Junk Charts

Round up

Here are some interesting reading from other places:

Tag clouds have caught on since we approved them a while ago.  One interesting use was at the Life Vicarious blog.  They use it to compare the inclinations of three New York-based restaurant reviewers.  What they should have done is to remove irrelevant words like  "one", "also", "many", "make"/"made", etc.  In statistics, this is called removing "noise" which helps bring out the "signal".

Andrew Gelman discussed the NYT article that reported the finding of unexpected male bias in the children of Asian American families.  He can be counted on to make useful comments on any accompanying graphics.  He rightly pointed out that this is one example of not starting at zero: the relevant baseline is 100 since the metric is essentially the over-age of males relative to females.  I also agree that a line chart with a longer time series plotting percentages rather than over-age would work better.

The racetrack chart made an appearance at Flowing Data.  This one is even more busy and just as impossible to decipher.

Reading comprehension

Note: I am in the middle of a holiday and so posting will be limited.

Andrew posted a pretty chart that caught my attention.  This is the sort of sophisticated chart that rewards careful reading. 

Below is a guide to reading the chart:

• It is a small multiples chart with the components arranged in two dimensions (income levels, and a race-religion hybrid category).  The top row is a summary of voters of all race-religion grouped by income.  Note that there is no corresponding summary column for voters of all incomes grouped by race-religion.
• Source of data: 2000 poll but applied to 2008 demographic patterns.  In other words, there is an underlying assumption that opinions have stayed stable within the demographic groups.
  
• The chart is in fact three dimensional because each map gives us the geographical (state by state) breakdown.
• It is useful to figure out the smallest unit of data: in this case, this is the percentage support of federal school vouchers by voters of a given race-religion-income-and-state category.
• The color scheme is such that red represents highest support and blue lowest support, with pink and purple in the middle
• It's almost always better to start from the aggregate (that is, the average) and then study variations along different dimensions, and this is how the chart is arranged from top to bottom
  
• On the top row, the higher income groups tended to favor vouchers more than lower income groups, with a break point around $75k; even here, the regional differences are significant, with northeast and southwest hotter for vouchers at all income levels
• As we move from row to row, we realize that the aggregate data hides many disparities.  For example, white Catholics (second row) are more likely to support vouchers regardless of income level while white non-evangelical Protestants (fourth row) are much less likely than average to support vouchers at all income levels.
• Notice that the statistician (Andrew) has carefully defined the race-religion categories to balance between collapsing subgroups that are distinct and showing too many subgroups so as to cloud the patterns.  That is why there are many more race-religion subgroups that are not shown.  The ones shown are of special interest.  Consider the white protestants, evangelical vs. non-evangelical (third and fourth rows).  If one were to fix the race, geography and income dimensions, and even fix half of the religion dimension, we still find the two subgroups to be on different ends of the spectrum relating to the voucher issue.  This is why the evangelical or not dimension has been included.
  
• The white space is interesting.  Here, the issue faced by the statistician is sparse data when one gets down to multi-dimensional subgroups.  Andrew chose to ignore all the data, which is the wise thing to do.  With so few samples, it is particularly easy to draw bad conclusions.   
• Because of the white space, we get additional information on the spatial distribution of the demographic subgroups.  The black population (at least the voters) are predominantly found in the southeast while Hispanics are in the southwest.  The subgroup of income higher than $150k is essentially all white.  Admittedly, this is a very crude read because we only have two levels (below 2% of state population and above).  Of the colored states, we cannot differentiate between densely populated and not.

  

Such rich graphics deserve careful reading.  Enjoy!
  

Spinning multi-color

New York Times has a great pointer to the Global Warming Art website.  The author Robert Rohde wants to popularize environmental science by visualization of the data.  There are many interesting charts and well worth repeated visits.

These pie charts cry out for some re-dressing:

The pie charts, the colors, the whole works.  Most troubling is that each pie has its own sorting scheme, and because the text labels were not reproduced in the smaller pies, the reader is sent scrambling around to find the right labels.

In addition, these pie charts, as with almost every other pie chart, fail the self-sufficiency test.  Without all the data printed next to each sector, the reader is simply unable to judge the size of each sector.

Further, the aggregate data (larger pie) may not be as relevant after realizing that the smaller pies show very different patterns.  The following junkart version tries to bring out this fact by treating both dimensions (type of greenhouse gas; source of emission) equitably.

While I picked on this particular chart, I must say I support Robert's effort and wish him luck in this very well-intentioned project.

Colorful maps

Bernard L. loved the recent NYT take on immigration in America.

The very pretty maps are found here.

An amazing amount of data is being visualized here.  Mousing on the map will pick up the specific data for each county.  There is a bar up top for discovering the evolution over time.  It would be great if there is an animation button so the map can be played out without clicking.  An animated gif will also do (similar to the disease map we featured some time ago).

The colors on the first map represent the origin of the top ethnic group in each county.  Within each group, the tint of the color further displays the percentage of the population that group accounts for.  The subgroups appear to be 0-2%, 2-5%, over 5%.  The last subgroup is very wide.

Not so keen on the second map with all those bubbles.  They show the number of people from each country by county.  The bubble size is proportional to population.  Every version of this map looks the same because the population is concentrated in the cities and the interior is sparsely populated, no matter what ethnic group.

Regardless, this is another laudable effort by the crew at the Times.

Reference: "Immigration Explorer", New York Times, March 10 2009.

The trouble with maps

Todd B. pointed us here.  These are maps that supposedly show the distribution of respondents for each answer choice in a survey exploring accents in different parts of the country.  The full set of maps for every question can be found here.  

Amusingly, the researchers also provided a map of "all respondents".  (I won't ask how the proportions of respondents were reduced to binary output to produce the above maps.)

Here is Todd to lead off the discussion:

Just because you put data on a map doesn't make it effective. Check out these mapped responses that either tell us that there is no difference in dialects or fails to illustrate differences effectively.

Reference: "Dialect Survey", University of Wisconsin-Madison.

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.

Food art

Adam, who is the designer behind the Wired graphics special on "The Future of Food", asked about the rest of the series.  We previously made some comments on a set of mini donut charts.

The first thought that came to mind after browsing through all the charts was: what a great job they have done to generate interest in food data, which has no right to be entertaining.  Specifically, this is a list of things I appreciated:

• An obvious effort was undertaken to extract the most thought provoking data out of a massive amount of statistics collected by various international agencies.  There weren't any chart that is overstuffed, which is a common problem.
• It would be somewhat inappropriate to use our standard tools to critique these charts.  Clearly, the purpose of the designer was to draw readers into statistics that they might otherwise not care for.   Moreover, the Wired culture has long traded off efficiency for aesthetics, and this showed in a graph such as this, which is basically a line chart with two lines, and a lot of mysterious meaningless ornaments:
• 
  
• A nice use of a dual line chart, though.  It works because both data series share the same scale and only one vertical axis is necessary, which is very subtly annotated here.
• The maintenance of the same motifs across several charts is well done.  (See the pages on corn, beef, catfish)
  

Further suggestions:

• It would be nice if Wired would be brave enough to adopt the self-sufficiency principle, i.e. graphs should not contain a copy of the entire data set being depicted.  Otherwise, a data table would suffice.  The graphical construct should be self-sufficient.  This rule is not often followed because of "loss aversion"; there is the fear that a graph without all the data is like an orphan separated from the parents.  Since, as I noted, these graphs are mostly made for awe, there is really no need to print all the underlying data.  For instance, these "column"-type charts can stand on their own without the data (adding a scale would help).
• Not sure if sorting the categories alphabetically in the column chart is preferred to sorting by size of the category.  The side effect of sorting alphabetically is that it spreads out the long and the short chunks, which simplifies labelling and thus reading.
• Not a fan of area charts (see below).  Although it is labelled properly, it is easy at first glance to focus on the orange line rather than the orange area.  That would be a grave mistake.  The orange line actually plots the total of the two types of fish rearing, not the aquaculture component.  The chart is somewhat misleading because it is difficult to assess the growth rate of aquaculture.  Much better to plot the size of both markets as two lines (either indiced or not).
  
•  

Reference: "The Future of Food", Wired, Oct 20 2008.

Dealing with skew

Bernard L pointed us to this income distribution chart printed in the Economist.

The accompanying paragraph points to the range of the bars, that is, the gap between the top decile average and the bottom decile average, as evidence of income disparity, concluding that the US and Britain are among the worst.

Bernard likes the use of vertical sections to represent the average incomes by decile and dislikes the USA-Today style background image.  Agreed.  But why plot the middle deciles at all when the only worthy data involve the endpoints of the bars?

A close examination of the spacing of the middle deciles leads to more befuddlement.  There does not appear to be much difference between the countries.

The answer to this is that decile statistics are not appropriate for data as skewed as incomes.  At the high end, the 10% intervals are too coarse.

One clue to this is that the top 10% in the US only earns $90,000 on average but we have all heard of the billion-dollar hedge fund managers and Wall Street bankers and $30 million a movie celebrities.  The problem is that within the top decile, the income distribution is also tremendously skewed. 

The neat idea of plotting the vertical sections indicates an awareness that the red dots (average income) are insufficient because of the skew.  Alas, there remains a lot of skew above the top decile and the designer inadvertently falls back into the same trap by considering the average income within the top 10%.  Thus, the amount of disparity on the right side of the chart is grossly underestimated.  Roughly speaking, we are looking at 10 samples of the distribution, nine of which at the low end of the range and only one at the top end (long tail).  Here is the idea:

Reference: "Spreading the wealth", Economist, Oct 21 2008.

Break it down, build it up

Thought of the day:

While commuting today, I wondered why we use the term "data analysis" or "data analyst".  I recalled that in chemistry class, we learnt that analysis means breaking things down while synthesis means building things up.

With regards to data, typically we try to collect data at the most detailed level and we build up messages and stories from the little pieces.  We don't break things down.  We can't break things down, in fact, if the data come to us in aggregated form.  (Think ecological fallacy.)

So why don't we say "data synthesis" rather than "data analysis"?

Loss aversion

Loss aversion manifests itself in chart-making, as it does in economics.  In chart-marking, loss aversion can be defined as the tendency to avoid losing data at any cost.  Given a rich data set, designers often make the mistake of cramming as much data into the chart as possible.  This is taking Tufte's concept of maximizing data-ink ratio to the extreme, and it often leads to awkward, muddled charts.

Gelman provided a great example of this recently.  See here. 


Every piece of data is given equal footing, which results in nothing standing out.  The reader gasps for air.


Here is a recent example from the New York Times, in which the designer showed admirable restraint.

  The best evidence is the set of small multiples shown at the bottom.  These give the amount of phosphorus flowing into the lake annually since 1973, as measured from four locations.

The point is that the pollution has been most serious on the northern shores, especially in recent years.  Thus, the Florida plan focusing on the southern region is likely to make limited impact.

The choice of vertical lines is smart, as the typical time-series connected-line chart would jump up and down crazily.  A simple vertical axis marks the amounts, avoiding the temptation to print all the data.  The designer realizes it is the trend, rather than individual values, that is the issue.

Taken together, the three components tell a good story.  This is a well-executed effort.  The Times once again proves itself the leader in developing sophisticated graphics.



Reference: "Florida Deal for Everglades May Help Big Sugar", New York Times, Sep 13 2008.