In Anyone But Romney: The GOP race so far, the National Post shares an enormous infographic with us (click for full size image).

The bulk of the graphic is taken up with what remind me of snake skins laying out to dry. Apparently the widths indicate the relative popularity of each candidate along a vertically-oriented time axis.

The unorthodox alignment of the time axis is initially disorienting, but the blobs are big, they must be important. Hmm, are those all months delineated by the horizontal white lines? Apparently so, even though they differ by more than the days in each month would account for. The spacing must be dictated by the occurrence of each successive poll, not by the passage of days.

The snake skins are decorated with parallel arrows, which change direction in mid-January. Is it the dropping out of Perry or of Huntsman that this change indicates? Or nothing; probably that’s just where the fancy fill pattern changes.

Auxiliary Charts

Okay, I’ve feasted my eyes on this lovely rotated timeline blob thing, what is shown in these small charts added as an afterthought to the bottom of our infographic?

The small chart at bottom left shows the popularity of the candidates. Wait. That’s what the big paint drips also showed. The date axis here is horizontal, left to right, but the data is indistinguishable from that in the upper graph. The months have the same irregular spacing.

At first, the small round markers beside each candidate’s name appear to show a significant time point, because Huntsman’s line is labeled at the point he dropped out. But Santorum and Paul and Romney and Gingrich haven’t dropped out, so that’s not the purpose of the circles. On further inspection, they just seem to say, “This label goes with that line”. Some lines are labeled once, some twice, and . . . QUICK! Without referring to the large chart above, which candidate goes with the yellow line?

Poor Herman Cain, couldn’t buy any respect.

I think the only purpose of the line chart is to show what the monster paint blobs showed, but in easy to read fashion (except for the labeling issue). Conversely, the big blobchart seems to be shouting, “Look Maw, I made a info graffick!”

The remaining chart shows basically that Mitt Romney has raised a lot of money, much more than his competition, and he’s also spent more than they have.

Overall, this monstrous graphic would have been more informative with just the bottom two charts, without the distraction of the rattlesnake hides that occupy 85% of the original. Of course, if the intent was to get people to look at your page, the snake hides may have succeeded.

Apparently the National Post is waiting for anybody, even Newt Gingrich, to overtake Mitt Romney’s lead in the polls. But this article, even the updated edition, predates Gingrich’s poor showing in the Florida primary. The question that remains is, Can money buy election happiness?

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Licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported License.
 

The reason for this arrangement is logical, once you figure it out. To illustrate, let’s start with this data. Yes, the data in column A is mixed up. Instead of 1-2-3-4, it goes 1-3-2-4, to help illustrate differences between XY and Line charts at the same time.

Here is an XY chart made from this data. Looking at Series 1, we see it starts at X=1, proceeds to X=3, then X=2, and finally X=4. No surprise, since it’s following the data, which as I pointed out above, is in mixed up order.

Big deal, no surprises. But let’s look at the chart axes for a moment, and review 4th grade math.

By default, the two axes will be located along the bottom and left edges of the chart. Where the axes intersect is called the origin, and it is where both axes have their minimum values (we’re dealing with non-negative data). Lower values are plotted closer to the origin, and higher values further away.

Let’s make a Line chart with the same data. It looks different from the XY chart. No, the series are formatted the same, with markers and lines. But check out the horizontal axis. The numbers are not sorted numerically, they are listed in the order they appear in the worksheet, as if they have no numerical value. In fact, in line, column, area, and bar charts, Excel treats X values as non-numeric labels. (Unless the X values are dates, and I’ll cover that another time.)

Note that the axes still cross at the origin in the lower left of the chart. Lower Y values are closer to the origin, and X values encountered earlier in the worksheet are closer to the origin.

Okay, easy enough. In a line chart, Excel lists the X axis labels in the same order as in the worksheet, and the origin is at the bottom left of the chart.

Same with a column chart. Note in the column chart that the order that series are clustered is also the same order as in the worksheet.

Now let’s make a problematic bar chart.  1 is in the top of the worksheet range, but at the bottom of the axis. But remember, the origin is at the bottom left, and the lowest values and first labels are located closest to the origin. So the “1″ label on the vertical axis is closest to the origin, that is, lowest in the chart, even though it was highest in the worksheet. The series are also in the order they are because series 1 is closest to the origin.

If you really need the chart to be arranged the other way, it’s a simple two-step fix. First, format the vertical axis, and check the box for “Categories in reverse order”.

See, now the top label in the worksheet is also the top label in the chart. Reversing the categories has moved the origin to the top left of the chart, so the bottom axis is now at the top of the chart. Note also that the series are now listed in the expected order.

If you want the horizontal axis back at its customary bottom position, format the vertical axis again. (You can do this step at the same time as the earlier Format Axis step.)  Select the option button for “Horizontal axis crosses: At maximum position.”

Since the vertical axis maximum is now at the bottom, that’s where the horizontal axis appears.

Now we know enough to go back and fix the original chart. Format the vertical axis, reverse the category order and make the horizontal axis cross at the maximum.

Top is Top, Bottom is Bottom, series are plotted in 1-2-3 order, and we can finally rest easy.

Peltier Technical Services, Inc., Copyright © 2011.
 
Licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported License.
 

At first glance, these lines seem useful, because the lines will converge or diverge depending on changes in value of a series from stack to stack.

Unfortunately, the differences in slope is not really observable unless it is substantial. There are better ways to display this data.

The Data

Here is the data used in this example.

Standard Charts

Let’s start with the simple stacked column chart below. We can readily see how the total varies from year to year: a steady increase from 2005 through 2008, a plateau between 2008 and 2009, and a drop in 2010. We can also judge variation in series “alpha”, because this series starts at the base of the chart.

Series “beta” is harder to judge, because its blocks are added to the staggered baseline formed by the tops of the alpha blocks, and the baseline is staggered further. Comparisons between points in different series is also made difficult by the lack of a single baseline for the bars.

We can add the series lines to connect endpoints of corresponding points. These lines may help judge changes in a series from year to year if the changes are large enough, but they don’t reset any staggered baseline to a straight line. They also do not help at all with comparisons of different series. In fact, the lines may guide your eyes away from the comparisons you are interested in.

Series lines add useless elements to the chart. This is the definition of chart junk.

Feeble Improvement Attempts

Let’s give the data a common baseline by unstacking the points. Now we’ll have an easier time comparing lengths of the bars, because the different lengths only move the tops, not the bottoms, of the bars.

There is a problem with this display: it is too cluttered to read easily. We can easily compare the bars within a given year, but when we compare from year to year, the bars in between interfere with the comparison. This is especially problematic with the shorter bars.

If we convert the bar chart to a line chart, we’ll remove the vertical rectangles of ink that interfere with our comparisons. Now there is a different problem. The overlapping of points makes it difficult to trace a series from left to right. Even the different colors don’t help a lot, and if you are looking at a photocopy, you’re lost.

A Better Approach

Well, we don’t need to overlap all of the data. We can plot each series in its own stretch of horizontal space, so each series occupies its own panel. Yes, it’s a panel chart, even if we don’t have lines between all of the panels. It’s also similar to a type of chart known as a cycle chart.

We can see immediately that gamma has an overall downward trend and epsilon a similar upward trend. This was not at all visible in the earlier charts. We can also clearly see that the general amplitudes of alpha and beta are similar, as are those of gamma, delta, and epsilon. We could have seen this in the stacked charts, if we’d squinted long and hard enough. That’s too much work; the panel chart is so much easier.

The panel chart is not too hard to create. It’s really a simple line chart. What’s complicated is the data layout, shown below. The data is spread out vertically so the blocks of data do not overlap. Each blue shaded cell is completely blank (not a formula returning a null string, but a completely empty cell). The tan shaded cells contain space characters.

The two blank cells in the top left tell Excel that the top row should be used for series names and the left two columns should be used for category axis labels. The blank cells between series names in the first column tell Excel to center the labels across the blank ranges. The space characters keep the year labels from moving out of place. I hid all but the first and last year labels, since these two were sufficient to describe the data.

We actually don’t need different formatting for the different series, since they are separated in the chart. We can use a single column to define our data range (keeping the same category axis data, with its blank cells and space-containing cells).

The resulting chart shows our data as clearly as the previous one. Adhering to a single format makes the chart a bit cleaner.

Obviously this chart does not include the totals for each year. We could include them in this chart, but that has the undesirable effect of shrinking the individual series, reducing the resolution.

There’s a radical approach to showing both the individual series and the totals. It doesn’t involve mucking around with dual axes, which cause more confusion than anything else. It doesn’t involve any kind of tricks to force all the data into the same chart. What is the radical approach?

Two charts.

The first chart shows the individual values, in the panel style chart above. The second chart shows the total values, I used a stacked bar, but you could have used a line chart of the totals without its constituents. I’ve revived the colors for the line chart on the left, so the lines can serve as a legend for the colored blocks on the right.

What do you think of this approach?

Peltier Technical Services, Inc., Copyright © 2011.
 
Licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported License.
 

Sales funnel graphs are used to represent the development of sales leads into actual sales, or conversely the attrition of sales leads before they become actual sales. In the example below, A might represent web site visitors, B visitors who accessed the specific sales page for a product, C visitors who clicked the link to receive additional information, and D customers who finally purchased the product.

Sometimes these funnels are drawn tapering to a point, as above, and sometimes they taper to a small but nonzero width, as below.

I don’t like this kind of funnel chart. Sit back and I’ll tell you why.

Funnel – Bad Metaphor

Sales funnels are so named because of a superficial resemblance to the kind of funnel found in many kitchens or inverted on top of the Tin Man.

This is where the metaphor breaks down, for me at least. In my kitchen, everything that goes into the top of the funnel comes out the bottom. That’s the purpose of the funnel: to make it easier to pour liquids and small particulates into a small-mouthed container without spilling. A sales funnel shows how much is left at a certain point, that is, how much has not spilled out. They really should be called sales “sieves”.

Funnel – Bad Graphic

Even worse than the bad metaphor is the bad graphical behavior of a funnel chart. Funnels badly distort their data. Let’s examine this distortion with the idealized funnel below. Each colored layer of the funnel has the same value, that is, I’ve constrained it to work like the funnels in my kitchen: what goes in at the top comes out at the bottom. These funnels are usually drawn to make the height of each section proportional to its value, and the stack of areas starts at a small width at the bottom (zero width in this one) and widens to a maximum height at the top. What our eyes see is a much larger colored region at the top, but our eyes are fooled by the hugely distorted areas.

In this graph, I have divided each colored area into triangles as large as the single bottom purple triangle. Although each colored band represents the same value, each band uses a much larger amount of area (number of small triangles) to represent this value. By the time we get to the top band of the chart, we have used 7 times the area of the bottom band, for the same encoded value. This is a poor means of encoding data.

Funnel Chart: From Bad to Worse

The specific graphic that kicked off my current rant was brought to my attention by Adam Vero of blog.meteorit.co.uk in a comment under my recent post, Excel 3D Charts: Charts with No Value. He read about a Simple Chart Modification in Microsoft Dynamics CRM 2011 in a Microsoft blog, in which a “Chart Wizard” (said I sarcastically) was showing how to improve on the length-squared distortion in a regular 2D funnel by pimping it into a length-cubed distortion in a fancy faux-3D funnel.

This is bad on so many levels.

A Better Representation of Sales Flow

When I talk about improving a chart, I don’t mean increasing the pseudo-dimensionality of the chart, or increasing the use of gratuitous graphical effects, or blinding the readers with pizzazz. I talk about improving the transfer of information. Thanks again to Adam Vero for starting this discussion.

We can correct for the massive area distortion in a funnel graph by cropping the sides of the funnel. Now the remaining stacked column chart has columns that have heights and areas which are proportional to their values.

Here is the simplified stacked column chart. A lot easier to interpret than the funnel.

We want to represent retention in each step of the sales process. Bar sizes can be compared more easily if the bars are arranged side-by-side with their bottom ends aligned. The side-by-side arrangement also gives a somewhat intuitive sense of how the sales steps proceed, since we westerners interpret the passage of time from left to right. This clustered (side-by-side) column chart better represents the sales progression than does the previous stacked chart.

We don’t need the different colors in a clustered chart, and we can place our labels right below the bars.

If our data is tied to events that have occurred on or by specific dates, we can convert the bar chart into a timeline. For example, we mailed out invitations to sales prospects on January 15, a large fraction of these emailed us for information by March 15, a smaller fraction attended our June 30 sales webinar, and by November 22, we had made sales to an even smaller group.

Peltier Technical Services, Inc., Copyright © 2011.
 
Licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported License.
 

I’ve recreated the clustered bar chart below. The common problem is that the longer bars tend to overwhelm shorter bars. Most of the red bars seem to be hiding behind the companion blue bars, and it’s harder to notice the shorter blue bars. In addition, the data is sorted alphabetically by state, which completely obscures the ranking of states by either quantity.

The first step to improving the readability of this chart is to change the chart type to a dot plot. I’ve written about Dot Plots, and created a Dot Plot Utility for anyone who needs dot plots but doesn’t want to follow the tedious procedure to make them by hand. Here is the first dot plot of the data. The data is still sorted alphabetically by state, but already it is easier to read than in the bar chart.

The next step is to sort the data, either by murder rate

or by suicide rate.

Both of these charts show that suicide and murder rates are uncorrelated. When sorted by one rate, the data for the other rate bounces around as much as in the alphabetically sorted chart. In both charts, it is easy to see that in two of the states plotted, Louisiana and Maryland, murder rate exceeds suicide rate, but that generally the suicide rate falls well below murder rate.

We can look at the ratio of murders to suicides, below. There are only two states in which this ratio exceeds one, again Louisiana and Maryland, and we can also see that the ratio for these states far exceeds the ratio for the rest of the states. A criminologist may want to investigate these two states.

The intent of the Freakonomics podcast is to investigate why there are so many more suicides than murders, so we could look at the opposite ratio, suicides per murder, below. This time two different states, New Hampshire and Montana, are substantially higher than the rest, and a third state, Hawaii, is still markedly higher than the other states. This is the chart that best supports the podcast, and you can tell that rather than suicide being “twice as” prevalent as murder, suicide is probably more like four times as prevalent as murder.

My charts show data for fewer states than the original Freakonomics chart. I followed the sources cited in their post, but the data I found was not complete. I show all states except Florida, and I also omit DC, Puerto Rico, and the Virgin Islands (which had no data on the Freakonomics chart).

Follow-Up September 9th, 2011

My friend and colleague Chandoo has taken a similar but alternate graphing approach in Suicides & Murders by US States – An Interactive Excel Chart. He’s used a combination of worksheet formulas, in-cell charting, and conditional formatting to produce a VBA-free interactive chart. Very cool.

Peltier Technical Services, Inc., Copyright © 2011.
 
Licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported License.
 

Original Line Chart

The original line chart looked very much like this, showing normalized mortality rates as a function of body mass index (BMI). This is how not to make your chart.

Data was reported as a single value for each range of BMI as in the table below.

Improving the Line Chart

The first improvement we can make to the original chart is to rotate all labels into the horizontal orientation, so they are easier to read.

The next step is to change the horizontal spacing so that the separation between points is proportional to the difference in their X axis values. I’ve inserted the yellow column into the data, and in this column I’ve entered the midpoint of each bin range.

I plotted the mortality values against this new BMI column, and converted the chart to an XY Scatter chart so the new X values are recognized as numeric values and not equally spaced text labels. I added markers to show the actual points, but made the markers small so they aren’t emphasized with respect to the connecting lines.

Pretty good, but we have lost the bin range labels. No problem, let’s just add data labels to the series. You can add any type of labels (series name, Y values, whatever) and change the text of the labels manually, or you can use Rob Bovey’s Chart Labeler to do it automatically.

Yuck, that’s too cluttered. It was even worse when I initially had all labels below their respective points.

Let’s keep the points and their proportional spacing, but put the labels along the horizontal axis, as in the original chart. We can’t do that with built-in axis labels, but we can add a second series to the chart, with data labels. I added a column to hold the Y values for the added series; the Y values are equal to the axis minimum of 0.6.

Here I’ve highlighted the new series, and used the Chart Labeler (see link above) to add the labels below the points.

I’ve hidden the dummy series.

We’re still missing something: tick marks. Let’s add short vertical error bars to the dummy series. (See my article Custom Error Bars in Excel Charts for some helpful hints, and for a simply free utility I wrote to make it easier, even in Excel 2003 where it’s already pretty easy.) I placed a value in a cell, and used that cell as my custom error bar source range. My first value was way off, producing huge error bars. But by linking the error bars to the custom value in a cell, I made it easy to adjust the error bars until they looked appropriate, at a custom value of 0.04.

That’s quite an improvement over the original.

Alternative: Step Chart

I decided to make a step chart, in which each horizontal line segment spans the bin range at the Y value for that bin. I split each data point from the original data into two points, one at either end of the bin range. I chose endpoints that extended a reasonable distance beyond their bin cutoffs.

And here’s the step chart. No need for bin range labels, because you can see where the bin edges are along the X axis. And it makes clear that each bin’s value is constant across the bin. Well, it isn’t really constant, but the way that the data was presented implies that it is.

Alternative: Histogram

Another variation is to make a histogram with variable width bins. Can’t do this with a column chart in Excel: all those columns have to be the same width. This chart was made with the original line chart data, which leads to equal width bins for unequal bin ranges. I did not make the common mistake of starting the vertical axis at the same minimum (0.6) that was suitable for the line charts.

Instead of a column chart, we’ll use an XY chart and draw just the outlines of the columns. To do this we take the step chart data, and insert a row between each pair of duplicate X values. We copy in the X value from the cell above and assign a Y value of zero. This will produce a line from the end of one bin, straight down to the horizontal axis, then straight up to the start of the next bin.

Plot the data in an XY chart to get the pseudo-histogram. I left the endpoints at their Y values, not at zero, to indicate that these bins were not enclosed, but extended indefinitely. And again, I started the vertical axis at zero.

Summary

In her book, Naomi Robbins says Do not use equally spaced tick marks for uneven intervals on an arithmetic scale. Here I’ve demonstrated a few techniques to use proportionally spaced data points. Some are based on the “How Not To” line chart example in her book, and some are more intricate. Of all the options, I think I like the step chart best. It’s clean and uncluttered, and shows real values along both axes.

Peltier Technical Services, Inc., Copyright © 2011.
 
Licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported License.