Junk Charts

Life-enabling charts

In response to my call for positive examples, reader Merle H. sent in an example of how good charts can make our lives simpler and easier.

All of us have seen the following presentation of air travel data.

Not trying to pick on Travelocity - it's the same format whether you use Expedia or any of the airline sites.  For those customers who are looking to decide what dates to travel so as to minimize their air fare, this format is very cumbersome to use.

What about this fare chart at FuncTravel.com?

As you mouse along the line chart, the average fare for each day is visible.  Clicking on a particular day will fix the departure or return dates.

So much easier, isn't it?

A few caveats, though:

• Instead of just providing the historical averages, they should consider including information on variability, such as bars that indicate the middle 50% or 75% of prices.  Also, what about a sliding control for customers to decide which period of past history the averages should use?  More recent data may be more representative.
• This particular feature appeals to the price-sensitive, date-flexible customer segment.  Not everyone will pick itineraries based on those criteria.  There is an easy fix. If some controls are available for customers to indicate other preferences, e.g. exclude all British Airways flights, include only evening flights, etc., and the chart can update itself based on such selections, then the chart becomes a lot more flexible, and useful to many more customers.
• As with many automatically generated charts, the chosen labels on the vertical axis are laughable.  That should be relatively easy to fix, you'd think.
  

A great start.  I happen to notice that Travelocity has a beta feature that shows a similar chart.  A revolution in how travel sites present data to us is long overdue. 

Supplemental reading

What are other graphics blogs talking about recently?

Information Aesthetics highlighted the so-called New York City Subway sparklines.   (original site)  (Andrew also mentioned it.)

IA said "The general idea is that the history of subway ridership tells a story about the history of a neighborhood that is much richer than the overall trend." 

Okay but what about these sparklines would clarify that history?  From what I can tell, this is a case of making the chart and then making sense of it.

The chart designer did make a memorable comment in his blog entry: "Hammer in hand, I of course saw this spreadsheet as a bucket of nails."  The hammer is a piece of software he created; the nails, the data of trips taken.

Nathan at FlowingData gave a reluctant passing grade to this Wall Street Journal bubbles chart illustrating the recent U.S. bank "stress" test.

One should fight grade inflation with an iron fist.  (Hat tip to Dean Malkiel at Princeton.)  A simple profile chart would work nicely since the focus is primarily on ranks.  The bubbles, as usual, add nothing to the chart, especially where one can create any kind of dramatic effect by scaling them differently.

Nathan also pointed to the maps of the seven sins, which garnered some national attention.  This set of maps is a great illustration of the weakness of maps to study spatial distribution of anything that is highly correlated with population distribution.  Do cows have envy too?  See related discussion at the Gelman blog.

Wannabell

This graph, called the Bell Curve, is a wannabe.

The first hint is its asymmetry, the right tail being longer than the left tail.

Further, the helpful labelling of the "average" does not coincide with the peak of the curve.

The author of the annotation seemed to understand, calling the distribution "skewed".  A Bell Curve is not skewed.

This is a pity because the designer might have selected a different chart type if she wasn't so enamored by the bell curve object.

The data tells us about users of 30-day unlimited passes in the New York City subway system: how many trips do they typically make?  The card costs $81 while each trip costs $2 so anyone taking fewer than 40 trips in those 30 days would have been better off buying individual tickets.  The "average" user took 56 trips.  The range of trips taken was very wide, perhaps surprisingly so.

Several key pieces of information has been left off the chart.  What is the total number of riders?  Without this, there is no way for readers to understand 15,185.  What is the smallest (and largest) number of trips taken by any rider?  Visually, it appears that the horizontal axis does not start at zero.

It would have been better to show a cumulative distribution with percentages of riders on the vertical axis.  On such a chart, we can read off the median and any percentiles.  In other words, it would be much more informative.

As it stands, I like very much the annotation of the 56 trip and the 100 trip points: they are great aids to help decipher the chart.  It would be great to indicate the 40 trip point too.

For those more technically inclined: the graph also begs the question of whether it is an actual or modelled curve.  It looks too smooth to be actual data.  If it is a model, then it is definitely not a normal distribution.  What could it be?  A spline?

Reference: "In Decade of Unlimited Rides, MetroCard Has Transformed How the City Travels", New York Times, July 16 2008.

Buffer time

As this report from the Department of Transportation makes clear, congestion on our roadways causes travellers to add "buffer time" to their planned journeys.  So, for instance, one may have to allocate 32 minutes for a trip that would have taken 20 minutes in uncongested traffic if one would like to guarantee on-time arrival.  The 12 minutes would either become time spent sitting on the road or wasted time due to arriving too early.

Buffer time can be applied to graphs too.  Some graphs require readers to spend time fishing out the information.  The chart used to illustrate travel time belongs to this category.  The clock analogy fails; in fact, it confuses matters as the hour hand just sits there serving no purpose.  The buffer time between staring and comprehending is too much!

Only four numbers underly this chart: travel time when uncongested and buffer time to guarantee on-time arrival, for 1982 and 2001.  The following version gets to the point without fuss.  It shows that the travel time increased significantly even under uncongested traffic; worse, the buffer time multiplied.

Reducing buffer time is always good but some buffer time may be inevitable.  In the traffic analogy, to eliminate all buffer time would mean lots of unused capacity.  In the context of graphs, more complicated charts would require more time; the key is whether the reader is rewarded for the time spent figuring out the chart.

Source: "Traffic Congestion and Reliability", Department of Transportation.

Noisy subways

This NYC subway report is impossible to read.

However, it is very difficult to find a good way to show the information.  In fact, the data contained very little of that.  Curiously, the ratings are very dispersed so that each line is graded high on some category and low on others.  Here's one view of it:

I have grouped the subway lines together (A/C/E, 4/5/6, etc.).  The metrics are plotted left to right in the same order as in the original.  Is it all noise and no signal?

(I just realized the vertical axis is reversed: best ratings are at the bottom, worst ratings at the top.  Doesn't matter anyway since I can't see any patterns.)

Source: "No. 1 Train is Rated Highest by Commuter Advocates", New York Times, July 24 2007.

PS. Two contributions from readers.  Still looking for insight from this data...

Lines of death

I've been reading my friend's anti-smoking tome, and traced this "infographic" back to its source (World Health Organization). 

I was very intrigued by the "lines of death" which seemed to make the point that the risk of death had a spatial correlation: specifically, that the death risk for male smokers was higher in northern hemisphere (above the line), primarily developed countries, as compared to the southern hemisphere, mostly developing nations.

I find that somewhat counter-intuitive but in a fascinating book like this, that brings together both scientific, psychological and societal commentary, I was expecting to learn new things.

Looking at the legend, the red areas were regions in which deaths from tobacco use accounted for over 25% of "total deaths among men and women over 35".  This explained some, as perhaps there were more reasons to die (warfare, other diseases, mine accidents, etc.) in developing nations than in developed nations, or that they had larger populations (so more deaths even at lower rates).

However, the description of the "lines of death" raised my eyebrows.  It is now claimed that more than 25% of middle-aged people (35-69 years old) die from tobacco use in the red regions. 

Did they mean 25% of the dead middle-aged people die from smoking?  Or 25% of all middle-aged folks die from smoking?  A gigantic difference!

Percentages are very tricky things to use.  Every time I see a percentage, the first thing I ask is what is the base population.  Here, the baseline appeared to have gotten lost in translation.

This set of maps also shows the peril of focusing too much on  entertainment value, and losing the plot. 

For those concerned about the effect of smoking on our society and our children, I highly recommend Dr. Rabinoff's highly readable new book, "Ending the tobacco holocaust".  It contains lots of interesting tidbits and really brings together every cogent argument that exists, including the common ones you've heard and others you haven't.

Reference: "Ending the tobacco holocaust" by Michael Rabinoff; The Tobacco Atlas by the World Health Organization

Time travel

One of my scientific heroes and seminal teachers is Professor Frank Kelly at Cambridge.  What a pleasant surprise to see his involvement in a data visualization project.  To cite his wise words:

The travel-time maps are more than just pretty to look at; they also demonstrate an innovative way to use and present existing data. We are entering a world where we have access to vast quantities of data, and ways of turning that data into information, often involving clever ideas about visualisation, are becoming more and more important in science, government and our daily lives.

The little black dot near the center of the map indicates the Mathematics building at Cambridge.  The contours (vaguely visible at our scale) represent intervals of 10 minutes by public transportation away from the black dot.  Any colored dot on the map refers to the time at which a traveller must leave in order to get to the Math building by 9 am, taking into account traffic situation, time of day, and decisions.  The hope of such maps is to help commuters (by public transit) plan their travel.

Professor Kelly has a very nice write-up on the intricacy of generating the data for such a map, which includes techniques of sampling, smoothing, extrapolation and so on.  It is rare that we get insights into the chart-making process.  He also carries a larger version of the travel-time map.

A similar article can be found at Plus magazine.

Flight of fancy

The venerable Wired magazine has surely gone too far with this flight of fancy!  Consider:

• The zig-zagging lines streaming across the map
• The redundant white dots, each of equal size, contradicting the black dots, with size proportional to prevalence
• The inexplicable use of 00, 01, 02, ...
• The use of a taller column for human cases, when tallied, amounting  to about 1/20 the number for bird cases
• The inclusion of Australia (with zero cases) while excluding the Americas (also zero cases)
• Ordering the countries neither by bird nor human cases but by convenience of placement on the map

As with a previous example, the map adds nothing to the data except for providing a lesson in geography.  We prefer a parallel bar chart, shown on the right.  Here, the continents are given different colors.  In an unusual move, I chose different scales for each side as I am more interested in the distribution among countries, rather than the relative prevalence of bird/human cases.

Reference: "Flight H5N1: Delayed", Wired Magazine, October 2006.

Tracks

"Tropical Storm Debby strengthened as it moved northwest yesterday.  Of the 15 previous storms with positions similar [...], 13 became hurricanes, but only two reached the United States".

This data-laden statement accompanied the following weather map.

Now.  Imagine if:

• no colors were used, and
• the two storms that landed had tracks bolded, and
• the 13 hurricanes had solid tracks, and
• all other tracks were drawn gray, and
• the then location of Debby was annotated, and
• only the two making landfall (Gloria 1985 and Storm 4 1938) were labelled, and
• the locations of landfall were crossed, and
• the large box was removed, revealing the land mass,
  

Then only the key data needed to support the accompanying statement would be present.

Reference: "Highlight: Tropical Storm Debby", New York Times (weather report),  Aug 24 2006

Bubble charts and their discontents II

Bubble charts force three dimensions onto a 2-D flat surface.  They are occasionally useful for illustrating concepts but seldom work as a data graphic.  The following chart illustrates some lethal problems:

In bubble charts, two dimensions are plotted in the usual x and y axes (here, longitude and lattitude) while the third dimension is depicted as circular areas.  Like wild dogs, the pair of gigantic bubbles insisted on marking their territories, obscuring many littler bubbles.  At the same time, it gets harder and harder to locate their centers (i.e. recover the other two dimensions) as bubbles expand.

Further, the standard way of displaying the legend, involving overlapping circles, obstructs our ability to compare the areas effectively.

This chart, however, is data-rich.  Simultaneously, it plots (1) geographical locations (map); (2) passenger volume (area of circle); (3) market share (shading of circle); and (4) top markets (call-out text).  The key to improving readability is to untether oneself from geography.  In other words, give up geographical information and focus on market share versus passenger volume.  For example:

[The graph looks better if it had only blue diamonds.  I had to insert green dots because I don't have the full data set.  The blue diamonds are real data; green dots are approximations, and there should have been many more in roughly the same locations.]

We now see that Northwest's markets fall into three types: large and dominant (national hubs), small and strong (regional hubs), and small and small (others).  There are only a few cities with market share over 50% while the rest are less than 25%.  Similarly, NWA serves fewer than 25,000 passengers in all but three markets.  (A log scale can be used here if one wants to explore further groupings within the small-scale markets.)
 

Reference: "Well-Laid Plan Kept Northwest Flying Despite the Strike", New York Times, August 22, 2005