Junk Charts

Dizzy display

 Xan G. tells us that these "inconsistent pie charts ... make [his] head hurt".  The dizzy array of colors is unfortunate, especially when "Application" gets a medium blue in three of four pies but an orange-red in one of them.  Just like the baby names charts, it's important to keep the background constant when constructing small multiples.

We cite from the horse's mouth:

The goal of this section was to uncover any [software development] task that might be overlooked [by these startup companies]. When writing a software product, the tendency is to focus 100% on the application. Items like support, marketing, and especially billing never cross your mind.

The junkart version below is designed to bring out this one message: that Blinksale has distinguished itself from the rest by having spent more time developing code for purposes other than the application itself.  

I removed the raw counts of lines of code and focused only on the relative proportions.  The former does nothing to argue the author's case.

The pie charts fail our self-sufficiency test.  The reader must rely on the data table and data labels to understand the chart.  If removed, the key message is obscured.

Source: "Web App Autopsy", ParticleTree, June 2007.

Foreground, background

Derek C. points us to this effort by a science journalist to use graphs to help "clarify the concept of climate change".  The graph on the left shows that actual greenhouse gas emissions have exceeded the level predicted by the most pessimistic climate models.  The 3D bar chart on the right examines which countries had most increased emissions since 1990.

While the bar chart contains many of Tufte's "ducks" (not sorted by percent change, 3D, color, gridlines, sufficiency, etc.), it's the left chart that can be made more powerful. 

The casual observer does not need to know which model led to which trajectory of predictions; the graph is vastly simplified, and the message much clearer in the junkart version.  (I only included the CDIAC data because I didn't locate the EIA numbers.)

The general point here is recognizing what is foreground, and what is background.  Aside from gridlines, data labels, axis labels and so on, some of the data usually constitute background material, often as in this case being used to establish comparability.

One message I got out of this chart is that these climate models have done a good job!  (Now, I have no idea if part of the curve included the training period.  It is curious that the predictions were very narrowly contained in the early 1990s.)

Source: The Island of Doubt Blog, June 6, 2007.

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.

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.

 

Peripherals 1

Like any technology, charts also come with peripherals: I'm talking about legends, data labels, grid-lines and so on.  These things typically give us the most trouble, especially with complex data sets.  The analogy is apt: one may feel inextricably knotted up like bunches of cords and wires.

Interactive graphics is a particularly elegant solution to this problem, and Google Finance has done a fantastic job leading the way.  One trick is to show the legend only when the user asks for it.  Using bar charts (on the left), Google summarizes neatly the performance of stocks within each industry sector.  The bar chart gives a sense of the dispersion which adds to the average returns printed next to them.  For example, most sectors gained on average but then about 30% of the individual stocks in most sectors actually declined on that day.  So the fact that technology stocks gained 0.48% on average doesn't necessarily mean that the two tech stocks you own gained 0.48% or gained at all.

Typically, we would put a legend on the side or at the bottom of the chart, which all be told, is an ugly duckling next to a well-executed chart.  Here, the legend is hidden behind the "What's this?" link.  The side benefit is that the legend can be as verbose as needed since it doesn't interfere with the chart.

There are a few minor things to consider:

• "What's this?" is not very informative: Why not call it a "legend" or "key"?
• The graph designer seems to think that the most important information sought by readers was the extremes, i.e. the percentage of stocks that gained/lost more than 2%.  By darkening the sides of the bar, it draws attention away from the middle which is the boundary between the gainers and the losers.  I'd like to see that boundary delineated.
• Similar to the above point, I'd sketch out a version which aligns the gainer/loser boundary to the middle so it's easy to see the balance between gainers and losers.  This version however would require more space
• I'd provide sorting by average return, and by percentage of gainers

Going out on a limb

Earlier in the month, Prof. Gelman linked to Brandon's fascinating analysis of on-line weather forecasting accuracy.  I have done some additional analysis of the data and the result can be visualized as follows.

I'll concentrate my comments on three observations:

• CNN was the clear winner in forecasting accuracy during this period based on two criteria: its median error in forecasting daily lows, and its median error in forecasting daily highs.  Moreover, both the median errors were zero, which gives us confidence about its accuracy.  The Weather Channel (TWC) and Intellicast (INT) were not far behind.
• The ability to forecast highs was better across the board than that of forecasting lows (except BBC).  I am not sure why this should be so.
  
• Overall, our weather forecasters were much too risk-averse.  Notice that the errors were heavily biased in the lower left quadrant.  A negative error on low temperatures means predicted low is higher than actual low; a negative error on high temperatures means predicted high is lower than actual high.  Taking these together, we observe that the range of actual temperatures have generally been larger than the range of predicted temperatures!  No one was willing to go out on a limb, so to speak, to forecast extremes.

Actually, I believe this inability or unwillingness to forecast extreme values is endemic to all forecasting methodologies.

Before closing, I mention that the graph was based on a subset of Brandon's data.  I only considered same-day forecasts, did not consider Unisys (because they didn't provide forecasts for lows), and also noted that there might be bias since there were breaks in the time series.  Also, I retained the sign information and didn't take absolute values as Brandon did.

Bubbles of death 2

Here is an alternative way to present the death risk data.  It's a variation of Tukey's stem-and-leaf plot.  Instead of presenting the exact odds, I believe it is sufficient to generalize the data by grouping them into categories.  Not much is to be gained by knowing that the odds of dying from fire and smoke is 1 in 1113 as opposed to the odds being in the range 1 in 1000 to 1 in 10,000 and comparable to that of drowning, motorcycle accident, etc.

PS. Be sure to look at Derek's chart in the comments.

Mirror, mirror

Mirror, mirror on the wall...

I don't see what the second line adds to this plot, given there were only two candidates in this election. 

Political graphs do not get much better than those at the Political Arithmetik blog.

For instance, in the chart below, he wisely chose to draw trend-lines rather than connecting the individual dots.  Also, typically, he plots dots for all the different polls, which allows us to assess the variability (reliability) of the observed trend.

 

Reference: "Sarko embraces the Anglo-Saxons", Economist, Feb 3 2007.

Complex is not random

There is a tendency to mistake complexity for randomness.  Faced with lots of data, especially when squeezed into a small area, one often has trouble seeing patterns, leading to a presumption of randomness -- when upon careful analysis, distinctive patterns can be recognized.

We encountered this when looking at the "sad tally" of the Golden Gate Bridge suicides (here, here, here, here and here).  Robert Kosara's recent work on scribbling maps of zip codes also highlights the hidden patterns behind seemingly random numbers.

Robert found a related example (via Information Aesthetics, originally here): the artist takes random numbers (lottery numbers), and renders them in a highly irrelevant graphical construct, as if to prove that spider webs can be generated randomly.

According to Infosthetics, each color represents a number between 1 and 49, which means the graph contains 49 colored zigzag lines (not counting gridlines and axes).  Each point on the year axis represents a frequency of occurrence.

Imagine if you are tasked with using this chart to ascertain the fairness of the lottery, that is, the randomness of the winning numbers.  The complexity of this spider web makes a tough job impossible!  We must avoid the tendency to jump to the conclusion of randomness based on this non-evidence.

In fact, testing for randomness can be done using any of the methods described in the postings on the "Sad Tally" (links above).  A first step will be to plot the frequency of occurrence data as a simple column chart with 1 to 49 on the horizontal axis.  We'd like to show that the resulting histogram is flat, on average over all years.

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.