Actually, this isn’t the original chart, theirs was substantially larger. Since theirs was obviously constructed in Excel 2007, I transcribed their data and built my own. Though smaller, this chart lacks none of the features of the original.

Jimmy made some remark in his tweet about the “worst chart ever”, but I have to say, this chart is not even close to the worst ever. It may be in the bottom quartile, but we’re talking about a long, long tail.

So what’s wrong with the chart, anyway?

We’ve heard many times about how people just aren’t very good at judging angles or areas, and that makes pies ineffective for all but the simplest parts-of-a-whole displays. Donuts take this one step further, cutting out the central bit of the pie, so we’re relying on areas alone, without any help from the angles where all the wedges meet.

Of course, the donut resembles the big fat zero most viewers would give NBC as their grade.

Let’s improve this chart in steps. First, if we sort the data points, we only have to try comparing adjacent points. This also puts the most biting criticism of a sports event, “Not Enough Sports”, right up front.

Now we can put the munchkin back into the donut. We have the angles to help us judge the areas, which may or may not help.

Finally, we can convert the pie pieces into candy bars.

Now the labels are right next to the data points, not off in some distant legend, and the bars are easily ranked by length. The above chart may cause confusion with its multicolored bars, and we don’t want any viewers hunting around for the key to find meaning in the bar colors where none exists, so we use a single color for the bars. Or in this case, two colors. I’ve highlighted “Happily Watching” in a distinct color to set this category off from all the negative ones.

The above chart has two sets of labels. There is the horizontal axis at the top of the chart and the labels at the end of each bar. Is it redundant to have both in the same chart?

We can choose to leave data labels off the points and rely solely on the axis labels.

Or we can keep the data labels on the points, remove the axis, and close up the space between the chart and the title.

Which labeling option to you prefer? Axis labels, data labels, or both?

UPDATE 3 March 2010

Steve Fleming suggested in a comment below that I move all of the data labels between the category labels and the category axis. Good idea.

Similarly, the labels can be moved from the ends to the bases of the bars.

Peltier Technical Services, Inc., Copyright © 2010.
 
Licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported License.
 

Okay, as you move left to right, the bubbles get larger. The bubbles in the top row are larger than the rest, but except for the first bubble in the second row, the bubbles don’t change much from row to row. If not for the numerical labels, we wouldn’t notice any difference at all.

Apparently bubble area, not diameter, encodes the values; if diameters controlled size, the leftmost bubbles would practically disappear. On closer inspection, I noticed that the top row of bubbles, Income, obviously uses a different scale than the others.

Given our difficulty in judging bubble areas (or diameters), and given the unannounced scale change between Income and Family Contribution, the data may as well have been presented in a table. It has the same grid and numbers, but is smaller and lacks those distracting circles.

However, you can make much sense of the data if you make a simple line chart. Now you can see the similarities and differences in the three plans.

But I thought this was a bit simplistic, a bit incomplete. I spent ten or fifteen minutes at the Kaiser Family Foundation Health Reform Subsidy Calculator and filled out the data. When you’re making a bubble chart, you don’t need many data points, in fact, you can’t accommodate many data points. But a line chart can represent a continuum of data points.

In this chart it becomes clear that the plans are similar in the middle of the income range, but differ at the ends, not only in the costs, but also in the income levels where the plans kick in at the low end and where the plans reach maximum contribution at the high end.

If we superimpose the data from the bubble chart onto the line chart, we see that the bubble data actually shows a smaller difference between the plans at the high end than we can see in the line chart.

Nice chart and all, but I’ve neglected some details. There are no titles in the chart, so someone reading the newspaper would actually have to read the article to get the story. Also, except for USA Today, most newspapers are limited to black and white graphics. And the charts I’ve made are rather large for their data content (though smaller than the original bubble chart).

So how can we make this chart more suitable for a newspaper? Shrink it, add titles, and convert the colors to black and two shades of gray.

You could use dashed or dotted lines as well. Excel up to 2003 does poorly with thicker dashed or dotted chart lines, but Excel 2007 renders these features nicely.

Apparently there has been much criticism of this chart. On the one hand, it is eye-catching. On the other, it does not clearly show anything without a lot of mental gymnastics. If you view it at full size, you can at least read the numeric labels in the margin, but reduced to fit into a medium sized monitor, it’s illegible.

The iGraphics Explained blog posted an attempted clarification of and justification for this beast in Data Visualisation and Quantitative Easing explained by Ciaran Hughes in the Daily Telegraph. The explanation said

On the left we can see the ‘running total’ of the value of assets purchased, against the ‘monthly total’ on the right hand side, keyed at the top of the graphic.

I think the reader is able to understand the depth of the financial stimulus package, and when.

Right. I showed this picture to an unbiased bystander (my wife, who has a PhD in the biological sciences and who now teaches math and science), and asked how well it showed monthly and cumulative spending. Her initial response: WTF!!??

As I pointed out, you can only see the running and monthly totals if the text labels are legible. A table without the pretty distraction in the middle would be an improvement, if only because the numbers are not spaced out by the nice colors.

Of course, seeing numbers in text form is not the same as truly visualizing the data. A bar chart is a major improvement over the table and over the fancy illustration at the top of this article.

If you want to see, or emphasize, the month-to-month trend, which was the intent of the original illustration (i.e., the “Easing” of government support), a line chart is the best option. You can readily see the negative slope of the Monthly data, and the decreasing slope of the Cumulative values.

In all of its glory, here is the original 3D not-quite-exploded pie chart.

What’s Wrong?

What’s wrong with this chart? Well, it’s a pie, and we’ve covered this ineffective visualization method before. It’s rendered in 3D, which through the magic of simulated parallax distorts the apparent sizes of the data points (i.e., the wedges). Also the legend is truncated: the last three items are left off the bottom. They’re each only 0% of the total, but you can see paper-thin wedges struggling to remain upright in the pie.

In a few moments I’ll describe the larger visualization sin. But first I’ll try to duplicate this same chart.

I pasted the data into Excel, made a 3D pie, and adjusted the colors and orientation until I had gotten pretty close to the original.

I’ve managed to include all of the legend entries. But my chart doesn’t resemble the original very closely, does it? What if we explode the pie?

It still doesn’t resemble the original. When I exploded the pie, the wedges moved outwards by the same amount. The edges that were at first touching are still parallel, and the angles at the vertices of the wedges are unchanged.

The original pie, on the other hand, has its wedges still touching in the center. The gaps themselves are wedge-shaped, which decreases the angles of all of the pie’s wedges and distorts our decoding of the underlying values. I guess this is what happens when there is too much art, too much aesthetics, involved in the graphing of data.

Reconstructing the Extra Distortion

Let’s start with plain vanilla pie charts of the data, in both 2D and 3D. I’ve omitted the legend and labels for clarity.

If we do a straightforward explosion, the shapes of the wedges are unchanged. The gaps are not uniform in width, but are larger between wedges with larger values. There is also some kind of optical illusion going on in the center of at least the 2D chart.

We can recreate the appearance of the original chart by inserting an invisible wedge with value 2500 (I fiddled to get this to look about right) between every pair of adjacent wedges in the first chart, without exploding the chart.

All the gaps are the same width, and some of the real wedges are smaller than the gaps. This proves the maxim, “Less is More”. The 3D pie closely matches the appearance of the original 148Apps chart.

you can take this approach to extremes. With ultra-wide wedges, there isn’t too much differentiation between the data values.

We can take this one step further, by moving all of the gaps to the “end” of the pie.

This clearly illustrates the distortion of the fancy wedge-gapped 3D pie chart. The amount of these pies that are made up of nothing is 31%, leaving only 69% for displaying data. The largest wedge, which comprises 17% of the data, fills only 11% of the circle.

We humans are bad enough at judging areas and angles, so when the angles are distorted in this way, we’re hopeless.

There are a number of strange and wonderful charts on the dating site, but the one that led to this specific discussion is shown here.

The major controversy it that the horizontal X axis is not located at zero on the Y axis, but at the average effectiveness of 27%. A second issue is that vertical bars pretty much force category labels with hard-to-read orientations. If these are really a problem, then a horizontal bar chart with the bars starting at zero solves it, as Kaiser demonstrates.

If you are interested in relative effectiveness of each photo category, then the zero axis origin may not be so important. Also, the resolution of this chart is better than if the bars had to start at zero.

This is an improvement in terms of legibility of labels and judging the absolute values of the bars. Perhaps a dot plot is equally effective?

Unlike a bar chart, starting the value axis at a value greater than zero poses no cognitive issues. We can then expand the scale, to gain back the resolution of the original chart.

What do you think of these alternatives?

Q: What’s worse than comparing categories within a pie chart?
A: Comparing categories between 2 pie charts.

I will use an article Jeff cited to show a better way to make comparisons.

The Analysis

Jeff pointed to Why are men more affected by labour market downturns?, a study by the NZ Department of Labour. The article stated that of the 34,000 jobs lost by the NZ economy in the eight quarters ending September 2009, 80% were lost by men.

This disparity in job losses can be seen through an analysis of the jobs held by men and women. Many more men hold jobs in manufacturing and construction, sectors which are hard hit during recessions. Women on the other hand are more likely to be employed in fields such as education and health, which are largely government funded and tend to be less sensitive to economic conditions.

The Visualization

This is a well thought out analysis, but as Jeff pointed out, comparing wedge sizes in two different pie charts is not an effective way to support the argument. Their two original pie charts were huge, and not even posted on the same page, though they did show barely legible thumbnails adjacent to the text of the article. The following two charts show the breakdown of jobs by men and by women. I’ve enlarged the pit thumbnails somewhat, to improve legibility and to compare with an alternate display I’ve created below using Dot Plots.

Seasonally adjusted male employment by industry September 2009 quarter

Seasonally adjusted female employment by industry September 2009 quarter

The Alternative Visualization

I’ve made two dot plots to show the same data. Within a couple pixels, the Dot Plots (including title) are the same size as these pie charts (without title), but each Dot Plot shows twice as much information, the Dot Plots have much more legible text, and the comparisons are much easier to make within a Dot Plot than between multiple pie charts.

It would be so easy to make a few simple annotations on one of these dot plots to drive home the point of the analysis.

Dot Plots

Dot Plots have been developed as a more effective tool for categorical comparisons than bar charts, pie charts, or (gasp!) donut charts. You can read about them in several places:

• Good Graphs for Better Business by William S. Cleveland and N.I. Fisher
• Dot Plots: A Useful Alternative to Bar Charts by Naomi Robbins
• Compare Metrics by Category Using Excel Dot Plot Charts by Charley Kyd
• Excel Dot Plots by Kelly O’Day
• Dot Plots on this web site

The last three links show various techniques for creating Dot Plots in Excel. Excel doesn’t make it easy to create Dot Plots: you need to use one helper series technique or another to generate the text labels along the vertical axis. The easiest approach is probably to use a horizontal bar chart with hidden bars to supply the labels, and an XY chart to supply the data points.

To simplify the creation of Dot Plots in Microsoft Excel, I’ve developed a utility that generates a dot plot in a simple button click. The utility is a standard Excel add-in, and it adds a Dot Plot button to the Excel menu (versions 2000 through 2003) or to the Excel ribbon (versions 2007 and later). The button pops up a simple dialog for the user to select formatting options.

Excel detects a preselected data range, and remembers the Chart Lines options from the previous time you used the utility. It produces a very simple Dot Plot adjacent to the data range.

Two minutes of formatting produces charts like those I used above to support the findings of the NZ Department of Labour.

The PTS Dot Plot Utility is available from the Peltier Tech web site for a nominal fee. It can be downloaded as soon as the purchase is approved, it installs itself using the downloaded setup file, and the button appears the next time Excel is started.

Click on the icon to the left or visit PTS Dot Plot Utility to check it out.

To learn about Peltier Tech’s other utilities, visit PTS Excel Charting Utilities.

I missed National Pie Day, but while reading The Real Reason Outsourcing Continues To Fail, I encountered a pie chart that gave me indigestion. It purports to show problems with inter-cultural relationships that lead to outsourcing failures.

What’s wrong with the chart?

What’s wrong with this pretty chart, you may ask (or you may already have a good idea). Where to begin…

It’s a 3D pie chart, and we’re looking at it almost end on, so the sizes and angles are all distorted. The values are unsorted, so position around the pie doesn’t help determine relative percentages. The legend is ordered by row instead of by column, so you have to go back and forth between the pie and the legend, then back and forth between the two columns of legend entries, then if you remember, back to the pie.

When I visited the original report that contained this chart, What Causes Outsourcing Failures?, the reason for the unsorted values became clear. Figure 1, earlier in the report, showed its slices sorted by value. Because of the severe angle you can only tell the chart is sorted because the data labels are in numerical order.

Placing “Other” in the middle of the data is unorthodox. Generally “Other” is placed at the end, because typically it’s comprised of several very small values.

Figure 3 used the same order as Figure 1, except that “Other” was placed at the end where it belongs. This consistency is not a bad thing, but it’s dwarfed by the other problems with the charts. There is another pie chart, Figure 2, which shows Least Frequent Causes of Outsourcing Failure. I’ll spare a kitten and not repost it here.

How can we make these charts better?

Let’s dispense with the 3D distortion. The circular arrangement also does not aid in understanding, especially in the unsorted Figure 3. Let’s remove the legend and put the labels right next to the points. This way, we can reduce the number of colors (which I haven’t mentioned, since it often boils down to a matter of taste).

Well, that sounds to me like a bar chart, so here are bar charts of the two pies above, Figure 1 above and Figure 3 below.

Easy to read, easy to correlate label with data point, easy to see a strong variation in Figure 1 but not in Figure 3. But they take up a bit of room, don’t they? Let’s see how they look in a panel chart.

That’s good to compare the general shapes of the trends. If we’re concerned with the specific values of each category, we can even plot the data in the same space with a dot plot.

The article shows a line chart with a line connecting a country’s health care spending on the left axis with its life expectancy (at birth) on the right axis. The US and Mexico are colored differently because they do not have “Universal” health coverage. Thicker lines indicate more doctor visits per person per year. Click on the chart for a full sized version.

The Original Chart

This chart was mentioned in Not the best time for a parallel coordinate plot . . . but it’s not actually so bad here by Andrew Gelman, who thought the chart wasn’t terrible, but wondered why they selected these specific countries for the chart.

Evan Falchuk was more critical in Warning: Graphic Politics. Evan noted that there were no apparent correlations between life expectancy and spending, number of doctor visits, or whether there was universal coverage. Evan also asked whether spending was even relevant to the quality of health care.

None of the critiques of the chart mentioned the effect of malpractice insurance on health care costs, though one response to Falchuk’s post mentions defensive medicine. It’s more complicated than the US being ripped off, and anyway, that’s a political discussion for another place and time.

John asked me when he sent me the original link how else I might graph the data. We agreed that the purpose of the original chart was to show the huge spending in the US, compared to its life expectancy, in as dramatic fashion as possible. To take away some of the drama, I redrew the line chart with more equal spreads in the respective Y axes. You could tweak the scales even more to reduce the relative steepness of the lines, or make the chart wider and less tall.

The chart is still a bit dramatic, but not as outrageous. The extreme slopes of most of the lines are just a distraction. As noted above by Evan Falchuk, this chart shows no correlation between the two main variables in the study. Not surprising, because the correlations are weak. Also not surprising, since it’s not a very effective way to show a correlation.

The New Chart

The best way to show correlation between two variables is in an XY chart. I got into Chart Busters mode, and plotted X=spending and Y=life expectancy in the following chart. The US and Mexico are colored differently to highlight their non-universal-coverage status, and data points are sized to reflect the number of doctor visits.

The US is an obvious far outlier. You can imagine an upward slope in the green markers, perhaps steeper than 45° in this plot. The correlation is not really strong, nor is it negligible. Excluding the US, the R² value is 0.52 including Mexico and 0.48 excluding Mexico.

A commenter to the National Geographic post listed a handful of other countries, which I’ve included in the XY chart below:

Inclusion of these countries increases R² to 0.56, probably since most of them fall within the dense upper range of the previously included countries, and one point, Turkey, falls below and left of the rest. In all of the regressions, the slope of the line is 1.9 years per $1000 of spending, and the Y-intercept implies that we’d live to 73.5 without spending a dime. At the level of spending of the US, the relationships predict a life expectancy of 87.5 years.

What’s the takeaway?

First, the XY chart shows the correlation between spending and life expectancy much better than does the line chart, without nearly as much drama. The US still shows a dramatic divergence from the other countries, spending more than twice as much for a slightly below average life expectancy.  We’ll leave debate about the reasons for this divergence for the political blogs.

A few months back they had a bar charts with a value axis that started above zero, and we can’t have that, now, can we? But I must say, these daily charts do not often violate good practices, and while they are somewhat decorated, it is usually limited to eye-catching series coloring and not splashy chart trash.

In iPhone Blows Past Windows Mobile the chart of the day showed the growth in users of half a dozen smart phones during 2009. From the title of the post, I expected to see lines crossing at some point. but they didn’t go for that effect. I’ve recreated their chart below.

The chart has several problems. First, the time scale moves vertically instead of horizontally. Second, the time points are not evenly spaced. The gaps between measurements alternate between three months and two months. Third, there is no immediate view of anything crossing anything else. The user has to work to extract that information.

A fourth problem is that the ends of the bars seem to trace a smooth curve from Google in February through RIM in October. Well, except for Microsoft, and you could even infer that the chart shows Microsoft as better than the rest. This is a spurious relationship resulting from the accidental alignment of the points grouped this way.

I put on my Chart Busters cap and went to work. The result is the chart below.

I’ve changed the time scale to horizontal, left to right. I placed the data points at proportional positions along the axis. I’ve changed the aspect ratio of the chart. And I used a line chart rather than a bar chart. What is now clear is the obvious growth of the iPhone past the stagnant Windows Mobile. And that was the point of the Chart of the Day article, wasn’t it?

Well, as Edward Tufte once said, “The only thing worse than a pie chart is several of them.” Especially in this case. If not for the different titles and the percentage data labels, I would think someone had goofed and used the same graphic twice.

Having to read the numbers off the chart to make comparisons defeats the purpose of graphing the data, but is not as efficient as a table, because the numbers are strewn about the visual field. I can see that Google takes up most of both pies, but I can only estimate that Google’s take is about 2/3 of either pie.

So what are we trying to show here? If we want to show how each search engine’s share changed, a clustered column chart is good, because the two bars for each company are adjacent, for easy comparison.

It’s easy to see that Google and Microsoft both went up slightly, and Yahoo went down. And nobody’s really concerned with AOL or Ask, are they?

An alternative to the column chart is a line chart. I shaded the plot area light gray, so it’s obvious that even though Google is way up here and the rest are way down there, all are part of the same chart.

Again, it’s clear that although the changes were rather small, Google and Microsoft both gained at the expense of Yahoo.

What if it’s the change itself that we want to show? Again, a column chart fits the bill.

There are a lot of options when you’re selecting the chart type. You need to decide what you want to show in your chart, then select an appropriate graphic that shows it. As usual, it’s not a bad move to select from the array of 2D line and bar charts.

And I had too much pie over the Thanksgiving weekend. They call it a long weekend, when a more accurate phrase would be wide weekend.