On 16-Jun-10 08:02:04, Wells, Julian wrote:
> Yikes! The Cabinet Office people might profitably be directed to the
> ONS house style guide or its predecessor "Plain Figures", not mention
> that old faithful "How to Lie with Statistics" (I see from Wikipedia
> that the latter has been claimed to have sold more copies than any
> other text on statistics).
>
> Julian
I was so struck, looking at the graphic, by the apparent disparity
between the perceived "sizes" of the circles and the associated
numbers that I even wondered if the sizes had been deliberately
fudged! So I did a check. Enlarging the picture and using a ruler,
I got, for the diameters of the circles:
1.2m: 42mm
1.5m: 53mm
1.8m: 64mm
Now:
1.5/1.2 = 1.25 ; 53/42 = 1.26
1.8/1.2 = 1.50 ; 64/42 = 1.52
1.8/1.5 = 1.20 ; 64/53 = 1.21
So pretty close agreement between diameter and value (given that
the edges of the circles were a bit fuzzy anyway).
Which just goes to show (essentially Julian's point) that the eye
is more influenced by relative areas than by relative linear
dimensions. Indeed, attempting to estimate "by eye" the relative
diameters (before using the ruler) I had judged that successive
circles were more like 1.5 times as wide as their predecessors.
And that is in keeping with ratios of areas (1.2^2 = 1.44). A nice
"optical illusion".
Well, now, the Cabinet Office statisticians should of course be
encouraged to make the areas in the right ratios, rather than
the diameters, in order to induce appropriate perceptions.
And then they would have to make diameters (presumably the defining
quantity for producing the graphic) proportional to the square roots
(which might require a coffee break). And then they would have to
explain that somehow. Or not -- the report makes no attempt to explain
the scaling of the circles.
So maybe they wouldn't explain. Then some journalist could do what
I've just done and then report "The Cabinet Office report includes
graphics that deliberately play down the massive increase in
claimants from 1997 to 2009. The increase from 1.2m to 1.8m is
an increase of 50 per cent. The circles increase in size by just
[journalist's synonym for 'only'] 22 per cent."
But what journalist is going to pick up on the apparent exaggeration
that is present in the graphic as presented? Maybe Tim Harford?
So perhaps the C.O. should explain! A simple parenthesis in the
caption (to the better form of the graphic) would do it:
"Figure 3.1: The numbers of working-age Disability Living
Allowance claimants have increased by over 40% since 1997,
from 1.2 million to 1.8 million (areas of circles proportional
to numbers)."
Or is that too abstruse?
But since they've stated the numbers so clearly, why bother with
the graphics?
Well, you sort of can't help it once you've woken up a spreadsheet!
In the memorable words of one of Jasper Carrott's best:
"Q: Why do dogs lick their ****s? A: Because they can."
I think we have a very long way to go before the public understanding
of statistical information is informed by presentations which induce
correct perceptions.
Ted.
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E-Mail: (Ted Harding) <[log in to unmask]>
Fax-to-email: +44 (0)870 094 0861
Date: 16-Jun-10 Time: 10:39:23
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