mscroggs.co.uk
mscroggs.co.uk

subscribe

Blog

 2017-02-25 
Recently, I've noticed a few great examples of misleading uses of numbers in news articles.
On 15 Feb, BBC News published a breaking news article with the headline "UK unemployment falls by 7,000 to 1.6m". This fall of 7,000 sounds big; but when compared to the total of 1.6m, it is insignificant. The change could more accurately be described as a fall from 1.6m to 1.6m.
But there is a greater problem with this figure. In the original Office of National Statistics (ONS) report, the fall of 7,000 was accompanied by a 95% confidence interval of ±80,000. When calculating figures about large populations (such as unemployment levels), it is impossible to ask every person in the UK whether they are employed or not. Instead, data is gathered from a sample and this is used to estimate the total number. The 95% confidence interval gives an idea of the accuracy of this estimation: 95% of the time, the true number will lie of the confidence interval. Therefore, we can think of the 95% confidence interval as being a range in which the figure lies (although this is not true, it is a helpful way to think about it).
Compared to the size of its confidence interval (±80,000), the fall of 7,000 is almost indistinguishable from zero. This means that it cannot be said with any confidence whether the unemployment level rose or fell. This is demonstrated in the following diagram.
A fall of 7,000 ± 80,000. The orange line shows no change.
To be fair to the BBC, the headline of the article changed to "UK wage growth outpaces inflation" once the article was upgraded from breaking news to a complete article, and a mention of the lack of confidence in the change was added.
On 23 Feb, I noticed another BBC News with misleading figures: Net migration to UK falls by 49,000. This 49,000 is the difference between 322,000 (net migration for the year ending 2015) and 273,000 (net migration for the year ending 2016). However both these figures are estimates: in the original ONS report, they were placed in 95% confidence intervals of ±37,000 and ±41,000 respectively. As can be seen in the diagram below, there is a significant portion where these intervals overlap, so it cannot be said with any confidence whether or not net immigration actually fell.
Net migration in 2014-15 and 2015-16.
Perhaps the blame for this questionable figure lies with the ONS, as it appeared prominently in their report while the discussion of its accuracy was fairly well hidden. Although I can't shift all blame from the journalists: they should really be investigating the quality of these figures, however well advertised their accuracy is.
Both articles criticised here appeared on BBC News. This is not due to the BBC being especially bad with figures, but simply due to the fact that I spend more time reading news on the BBC than in other places, so noticed these figures there. I quick Google search reveals that the unemployment figure was also reported, with little to no discussion of accuracy, by The Guardian, the Financial Times, and Sky News.

Similar posts

World Cup stickers 2018, pt. 3
World Cup stickers 2018, pt. 2
A bad Puzzle for Today
A 20,000-to-1 baby?

Comments

Comments in green were written by me. Comments in blue were not written by me.
I've seen archaeologists claiming proof that event A happened before event B because the radiocarbon date of A was 50 years before B. Except the standard error on both dates was 100 years. They even showed the error bars in their own graphics, but seemed to not understand what it meant.

My favorite species of ignoring the measurement error is the metric conversion taken to way too many decimal places. The hike was 50 miles (80.467 kilometers) long.
Perry Ramsey
                 Reply
 Add a Comment 


I will only use your email address to reply to your comment (if a reply is needed).

Allowed HTML tags: <br> <a> <small> <b> <i> <s> <sup> <sub> <u> <spoiler> <ul> <ol> <li>
To prove you are not a spam bot, please type "s" then "e" then "g" then "m" then "e" then "n" then "t" in the box below (case sensitive):

Archive

Show me a random blog post
 2020 

Feb 2020

PhD thesis, chapter ∞
PhD thesis, chapter 5
PhD thesis, chapter 4
PhD thesis, chapter 3
Inverting a matrix
PhD thesis, chapter 2

Jan 2020

PhD thesis, chapter 1
Gaussian elimination
Matrix multiplication
Christmas (2019) is over
 2019 
▼ show ▼
 2018 
▼ show ▼
 2017 
▼ show ▼
 2016 
▼ show ▼
 2015 
▼ show ▼
 2014 
▼ show ▼
 2013 
▼ show ▼
 2012 
▼ show ▼

Tags

hexapawn a gamut of games weak imposition polynomials rhombicuboctahedron sobolev spaces gaussian elimination twitter royal institution hats python numerical analysis error bars manchester reddit menace chebyshev mathsteroids dataset flexagons dragon curves trigonometry games probability game of life programming people maths ucl pac-man stickers geometry realhats news wool determinants mathsjam frobel binary london underground countdown game show probability platonic solids folding paper approximation gerry anderson javascript simultaneous equations cambridge curvature accuracy speed video games fractals matt parker latex golden spiral ternary football triangles misleading statistics craft bempp sport talking maths in public world cup cross stitch logic bubble bobble graph theory books harriss spiral statistics preconditioning asteroids tennis royal baby reuleaux polygons big internet math-off pizza cutting plastic ratio boundary element methods matrix multiplication map projections draughts tmip manchester science festival inverse matrices dates light advent calendar chalkdust magazine pythagoras martin gardner sound electromagnetic field finite element method nine men's morris rugby signorini conditions christmas card go interpolation european cup chess final fantasy arithmetic coins data visualisation estimation radio 4 palindromes national lottery folding tube maps matrix of cofactors php noughts and crosses weather station the aperiodical braiding propositional calculus inline code bodmas oeis christmas matrices sorting hannah fry mathslogicbot captain scarlet golden ratio raspberry pi london phd computational complexity wave scattering puzzles matrix of minors machine learning data

Archive

Show me a random blog post
▼ show ▼
© Matthew Scroggs 2012–2020