David Leonhardt's article on the graduation rates of public universities caught my attention for both graphical and statistical reasons.
David gave a partial review of a new book "Crossing The Finish Line", focusing on their conclusion that public universities must improve their 4-year graduation rates in order for education in the U.S. to achieve progress. This conclusion was arrived at through statistical analysis of detailed longitudinal data (collected since 1999).
This chart is used to illustrate this conclusion. We will come to the graphical offering later but first I want to fill in some details omitted from David's article by walking through how a statistician would look at this matter, what it means by "controlling for" something.
The question at hand is whether public universities, especially less selective ones, have "caused" students to lag behind in graduation rate. A first-order analysis would immediately find that the overall graduation rate at less selective public universities to be lower, about 20% lower, than at more selective public universities.
A doubter appears, and suggests that less selective schools are saddled with lower-ability students, and that would be the "cause" of lower graduation rates, as opposed to anything the schools actually do to students. Not so fast, the statistician now disaggregates the data and look at the graduation rates within subgroups of students with comparable ability (in this instance, the researchers used GPA and SAT scores as indicators of ability). This is known as "controlling for the ability level". The data now shows that at every ability level, the same gap of about 20% exists: about 20% fewer students graduate at the less selective colleges than at the more selective ones. This eliminates the mix of abilities as a viable "cause" of lower graduation rates.
The researchers now conclude that conditions of the schools (I think they blame the administrators) "caused" the lower graduation rates. Note, however, that this does not preclude factors other than mix of abilities and school conditions from being the real "cause" of lower graduation rates. But as far as this analysis goes, it sounds pretty convincing to me.
That is, if I ignore the fact that graduation rates are really artifacts of how much the administrators want to graduate students. As the book review article pointed out, at the less selective colleges, they may want to reduce graduation rates in order to save money since juniors and seniors are more expensive to support due to smaller class sizes and so on. On the other hand, the most selective colleges have an incentive to maintain a near-perfect graduation rates since the US News and other organizations typically use this metric in their rankings -- if you were the administrator, what would you do? (You didn't hear it from here.)
Back to the chart, or shall we say the delivery of 16 donuts?
First, it fails the self-sufficiency principle. If we remove the graphical bits, nothing much is lost from the chart. Both are equally impenetrable.
A far better alternative is shown below, using a type of profile chart.
Finally, I must mention that in this particular case, there is no need to draw all four lines. Since the finding of a 20% gap essentially holds for all subgroups, no information is lost by collapsing the subgroups and reporting the average line instead (with a note explaining that the same effect affected every subgroup).
By the way, that is the difference between the statistical grapher - who is always looking to simplify the data - and the information grapher - who is aiming for fidelity.
Reference: "Colleges are lagging in graduation rates", New York Times, Sept 9, 2009; "Book review: (Not) Crossing the Finish Line", Inside Higher Education, Sept 9 2009.
As promised, we stick to bubbles. Like the street artist blowing soap bubbles at passers-by, this map -- published in the Guardian (UK) -- is a gift of bubbles.
And our reader Frederic M. is not amused. "A tremendous failure", he said.
In terms of conveying the data, a simple bar chart would do a better job in exposing the biggest polluters, as well as the relative magnitude between the biggies and the small fish.
The chart reveals more problems if one clicks on, say, Europe, and sees the following:
For starters, compare the bubbles labeled 858, 468, 586, 418 with those labeled 23, 20, 18. And look at the little ones in the periphery labeled 133, 174, 128. Baffling, isn't it?
What they did was to print the ranks for every country, except the top four in Europe for which the ranks are placed next to the country name (in small font), and the actual amounts are placed in the middle of the bubbles. The ranks, of course, are pretty useless, and they obliterate the scale of the differences between countries.
Besides, the bigger the polluter, the smaller the rank but the larger the bubble. This built-in disconnect can also be disorienting.
Every bubble chart typically contains lots of data labels, and the reason is that the bubble form lacks self-sufficiency. Without the data labels, the reader has trouble comparing the areas.
Reference: "The Carbon Atlas", Guardian, Dec 9 2008.
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:
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.
(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.
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.
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.
Since the proportions add up to 100 percent, this multiple-choice question appears to allow only one answer, even though, as the text said, there were two acceptable answers! It would be useful to label those two choices separately. We'd also want to see how the question was phrased.
Seen differently, the Tetris chart is a 4x25 matrix with each cell representing one hundredth of the respondents.
Reference: "Name, Please? High School Seniors Mostly Don't Know", New York Times, April 19 2009.
Right on the heels of the disastrous bubble chart comes another, courtesy of the NYT Magazine. Bubble charts are okay for the conceptual ("this is really big, and that is really tiny"). This chart wants readers to compare the sizes of the bubbles, which highlights the worst part of such graphs.
Poor scaling is the huge issue with bubble charts. They are the prototype of what I call not "self-sufficient" charts. Without printing all the data, the chart is unscaled, and thus useless (see below middle). When all the data is printed (as in the original, below left), it is no better than a data table.
In the above right chart, we simulated the situation of a bar or column chart, i.e. we provide a scale. For this chart, the convenient "tick marks" are at 10, 20, 34, 41. Unfortunately, this scaled version also fails to amuse.
Note further that the data should have been presented in two sections: the party affiliation analysis and the gender analysis. Also, it is customary to place "Independents" between "Republicans" and "Democrats" because they are middle-of-the-road.
A profile chart is an attractive way to show this data. Here, we quickly learn a couple of things obscured in the bubble chart.
On the issue of abortion, Independents are much closer to Democrats than Republicans. Also, there is barely any difference between the genders, the only difference being the strength of support among those who want to legalize.
Reference: "A matter of Choice", New York Times Magazine, Oct 19 2008.
PS. Based on RichmondTom's suggestion, here are the cumulative profile charts.
Frederic M. sent in this chart, together with his commentary.
Bubbles across rows have vastly different numbers but their circles are
of identical size (or vice versa). It borders on the ridiculous that all
bubbles of the US
row have the same size... The question if teenage birth rates and teen sex are
correlated cannot be eye-balled with this kind of display. The fact that you
cannot compare across rows make this an instance of “chart junk”.
White spaces -- always dangerous. Does lack of bubble imply no data or no abortions/sex?
Sorting -- this is what Howard Wainer called "Arizona first" with a twist (United States)
Loss aversion -- would U.S. readers be resentful if countries like Iceland are excluded? A much reduced version comparing U.S. to say Canada, U.K, Japan and Germany may yield more information for the reader.
Sufficiency -- if all the data are printed as in a table, why do we need the bubbles?
Reference: "Let's Talk About Sex ", New York Times, Sep 6 2008.
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.
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.