Junk Charts

Following one's nose 2

This is the second post on the immigration paradox study, first discussed on the Gelman blog.  My prior post on the graphing aspect is here; this post focuses on the statistical aspects. I am working backwards on Andrew's discussion points.

Which difference is most interesting?

5. Agree with Andrew; they should publish similar analyses on other minority groups as soon as possible.  One thing that strikes me when looking at the interaction plot is that the U.S. born non-Latino whites have a much higher incidence of mental illness.  The difference between different subgroups of Latinos paled in comparison to the difference between non-Latinos and the Latinos.  This latter difference is particularly acute among the U.S. born than the immigrants. The importance of the Latino analysis hinges upon whether the "paradox" is also found among other minority groups.

(Chris P also pointed this out in his comment on the previous post.)

Disaggregation, Practical Significance, and the Meaning of Not Significant

2. Andrew is also right in expressing moderate skepticism about this sort of disaggregation exercise.  He connects this to the subtle statistical point that "the difference between significant and not significant is not significant."  A related but less obtruse issue is that as one disaggregates any data, the chance of seeing variations that stray from the average gets higher and higher.  This is because the sample size is decreasing, and so the statistical estimates are less reliable.

(To give a flavor of the scale, there were a total of 2500 Latinos in the sample, with 500 Puerto Rican Latinos. The analysis drilled down to the level of different types of mental disorders, subgroups of Latinos, and also adjusted for demographics.  The details of the demographic adjustment are not available but in any case, one should be concerned about whether there were sufficient numbers of say, male immigrant Puerto Rican Latinos age 18-25 with income < $10,000 living in a rental apartment, for such an elaborate exercise.)

Expanding on this point further, one observes that the measured gap between U.S. born and immigrant Puerto Rican Latinos was about 5%.  But this 5% is probably of considerable practical significance since the base rate of incidence is about 30% (I say probably since I am not an expert in mental illness).  The current statistical analysis judged this to be insignificant -- if the sample size were larger, this difference could conceivably be statistically significant, and also practically significant.

But, doesn't the significance test deal with the small sample size problem?  Yes, if the authors merely described the Puerto Rico result as inconclusive.  Here, as is done very commonly, insignificance is equated to "no difference": they said

No differences were found in lifetime prevalence rates between migrant and U.S.-born Puerto Rican subjects.

In reality, a difference of 5% was found in the sample that was analyzed.  The statistical procedure found that this difference could have been a result of chance -- notice "could", not "must".  If the measured difference was 0.5% on 30%, then I might be willing to accept a finding of "no difference"; when it was 5% on 30%, I would like to see a larger sample analyzed.

The Meaning of Paradox

1. Andrew was perplexed by why the phenomenon is known as a "paradox". I had the same issue until I read the paper. The authors were a bit sloppy in the abstract. In the paper itself, they explained that the conventional wisdom has it that immigrants should be more likely to have mental illness because of the stress from the immigration process, and yet the statistics showed the exact opposite. That is the paradox.

Publication Bias

I was a little shocked to see the data tables that gave all the estimates of the various effects at the various subgroup levels: shocked because the authors were allowed (or asked) to include only the p-values that were below some unspecified level (which I surmised is 10% although a 5% significance level is used to judge significance as per convention). This is publication bias within publication bias. P-values that are not significant still provide valuable information and should not be omitted. They did provide confidence intervals but for each subgroup separately, rather than for the difference -- and as they noted, such intervals by themselves are inconclusive when they overlap moderately.

Lining them up

Consider this simple and effective display accompanying the NYT article titled "Recession Drives Women Back to the Work Force".  This is somewhat surprising because jobs are harder to come by during a recession. 

The journalist also told us that the interpretation of this data is controversial among economists.  The trend seemed to have been a decline in participation till 2004 and then a rise since then for 25-to-34-year-old women.  If there were an up-trend, it appeared before the start of this recession.  And participation rate dropped after the 2001 recession.  So much is still under study.

The use of small multiples is a good idea, and the color coordination between the two charts is well thought out.  A minor miss is the vertical scale: for any small multiples chart, one should always use the same scale.  In this case, using the same scale will allow readers to compare the levels of participation between men and women.

The following chart plots a related data set, focusing on the difference between men and women, among those married.  As before, the participation rates are of very different levels.  The male rate has steadily declined in recent decades while the female rate rose from the 30s in the 60s to about 70% in the 90s. 

Reference: "Recession Drives Women Back to the Work Force", New York Times, September 19, 2009; Bureau of Labor Statistics.

Community outreach

Omegatron re-cycled some Wiki charts and we are happy to report that they are great improvements over the originals.  I welcome other readers to alert us when you have done your bit of community outreach, by ridding the world of chartjunk.  The email address is the name of the blog at gmail for any submissions.

Not surprisingly, the originals were pie charts.

The recycled art: (can be seen here and here)

Why are pie charts such poor tools for communications?  Think about where we can place the message, and you'll find that this chart type is far too rigid.  In a pie chart, the key resource is the relative size of the sectors, followed by the number of sectors, and sometimes the size of the total pie.  Other than those, there are little else useful in a pie chart.

The histograms used by Omegatron are much more flexible.  There can be information encoded in the height of the bars, the width of the bars, the total area, the relative distribution of bar areas, the existence and location of peaks and troughs, etc. etc.

For comparing data collected in slightly different formats, the pie charts are hopeless.  Notice that the lowest category on the left (pink) corresponds to 8 weeks or less, which would include two and a half sectors on the right plus potentially a missing sector for 4 weeks or less.  The histograms below handle this easily.

Omegatron asked for some feedback.  I think the new ones are significantly better.  A few minor points:

• Instead of coloring the background to the chart, I'd color the bars themselves into green/yellow/orange according to the trimester
• I'd put the trimester labels under the horizontal axis, close to the "week" labels 
• The charts obviously need to identify the country and year of the data (which I added).  Omegatron pointed me to an inexplicable Wiki convention of not putting text inside charts (see here).  I must disagree with this convention.  Annotations on charts are some of the most useful things.
• If these two charts are to be placed side by side for comparison, then we need to sort out the vertical scale.  It cannot be the absolute number of abortions but some kind of relative scale in proportion to the population size, or some similar metric. 
• In addition, if comparison is the point, I'd suggest an overlapping histogram with bars having no fill.  

Great work!  And I love to see more of it! 

Bubble after bubble

I finally checked the Junk Charts mailbox again, and I found an uprising against bubble charts and pie charts.   It appears that despite their shortcomings amply demonstrated here and elsewhere, editors everywhere continue to believe that the public has a lovefest with these creatures.

I will start off the parade with this one from the Wall Street Journal, purportedly showing that the Bank of England has continued to inject cash into the economy, and at ever increasing rates.  The headline said Bank of England to expand bond-buy plan.


This chart has a variety of problems, in addition to the use of overlapping bubbles.  As has been documented, it is almost impossible to gauge the relative sizes of circular areas, especially when they are overlapping.

If we remove all but one of the data labels, the chart is non-functional.  This is what we mean by not self-sufficient: the interpretation of this chart requires, indeed demands, that all the underlying data be printed on the same chart.  The only way readers can understand what is going on is by reading the data itself!

The horizontal axis (indicating time) is also non sensical.  The separation from month to month is variable.  Besides, and this is the key flaw of the chart, the projected number is a three-month total cumulative growth being treated like a monthly figure.

 

Since the Bank is projected to inject 175 50 billion extra pounds in the next three months, that would work out to be roughly 60 16 billion per month.  That would turn the story upside down: one would conclude that the Bank is gradually slowing the rate of injection.  The following bar chart points this out with little fuss:

 

When bars are used, there is no need to print every single data point.  The relative lengths of the bars can be estimated easily.  The months are equally spaced.

One final point: the exchange rate cited is not very helpful.  What would have been more useful for readers would be the scale of the cash injection with respect to each nation's GDP.

Reference: "Bank of England Expands Bond-Buy Plan", Wall Street Journal, Aug 7 2009.

PS. Per Andrew's comment, here is a line chart, where the growth/decline in the injection is encoded in the slope of the line segments:

Degrees of likeness 2

We left off the other day with an interactive graphic with the ability to peer into subgroups.  This feature assumes implicitly that the overall average obscures differences within subgroups.  What statisticians do with this type of data is to compare the subgroups, and identify the factors that make someone different from the average.

For example, there is a clear distinction between the employed and the unemployed in how they spend the day (not surprising).

This happens to be what NYT printed in the paper edition that day.  (Note, though, that the graphic loses quite a bit without the interactivity.)

On the other hand, there appears to be little differentiation between men and women.

Nor is there much difference between blacks and whites.

One factor that matters is age.  Older people are not exactly like the young.  A lot of these factors (for example, age and employment status) are correlated, by the way.

I showed all these in order to talk about the statistical concept of "aggregation".  We noted that the distribution of time use of the employed is different from that of the unemployed.  Thus, we cannot use the "average" distribution to describe both groups, and so we show the data in disaggregated form.  Similarly for time use and age.  

But there is not much gain in disaggregating race and gender: the "average" is representative of the subgroups for these two factors.  This is one distinction I see between information graphics and statistical graphics: the former typically shows all possible subgroups while in the latter, the designer zooms in on the factors that matter.

A shocking failure to communicate

So said a reader, Stephen B., of the following graphic (note: pdf) in the London Times concerning Andy Murray's recent tennis triumphs.

How can we disagree?  Shocking?  Yes.  Failure?  Definitely.  Failing to communicate?  No doubt.

Let's first start with the five tennis balls at the bottom.  It fails the self-sufficiency test.  It makes no difference whether the balls (bubbles) are the same size, or different sizes.  Readers will look at the data and ignore the bubbles.

Amazingly, the caption said that "Murray has one of the best returns of serve in the game."  And yet, the graphic showed the five players who were better than Murray, and nobody worse!  For those unfamiliar with tennis statistics, it does not provide any helpful statistics like averages, medians, etc. to help us understand the data.

But that is only the beginning.

Take a look at these two donuts.

(The color scheme from light to dark: first, second, third, fourth round of tournament)

So we're told: the 75% of first-serve points won in the fourth round was 25.6% of the sum of the percentages of first-serve points won from first to fourth rounds (75%+70%+71%+76%).  What does this mean?  Why should we care?

The challenge with these two statistics is that they are correlated and have to be interpreted together.  If a first-serve is won, then there would be no second serve, etc.  Here's one attempt at it, using statistics from the Soderling-Federer match.  It's clear that Federer was better on both serves.

Reference: "Murray's march to the last eight", London Times.

 

The case of the shrinking mall

I had a similar reaction when reading this chart but I will let our reader take center stage.

Top portion

Bottom portion

The back of today's New York Times' Week in Review section devotes half of its space to a lame infographic that wastes space and has a major error (which has been corrected lazily in the version now online at http://www.nytimes.com/interactive/2008/10/14/opinion/20090531_OPCHART.html ) The chart shows the recent decline (or in some cases, rise) of retail sales at 27 common mall chains. My main objection is that the top half of the chart is useless. Yes, it provides a baseline from which shrinkage in area (visual metaphor of income = floor space) in the bottom half can represent the relative declines in sales, but this is redundantly handled better by color. The only part of the chart that I got any information from was the bottom half, and it took me a while before I figured out why the top half was even there. Meanwhile, the error in the printed version is that the +5-10% stores were colored light green while the +0-5% store (Burger King) was colored dark green. It should have been vice-versa. The online version simply swapped the colors in the legend, rather than on the map itself, which works logically but begs the question: why do you have dark red at one end of the spectrum and light green at the other, with dark green in the middle? Thank you for listening-- just blowing off a little steam here. It's a lot of wasted space and I'll bet the New York Times paid a lot for it.

Reference: "Op-Chart: The Fall of the Mall", New York Times. (Ed: I am not sure why the date is given as October 2008.)

Some things never fall

It's New York City.  House prices do not fall.  Enjoy the graphic!

Click here for the interactive version

Reference: "For Housing Crisis, the End Probably Isn't Near", New York Times, April 21 2009.

PS. Memo to grammar teachers: When did they start using contractions in titles? 

Don't mess with the scale

My friend Patrick pointed out the single biggest issue with the chart below -- that the designer chose a scale that precisely undermines the message of the chart.  Undermine may be too mild a word to use here; annihilate may be more apt.

The lines in this chart are anchored at the zero point on the time line (horizontal axis) used to indicate the bottoms of various bear markets in the Dow from 1929 to 2007.  From that anchor, time runs to the left showing the amount of time for the Dow to go from peak to bottom (the decline); time runs to the right showing the amount of time for the Dow to climb back to the prior peak (the recovery).  As the caption said, the point of the chart is "if the decline was fast, the recovery took a considerable time".

Funny thing then that the distances from the zero point are roughly comparable on the left as on the right.

This illusion resulted from some very convoluted and perplexing messing around with the horizontal scale.  First, the left-of-center scale is in months while the right-of-center is in years.  Second, the left-of-center scale has normal spacing while the right-of-center seemingly was suffering from spasms.  Take a closer look:

The first five years (0-5) took up about half the scale while the next five (5-10) took maybe one-eighth.  The first year (0-1) took about as much space as the next two years (1-3).

I am not quite sure what is the logic behind this but since the message of the chart has everything to do with the time duration, it is most unfortunate to introduce such distortions.

There is yet another "innovation" in this chart.  Notice that on the right side, the axis labels are irregular (more spasms)... 0,1,3,4,5,10,15,20, 25...  This is as if the designer is posing one of those IQ questions requiring readers to figure out the next number in the sequence.  The specific time intervals selected may have meaning: note that all the lines are straightened out in between these tick marks.  Given that each line represents a different historical sequence, it is difficult to comprehend the regularity of these intervals across history.  Perhaps this will prove to be the key to unlocking the secret of this chart.  Please comment below if you are able to unravel this mystery.

Besides, the same type of "innovation" was not applied to the left side of the chart.  Here, the designer opted to throw out all the data between the peak and the bottom and straightened out all the intermediate fluctuations.

Below are two different versions of this chart, basically restoring the time scale to the normal, equally spaced, symmetric appearance.  The top one used monthly Dow returns where the volatility obstructed our understanding of the trends, requiring the use of color to differentiate the lines.  In the next version, I used R to generate the loess estimates (a type of smoothing) and the trends became clearer.  (There was a prior discussion of loess on Junk Charts here.)

 

Now, these pictures are very different from the original graph!

I'd be very cautious about reading into these charts anyway.  This question is not one suitable for statistical analysis.  The sample size of six is far too small.  Each recession is different in terms of causes, remedies and context.  The fact that we call them recessions do not make them comparable.  Further, it is also impossible to know at this stage if the 2007 decline has reached bottom.  The chart designer essentially assumed this to be the case but who knows?

PS. Nick Rapp, one of the designers of the chart, responds in the comments.  He has started a blog to feature the work of his graphics team at AP.  His colleague has created an interactive version.  More than anything, this post highlights an aspect of the chart that Nick and his team clearly spent a lot of time doodling over.  The concept of the chart itself is wonderful actually, if I didn't say so already; it is essentially the same chart as the oft-printed chart where the anchor point is the start of each recession, only here the anchor is the bottom of each recession.

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.