A challenge to readers. Who said this: “If on the one hand we are seeing a reduction in absolute poverty, on the other hand we cannot fail to recognize that there is a serious rise in relative poverty, that is, instances of inequality between people and groups who live together in particular regions”?

The difference between relative measures and absolute ones has often been mentioned in these pages, together with the confusion in – indeed misleading of – the minds of the public that this can cause when one is reported without the other. A standard example is in The Norm Chronicles, by Michael Blastland and David Spiegelhalter (2013). You can also find it in Spiegelhalter's article in Significance, March 2008. The relative risk of getting bowel cancer rises if you eat smoked meats; the absolute risk remains tiny. For which reason it is also called the bacon sandwich fallacy.

But the quote above does not come from Prof. Spiegelhalter, who is Winton Professor of the Public Understanding of Science at Cambridge University and who therefore knows more than most about how to communicate statistics. Nor, indeed, does it come from any statistician. A slight clue – all right, quite a large clue in both relative and absolute terms: Roman Catholic readers should have less difficulty in identifying its source. It was Pope Francis, in his Message for World Day of Peace, given on New Year's Day this year.

This issue of Significance is devoted to global poverty and ways of understanding and alleviating it. It is not unexpected to find that a pope has something to say on the subject. Perhaps less expected is that he should point out an important statistical issue in the way that we should look at poverty. I stumbled across the quote while trying to pin down what he said about the champagne glass diagram of distribution of wealth on page 39. Verifying references can have all sorts of side benefits.

The statistics of poverty are horrifying. Zeid and Cochran's article on Somalia (page 4) is little more than a catalogue of huge numbers. The numbers of people forced to flee their homes may since have been exceeded by Syria. Mortality rates are dry things. We may intellectually grasp what a maternal mortality rate of 1000 deaths per hundred thousand live births (as in Somalia) means, as opposed to one of 11 deaths per hundred thousand (as in the UK); but it is hard for most of us to emotionally feel the statistic. A single picture would carry more emotive power. Contrast, perhaps, the Pope's statement with Stalin's: “One death is a tragedy. A million is a statistic.”

In one sense it is an affront to count these things. The loss of a child, a death in childbirth because no medical care is available for many miles around – these are individual pains which we can share only remotely: how can you quantify sorrow? In another sense, quantifying is a necessity before we can do anything useful to help.

Inmates of concentration camps were depersonalised by being tattooed with numbers, not names. A cult TV programme of the 1960s called The Prisoner had its hero caught up in an incomprehensible world and asserting his own individual worth with what became a catchphrase: “I am not a number, I am a free man.” The Pope's quotation should remind us that it is possible to be both.

Properly understood, the numbers do not hide suffering – they reveal it. Such proper understanding is hard to come by, but that does not mean we should not try. Counting people does not dehumanise them. Instead, it is an essential tool in understanding the poverty that dogs humanity, and in trying to reduce the amount of suffering that is in the world.

Julian Champkin

Timeline for all

Is the fold-out “timeline of statistics” in the December issue going to be made separately available? It is superb, and I think should be on the wall of every secondary school in the country.

Meic Goodyear


The timeline is downloadable, with open access, at high resolution and with no need to register, from www.statslife.org.uk/images/pdf/timeline-of-statistics.pdf or from http://onlinelibrary.wiley.com/doi/10.1111/j.1740-9713.2013.00707.x/pdf. Teachers, and everyone else, are encouraged to download it and print as many copies as they like, at as large a scale as their printers (or a copyshop's printers) will permit, and post them wherever they are likely to be seen. It was designed with that hope in mind – Ed.

Still pedalling frequently …

There is an error or misprint in the last paragraph of Aberdein and Spiegelhalter's article “Have London's roads become more dangerous for cyclists?” (Significance, December 2013). It says there are 22.4 deaths per million kilometres cycled in the UK. That should be billion kilometres1. (If it were million there would be hundreds of deaths in London every day and we should all have to give up cycling!)

John Cutler, a cyclist still alive



… or frequentistly?

The item by Aberdein and Spiegelhalter in your December issue (“Have London's roads become more dangerous for cyclists?”) would almost serve as a demonstration of how to misuse significance tests. The hypothesis being tested was never explicitly stated, but the authorities were exhorted to investigate the hypothesis that the risk to cyclists had increased. The authors were perfectly able to do this for themselves, testing for a shift in the mean using the data they presented in Figure 1. It appears from visual inspection that no shift has occurred, but that would lead to an uninteresting article, so a rather noisy statistic which is significant at 0.025 was used to set hares running.

There was an earlier significance test implicit in Figure 2, where the similarity of two histograms was used to accept the hypothesis that deaths of cyclists could be modelled as a simple Poisson process. Those who have worked with occurrences of this nature tend to assume that they are almost always compound Poisson processes. (In this instance one expects to see clustering resulting from a correlation with rain and darkness, perhaps complicated by a reduction in the population at risk when rain and darkness are anticipated: many cyclists travel by some other means in such weather.) So it is better to estimate a variance-to-mean ratio rather than to take it as unity simply because the data do not require the more elaborate model. And with a compound Poisson process, the probability of six deaths in a fortnight will be higher.

Unless statisticians pay some attention to the inherent plausibility of the hypotheses they are testing and unless they seek supporting evidence for marginally significant results, they end up endorsing one false positive for every twenty investigations they conduct. Since “boring” results remain unpublished, the overall result is to bring the frequentist approach into disrepute.

R. C. Wheeler


Average answers

Nate Silver's advice (Significance, December 2013) to remember the lowly average struck a chord with me. I like to ask my undergraduate students why we calculate averages. This is something they have been doing for years, through many years of school, but no one is sure what the right answer is.

For sport, I sometimes ask the same question of my colleagues. The only difference I have observed in their responses is that my colleagues are much better at changing the subject. When an answer is proffered, it is comes as quite a technical notion of the value of an average as the first term in approximating the distribution of the data. No one, so far, has related averages to the more intuitive notion of central tendency, or to the idea of comparing with anticipated or known values. But perhaps these responses don't seem precise enough to be the “right answer”.

Tom King


Letters should be sent by e-mail to significance@rss.org.uk, or by post to: Significance Letters Page, Royal Statistical Society, 12 Errol Street, London, EC1Y 8LX. They should be short (preferably under 250 words), may be edited for length and should clearly indicate whether or not they are for publication. They must be received by March 15th, 2014, in order to be considered for publication in the April issue.


Wiley Prize Crossword Rock Foundation by Sam Buttrey


Send your solution to: Significance Crossword Competition, Royal Statistical Society, 12 Errol Street, London, EC1Y 8LX or scan it and email to signifrcance@rss.org.uk. The competition is sponsored by Wiley (http://www.wiley.com/statistics), who will give the winner £100 or $150 to spend on Wiley books. Closing date: March 25th, 2014. The winner will be chosen randomly from the correct entries, and the correct solution published in the April issue. Photocopies are acceptable.

Answers to eight italicised across clues need to be adjusted in sequence before being entered into the grid. The answers do not match the number of squares apparently available.

The set of operations can give rise to the solution at 15A, which is unclued but enumerated.

Downs are normal. One answer is a familiar abbreviation.


  • 1 Let out at small cell, perhaps (3) 3 Item used in gymnastics or dance (4)
  • 5 Loves screaming and fresh entrails
  • 8 Feel sad about little bird after mother's end
  • 9 Added juice to Bordeaux, e.g., incurring cost (9)
  • 11 Adds on assessment for the telephone (5)
  • 12 Take coach going west, take airplane, am I stuck inside a generic container
  • 14 Antibiotic makes you ill; brief AMA finally 15 (5, 5)
  • 18 Repayments for re-working vegan scene (10)
  • 20 Bad loss I'd taken in geometry class
  • 22 Send nitrogen mixture into space, audible from a seat on the grass (two words.)
  • 24 Angry about the Ugandan political leaders (3,2)
  • 27 Cracks unlocked beer safes (9)
  • 28 Pen dropping in beasts’ end smells terrible
  • 29 Cook some lamb dressing tips in a rare fashion
  • 30 In her, a genteel anger (4)
  • 31 Ask yourself inside to blue surroundings (3)


  • 1 Card sharp holds second round (5)
  • 2 True or false: I go call like crazy (7)
  • 3 Wager with a second or seconds (5)
  • 4 Possibly counts pounds or dollars on the outside (5)
  • 5 Pair of shorts and a long singlet one set out after a short sleep (8)
  • 6 As for woman, one has a fine set of clothes (7)
  • 7 Beer goes up, down, inside, outside sophomores (4)
  • 10 Car at end has scary noise inside bag (7)
  • 13 Food that's unordered? (4)
  • 14 Devastation left little to preserve (4)
  • 16 With a bit of ammonia inserted, kills lettuce and peas, e.g. (7)
  • 17 Surfer babe, much wiped out (5, 3) 19 Depression fighter: speak of naked fish? (3, 4)
  • 21 Purposes and locations for nomads, maybe (7)
  • 23 Like Bob Marley, a star in transit (5)
  • 24 Speed in bandwidth, as terabyte (5)
  • 25 On the up-and-up, bashful is really the opposite (5)
  • 26 Kills the first of forty-five soldiers (4)

Solution to December issue's crossword: Recurring by Goujeers

1 to 9 in the clues represented the first nine wedding anniversaries


Across: 1 BUCK LE, 4 anag, 10 SILLY round IM and A R, 11 2 defs, 12 IRON(IC), 13 UNI T(cell) T(test) RUSTS, 15 OCHE in TRE(Y), 16 2 defs, 19 X replacing Q in EQUALS with last letter first, 21 anag, 23 OOPS A DAISY, 25 WOO L, 27 DATE D, 28 anag, 29 NOR THE R.N., 30 AD HERE.

Down: 1 B ASSISTS, 2 OR in COMMODE, 3 homophone LIE LOW, 5 chemical element abbreviations, 6 anag, 7 hidden, 8 IS in MUSE, 9 2 defs, 14 THOU SAND TH(E), 17 anag, 18 anag, 21 HAS, odd S-L-E, 22 2 defs, 24 APE in PR, 26 3 defs.

Winner, October: Tony Desmond, Guelph