Junk Charts

Organizing the bookshelves

When you go to the library, you expect to find the books in an organized fashion, typically sorted first by subject matter, then by author, then by title, and so on. Imagine the frustration when you walk in and discover that books are spread out everywhere with no discernible order. We are very particular about tidiness: it would still be terrible if the books were arranged by author and title without first splitting by subject matter. We are annoyed because it would take too long to find a book.

I did run into such an exasperating bookstore -- I believe it is in Brooklyn. The (used) books in this store are arranged by the date on which the owner acquired them. Fiction, I recall, is ordered by alphabets of last names, and then, say within the 'A' authors, the books were sorted by date of acquisition. What a headache!

Reader Pat L. had a big headache trying to figure out this chart, found on Wikipedia: (I'm just excerpting a small part of it; the full chart is here).

To quote Pat:

I was overwhelmed by the information -- so many chemicals and so many units of measure.  I quickly gave up and opened up the image in an picture editor.  One-by-one, I erased the blood chemicals I wasn't interested in.  Maybe if I was a doctor, the chart might have been useful.

 ***

One way to simplify this is using small multiples. Recognize that few if any users would need to directly compare every one of these chemicals. I'm guessing that groups of chemicals can go on separate charts. This is no different from a bookseller organizing shelves to help readers find books.

Also get rid of the minor gridlines.

For a summary chart of this kind, I doubt that it adds anything to include the information on whether the end of a range is definite and consistent, definite but inconsistent, or unknown.

Rightsizing: the graph edition

Reader Alex C. alerted me to this sensible note from Allan Reese, complaining about a piece of marketing by a software vendor (Aptech Systems), shown here:

This graph purportedly demonstrates the power of 3-dimensional plots, which presumably is a feature of the software GAUSSplot. As Reese pointed out, it rather unfortunately demonstrated the weaknesses of 3D plots, and it did so amusingly well.

Reese: "Apart from a Daliesque charm as abstract art, I can see nothing professional or commendable in this graph."

Yes, every decision rasps. Reese noted that the chart is named a "3D contour plot" by the vendor and yet we see a paired column chart arranged in an L-shape. The diskettes indicate the average of the 3 column values, which serves to obstruct our view of the underlying data. The legend--which is a palette of colors--plays the redundant role of gridlines. The diskettes take on various colors but the label shows it in orange. The two identical axis labels run in opposite directions, with a third running horizontally atop the color legend. The title announces a comparison of natural and synthetic fabrics, which explains how the eight fabrics were divided into two groups but will be missed easily. We surmise that the chart designer typically reads from top to bottom, right to left given the orientation of the fabric categories.

What most disturbs Reese--and surely anyone who is informed of it--is the optical illusion rendered by the use of three different shades of gray for the three panels. The chart literally creates two duelling images, the cube with rainbow strips crawling all over it, and the corner with two walls with rainbow columns sticking up from the floor. The second image, the intended one, is unstable because it would be hard to create a lighting scheme that would render one wall dark while the other wall is lighted.

***

The following 2D dot plot has no razzle-dazzle but makes the point.

I realized the grouping by synthetic v. natural late and just decided to box the synthetic ones. One can certainly make this a two-panel chart with the synthetics on the left and the naturals on the right.

The use of only 3 samples is highly questionable. This chart shows that the only reasonable conclusion is that Acrylic and Nylon have higher burn times than the rest. With so few samples, it is hard to tell if the remaining fabrics are truly different.

***

There may be situations where a 3D chart is preferred to a 2D chart but this set of data is certainly not such a situation. The software may in fact produce great 3D charts but this particular chart does not show off the software as the marketers may have hoped. One of the designers most important task is to examine the structure of the data, and "right-size" the chart-- throwing in extra dimensions is often counter-productive.

 

 

 

Light entertainment: a world of spikes

Something light to start the week... this infographics poster submitted by Curtis R. has to be seen to be believed. Prepared by the Rate Rush website, it compares Digg and Reddit, two services that rank and track the popularity of web pages. They were in the news a few years back; do people still use Digg or Reddit?

Here is a section of the chart:

 

Oh, and if you scroll down further, the designers received some appropriate feedback and re-did this chart:

 

I have to commend them for responding to reader suggestions. This line chart is obviously much better, and we can see that Digg has more front-page stories than Reddit at any time of the day. (Please put the data-series labels next to the lines on the right. And fix the nonsensible decimals on the gridlines.)

The fact that there is a huge gap between Digg and Reddit during the early morning hours could indicate that Reddit users tend to visit the site at work, or it could indicate that Reddit's algorithm realizes that there is no need to update the front page as often when the traffic is slow, or it could be some data processing error. It's something worth investigating.

Here's one more for further amusement:

Curtis reacts to this spiky chart:

2 pie charts, tilted at different angles (making it impossible to accurately judge the size of each sector), with a color legend that switched from chart to chart (e.g. imgur is blue in the reddit chart, gray in the digg chart).

Definitely not working

Catherine Rampell ponticificated on the nature of working families in the NYT Economix blog recently.  Are both members of the family working?  Or not working?

One thing is for sure.  Her chart just doesn't work.  Too many colors, unnecessary gridlines, should label the series directly in lieu of the legend.  Fails our self-sufficiency criterion: once every piece of data is printed on the chart via data labels, everything else is rendered redundant!

And the chart conveys the wrong message!  Looking at this chart, the reader would think the message is: the distribution of work status among married couple families has not changed materially between 2001 and 2009.  That is pretty much Rampell's conclusion.  She said that the gray bar moving from 17.5% to 18.8% in 2009 was "not a huge jump from year to year", and the the pink bar going from 8.2% to 9.9% in 2009 was a "slightly bigger increase".

This unfortunately paints the whole picture.  For a start, most stacked column charts can be replaced with line charts like this:

Because the vertical scale is no longer constrained at the upper end, the changes from year to year will appear more magnified in this version.  We may think some of the 2009 data to be different from the other 8 years, and we would be right.  Sometimes a small change is a big change - because the thing being measured just doesn't vary much.  The next chart highlights this:

I went back to the raw data, expressed in the number of married couple families, and then created an index, with the 2003 count as 100 for each category.  The black line shows the underlying demographic growth in the total number of such families over the 9 years.  It's now obvious that there has been a pretty remarkable jump in families with only the wives working.

The difference between this chart and the other two charts is the choice of comparisons.  The first two purports to look for year-on-year changes; such comparisons are hard because how big a shift is to be considered noticeable?  In the last version, we regard as noticeable a growth curve over time that differs significantly from the underlying growth trend (black line).

More sophisticated statistical tests can also be used to establish whether the shift in distribution is "statistically significant" but I think the visualization is sufficient.

Reference: "Working Families, Not Working", New York Times, Jan 15 2009.

 
 

Tiger tiger

Picked up the Metro paper the other day and found them ventilating about the possibility that Tiger Woods used steroids; the news was that a Canadian doctor he (and other professional athletes) hired has been caught with HGH and drug equipment. In the section on why Tiger couldn't be doping, the following chart appeared:

 

According to this line of argument, since steroids should improve driving distances, and since driving distance determines overall performance, the fact that his average driving distance "remained almost constant throughout the years" proved that he did not dope.

Now, I have no idea if he dopes or not.  But this particular argument is full of holes.  In the modern era, steroids are used not just for enhancing brute strength but also shortening recovery times, prolonging training, etc.  Also, it holds only if overall performance is heavily affected by driving distance.

  The bar chart has multiple problems:

• The choice of starting the vertical scale at 250 is completely arbitrary, and as been shown before, cutting off the bottoms of bars is a bad idea -- the lengths of the remaining parts are no longer proportional to the stated data.
• The choice of the three years is also unexplained, especially when 2001 is not in the middle of 1997 and 2009. 
• The horizontal gridlines are totally redundant since all three numbers sit in the very last section (290-300).  

Why were those three years chosen?  The following line chart that plots all the data may give us a clue:

The choice of 2001 and 2009 means we missed the peak of his driving distance performance.  Looking at the standardized units, we see that at its peak, the driving distance was about 2.6 times the standard deviation above his career average (the zero line using the scale on the right). 

The difference between 1997 and the peak was about 20, which looked large compared to the standard deviation of 6 over this entire period. Establishing a reference point is very important to interpreting any observed difference.

This is one of the few occasions where double axes can be recommended.  The two axes in fact plot the same data, only reflecting a difference in scale.

Reference: "Three reasons to believe he's totally clean", Metro USA, Dec 16 2009.

Worthy of the Times

Andrew Gelman has put up a great post, discussing how he collaborated with the New York Times editors to transform his chart to a publishable form.  Some time ago, there was a discussion here about the publish-worthiness of my charts (actually, the lack thereof), and I explained that to take my charts to that level would require quite a bit of extra work.  Gelman speaks here from first-hand experience.

Here are the two versions side-by-side.  Readers on the Gelman blog are debating which version is "better" with Gelman himself voting for the revised NYT version:

Let's compile a list of the changes:

1. Removed 2000 data and relied on only 2004 data
2. Reduced number of groups of senators from 7 to 5 (with a special calling out of Senator Lieberman)
3. Re-ordered senators to facilitate classifying into Democrats, Independent, Republicans
4. Added annotation explaining the grouping of senators; in particular, qualified why the 49 Democrats and 32 Republicans were set aside
   
5. Removed scale labels on the top of the chart, retaining only the bottom labels
6. Vastly increased the area devoted to text labels, which now covered half of the chart
7. Added white vertical gridlines
8. Instead of coloring the cross marks, colored the background of the chart; introduced the yellow color for Lieberman (which Gelman originally colored blue)
9. Removed reference to the national average but explained clearly in the legend that the percentages are relative to the national average.
   

Of these, 2,3,4 are definite improvements. 1 is acceptable since 2000 and 2004 data are quite highly correlated (note, however, Iowa, Virginia and Ohio.) 7 looks brilliantly here although we typically don't recommend adding gridlines and such. 5 is also acceptable because of 7 -- with the gridlines, one doesn't need to have two sets of labels. 8 can be debated: I'd like to see a version with large colored squares instead of cross marks in lieu of the background; the current look is not bad. 9 can also be mulled over: would it be so bad as to insert in parentheses 73% after the words "national average" in the legend?  I suspect some feel that this may cause confusion because readers now need to understand relative versus absolute values. 6 is the most debatable because the data-ink ratio has been vastly reduced. 

There are several good features of the original chart that they left unaltered, which should also be duly noted:

• Allowed the positive side of the scale to extend to 10% even though the largest data only reached about 6%. While this creates empty space, it helps readers judge the magnitude of negative numbers relative to positive ones.
• Subdued horizontal gridlines
• Retained the title of the chart (I actually prefer that they use the title to summarize the finding as opposed to the current one which takes a neutral stance.)
• Retained the horizontal scale labels at 5% apart

One final comment on something omitted from both charts: I'd prefer that they plot all the dots for the 49 + 32 senators, on the top and bottom lines respectively, instead of just plotting the group averages.  It would be really interesting to see what the spread is around the 0% point.

Degrees of likeness 1

The NYT team just put up a fantastic visualization of the American Time Use Survey data, which purports to measure how the average American spends the time of a day.  (Apparently, thousands of people recalled what they did every minute of an average day.)  The amount of data collected is massive, and this graphic allows readers to explore the data in intuitive ways.

The chart shows for each minute of the day (horizontal axis) the proportion of people doing specific activities.  Not surprisingly, we spend more time sleeping than any other type of activity.  The axis and data labeling as well as gridlines are very restrained.

Normally, I am not a big fan of these proportional area charts because the only relevant dimension to look at is the vertical distance from one curve to the next but the focus on areas put equal weight on the horizontal and vertical distances.   The horizontal distance is meaningless, and thus the area is meaningless.

These designers found a solution to the problem, and good for them!  Because of the mouse-over effect, I could not save the actual appearance -- here, I show what it looks like.

By mousing over different parts of the graph (say, moving vertically), we can compare the actual proportions.  Terrific!

The key interest of this graphic is the following legend.

While the above graphic shows the use of time by all Americans in aggregate, this panel allows us to zoom in on specific groups of Americans.  How alike are Americans?

Reference: "How Different Groups Spend Their Day", New York Times, July 31 2009.

 

The trouble with two lines

It's never a good idea to put two scales on one chart, and this is another example of what not to do:

The ugliest part of this chart are the duelling gridlines. Because neither axis starts at zero, it is difficult to access whether the number of newspapers was declining at a faster pace than the circulation was. Also, line charts would be better able to trace the evolution over time. The interspersed blue and red columns interfere with each other. Note that the designer lessened our pain by plotting every other year, thus halving the number of columns.

The junkart version also puts two data series on the same chart but on the same scale. Instead of plotting the raw data, we plot indices, with 2008 as 100. This reveals a pattern that was not apparent in the original chart. There appeared to have been four periods of evolution: up till 1980, both the number of newspapers and total circulation were at a plateau; from 1980 to 1990, the circulation stayed stable while the number of papers dropped drastically, indicating perhaps consolidation; then from 1990 to 2003, both series declined at roughly equal rates; and finally, the bottom dropped off the circulation from 2003.

See our previous discussion of dual axes here, here, and here

Reference: "Channel Shift: Online Circulars: the first step by retailers toward web-to-store harmony? ", Internet Retailer (print), May 2009. Data from the Newspapers Association of America.

Bonus 1: Thinking about the column interspersing trick some more, I realize that it is, em, possible, em, that one series was plotted for odd years and the other series plotted for even years!

Bonus 2: Here is the requested scatter plot (still indiced):

Exemplary

From Bernard L., another exemplary effort by the Times.  This one really got me excited.  

The set of line graphs shows how demographics of students in American schools have evolved in the last two decades.  Here, I selected New York City schools, and the tool sensibly decided to compare those with New York State schools (gray line).

There is so much to learn from one simple chart:

• The blue and gray lines are almost parallel everywhere, which tells us that in terms of the change in demographic composition, New York City pretty much resembled New York State during this entire period.
• However, in terms of demographic composition, rather than the change in composition, New York City schools are very different from the rest of the state, in that the proportion of white is lower by a third while that of minorities are much higher, especially black and Hispanic students.
• State-wide (as well as city-wide), black and white students have been declining as a proportion while Hispanics and Asians have increased. 
• The extent of the change is immediately visible, Asians have jumped from 7% to 14% for example.  

  
From a graph design perspective, the execution is very clean.  Data labels are limited to the first and last values.  A small multiples concept is used with the ethnic groups placed side by side.  A great awareness of foreground and background as well.  And imagine how much data has been visualized here, and be impressed.  You can look at any county in the country.

Here's one where the county change does not exactly mirror the state change (Napa in California):

Reference: "Diversity in the classroom", New York Times, March 12 2009.

The shackle of time 2

In the last post, we removed the time dimension in order to clarify certain aspects of the S&P 500 returns.  We found that with an investment horizon of five years, there was historically about a 25% chance of losing money and a 25% chance of more than doubling.

Even though we looked at cumulative returns, it was still the case that the data was serially correlated; in other words, it could be that the eventual return was not independent of the starting year of the five-year period.  To gauge this, we must return to the time dimension that was previously removed.

The chart on the right plots the five-year returns for all five-year periods starting from 1910.  What it shows is that even with longer time frames, timing or luck still plays a key role. 

For example, any such investment in the S&P 500 between late 1950s and 1980 did not double in five years no matter which year the investment was made.  Then again, if the investment was made in the 40s and 50s, no one lost money in a five-year period, similarly in the 1980s.

So the fact that we saw a 25% chance of doubling (or losing money) over history says much less about what might happen in the next 5 years than the simple number suggests.

In response to a reader's comment - the data series was described as "real total return" so these are inflation-adjusted.