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Subject:

Re: Mean vs Median (was: Re: New free statistics resource (fwd))

From:

Stephen Morris <[log in to unmask]>

Reply-To:

Stephen Morris <[log in to unmask]>

Date:

Mon, 25 Jul 2005 15:22:20 +0100

Content-Type:

text/plain

Parts/Attachments:

Parts/Attachments

text/plain (133 lines)

Dear Mike,

Thank you for your very full response. On re-reading the piece myself I
think it is broadly fair - except that perhaps the word "commentators" is
ambiguous - we didn't mean to point fingers at the IFS but at the media. We
will change that.

We do say "...despite this, even a brief reading of this section of the
report gives the true picture. Maybe next week's headlines will read 'Media
mean median'."

I take your point that the two taken together give a fuller picture than
either of them separately. Hmm - maybe there's another piece in that.

Stephen

-----Original Message-----
From: email list for Radical Statistics [mailto:[log in to unmask]] On
Behalf Of Mike Brewer
Sent: 25 July 2005 14:42
To: [log in to unmask]
Subject: Mean vs Median (was: Re: New free statistics resource (fwd))

Stephen,

It was good of you to send the web link, and brave of you to subject
yourself to 
the Radstats critique!

Naturally, I checked out your page about the March 2005 IFS report on
household 
incomes, on which I was a lead author, and the mean vs median income
controversy 
(I confess to some surprise that was not a Radstats discussion about it at
the 
time).

Your web-page find us guilty of incorrectly using the mean to characterise
the 
average. I think that is a little harsh on us.

It is true that we implicitly use "average" as a synonym for "arithmetic
mean" 
in the first line of our press release
(http://www.ifs.org.uk/pr/hbai05pr.pdf). 
This is because we took the view that people might be confused by a headline

that said "Tax rises and new tax credits cut mean income, but reduce
poverty and inequality". But, in our defence, the third paragraph of the PR 
discusses the skewness of the income distribution, explains that we use 
"average" to mean "mean", and "median" to mean "median", and says that
median 
income rose while mean income fell. Furthermore, the relevant paragraph in
our 
executive summary reads: "Income growth was particularly sluggish in
2003/04. 
Median income increased in real terms by just under £2 per week (an increase
of 
0.5 per cent) while mean income fell for the first time since the early
1990s (a 
small change of –0.2 per cent)." This makes no mention of "average"; our key

point is that both numbers are low compared to the past few years (the real 
statistical crime we committed was that neither of these statistics was 
significantly different from zero!).

Of course, what happened in reality is that people in the media had to
decide 
which of these 2 numbers was the more interesting and the more applicable,
and, 
naturally enough, since we were a week away from a general election
campaign, 
the Tory-supporting newspapers decided on a "fall in average income"
headline, 
the Treasury objected furiously, and the story became big political as well
as 
economic/social affairs news.

But on top of these points, I would argue that it is interesting to look
both at 
trends in mean income, as well as median income. Trends in mean income tell
us 
about trends in how much "pie" there is to go round, and trends in median
income 
tell us about how much of the pie is going to the person in the middle of 
society. Our policy point was that direct tax rises had reduced the size of
the 
pie enjoyed by households, with richer households bearing most of this fall
in 
incomes: this point cannot be made by looking at trends in median income.

Having said all this, your general simplified statistical point - look at
trends 
in median when examining skewed distributions, not trends in the mean - is
not 
something I am trying to dispute!

best wishes,
Mike

[Incidentally, we, like the Treasury, enjoyed(!) trying to explain the 
difference between the mean and the median on live television!]


Stephen Morris wrote:

> And the third discusses when you should use the median or the mean, using
> the example of average household income:
> http://www.conceptstew.co.uk/PAGES/mean_or_median.html 

-- 
Mike Brewer
Programme Director, Direct Tax and Welfare
Institute for Fiscal Studies
7 Ridgmount Street, London, WC1E 7AE
Tel: +44 (0)20 7291 4800  Fax: +44 (0)20 7323 4780

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