Tornado Charts and Dot Plots
by Jon Peltier
Sunday, March 2nd, 2008
Peltier Technical Services, Inc., Copyright © 2012.
Licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported License.
Tornado charts are often used to compare distributions, in the form of back-to-back histograms. Tornado charts are particularly popular for comparing closely related populations, such as male and female age distributions. In this context they are known as “population pyramids”. Tornado charts are attractive, but I don’t think they are as effective as they at first seem to be. To illustrate this point, I went to the US Census Bureau and found the following age data for males and females:
| Age | Female | Male |
| 0 – 4 | 20,362,338 | 21,270,982 |
| 5 – 9 | 19,433,506 | 20,312,348 |
| 10 – 14 | 19,759,032 | 20,720,770 |
| 15 – 19 | 21,098,748 | 22,210,796 |
| 20 – 24 | 20,459,024 | 21,463,444 |
| 25 – 29 | 20,468,426 | 21,051,428 |
| 30 – 34 | 19,181,668 | 19,505,666 |
| 35 – 39 | 20,974,366 | 21,055,280 |
| 40 – 44 | 22,001,868 | 21,731,666 |
| 45 – 49 | 23,132,456 | 22,551,750 |
| 50 – 54 | 21,442,384 | 20,542,978 |
| 55 – 59 | 18,847,148 | 17,709,266 |
| 60 – 64 | 15,061,074 | 13,778,138 |
| 65 – 69 | 11,515,338 | 10,053,366 |
| 70 – 74 | 9,454,922 | 7,713,210 |
| 75 – 79 | 8,416,580 | 6,167,808 |
| 80 – 84 | 6,952,558 | 4,312,468 |
| 85+ | 7,642,992 | 3,470,102 |
We can make the two histograms from this data, one for the female population and the other for the male population.
The histograms present the data in separate charts, which makes them tricky to compare, while the vertical age group labels on the horizontal axis are difficult to read. A tornado chart combines the data by rotating these two charts so their categories are arranged vertically, and placing them back to back.
Although the category labels are now horizontally oriented, they are still difficult to read because they are partially obscured by the bars they overlay. This is often fixed by putting the labels on the side of the chart, which unfortunately puts them close to only one of the populations.
This is also sometimes addressed by splitting the chart halves and inserting the labels between the two populations. This is probably the best of the tornado chart options, because the labels are located at the baselines of each distribution.
While a tornado chart seems like a good approach for comparing similar distributions, I am always somewhat distracted by the optical illusion in which an image seems to switch between a goblet and two profiles in silhouette.
Source: AVIV – optical illusions – brain teasers – riddles
Another problem is that the two populations are more difficult to compare than we think when we view the chart. In the last tornado above, we can clearly see the greater female population in the oldest age groups, and we can see the baby boomer peak in the 45-49 age group. We cannot easily detect the differences between any age groups younger than about 60-64, because the bars move away from each other.
This problem can be solved by putting the bars on the same side of the category axis, in a clustered bar chart. We can easily see the differences between male and female populations in all age groups. In groups up to 30-34, the males have greater numbers; at 35-39 the numbers are very close to the same, and from 40-44 upwards, females have larger numbers, and the differences increase with age. An advantage is that the chart shows the populations with the same resolution as above in less space, because the data only extends in one direction from the category axis.
The problem with the clustered bar chart is that the alternating bar colors disrupt the smooth display of the distributions, and in some cases the distributions may be made to appear offset, because of the placement of the bars side-by-side rather than one atop the other. Jorge Camoes has written about population pyramids in How-to screencasts: Population pyramids in Excel and Animation and demographic information visualization. Jorge also thinks these charts are not as effective as they might be, and he suggests the use of overlapping bars, with one displayed as an outline rather than a filled bar. This approach gives a better impression of smooth distributions than the clustered bar chart above, but the different formatting gives different emphasis to the filled bar and outlined bar. The two charts below show the same data, but the initial impressions each gives are different.
A different choice of colors may improve the uniformity of the two series, but not completely. A black line and a light gray fill give the series more equal weight than the blues and reds above.
I’ve written about dot plots on my web site, where I’ve also linked to other sources: Good Graphs for Better Business, by William S. Cleveland and N.I. Fisher, Dot Plots: A Useful Alternative to Bar Charts, by Naomi B. Robbins, Ph.D., Compare Metrics by Category Using Excel Dot Plot Charts, by Charley Kyd, and Excel Dot Plots, by Kelly O’Day. Jorge Camoes also finds them a suitable replacement for population pyramids in Population pyramids in Excel. This is a good data set to display in a dot plot. The lines clearly show the distributions for both populations, as well as the relative populations in each age range.
Related Posts:
- Close Races
- Funnel (Tornado) Chart
- Use Dot Plots for Better Categorical Comparisons
- Re: Abortion Ratios 1980-2003
- Conditional Stacked Clustered Column Chart with Targets
- Charting 2011 Major League Baseball Attendance
Posted: Sunday, March 2nd, 2008 under Chart Types.
Comments: 20
Comments
Comment from Jorge Camoes
Time: Monday, March 3, 2008, 2:27 am
Jon, the problem population pyramids (as a subset of tornado charts) is that they became an icon of a the demographic science. So, you can make them more efficient, but I am not sure if the people in the field are prepared to accept them. (Please note also that they usually put the first age group at the bottom.) There was an interesting discussion around this topic in Stephen Few’s forums some months ago. I also wrote about it.
I do prefer the last design, but if you overlap the bars in a clustered bar chart I think that’s acceptable (in this case, the fill option in one of the series must be set to “none”).
Comment from Jon Peltier
Time: Monday, March 3, 2008, 6:40 am
Jorge -
I looked up tornado on your site, but it was the term “population pyramid” which found the posts you mention, Population pyramids in Excel and Animation and demographic information visualization. I’ve referenced that term and your posts. I’ve also flipped the charts over (Excel makes it relatively easy to reverse an axis), added an overlapped bar chart like you’ve suggested, and replaced most of the legends with labels.
The problem I saw with your bar chart that had one population filled and the other outlined, is that the outlined series had a different emphasis than the filled one. When the outline is used as a target, and the filled as an actual value, this difference is fine, but when you are comparing more equal data, such as these populations, I think it detracts from an objective conclusion. However, one step at a time.
Is changing this demographic visualization the same uphill battle we face with pie charts and gratuitous 3D effects?
Comment from Jorge Camoes
Time: Monday, March 3, 2008, 9:58 am
Jon, we can be gentlemen and fill women outline men… Seriously, I agree with you, filled/outlined bar charts are better suited for target/actual charts. But I believe this is the best option if you are using column/bar charts. But probably we should avoid them and use a line chart or a dot plot.
Demographers look at population pyramids to see the overall shape. If you “fold” it you get a higher data density and you can easily spot meaningful differences between sexes for each age group. But you already have a standard that gives you some insights. Pie charts and 3D effects just mean that people can’t manage data. That’s more challenging to fix…
Comment from Jon Peltier
Time: Monday, March 3, 2008, 10:56 am
Obviously part of the effectiveness of a chart type is the users’ familiarity with it. This would explain why a demographer would prefer the pyramid to a dot plot, and his familiarity would give him insights quickly which would take me longer. Whether another type is more effective may be less important. The overlapping outline/fill chart is a pretty good compromise.
But familiarity also makes people use pies and 3D charts, and their familiarity blinds them to the ineffectiveness of their chosen chart styles.
Comment from Doug Glancy
Time: Monday, March 3, 2008, 4:33 pm
Jon,
I like the clustered bar chart best, but I’d maybe go back to square one and make the bars vertical. I don’t find the age labels hard to read, and then it would be a “side-to-side” comparison of each age group.
Comment from Jon Peltier
Time: Monday, March 3, 2008, 4:56 pm
Doug – If you like the horizontal age axis with the vertical bars, you could easily fix the category labels. Since we’re measuring 5-year blocks, it makes sense to put the years that separate the bins on tick marks between the histogram bars. Mike Middleton’s Better Histograms includes instructions and an add-in to do this, but I just manually added a dummy XY series to add the labels “0″ through “85″.
Or if you like the overlapping bars, something like this:
Or even a horizontal version of the dot plot, which is our old favorite, the line chart:
Comment from Doug Glancy
Time: Monday, March 3, 2008, 5:41 pm
Jon, I like the first one. I find it captures the chronology well, because it reads left to right, it’s easy to compare each pair, and the new labels are very clean. The dot plot doesn’t quite jibe for me, because when I see one I expect it to be over years, e.g., from year 1980 to 2005. Thanks.
Comment from Jon Peltier
Time: Monday, March 3, 2008, 5:48 pm
Doug – Hat’s off to Jorge, I think I prefer the middle one. You’re right about the line chart: it isn’t really a time-line, but it causes the reader to think it shows a continuous span of years.
Comment from Kevin Johnson
Time: Friday, March 14, 2008, 6:31 pm
Can someone tell me what the right and left side of a tornado chart means. I am having problems understanding it. For instance, my text book says that the cell that has the most impact on the EMV should be placed at the top of the chart. However, my problem involves setting several input cell to + and – 20% of there base case. Nevertheless, two of my imput cells have an amount of -40,000 but yet both are shown at different locations on the chart. Could someone explain. Thanks.
Comment from Jon Peltier
Time: Friday, March 14, 2008, 9:28 pm
Hi Kevin – There’s not necessarily any significance between the left andd right sides of the tornado plot. You have two opposite items being compared so you draw one in each direction. Often tornado charts are used to compare effectss of separate categories, rather than of an ordered set of categries (like the ages in my example). In the case of independent categories it’s customary to rank them from the widest spread at the top to the narrowest at the bottom. But you don’t sort each side, you sort the categories by the total of both measurements in each. I’ve also used charts which weren’t charts showing two populations, but more like floating bars going from a minimum to a maximum for each category. We sorted those from widest to narrowest and called them tornados too.
Comment from Kevin Johnson
Time: Saturday, March 15, 2008, 1:05 am
Thanks Jon.
Comment from Sarah
Time: Thursday, May 15, 2008, 5:23 pm
I’m a couple of months late on this, but I like the idea of folding a population pyramid onto itself to more easily compare male to female. I have a slightly more complex case (which, by the way, I created using your tornado chart tutorial):
[image no longer available]
I guess one option would be to turn all of the series into lines, but since we have age ranges and not single-year ages, I think I prefer bars. But it’s difficult to compare male to female education levels except in the most pronounced cases, such as Afghanistan:
[image no longer available]
Comment from Jon Peltier
Time: Friday, May 16, 2008, 8:17 am
Sarah – Those are interesting graphics. Breaking down the bars into prportions (i.e., by education level) complicates the issue if you want an overlaid comparison. Sometimes I find it better to use several charts. For example, I might do a master dot/line plot of total population M/F. then a version of this for each education level, then maybe a line/dot plot for each gender showing all education levels, unstacked. Then I’d pick the few charts that supported the story I was telling, and place them all in an appendix.
Comment from Paula
Time: Tuesday, July 21, 2009, 9:17 pm
I might be dense, but I cant find the tutorial that Sarah would have used to create the the tornado graphs with the x-axis down the middle. Can you point me to the link or are these in books. thanx
Comment from Paula
Time: Tuesday, July 21, 2009, 9:30 pm
In addition, I have seen a tornado chart tutorial by you, but I cant get mine to look like sarah’s with the split axis with 2 zeros. thanx.
Comment from Jon Peltier
Time: Wednesday, July 22, 2009, 12:19 am
Here are a couple links:
Tornado Charts
Tornado Charts and Dot Plots
Keep in mind that tornado charts are not as good as you might think for comparing two sets of data. The fact that the bars extend in opposite directions makes comparisons difficult.
Comment from Copa
Time: Thursday, June 24, 2010, 7:58 pm
thanks for the info
Greetings from the south
Comment from Juan C. Mendez
Time: Thursday, September 16, 2010, 11:02 pm
John
Good post. Other kind of chart that is also named tornado is commonly used in financial and business settings to show how a given result (usually NPV) is affected by changes in the key assumptions, variables or uncertainties.
I show how to create these charts on my blog [link no longer available]
Best wishes,
Juan C.
Comment from Dave Fenton
Time: Friday, March 4, 2011, 12:24 am
I like the tornados but they are all with respect to zero. Say you have values of ranges (5-70, 60-90, 30-80 etc.) and you want to tornado them all on top of one another where their centerlines don’t necessary match up. This is useful in Sensitivity Analysis.
Thank you,
Dave
Comment from Jon Peltier
Time: Friday, March 4, 2011, 3:52 pm
Dave -
In this case you want a floating bar chart, with a transparent bar with a value equal to the lower limit of the spread, and a filled bar with a value equal to the width of the spread (upper limit minus lower limit).
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