Friday, June 1, 2012

Telling stories with numbers

Ensuring that future citizens are quantitatively literate (as well as literate) should be the responsibility of every teacher and professor, but in the end it often falls on the mathematics instructors. In part this is because in the public, political, and bureaucratic minds, quantitative literacy is about numbers and numbers are the responsibility of mathematicians.  But in part too it is because all too often the mathematicians are the only ones not scared by numbers.

The trouble is, of course, as only those of us in the math biz know, for the most part we are not well versed in QL issues. Sure, along with millions of other people, we’ve read journalist Darrel Huff’s 1954 bestselling book How to Lie with Statistics, and academic Edward Tufte’s masterpiece The Visual Display of Quantitative Information, and some of us have likely managed to get hold of a copy of the excellent set of essays Statistics: A Guide to the Unknown, now into its N’th edition, though the publisher’s insanely high price can surely be motivated only by the desire that as few people as possible actually buy a copy. But that is about as far as it goes for most of us who find ourselves asked to teach a QL course.

Yet all of those excellent sources of QL educational material are mostly relevant to ensuring the future citizens can make intelligent use of the quantitative issues they face in their daily lives – making wise financial decisions, evaluating loan and credit-card agreements, buying houses, voting in elections, understanding graphs and charts in the media, and the like. What they miss is what is probably the single most important aspect of QL for people who use numerical data in the worlds of business and government: using numbers to communicate.

Every day, crucial business and political decisions are made on the basis of numerical data. Only rarely do the key decision makers produce that data; rather they rely on others, not only to produce it, but to present it to them.  Yet how many quants – the data producers – know how to present data effectively? To put it another way, how many of them know how to tell a story using numbers? With the educational QL focus on how to produce the numbers and how to present them using effective graphs and charts, what too often gets overlooked is how to communicate with the numbers themselves. I am referring primarily to what is surely the most ubiquitous numerical data preparation and presentation tool there is: the spreadsheet. For all the fancy graphics packages people use, I doubt that a single important business decision is ever made without the decision makers eyeballing a spreadsheet. For that, after all, is where the actual numbers can be found.

Or can they? Take a look at this example:

If you are a busy executive, with just a few minutes available to make a decision, how effective is that spreadsheet? Compare it with this one:

This is the same spreadsheet formatted differently. Some intelligent underlining and use of white spacing has provided structure that greatly aids comprehension. Actually, the formatting did not provide the structure, it simply represented in the spreadsheet printout the structure that the data already had, but which had been lost in the first presentation.

This example comes from a recent book, Painting with Numbers, by Randall Bolten, a lifelong quant based in Silicon Valley. As many high tech executives in the Valley will testify, Bolten is to the spreadsheet what Tufte is to the graph. Now, with the appearance of this book, his expertise is accessible to all. Aimed at the professional quant who has to present data to decision makers, much of the book goes well beyond what a high school or college QL instructor would require, but at under $20 for the Kindle edition, it is worth getting just to pull material from the early chapters (and perhaps the later one on PowerPoint presentations of spreadsheet data).

Much of what Bolten says boils down to adopting a common-sense attitude to the presentation of data. But as is so often the case, it can take someone else pointing something out before that common sense kicks in.

For example, simple Excel selections can make a huge difference to the intelligibility of the data. In the example below, right justification makes Version A much easier to grasp the overall picture at the first glance. 

As Bolten points out, Version A works so well because it takes advantage of the place-value representation of Hindu-Arabic numerals, which makes the leading digit the most significant. Simple, but very effective.

Likewise, how to represent the units can have a significant influence on readability. In the following example, Version F is much clearer than the other two.

None of this is rocket science – though more to the pity, for as Tufte pointed out, bad presentation of numerical data lay behind the disastrous decision to launch the space shuttle Columbia in 2003. It really is common sense. But having myself sat through many financial presentations as a university administrator, I know first hand that it is common sense that requires some prodding. Anyone faced with giving a QL course should devote some time to the crucial skill of being able to communicate effectively with numbers. As part of the language (sic) of mathematics, numbers too can tell stories. In today’s world, everyone should have the ability to ensure that they tell those stories as effectively as possible.