Junk Charts

More prevalent versus more likely

Aleks pointed to an interesting Business Week chart used to explain what people in different age groups are doing on-line.  This is a pretty chart that does an admirable job with a difficult data set.

The key to this chart, unfortunately missing, is that the percentages must be read as vertical columns to make sense.  So the top left square says 34% of "Young Teens" who answered the survey said they create web pages on-line.  In addition, the total of each column can be much more than 100% because multiple responses were allowed.

Realizing the above, we should interpret the bottom (grey) row as saying: "Older boomers" and "seniors" are more likely to be "Inactives" than younger people.  A tempting interpretation is: "Inactives" are more likely to be "seniors" and "older boomers".  But this is wrong because the chart hides the age distribution.  While 70% of "Seniors" are inactive, "Seniors" may represent a small proportion of the population, and thus they may not account for a large proportion of "Inactives".  This is the difference between prevalence and incidence rate.  (Another way to grasp this is to add the percentages across a row and try and fail to understand what the row sum could mean.)

The construct of the square grids is less damaging than it seems.  In effect, the data has been rescaled by dividing by 10.  The reader is then forced to apply "rounding".  If you are someone who sees $19.95 as $19, then you'd round down the partial rows.  If you see $19.95 as $20, you'd round up the partial rows.  So the designer has pushed you to think in terms of whole numbers between 0 and 10, in other words, in units of 10%, rather than units of 1% or, horror of horrors, 0.1% or at some other unrealistic precision.

Here's another example where the profile chart shines.  Because the percentages don't sum up to 100%, the other alternatives like stacked bar charts and "Merrimeckos"/mosaic charts don't work.  (Prior discussion of this issue here.)

This version gives a column view of the data, the lines linking percentages of each age group performing on-line activities.  The profiles nicely cluster into three groups: the younger people are more likely to say they are "joiners", "spectators" or "creators" but less likely to be "inactives".  We also see that the likelihood of being "Collectors" has little to do with age.

Source: "Inside Innovation -- In Data", Business Week, June 11 2007.

Wizardry

An anonymous reader dropped a comment pointing us to Martin Wattenberg's gallery at Business Week.  Martin's work falls into the category of information visualization, which typically concerns cramming as much high-dimensional data as possible onto 2D or 3D displays, augmented heavily by colors, shapes, interactivity, superpositioning and other tricks.  Often pleasing to the eye, these graphics usually take time to warm up to.  Sites like Infosthetics and Visual Complexity cover them well.

Martin is responsible for the baby names visualization, which tracks the popularity of names over the years.

Martin also created treemaps like this one.  Does this show relative stock performance better than other designs?

Looking for survival

Daniel W of esnips has started a collection of graphics on visualizing web statistics.  The following graph is an attempt to capture the ability of the web-site to attract returning customers.

The time axis serves double duty here: it is an indication of which "cohort" the users belong to, in other words, when they signed up; it is, also, the month of returning visits.

A more typical chart used by statisticians is the survival curve.  As shown here, these are the same curves as above but having the same starting point.  Now, the time axis is interpreted as number of months after registration.  Of 100 members who registered in January, how many returned one month later, two months later, etc.

If the purpose is to evaluate the consistency of retaining customers by cohort, then this graphic is less cluttered.  I also used a fading metaphor to color the lines so that the oldest cohort (also, the longest line) is the faintest.  Line labels are best hidden, and revealed interactively when the user mouses over a line of interest.

Not sure if Daniel was plotting real data; in general, we expect a certain amount of criss-crossing.  If the data is real, then his site has seen uninterrupted improvement every month thus far.

Source: The Web Analytics Graph Collection, eSnips.

Visualizing sensitivity

A reader wrote:

I'm a loyal reader who hopes you'll indulge him in just one or two questions.

In finance (valuation, specifically), we often create two-way sensitivity tables. Unfortunately, a three-way sensitivity table is what's most often called for. Of course, we work around this by producing multiple two-way tables.

Now, obviously, it's pretty hard to build  three-way table or chart in two dimensions, and the use-bigger-bubbles method doesn't really make sense in this kind of application-- but can you conceive of a good way to present the data in any other form?

Like he indicated, we typically see multiple two-way data tables for such data.  The virtue of this approach is that the data is exceptionally well-organized; it's great for looking up the outcome given the three dimensions (I called them Red, Green and Blue to protect the innocent.)

Further, starting from a baseline i.e. a particular cell in the table, it's easy to move our eyes up, down or jump tables to observe the impact of changing dimensions (so-called sensitivity analysis).

These data tables facilitates "local" sensitivity analysis but obscure "global" sensitivity: staring at those numbers, we feel lost in the trees and can't see the forest.  What's the effect of increasing Green on average?  What's the effect of increasing Green while decreasing Blue? etc. etc.

The junkart construct (right) is made to address these questions.  The black stripes establish the baseline, the overall range of values.  Then, if interested in the effect of Red = 0.11, we can compare those red stripes with the black.  Since the spread is wide, we note that Red = 0.11 is not a strong indicator of value, and to the extent it is, it points to lesser values.

What about Red = 0.11 and Green = 2?  Now, we focus on the first red stripes and the first green stripes.  We note that the overlapping region (which is where both conditions apply) is highly concentrated to the low end of value range.  Thus, we conclude that under those conditions, value is low (below 10,000) and further, that it is low primarily because Green = 2.

On and on for any one-way, two-way or three-way effects.

Although it's not the purpose of the chart, local sensitivity can also be observed.  For example, the highest value comes from Red = 0.09, Green = 16 and Blue = 0.30.  What if Blue decreases to 0.28?  We start on the Blue = 0.28 layer; going from right to left, as we see a blue stripe, we scan vertically to find the corresponding red and green stripes; the 3rd stripe from the right, we find the scenario of interest.  Such analysis would benefit from adding an interactive vertical guiding line.

Do you prefer 3-D plots?  Contour plots? Feel free to share your ideas!

Shower of bullets

Here's one of those infographics that makes the reader work hard (via Dustin J).  The graphic in its full glory is here; it's much too large to be reproduced, and I have clipped off the bottom half.

Much to the designer's credit, he extracted data of interest, rather than trying to cram everything onto the page.  In particular, he was most interested in the distribution of deaths among different age groups, the types of deaths (suicides, homicides) and the identities of the deceased (race, gender).

Just like the election fraud graphic, such rich data lend themselves to multiple levels of aggregation.  Here, the designer focuses on the most detailed level, making it easiest to see facts like "among the 18-25 age group, there were 6 black men murdered per day".

However, it takes much more attention to notice higher-level facts like "homicides per day are relatively flat across age groups while suicides heavily skew toward 40+".

In the junkart version, I decided to emphasize the more aggregated data, showing the number of deaths of each type across age groups. The detailed break-down of race and gender is shoved into parentheses, as they can be omitted by less serious readers.

The reader who discovers that the homicide/suicide pattern described above may surmise that homicide gunfire deaths are more "random" while suicides, being  premeditated, may affect older people disproportionately.  More research would be needed to confirm such and other suspicions.

Source: "An Accounting of Daily Gun Deaths", New York Times, April 21 2007.

 

Embedding logic

Bernard L. (from France) submitted this bubble chart for consideration.  It accompanied an NYT article claiming the absence of evidence of election fraud.  (Of course, as is well-known, absence of evidence is not the same as evidence of absence.  Here, I'm purely interested in data presentation.)

As a seasoned consultant, Bernard asked if a Marimekko chart would be superior.

This is one ambitious chart.  Ignoring the bubbles (which are more nuisance than anything), we are asked to interpret data at three different levels of aggregation in one go.

First, there were 95 cases classified into five indictment types.  Second, these cases resulted in either convictions or acquittals/dismissals.  Third, among the cases ending in convictions (the highlighted area), we were shown the occupations of those convicted.

By flattening three levels into one table, some key information is obscured.  For example, how many cases resulted in conviction?  The reader has to compute either 95-25 or 26+31+10+3.  What percent of civil rights violation convictions were committed by party/campaign workers?  It's not 2/3 = 67% (bottom row) but rather 2/2 = 100%.

The following junkart brings out the logic that is embedded in the complicated bubble-table.  While there is a lot on the page, the text labels plus the flow directions allow readers to absorb the data one level at a time.

I have not attempted the Marimekko as I am not a fan of such charts.  You're welcome to try.

Source: "In 5-Year Effort, Scant Evidence of Voter Fraud", New York Times, April 2007.

PS. I will be working through the backlog of reader submissions.  Thanks for your patience.  Keep them coming!

 

Remark (Apr 25 2007): Thanks to readers for keeping me honest (see comments below).  The conviction rates shown previously were indeed the inverse.  I have now fixed them.

Peripherals 2

In terms of interactive charting, Google Finance did much more than hide the legend.  In their main stock price chart, they used a number of neat features.

This chart effectively conveys a huge amount of information in a small space.  The bottom strip which shows relative prices for the past two years provides context to interpret the five-day movement shown in the main chart area.  I prefer to see a scale on the bottom strip as well. 

The sliding scrollbar can be dragged to show historical data.  Besides, the width of the window shown in the main area can be controlled.  For instance:

Without any effort, we are now looking at a 3-month chart for Q2 2006.  Notice the summary statistic on the top right corner also morphed.  The axis scale changed, and it never did start from zero to begin with.  (This shortcoming is alleviated by the profile chart in the bottom strip.)

Further, by placing the cursor in the chart area, we can highlight a particular day: a dot appeared on the price curve, the volume on that day was highlighted, and the text on the top right switched.  That text is what we typically place inside the chart area as a "data label".  The effect of moving it to the corner is similar to hiding the legend: it makes the graph more legible and provides space for longer descriptions.  As we move the cursor from left to right, the graph dynamically adapts.  Marvellous!

It may not be obvious the amount of data processing that has to take place to implement these sorts of features. I don't have space to address the data issue but maybe some of our readers can comment on it. 

Smoking-Screening

Behind the smokescreen lies the informative conclusion: among households with smokers, about 40% smoke in residence all the time while about half never smoke in residence.

This graphic, unfortunately chosen, contains many distractions from the main message, including:

• the liberal sprinkling of colors
• the inclusion of data for 1, 2, 3, 4, 5, 6 days, almost all of which were effectively zero
• the redundant vertical scale, as all the data already appeared on the chart itself
• the comparison of smokers to "total sample" (rather than non-smokers)

 

The last point merits special attention.  The total sample contains households with smokers as well as households without smokers. Any data from the total sample is a weighted average of these two types of households.  It is better to directly compare the two household types than to indirectly compare one type to the overall.

Further, households without smokers should be extremely likely to have no smoking in residence all week.  And if most households have no smokers (76% of this sample), then the statistics of the total sample will mimic those of no-smoker households. That is to say, the total sample statistics do not add much to the analysis.  Our junkart version below corrects for this as well as other things.

One of the key functions of a graph is data reduction, i.e. to aggregate data in such a way as to expose the information contained within.  Typically, a graph that uses aggregated data is clearer and stronger than one that plots every piece of data.  In this example, by combining 1-6 days into a single category ("smokes in residence part of the week"), we have a graph that is much more readable.

I want to thank Dr. Mike Rabinoff for inspiring me to look up these second-hand smoking statistics.  Mike recently published a book called "Ending the Tobacco Holocaust", which tells you more than you want to know about the tobacco industry.

Reference: "Second Hand Smoke Survey: Final Report", Madison Department of Public Health, Dec 2003.

Wading in waste

A poor graphic leaves readers wading in waste, in this case, the waste of time.  (Thanks to a tip from Dr. Bruce W.)

This very busy chart conveys a simple research finding, that the density of bacteria increases with the prevalence of impervious surfaces.  As Bruce pointed out, underlying this chart is but six observations taken at selected tidal creeks, each observation being a (paired) measurement of bacteria count and prevalence of impervious surfaces.

A factory worth of graphical elements was employed, including columns, pies, colors, data labels, legends and so on.  The result is utter confusion.  How is it that the tip of each column does not coincide with the center of each pie?  Do equal-sized pies imply equal surface areas?  What is the bacteria count at each location?

A scatter plot brings out the key correlation with minimal fuss.

Reference: "Wading in Waste", Scientific American, June 2006

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.