that might support a workshop on spatial thinking and visual learning I am conducting next week. I had already encountered the article from The Economist, and in the absence of Nightengale’s data, I had doubted whether area was truly being represented. You affirmed my suspicion, provided a corrected version and then provided a more appropriate modern version (albeit one not destined to become quite so famous). I wonder if the modern bar graph you provide could have its clarity improved. The type you use in which all three categories are proportionally represented on a single bar for each month would be most appropriate if the total number of deaths per month was the figure of primary interest. However, it is the comparison between the three categories of death that matters most and using three separate bars for each month would lend both a clear comparison and much greater quantitative clarity for each category. On the other hand, since Nightengale’s purpose was primarily persuasion rather than presenting data simply for the sake of knowledge, by showing no separation between your bars and thereby running the colors together, the resultant massive area of blue compared to the other colors becomes quite persuasive.
Posted by hstern on January 12, 2008 at 4:02 am
hstern, excellent points. As it happens, Piotr prepared several alternative bar charts, including one that corresponds to your recommendation. I didn’t want to overburden the initial post with all of them, but in response to your comment I think an update is appropriate.
Posted by Henry Woodbury on January 14, 2008 at 12:00 pm
How about a line chart instead of the final bar chart?
Posted by Hadley on November 11, 2008 at 11:14 pm
Thanks for these notes; the graphics are beautifully constructed. We came across your work whilst developing material of a similar theme for our project on understanding uncertainty. See http://understandinguncertainty.org/ . The data for ‘Diagram of the Causes of Mortality in the Army in the East’ was published by Nightingale in ‘A contribution to the sanitary history of the British army during the late war with Russia’ (1859). This data can be found on a table at http://understandinguncertainty.org/node/214 . We used this data to replicate Nightingale’s graphs, and the resulting charts resembled her original chart and the chart shown in the Economist article. So we believe that Nightingale’s original diagram is correct. Please describe the source of your data that makes you think otherwise!
Posted by Ian on November 20, 2008 at 12:07 pm
I arrived here via the BBC – the information will appear differently as a line chart and if ‘events’ were included, some sense of cause / effect might be achieved
Posted by Oman on November 22, 2010 at 8:15 am
Why do you have 1954 on both charts… on the right hand one it should be 1854 on the left 1856 I assume?
Also the March date on the right looks like 1885 and not 1855, this may just be the type setting.
Posted by Giles on November 22, 2010 at 9:51 am
Seems like a line graph would be easier to follow in the final diagram; it’s hard to pick out the red from the purple as bars. “Event” annotations would also be useful. Why did deaths from disease fall from Jan 1855? Presumably that was when Ms Nightingale began her work. Don’t make the reader look up the Wikipedia article to confirm that – show it on the graph!
Posted by Andy P on November 22, 2010 at 10:35 am
Another way of presenting it that would also allow for clear comparision between the areas, and also emphasise just how many deaths were preventable would be as a percentage share graph similar to the one on this page: http://www.marketmodelers.com/service2.aspx It would show the % of total deaths by cause in each month, and each month would add up to 100.
The benefit is that even in months with very few total deaths, you could also see that a large proportion of deaths were still avoidable, which is somewhat hard to see on existing charts in the article.
Posted by Tomato on November 22, 2010 at 10:37 am
A very interesting explanation and presentation.
Posted by Seth Frantzman on November 23, 2010 at 8:10 am
Posted by Rocker! on December 8, 2010 at 8:49 am
An absolute effective way of conveying information, i didn’t know before
Posted by Rasoul Shahilow on December 9, 2010 at 4:03 pm
I saw this on Marcus du Sautoy’s excellent prgramme on diagrams last night (BBC4). Forget all the numbers, it’s just a far better design than your dry stick charts; after all, persuasion and impact were the name of the game. It just looks great, like two eyes looking at you. Go Flo I say.
Posted by criggs on April 12, 2011 at 5:44 am
The Australian Council for Educational Research (ACER) seeks permission to reproduce a small amount of text from the following material:
Source Details: http://dd.dynamicdiagrams.com/2008/01/nightingales-rose/
Publication: Nightingale’s Rose
Author: Henry Woodbury
Publisher/Year: Dynamic diagrams: January 9, 2008, 4:06 pm
Material requested: 37 words slightly adapted – see below
Nightingale overdramatised the evidence that made her case.
Nightingale’s diagram represents one of the inherent risks in visual explanation. An image may be so visually interesting….. that we assume its conclusions without examining its data.
Nightingale overdramatised the evidence that made her case.
Nightingales’ diagram, however, illustrates one of the inherent risks in graphical representation: an image may be so visually interesting that we draw conclusions without adequate scrutiny of the data.
ACER is a not-for-profit organisation primarily engaged in the research, development and dissemination of knowledge and tools in education.
ACER is developing an examination for use in international schools in which English is the language of instruction.
Purpose: Examination booklet
Print run: 20,000
Print date: 4 July 2011
Territory: Worldwide excluding Canada
Please do not hesitate to contact me if you have any questions, though when responding please quote reference: 123924 Nightingale’s Rose.
Posted by Sue Franklyn on June 13, 2011 at 11:09 pm
What’s your data source? The table on http://understandinguncertainty.org/node/214 gives different values.
Total number of deaths by zymotic deceases in January 1855
2761 vs. ~1500 in your chart…
Posted by Herbert on November 13, 2011 at 5:50 am
One advantage of the circular presentation of 12 months per year is that it can show seasonal variation, which may be important for disease figures.
Posted by gasstationwithoutpumps on October 15, 2013 at 12:21 pm
I have read elsewhere that the chart was correctly adjusted for area e.g.:
“Some argue that a bar graph would have made her point more dramatically, though. One of the peculiarities of Nightingale’s circular presentation is that the deaths are proportional to the area, not the radius. Since the area of a circle is pr2, the area is proportional to the square of the radius rather than to the radius itself. This difference tends to de-emphasize the contrast between the small areas and the large ones. (In an early version of this diagram, Nightingale didn’t catch this distinction and drew the graphic incorrectly, with the radii proportional to the deaths. She quickly corrected her mistake.)” taken from
I have als seen this elsewhere with some of her early charts. Therefore I want to know if you have used her actaual recorded data – or data just taken from her graph assuming it has been drawn incorrctly?
Posted by Teresa Brunsdon on November 6, 2013 at 6:25 am
Firstly, I’d question how you obtained your data from as (as others have pointed out) Nightingale’s original diagram does show area proportional to the data, not radius, as can be checked against the original data.
However, the main point I’d like to say is that the bar charts are not an improvement on the original rose diagrams as they make Nightingale’s MESSAGE less clear: the original two rose diagrams show before and after (or at least, after and before as they were printed) the arrival of the sanitation commission. The point she wanted to show was that sanitation reduced deaths – at a glance, the two halves of the diagram makes this beautifully clear.
Posted by R Fisher on January 21, 2014 at 9:58 am