Junk Charts

A Harvard mess 2

Jon's comment on the previous post pretty much anticipated this post.   The prior post concentrated on graphical matters.  However, the biggest issue with that chart is the choice of metrics.  If the idea is to explore the potential adverse effect of a sharp decline in endowment investment performance, then it is not clear why one should be comparing the proportion of endowment funds and the proportion of operating revenues paid for by endowment funds.  A missing element from these two series is the relative size of the budgets of these different departments.

The next chart shows the proportion of each school's operating costs accounted for by endowment funds together with the total size of its operating costs.


We can turn the ratio around and directly compute how much of the total amount of endowment funds distributed for operating costs is accounted for by each school.  This is really the simplest metric that gets to the question.

 

There are really two possible worries: for the School of Arts and Sciences, who pays for just about $1 billion costs with endowment funds, any significant reduction in distribution will leave a gaping hole; for a department like Radcliffe that pays for over 80% of its operating budget out of endowment funds, obviously a reduction in distribution can cause problems but we are talking about a base of $18 million rather than $1 billion.

Reference: Harvard University Financial Report, 2008; Harvard Fact Book 2007

PS. The first source did not contain any data on operating budgets so the first set of graphs (now replaced) did not show what I intended to show.  The new ones used the right data and had the right order of magnitude in terms of budgets ranging from millions to 1 billion.  The 2008 data are not available as of yet.

Opinion graph

Sharon P. pointed us to this graph, which can make one speechless.

Reference: "Bulls, Bears, Donkeys, Elephants", New York Times, Oct 14 2008.

Mind the gap

When comparing two time series, one typically wants to discuss the size of the gap as it changes over time.  This Business Week chart, for example, depicted for readers the expanding gap between intra-day high and low prices of the S&P 500 for 2008.


This chart construct is effective at pointing out large changes but lacks precision in conveying smaller differences, or trends.  It is always a good idea to plot the gap directly, as we will show below.

More importantly, a better choice of scale can help a lot.  By focusing exclusively on variability (extreme values), this chart hides the relevant information of the closing prices of the S&P.  A point spread of a 100 points means more when the index is at 800 than at 1200.  In order to capture this, we can divide the point spread by the opening price of that day so we say the gap is one-eighth or one-twelfth of the opening price. 

The junkart version makes both changes.  The top chart fixes the scale, plotting the point spread as a percentage of daily opening prices.  Relative to the original chart, the variability in the front part of 2008 was muted because the index was at higher levels back then. 

The bottom chart plots the gap sizes (lengths of the high-low lines).  It is without doubt that directly plotting the gaps showcases the key message.  The current level of volatility is more than double what occurred at the beginning of the year.

If one wants to illuminate the trend as opposed to daily fluctuations, a further improvement will be using moving averages.

For those interested, shown below is a scatter plot that compares the original point spread and the derived point spread, which shows that the change is not trivial.

 

Reference: "The Market: A Daily Roller Coaster", Business Week, Oct 27 2008.

Vanishing act

This is a well-executed chart showing the complex dealings between Wall Street firms in the last 40 years.

They found a way to present all the information without criss-crossing lines.  The right column is the clincher.  It listed all the important recent events.

Reference: "Wall Street: RIP", New York Times, Sep 28 2008.

Lining things up

Guess where I went for vacation (clue in the chart).

This long, narrow country is divided into 15 regions.  In the chart below, an uneven parade of 13 bubbles was used to present some sort of economic projections.  The capital of the country was singled out as the top of the table.

The unevenness has a side effect, that the guiding lines are forced to have differing lengths and bewildering turns.  Further, because bubbles have no intrinsic scale, the designer must put all the data onto the map as well, thus failing our self-sufficiency test..

The following bar chart version respects the wide, thin space and yet delivers the data more clearly.  The top version displays all the data while the bottom one uses a simple axis.  The bottom chart is my preference since most readers are probably interested in approximate and relative comparisons, rather than exact projections.  (The map would be better off without colors.)

Reference: "Inversiones entre 2008 y 2012 llegaran a US$ 57 mil millones impulsadas por mineria y energia", El Mercurio, Aug 25 2008.

Off-sheet accounting

For mid-week entertainment, this full-page ad appeared in the Wall Street Journal recently:

The vertical axis says "% NYSE of All Market Share Volume".  The time-line is from July 05 to beyond July 08.  The text in the black box is "Matched Market Share: July 11, 2008".

When it's so obvious, it's probably not obvious.  The big story is off the chart: what happened to the other 50% of the volume over the years?

Faced with this, one reaches for the pie chart (... almost).

Small add (8/21/2008):

A tale on two charts

By now, everyone knows subprime mortgage lenders in the U.S. are in a world of hurt.   The following pair of charts illustrates how serious the problem is.  Lenders track the proportion of borrowers who are "60-day" and "90-day" delinquent, meaning late or no payment in the last 60 or 90 days.  Lenders count on a contained delinquency rate in order to run a viable business.  These loans stretch for often 20-30 years so it is crucial to catch problems early.

This trend can be seen in the IMF chart (right).  Take the 2000 vintage of subprime borrowers.  The peak 60-day delinquency occurred around 45 months after loan origination, and then tailed off.  (A 60-day delinquent borrower will eventually become 90-day delinquent, or less likely, non-delinquent, in either case causing the curve to tail off.  The tailing off feature is, in fact, undesirable, and can be removed by plotting delinquency rates of 60 days or more, as opposed to just 60 days.  This is what the NYT chart on the left did.)

What do these graphs say about the current malaise?  The NYT chart (right) carries its information in the relative slopes of the lines.  The steeper is the line, the quicker borrowers are becoming 90+ days delinquent. Another piece of information is when each curve starts to take off: the 2007 curve lifts off much earlier in the year than the 2005 and 2006 curves.  This last point is less secure because the graphic does not preclude the scenario in which loan origination is biased toward the latter part of the year.   Similarly, the crossovers between one curve and another tell us the extent of the problem compared to the past but again, the reader has to do much work to learn this information, as shown.

The IMF chart took a different view.  If we selected only the 2005-2007 curves and shifted the 2006 curve to the 12 month point, and the 2007 curve to the 24 month point, we would have recreated the NYT chart.  (We gloss over the matter of counting 90+ days rather than 60-day delinquency, and the other matter concerning the recency of the data used.)  Here, the key information is coded in the vertical distances between the curves.  Taking the vertical as shown below, the reader can see that the 2006 and 2007 vintages have performed almost twice as badly right off the starting gates while the 2005 vintage looked normal but worsened significantly after the two-year mark.

For lenders monitoring performance, the IMF chart is much more useful.  For someone wanting to know the current state of delinquency, the NYT chart is easier to work with.  It must be said that it is always better to plot more history and longer time horizons (like the IMF did).

Finally, can someone please prove a four-color theorem for graphs?  Spraying rainbow colors on charts is a bad habit (for example, also in the house price index charts).

Reference: "Housing Lenders Fear Bigger Wave of Loan Defaults", New York Times, Aug 4 2008; "IMF Sees World Growth Slowing, with U.S. Marked Down", IMF, Jan 29 2008.

A graphical playground

RichmondTom pointed us to this New York Times article, which made what I consider a sloppy argument for the inflation rate being over-stated rather than understated.  This article was accompanied by a colorful and playful chart to describe which components make up the index, and which price changes were most drastic.

 

Like most "infographics", this chart has an interactive feature which you need to click here to sample: mousing over the strangely-shaped areas leads to annotations describing the weight of the relevant component, and the change experienced in that component during the past year.  Like Sherlock Holmes holding a magnifying glass, the reader can use the Zoom In, Zoom Out buttons to drill down.

Here is an expanded view on the color scale, with my comments.

We have no issues with the blue or the red & orange regions but what with using light blue and light green for increases between 0 and 4 percent (when all other increases use red)?  Readers not looking at the color palette will be caught off guard, misinterpreting the data.  This is a big problem since those two appear to be the most frequently occurring colors on the chart.

The designer of this chart surely is aiming for entertainment, creating a playground for the data sleuth.  It succeeds if readers take up the invitation to explore the data.  Unfortunately, it is not the most accessible for more sophisticated numerates interested in understanding the data.

It is impossible to ascertain the relative size of pieces that are close in size but often in arbitrary shapes.  We can roughly read out which components are most important to the index: turns out to be "owner's equivalent rent" by a mile.  Owner's equivalent rent, as discussed by Leonhardt, is the most problematic and inaccurate component, and also, I might add, most susceptible to manipulation since it is an estimate, not a measure.  The next biggest pieces -- food and gasoline (excepting rent) -- are taken out because of "volatility".

The most interesting information in this data set is missing: how much does each component contribute to the overall inflation rate?  This requires multiplying the weight of each component with the change of each component.

It would also be helpful to label which components are taken out of the Bernanke calculation that claims only a 4% inflation when my cable company seems to have raised prices every six months, and groceries and meals and so on are rising at 10-20%.  (Of course, Leonhardt thinks this is all loss aversion.)

Reference: "Seeing Inflation Only in the Prices That Go Up", New York Times, May 7 2008.

Joining the fun

We hope this is indication that the British paper Guardian (with one of the best websites out there) is joining the fun.  It appears that they have quietly debuted an interactive graphics feature.  The first edition addressed the oil price crisis.

This time-series chart has much to be commended:

The use of inflation-adjusted figures seems obvious but we don't see much of these in the press.  Highlighting the peaks and providing annotation (when moused over) is an excellent touch.  The gridlines and axis labels (especially the year axis) are thankfully restrained.  We don't see the need for the unadjusted series (blue line), however.  The fact that the gap grew larger the more time we went back told us little, as it invited readers to read into it more than what it truly was, the time value of money.

Later on, they used an oil barrel object to illustrate the components of retail oil price.  The height of the cylinder is indeed proportional to the data plotted.  If only they colored the end of the cylinder gray instead of green!  As it stands, the green portion has about the same area as the red.

Reference: "Interactive: oil price", Guardian, July 14 2008.

Bound to extremes

The New York Times continued to push the envelope by printing super-complicated data graphics (while the Economist regrettably seemed to have picked the USA Today route... more on that in a future post).  The following graphic was used to illustrate the relationship between CEO compensation and their company's stock performance.

The two dotplot lookalikes depicted the percent change in CEO pay and the change in companies stock price, in both cases, from 2006 to 2007.  The size of the dots indicates the relative value of the CEO's pay.  The gray dots depict "similarly sized" companies for comparability.

In this post, I will focus on the comparison between change in pay and change in stock price for a given CEO.  In particular, the calibration of the axis/scale is problematic.  The scale is automatically determined by an algorithm; as one switches from one CEO to another,  the graphs take on different ranges, use different axis labels, and the zero-percent points shift.

This means that the two charts have different scales.  In this example, each tick mark advances 6% in the top chart but 12% in the bottom chart.

Since the zero points do not line up, the distance between the zero and the orange dot loses meaning:  the 2.5x longer distance in the top chart actually represented the same percentage change as in the bottom chart (31% versus 28%).

In order to respect the grid-lines (white lines), the tick marks fall onto stray percentages (24%, 36%, 48%, etc.).  That's unfortunate.

What's the culprit?  This chart is "bound to extremes".  In other words, the range of the depicted data is used to determine the plot area.  The bottom chart had zero on the left edge because all the stocks depicted rose between 2006 and 2007.  It is often better to use domain knowledge to determine the plot area.  Extreme values should be omitted if they don't add to the message.  Oftentimes, by leaving extreme values in the picture, we squash the rest of the data.

This is also why programs like Excel do a poor job picking a scale.

As an aside, the use of bubbles is almost always troubling. Bubbles do not have a scale so the only information we get is relative size.  However, we can't estimate areas properly so we get the relative size wrong.  Sometimes, even the chart designer may get stumped.  In the chart of Steve Jobs, you would think his bubble (total compensation $1) would be dwarfed by all the other bubbles, as in the WSJ chart we showed the other day.  Not so.

Thanks to Todd B. for submitting this chart.

Reference: "Executive Pay: the bottom line for the those at the top", New York Times, April 5 2008.