Yuan Yang

How to present statistics to donors (Part III: International Dollars vs Real Dollars)

 program ("Choosing Interventions that are Cost-Effective") presents DALYs saved per international dollar - most commonly the "Geary-Khamis" dollar. In short, an international dollar is an imaginary unit of currency that has the equivalent purchasing power parity of a US Dollar at some specified date. For example, a 2000 Geary-Khamis dollar is a unit of currency that buys you as many goods and services as a US dollar would have bought you in the US in the year 2000.

The WHO uses the Geary-Khamis dollar because it is an international organisation giving information to a range of donors who use different currencies, who are also choosing between investments in different countries with different goods and price levels; a Geary-Khamis dollar compacts all of the variation in nominal currency and in price level into one measure of real currency, i.e. currency that buys a certain amount of goods and services.

Now, there are many problems with the Geary-Khamis dollar from the point of view of economic theory and international justice. Thomas Pogge and Sanjay Reddy argue (in their paper 

) that the use of international purchasing power metrics such as the Geary-Khamis dollar obscures economic reality and leads one to overweight the importance of aiding some countries over others.

From the point of view of writing about cost-effective charity donation, the take-home message is that Geary-Khamis dollars are fairly complex economic fictions that are not easy for donors to understand. Nobody actually uses Geary-Khamis dollars (apart from, well, people who lived in the US in the year 2000). So it is of no motivational or emotive relevance to say to someone: "You could get that for 40 Geary-Khamis dollars!"

For a general audience we should use real dollars (or pounds, or whatever currency your audience understands), and make sure to either date the currency to a particular year, or adjust your statistics for inflation year upon year. If there are significant purchasing power disparities to take into consideration, you should give the headline statistic first and then explain what the purchasing power disparity does to your cost-effectiveness measure; don't just bundle it into the piece of confusing economic terminology that is the Geary-Khamis dollar.

I have argued that we should take responsibility for the rhetoric we generate when making statistical arguments for cost-effectiveness and moral decision-making. My three key recommendations are:

Write an executive summary highlighting the decisions the desired reader should make;

Present cost-effectiveness data in DALYs/dollar not dollars/DALY - the former is a better frame;

Draw linear graphs - they are clear to understand - and highlight a single comparative message; and

Use real economic metrics, such as US dollars, that are used by people in their daily lives.

Joined us at part three? Check out Yuan's posts on 

How to present statistics to donors (Part II: Representation)

Although we are familiar with the idea of criticising journalists for using misleading language in their verbal rhetoric, we are not as quick to point to the use of misleading data representation in statistical rhetoric, which is often non-verbal and highly visual. Graphs give a writer the opportunity to present statistics clearly, but also the opportunity to be confusing in two dimensions and multiple colours.

In a second post on on the importance of conveying information persuasively when discussing moral issues, Yuan gives her recommendations on representing data in graphs in an easily understandable way and on minimising the 'lie factor'.

Watch this space for Yuan's third post in this series where she'll wade into the international Dollar vs real Dollar debate.

Graphs give a writer the opportunity to present statistics clearly, but also the opportunity to be confusing in two dimensions and multiple colours.Representing numbers visually is much more arresting than presenting statistics numerically - so long as the graphics are easy to correctly interpret.

A common mistake among those graphing cost effectiveness data is to present differences on a logarithmic scale. This compresses differences in cost effectiveness of ten, a hundred or a thousand-fold into apparent visual differences of just two, three or four-fold. A good example is the linked figure on 

 from the Poverty Action Lab. While the true variation may be understood by the academics reading these reports, it’s isn’t appreciated by most others. Even if someone does understand on an intellectual level that the differences are ten times larger than they appear - and many do not - the logarithmic scale makes this point less emotionally compelling. As a result, we strongly recommend retaining a linear scale to show just how much better some approaches are than others.

A badly presented graph can place even more mental strain on interpreting the graph than simply presenting a table of numbers. Edward Tufte’s book, the Visual Display of Quantitative Information (

) is an excellent guide to principles of graphical representation of statistics. In short, your images need to have graphical integrity: to present information as succinctly as possible, and to present information in a way that is not visually misleading (to minimise what Tufte calls the “Lie Factor” of a graph). Graphical integrity has a huge impact on people’s perception of the data presented.

Although we are familiar with the idea of criticising journalists for using misleading language in their verbal rhetoric, we are not as quick to point to the use of misleading data representation in statistical rhetoric, which is often non-verbal and highly visual.

Tufte’s key recommendations are as follows (with my comments in square brackets):

“1. The representation of numbers, as physically measured on the surface of the graph itself, should be directly proportional to the numerical quantities represented [i.e. no log scales; use the numbers in absolute values]

2. Clear, detailed and thorough labeling should be used to defeat graphical distortion and ambiguity. Write out explanations of the data on the graph itself. Label important events in the data.

3. Show data variation, not design variation. [Meaning: Do not let the presentation style obscure the variation in the data that you are trying to display, or introduce new variation when there isn’t any. Ask yourself: What comparison am I using this data to display? Consider that humans find it hard to make multi-layered comparisons, and simplify your graph into multiple graphs if necessary.]

4. In time-series displays of money, deflated and standardized units of monetary measurement are nearly always better than nominal units. [I will look at this in the next section.]

5. The number of information carrying (variable) dimensions depicted should not exceed the number of dimensions in the data.

Yuan Yang

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How to present statistics to donors (Part III: International Dollars vs Real Dollars)

How to present statistics to donors (Part II: Representation)