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.
 

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.
 

Kitting out MPs for next term

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We’re hoping to use the summer break from parliamentary politics – isn’t it amazing how political news dries up when MPs are absent? – to think about what stats our parliamentary representatives work with. What is the basic equipment an MP needs to operate as a legislator, select committee member, policy debater, constituency activist and so on?
 
We’d like your ideas. For example, MPs fixate on figures to do with electoral prospects. They and their staff swim daily through shoals of data, including sometimes dody surveys from interest groups, firms and fellow politicians. So don’t they need to understand the basics of sampling and margins of error?
 
Political argument is often about risk – the likelihood of an event occurring. Does that imply MPs should have an adequate grasp of probability?
 
Statistics get used to beat opponents around the head. That’s OK, as long as we’re clear what the baseline is, or the denominator if we are talking about ratios. We’ll be looking through Hansard, the record of parliamentary proceedings, for examples of statistical use and misuse and talking to our contacts and colleagues to find out what would be most helpful.
 

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.
 

Debunking the demographic depressives

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First results from the 2011 census back those who say demographic change — the much worried-about ageing of Britain for example — is a lot more gradual than often recognised.
 
The Office for National Statistics reported that the percentage of the English population aged 65 and over was the highest seen in any census but also that the rate of growth is gradual.  There were 430,000 residents aged 90 and over in 2011 compared with 340,000 in 2001 – that’s an average increase of 9,000 nonagenarians and centenarians each year during the decade.
 
In a population of 53 million that’s not a demographic disaster, especially when the population has been growing at an historically remarkable rate. Over the decade numbers increased by 7 per cent, the largest growth in any decade since the state census began in 1801.
 
So much depends on how numbers are interpreted. The ONS has traditionally be shy of putting out glosses but with this census, in the midst of national gloom and doom, we need to be careful not to overdo the negativity.
 

Judging relative medal success at the London Olympics

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Measuring relative success is all about getting as near as possible to comparing like with like. Looking closely at the data helps.
 
We instinctively understand the difference between relative and absolute figures. For example,  we know that comparing the numbers of babies born in one country with another provides much less interesting and/or useful information than looking at the birth rate  i.e. babies born per 1,000 population, in each of those countries. We also know that just hearing that two people got a 5% pay rise means something very different if we also know that one earns £5,000 and the other £50,000 per year.  In other words, we know that expressing measures as ratios (one number divided by another) usually offers better insight into what is really happening.  
 
In the same way, when reading through the official (the absolute figures-based) Olympic medal tables, we know that the medals gained by a country depend not only on the training its athletes have undertaken but also on a range of quantifiable other factors such as a country’s population size and wealth as well as other fundamental factors such as the number of athletes from that country who are participating in the Games!. 
 
This morning’s Radio 4 ‘Today’ programme included an interview with Professor Stefan Szymanksi, Sports Economist at the University of Michigan in which he talked about the factors underlying Olympic medal performance. He encouraged us to consider the all time medal table and which countries have done well since the Olympics started.  Two highly populated and wealthy parts of the world stand out. The US has won 15% of the Olympic medals ever awarded and European countries have won 16%. Whilst there is an easily understood correlation betweeen population, wealth and medal-achieving performances over the long-term, trying to use those same factors to predict in the short-term seems to work less well because many other individual factors have to be taken into account, including just how much their country invests in the sport (and presumably, how much they as individuals want/are inspired to win and things like ‘home advantage’  too.)
 
Taking population and wealth into account,  some of the countries which are punching above their ‘population and wealth’ weight include: New Zealand, Australia and Norway and Finland (not just in Winter-sports)
 
In outstripping its one gold medal performance in 1996 in Atlanta, in (as we speak) taking third place in the medal table and in (fingers crossed) heading towards a 20+ medals total, Team GB is way ahead of China in per capita terms and doing very well indeed. Taking into account team size and GDP, Team GB is doing slightly less well. 
 
The RSS helped to get together a team from Imperial College which worked with the Guardian Datablog to develop the alternative medal league table.  This new table’s rankings includes weighted data, data which are based on figures adjusted by population, GDP and team size.
 
The RSS’s Significance magazine is also a must for anyone keen to receive regular updates and statistical perspectives on the Games.
 

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