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A massive problem in communicating the results of statistical calculations to the media and to the public is how we communicate uncertainty. Certainly most mass media seems to like a hard and fast number, even though except in a relatively small number of cases, numbers always have some uncertainty.

So, how can we, as statisticians (or scientists describing statistical work), best communicate our results, while keeping the uncertainty in tact, and making it meaningful to our audience?

I realise that this isn't actually a statistics question, rather a psychology question about statistics, but it's certainly something that most statisticians and scientists will be concerned about. I'm imagining that good answers might reference psychological research more than stats textbooks...

Edit: As per user568458's suggestion, a case-study may be useful here. If possible, please keep answers generalisable to other areas.

The particular case that I'm interested in serves as a nice example: the communication of climate science to politicians and the general public, through mass media. In other words, as a scientist, it is your job to convey information to a journalist in such a way that they have little difficulty in accurately conveying that information to the public - that is, the truth, although not necessarily the whole truth, which won't usually fit in a news-bite.

Some particularly common examples might be the communication of the uncertainty in the estimate of degree of warming over the remainder of the century, or in the increased likelihood of a specific extreme weather event (i.e. in response to a "was this storm caused by climate change" type question).

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    $\begingroup$ David Spiegelhalter has been working on risk and uncertainty and how to communicate these ideas. I do not believe there is a general answer to this question because it strongly depends on the context, mathematical-statistical tools developed at the moment, understanding of the phenomenon in question, ... $\endgroup$ – user10525 May 2 '12 at 7:33
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    $\begingroup$ @Procrastinator - post that comment as an answer! Statistical graphics are IMO a compelling way to disseminate much (perhaps most or all!) statistical content. I particular enjoyed Spiegelhalter's recent Science article (ungated PDF here). $\endgroup$ – Andy W May 2 '12 at 12:24
  • $\begingroup$ I like so much of @naught101's contributions to this site, but this question is just too broad. Any time the answer could come in the form of a book, or a library, I consider the question too broad. $\endgroup$ – rolando2 May 2 '12 at 21:26
  • $\begingroup$ @Procrastinator: I think the communication of risk is a separate question, and I don't know if the discussion of one is applicable to the other. $\endgroup$ – naught101 May 3 '12 at 1:21
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    $\begingroup$ This is a great question and an instant favourite - but I agree it is too broad (but only just). It can be made into an answerable, solvable problem by a) explicitly stating the audience of the communication (e.g. you imply an interested lay audience of press and general public), b) explicitly targeting a problem (e.g. "How best to communicate uncertainty around a quoted figure?" rather than uncertainty in general with that as an example), c) illustrating this problem type with a specific real world example problem where communicating uncertainty around a figure is needed but is unsuccessful. $\endgroup$ – user56reinstatemonica8 Jul 4 '12 at 14:32
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That's what Gerd Gigerenzer has been working on in the past: http://www.amazon.com/Reckoning-With-Risk-Gerd-Gigerenzer/dp/0140297863/ref=sr_1_1?s=books&ie=UTF8&qid=1335941282&sr=1-1

Edit to summarize what I think might be what Gigerenzer means:

As I understand it, Gigerenzer proposes to communicate risk differently. In the traditional way, a treatment (he's into medical statistics) is reported as having an effect of reducing an illness by a certain percentage. E.g. "eating 100 bananas a day reduces your risk of getting toe nail cancer by 50%". This is a huge benefit of eating bananas, it seems. The problem is that the prevalence of toe nail cancer isn't exactly high. Let's assume, there is a disease called "toe nail cancer" and its prevalence is 1 in 100000 people. Gigerenzer proposes to report the absolute probability of getting toe nail cancer before and after - e.g. "reduces the risk of getting toe nail cancer from 0,001% to 0,0005%" - which is lot less impressive in the case of rare diseases.

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    $\begingroup$ This would be a better answer with a short description of Gigerenzer's main claims. $\endgroup$ – naught101 May 2 '12 at 6:52
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    $\begingroup$ Thanks for the summary xmjx, although I'm not sure if it's actually that useful to conflate the communication of risk with the communication of uncertainty.. $\endgroup$ – naught101 May 3 '12 at 1:19
  • $\begingroup$ @naught101 -- Does the public understand the difference between risk and uncertainty? $\endgroup$ – Daniel R Hicks Jul 5 '12 at 2:41
  • $\begingroup$ @DanielRHicks: as I implied, I'm not sure. Feel free to make an argument for or against... $\endgroup$ – naught101 Jul 5 '12 at 3:58
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    $\begingroup$ @naught101 -- My point is that sometimes one needs to be intentionally imprecise in order to convey reasonably valid concepts to those who do not have the appropriate background. Too much rigor may produce a more precise understanding, but in a much smaller audience. Using "looser" terminology can result in a much higher rate of overall comprehension, even if the comprehension is less precise. $\endgroup$ – Daniel R Hicks Jul 5 '12 at 4:21
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In 2003 there was a series in the Journal of the Royal Statistical Society (A) on the Communication of Risk.

The reference that I have for the 1st one is:

J. R. Statist. Soc. A (2003) 166, Part 2, pp. 205-206

From there you could probably find the entire series and they may be of interest for this question.

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I think bookmaker's racing terminology may be more easily understood by the general public, for example the chances of some specific event happening might be said to be 50-50 or, as another example, there may be odds of 9-1 that an effect will be within a stated range, with a risk of 100-1 that some rather unlikely specified event will happen. This needs to be balanced with risk, in the sense of the potential benefit or damage that may arise. For example, if one crosses a road as a pedestrian without looking, one may be lucky 75% of the time, but the consequences of an accident could be catastrophic.

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