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.
 

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.
 

NASA and climate change: from weather dice to bell curves

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Earlier this week the National Aeronautics and Space Administration (NASA)’s Goddard Institute of Space Studies published a new statistical analysis which has found that the Earth’s land areas are more likely to experience extreme summer heat now than they were in the middle of the 20th century.
 
They looked at average (mean average) summer temperatures since 1951 and found that the odds have increased in recent decades for what they define as “hot”, “very hot” and “extremely hot” summers.
 
Between 1951 and 1980 less than 1% of the Earth’s land area experienced “extremely hot”  mean summer temperatures. Since 2006 about 10% of land area across the Northern Hemisphere has experienced those temperatures.
 
As the weather is governed by natural ups and downs or variability, lead author, NASA climatologist Dr James Hansen and colleagues were concerned that very large variations might be disguising a trend. They turned to  Statistics to help them work things out.  NASA used global temperature anomaly data (data on how much warming or cooling regions of the world have experienced) collected betweeen 1951 and 1980 as a base period with which they could compare subsequent surface temperature data from 1981 to the present. In this way, they were able to better understand the relatively stable climate bewteen 1951 and 1980 and to compare this with the increasing frequency of extreme heat events in the following 30 years.
 
They developed a bell or normal curve*, a much used type of graph, to describe how those anomalies are changing. They found that summer temperature anomalies during the base period of 1951 to 1980 when the climate was relatively stable, fitted well with the normal curve.
 
With mean average temperature at the top of the curve, decreasing in frequency to the left of centre with “cold” “very cold” and “extremely cold” events. Decreasing in frequency to the right of centre are “hot”, “very hot” and  then “extremely hot” events.
 
When plotting bell curves for the 1980s, 1990s and 2000s, the curve shifted to the right, meaning that more hot events have become normal. The curve also flattened and widened, including a wider range of variability.  An average 75% of land area across Earth experienced summers in the “hot” category during the past decade, compared with only 33% in 1951-1980. Widening the curve also led to a new category of  “extremely hot” events being developed….events which were all but non-existent between 1951 and 1980.   
 
Dr Hansen says summer 2012 in the US looks set to fall into the extreme category.  Global maps of temperature anomalies show that heatwaves in Texas, Oklahoma and Mexico in 2011, and in the Middle East, Western Asia and Eastern Europe in 2010 also fall into the new “extremely hot” category.
 
NASA colleagues are now settled on bell curves as the statistical tool which most easily communicates the change in temperature anomalies, particularly at the extremes.
 
However, in the past NASA has used other tools to communicate variability and the growing frequency of extreme temperature events. In the 1980s, Dr Hansen introduced the analogy of loaded dice  On one of the six-sided dice, he painted two sides blue, two white and two red to represent the chance of a cold, average, or warm summer season.  On the other – loaded –  die, he painted one side blue, one white and four red to represent how climate models suggested the dice would roll by the first decade of the 21st century. 
 
Looking back, the dice analogy seem to be a fair reflection of how many sides would now be red as opposed to blue to represent today’s climate.  Of course, Dr Hansen would now have to replace one of the red sides of the dice with an entrely new colour – brown, to represent ‘extremely hot events’ !
 
* e.g. a typical class’s grades would include a B grade at the top of the bell curve and then B- and then C grades to the left side and B+ and A grades to the right, showing that there are fewest As and Cs, with more B-s and B+s and most of all – Bs.
 
 

Getting fit won't win medals (but may save your life)

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The Olympic games have been a feast of numbers but one important set has gone missing. They are even more missed now the party is over and all the talk is about legacy, especially the effect of British sporting success on our everyday exercise and activity.
 
High levels of obesity prompt commentators and policy makers to reach for ways of stimulating an ageing population to get up and go, and what could be more inspiring than Olympic medals? The King’s Fund, the health policy thinktank, is one among many speculating about a post-Olympics boost, benefiting the area the games were supposed to regenerate in the east of London.
 
But where are the statistics linking attainment on the athletics or cycling tracks and activity levels among the population at large? Intuitively, young people might look up at the stars and tell themselves they too could mount the podium. But what 60-year old couch potato is going to hoist themselves on to a saddle and announce they are going to emulate Bradley Wiggins and get up the Col du Tourmalet ?
 
The relationship between elite sporting achievement and popular sporting participation does not have to be direct and could even be inverse – in the German Democratic Republic, for example, top sports people were in special programmes, while the public got on with life as best they could, smoking and drinking and ingesting polluted air.
 
There’s no ready evidence that high-profile events lead to waves of emulation and, besides, what is there to emulate. To get to Olympic standard is work – as the athletes pointed out – of decades and the most intense dedication. Is the contention that you see a gold medal performance then rush out to try to be at best adequate in your chosen sport – because being adequate is the most the majority of triers could ever hope for.
 
Exercise is good. Activity reduces the likelihood of the onset of life-threatening conditions. These are excellent nostrums of public health. But don’t let’s confuse them with our largely passive admiration of sporting achievement or assume that because Team GB did well that fact will cause any changes in behaviour.
 

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.
 

Pills and probability

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Pop a pill and you’re cured. In media reporting it often seems as simple as that. Take aspirin daily and you won’t get cancer. Put more subtly, take aspirin and your chances of getting cancer are reduced by a finite amount.
 
Except they’re not. What we have is a body of evidence, being added to over the months and years by new studies, but not evidence of the kind that allows a straightforward ‘positive’ result.
 
The Daily Telegraph says a daily dose will cut cancer risk for the over-60s by 40 per cent, but that is not what the evidence says. An academic article establishes an association between daily aspirin use and modestly reduced rates of death from cancer. But however much we might wish the relationship to be solid and causal, an association is all it is: the reduced death rate in the studies could be the result of some other, unobserved factor (people’s weight, their education and so on).
 
The admirable NHS Choices gives the detail and reaches the sober conclusion that ‘overall, the evidence is not strong enough to recommend that everyone take daily aspirin purely for cancer prevention’ — and that’s because we don’t know enough about the risks of taking aspirin, especially for people without cardiovascular complaints.
 

Let's stop playing around with playing field stats

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For most of us, our first experience of sports is on the school playing field..this  assumes you are lucky enough to have one.  But finding out the number of schools with playing fields in England is not that easy as evidenced by the government’s recent revisions of the number of sold/on sale playing fields.
 
After all, someone has to count school playing fields…. and maybe counting them is more of a challenge than we might think: what do we mean by ‘school playing field’? which type of school? geographical coverage? period?  etc. 
 
In light of this, it was good to know that we were not alone in suspecting that recent claims that an estimated 10,000 school playing fields were sold off between 1979 and 1997 needed to be challenged. Where had this strangely high (and nicely-rounded) number come from? BBC Radio Four’s ‘More or Less’  team found that the figure was less of an estimate and more of a guesstimate or ’ball park’ figure.  A check of Hansard found that until 2007 opposition MPs had been citing 5,000 – and not 10,000 – as the level of playing fields sold by previous governments. Why had this statistic suddenly doubled?  And where had the 5,0000 and 10,000 figures come from?
 
Well..the 10,000 figure had been taken from a 2008 Dept for Culture, Media and Sport report. Yet delving deeper into the figure’s provenance, the paper trail soon went cold. 
 
The source of the 5,000 playing fields figure was dubious too……a Lords debate in 2001 revealed it to to be a “guesstimate” and not a reliable count.  ’More or Less’ researchers found that the ’method’ used to guesstimate the 5,000 playing fields was pretty much a case of how not arrive at an estimate. It began with a 1983 snapshot survey* to which snapshot figures for grant-maintained schools were added (in this case, they added 64 fields across a particular 30-month period in the mid 1990s.)  Then came the assumptions. It was then assumed that all schools were sold off at the same rate as grant-maintained schools (unlikely as grant-maintained schools are more free than most to use their budgets as they wish) and it was further assumed that between 1979 and 1997, playing fields were sold at the same rate as during this chosen 30-month period. As a precaution (!), the figure was halved and then rounded to 5,000. 
 
Either way, this figure has stuck. It’s what More or Less’s Tim Harford calls a ‘zombie statistic’ that just keeps coming back at you….even a parliamentary question failed to exterminate it. 
 
In defence of guesstimates, they can offer a useful first step on a path towards a more thorough count as more accurate information is found.  Sometimes guesstimates ignore better information. Sometimes they reflect the absence of better information. In this case, “no one really knows the true figure because nobody counted“.  ‘More or Less’ researchers found that playing field sales have only been counted since 1998 (and we still have no idea how many there were then or how many there are now).
 
They suggest that as governments say that they have mainly sold playing fields when schools have been sold, a better way of estimating school playing field numbers might involve looking at school closures…apparently 3,000 schools closed in England between 1979 and 1997, many in response to changes in the birth rate and so somewhere in here are some of the school playing fields lost during this period.
 
Suddenly, everything seems a lot less certain and begs the question ‘was a guesstimate of this kind the right figure to take centre stage in parliamentary debate?’.
 
* not a survey of fields sold but of fields under threat (and, in fact, not just school fields) 
 

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