Oh no, penalties again

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Euro 2012? ….England may be out but the statistics were not entirely out. In Ian McHale’s model, penalties were assumed to be 50-50. And as Roy Hodgson told BBC Sport earlier today: “A player’s reputation should not be forged on a penalty shoot-out, their reputation should be forged on the four games and in those four games we have not lost.”.
 
To find out more about a stats approach to penalty taking…and why, for example, it might help a penalty taker to look at a clock before he kicks the ball, read ’How to take a penalty: the hidden mathematics of sport’  by Rob Eastaway and John Haigh (republished as ‘Beating the Odds: the hidden maths of sport’). See also ‘What’s the point of probability?’ which gives us a few tips on penalty-taking.
 

Evidence comes with numbers

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Politicians, including prime ministers, don’t always – if ever – study the available evidence before they make policy. This week’s kite flying by David Cameron about welfare was an example. There’s a lot of modelling and empirical data on the interaction of the benefits system, family size, work and so on, and it’s worth looking at.
 
But lately more voices are insisting policy interventions are put on trial beforehand, and proposals subjected to rigorous assessment before being rolled out. The Alliance for Useful Evidence is doing great work – it is co-funded by Nesta, the Economic & Social Research Council and the Big Lottery and the RSS has been an enthusiastic supporter.
 
A pre-condition for good evidence is usually robust numbers, and that requires the evidence gatherers and analysts to be able to handle and understand statistics. Nesta argues ’for rigour in the generation of evidence’. That will often mean applying quantitative methods. That message is starting to feed back to social science teachers, and students intending to study sociology, social policy and politics. They need to have a capacity to gather and make sense of data.
 
Professor John Macinnes of the University of Edinburgh, a member of the RSS getstats campaign board, is leading the ESRC’s initiative and the Higher Education Academy is on board, as teachers build up a bank of tools and presentations to help embed stats in social research, such as the Destress collection.
 
Nesta says, and we agree, that alongside the ’Geek Manifesto’ (there’s an event at Nesta next week), we need a geek manifesto for the social sciences.
 

Higgs Boson and the statistics of certainty

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With experiments run 40 million times per second every day, the Large Hadron Collider (LHC) is a Big Data fanatic’s idea of heaven.
 
The last couple of days of  pre-annoucement v. official annoucement reporting concerning how near CERN scientists were to finding the subatomic Higgs Boson or ‘God’ particle showed how important a role statistics plays in the sciences, not least in pinpointing outliers and measuring degrees of uncertainty.
 
In Statistics, if something is quantifiably less uncertain, it is more certain. Pre-announcement reports of CERN scientists’ findings from the LHC were shared in terms of a ‘four-sigma’ observation. This, said David Hand, Professor of Statistics at Imperial College, equated “in rough ballpark terms” to a 1 in 30,000 chance that they had made an error.
 
A four-sigma observation meant that the scientists were not able to say that they had definitely found the Higgs Boson particle. A four-sigma observation is one that is so far out (4 standard deviations from the mean) that it, or something more extreme, would occur by chance only 1 time in 30,000.
 
The ”threshold of certainty’ as to whether or not this was indeed the particle, was a five-sigma observation (or result).  A five-sigma result is further out and it, or something more extreme, would occur by chance only 1 time in 3.5 million.
 
Today the scientists’ have officially announced a five-sigma result which gives us more confidence than a four-sigma observation that there is something real there and not just a fluke or experimental error.
 
NB Please see the Understanding Uncertainty site for a great explanation of Higgs Boson and the role of sigma observations. See  Explaining five-sigma – How well did they do? for more on how various media outfits coped with explaining the statistics behind the news.
 

Risk and reactors

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MPs on the Commons Science and Technology committee would like us to have a more informed public conversation about the risks attached to different kinds of energy, especially nuclear. After the disaster at Fukushima last year (pictured), opinion in the UK has not moved dramatically – in comparison, say, to Germany – but the MPs feel debate is clouded by mistrust and misperception.
 
‘Public trust is key to how risks are perceived. The government’s position as an advocate for nuclear power makes it difficult for the public to trust it as an impartial source of information,’ they say.
 
But who can command trust; who possesses the authority to counter propaganda for or against the different energy sources, for all of which a risk calculus has to be made? The MPs wonder if independent regulators might carry more credible messages to the public – but they would have to be proactive and reach out energetically to members of the public whose scientific and statistical literacy might not be great.
 
 The report Devil’s Bargain, energy risks and the public calls for a government risk strategy team and more coordination between Whitehall departments – an old demand and one even less likely to be fulfilled in the circumstance of a coalition between two parties with distinct views about markets and the environment.
 
 The report can be faulted for a certain lack of humility too. MPs themselves are not the greatest advertisement for understanding risk, or probability. Their staff are not as literate as they should be in dealing with numbers. A more statistically informed parliament could give a lead, and not just in discussions about nuclear power.
 

Data revolution depends on stats understanding

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Underpinning the government’s plans for more open data are two big assumptions. Both are about the public. One is that people will take a positive view of data sharing and see the advantages in departments and agencies mixing and matching the information they hold.
 
The other is that people will make sense of what is released. That they will take in the numbers and percentages and understand what they are being told. Though Cabinet Office minister Francis Maude did not use the phrase when he published the white paper on open data, he clearly has in mind the ‘armchair auditors’ painted by his colleague Eric Pickles – citizens able to hold government more closely to account thanks to the voluminous information about the state that is becoming available.
 
But our colleague, the stats postdoctoral research fellow at the University of Cambridge  Robin Evans, sounds a warning. (he blogs at  itsastatlife.blogspot.com ) Say doctors are now going to release information about their patients’ cancer treatments. From it you could easily construct a rough and ready performance table showing the proportion of patients who recover. A fair appraisal would, among other things, ask how many cancer cases a doctor sees, and grade them according to severity - but that complicates the picture. The trouble is, that without the caveats, the open data result may be misleading.
 
Who’s going to insert the caution? Evans says there’s a challenge here for the statistically literate. ‘We have to ensure that naive and misleading interpretations of data are not allowed to predominate.’
 
But the white paper does not have much to say about who might step up and educate the public, shooting down erroneous interpretations and inserting qualifications into the picture.
 

Children can do stats, probably

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Understanding stats is vitally important – whether it comes to working out your pension, understanding screening programmes for disease or placing a bet on the winner of the Tour de France. But stats isn’t always easy. Measures of risk, for example, can be ‘tricky stuff’, says David Spiegelhalter, the eminent Cambridge statistician.
 
That’s why a new study commissioned by the Nuffield Foundation is welcome. It looks at how children grasp probability, and ways in which this basic statistical concept might be taught in primary schools. According to Professor Peter Bryant and his colleagues a good starting point is children’s intuitive responses to ideas of fairness. What better way to begin a card game than to shuffle the pack – by randomizing the distribution of cards you make the game fair.
 
The study says ‘despite the central importance of randomness and probability in our lives, it is clear that children (and many adults as well) often have great difficulty in thinking rationally about, and quantifying, probability’.
 
To get there we need to understand randomness, to work out the ‘sample space’ (all the possible events that could happen), understanding how events might be related (correlation) and then probabilities to be given a numerical value.
 
Psychologists show that people tend to think of ‘natural sequences’. If you pick four purple balls out of a bag containing only yellow and purple balls, there’s an almost intuitive belief that ‘it’s more likely’ the next ball to come out will be purple. But some people think ’the chances are’ the next ball has to be yellow. Teaching probability elicits the right answer: the chances of the next ball being either yellow or purple are the same.
 

Growing assets

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Releasing the latest findings from its Wealth and Assets survey the Office of National Statistics reports that despite the recession and financial crash the total stock of wealth held by British households has remained remarkably stable. Wealth largely held up because the value of private pensions rose significantly.
 
Wealth totals £10.3 trillion, which is enough to pay off the UK National Debt ten times, or five times if you include among the state’s liabilities all the money used to bail out the banks.
 
The data come from the second wave of the ONS sample, first collected in 2006-2008 and again in 2008-2010. Average (mean) household wealth is now around £418,000 (including the value of private pensions). The median is £235,000. The difference between the two averages stems from the way wealth is distributed. The wealthiest 10 per cent of households were 4.3 times wealthier than the bottom 50 per cent of households combined. Two thirds of all assets are owned by the wealthiest fifth of households.
 
For many, home is where the wealth is: property accounts for about a third of total wealth, though that’s now dwarfed by the private pension pots (some) people have built up. (The ONS survey excluded the value of public sector pension entitlements.) The least wealthy tenth of households not only lack wealth, in aggregate they are in the red, and owe more than the value of their assets.
 

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