Damned lies and statistics

A closer look at statistics in the news

Racial prejudice is growing in Britain, at least according to the headline on the front of the Guardian newspaper this morning. The paper describes a “Rising tide of race prejudice across Britain” based on new data from the British Social Attitudes Survey.

The BSA asked respondents whether they’d describe themselves as prejudiced against people of other races. The Guardian aggregated those who said they were very prejudiced and those who said they had a little prejudice.

It is true that this proportion has risen recently, from 27 per cent in 2012 to 32 per cent in 2013, but the long term trend is decline.

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Kate Allen

Last month, in advance of a report on 14 hospital trusts with relatively high death rates, it was widely reported that there had been 13,000 “unnecessary” deaths.

But, as a leading academic points out in today’s British Medical Journal, this demonstrates an epic lack of understanding of the concept of an average.

The 13,000 figure is the difference between the actual number of deaths in the 14 hospitals compared to the “expected” level. But what some writers failed to understand is that the “expected” level equated to the national average. As a result much of the coverage was seriously misleading, according to David Spiegelhalter, Winton professor for the public understanding of risk at the University of Cambridge. Read more

Data visualisation is the latest fashion in numerate journalism, albeit one that harks back to the likes of Florence Nightingale. Data visualisation creates powerful, elegant images from complex data. It’s like good prose: a pleasure to experience and a force for good in the right hands, but also seductive and potentially deceptive. Because we have less experience of data visualisation than of rhetoric, we are naive, and allow ourselves to be dazzled. Too much data visualisation is the statistical equivalent of dazzle camouflage: striking looks grab our attention but either fail to convey useful information or actively misdirect us.

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Chris Cook

Next week, the Department for Education is unveiling access to the Key Stage 4 league tables. The interesting policy thing to watch for is how many schools are under the floor target – these schools are at risk of a takeover by an academy chain. This is not straightforward: academy chains are not all equal, there is a limit to how far they can grow -and some of them are already struggling with the load they have.

Based on early drafts of the data returns (and assuming the DfE doesn’t calculate this stuff in an odd way*), about 240 schools last year failed to get 40 per cent of their pupils Cs in English, maths and three others. Of these, about 220 had a below-average number of pupils making “adequate progress” in English and maths, putting them at risk of takeovers.

Before the DfE starts its getting-tough-on-failing-schools routine, I thought I would update and republish two graphs. First, I have worked out what happens if you remove the failing schools. Answer: not an enormous amount. As ever, these are average results for poor pupils (on the left) running over to the richest (on the right).

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Chris Cook

At the moment, the Department for Education is considering changes to the league tables and the exam system. This seems an opportune moment to make a simple point about qualification-awarding and accountability: English school examinations are subject to measurement error in a really big way.

Here is a simple thought experiment to flesh it out. Imagine a class of 100 students. Let us specify that each one has a “true” ability that means that one pupil should get one point, one pupil should get two, one should get three and so on – up to 100 marks. Now, let’s award this class one of 10 grades: 90+ gets you an A, 80+ a B and so on.

Let us assume that the tests are perfect. If that were the case, you would get ten individuals in each grade. Easy enough. But what happens if we start introducing errors into the test? We can do that with a set of exotically named (but very simple) “Monte Carlo” estimates, which I calculated using this simple spreadsheetRead more

Chris Cook

Last week, I went to Wolverhampton where I spoke at a local debate, organised by the university and Pat McFadden, the local MP, about the local authority’s school. I was the warm-up act for Lord Adonis, former schools minister, setting the scene about the city’s education system before his talk on lessons on school improvement.

It was interesting event – and the city is clearly considering its future and the role of education within it. There is – judging by my inbox – serious and deep interest in improving schools in the city. One of the things I sought to do was set out Wolvo’s position in relation to the rest of the country – and what statistics about the city tell us.

Here is my presentation: Read more