Lesson 2: How to lie with with statistics - an apology
I'd like to apologise wholeheartedly and unreservedly for my post on Sunday in which I accused arts collective CultureLine of telling lies in a press release. I have since engaged in email conversation with the good folk at Colman Getty, the PR Agency responsible, and they've made me aware that one of my underlying assumptions about the survey was incorrect. By jumping to conclusions without seeking the facts, I have entirely misrepresented how the headline in the press release was obtained. Sorry, that's unforgivable. So on their behalf I feel it's only right to set the record straight. Because it turns out that the truth is much worse than I previously thought.
Half of north Londoners never cross the river for work or play 54% of Londoners living north of the River Thames never venture south for either work or cultural pursuits and south Londoners are twice as likely to cross the river for culture.
I wondered where that 54% came from, because it sounded unlikely. But I made a wrong assumption by using inappropriate data appearing later in the press release. I thought the 54% came from here:
48% of north Londoners visit the south of the capital for culture less than once a month and 7% never do this.
I thought the 54% must have come from adding together the 48% of North Londoners who sometimes cross the river to the 7% who never do. There were no other figures in the press release which could possibly have matched the 54% total, even after rounding, so I assumed these figures were what had been used. But this would have been a wholly unjustifiable use of statistics. Indeed, as a nice lady from Colman Getty kindly pointed out to me...
"Had we added the % of those North Londoners who never cross the river for culture to the % of those North Londoners who cross the river less than once a month for culture, you’re right, that would have been inaccurate and misleading."
Because that's not what they did. Instead I'm told they used a statistic from the survey which didn't appear anywhere in the press release. A statistic I couldn't have known about until it was revealed in their email.
"The ‘half of Londoners never cross the river for work or play’ statistic was calculated as follows. We asked respondents how often they crossed the river for work and how often they crossed the river for play. Of those North Londoners who responded, half either never crossed the river for work (47.7%) or never for play (7%)."
So the 'half' was obtained by adding the 47.7% for "work" to the 7% for "play". This made a supposed total of 54% for "work or play". Sounds convincing, doesn't it? But in fact this is an even bigger massive lie than the one I thought I'd seen before.
They've added this and this
48% of north Londoners never cross the river for work 7% of north Londoners never cross the river for play
to make this
Half of north Londoners never cross the river for work or play
And I'm sorry, but that's statistical drivel.
To help see why, here are those first two statements written the other way around.
52% of north Londoners sometimes cross the river for work 93% of north Londoners sometimes cross the river for play
Or, in other words, when it comes to play, almost all north Londoners sometimes cross the river. North Londoners are river-crossing kinds of people. They don't shun south London, they go there. Almost all of them. It is absolutely definitely not the case that "Half of north Londoners never cross the river for work or play", because almost all of them cross the river for just one of those activities. An even greater number (at least 93%, probably higher) cross the river for either one or the other. A more accurate headline would therefore have been
Half of north Londoners never cross the river for work
but that wouldn't have been news. Or maybe
Less than 7% of north Londoners never cross the river for work or play
but that wouldn't have been news either. Instead the good folk at Colman Getty have jumped to a fallacial conclusion based on underlying survey data which wasn't revealed to the public. More precisely, they combined two probabilities incorrectly using mathematical rules which should apply only to mutually exclusive events, which these are not. They invented a plausible-sounding statistic which had absolutely no grounding in reality, then launched their tainted conclusion headlong into the nationalmedia. They have lied with statistics, presumably because someone was too innumerate to know better.