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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 ****************************************************** Please note that if you press the 'Reply' button your message will go only to the sender of this message. If you want to reply to the whole list, use your mailer's 'Reply-to-All' button to send your message automatically to [log in to unmask] ******************************************************* ****************************************************** Please note that if you press the 'Reply' button your message will go only to the sender of this message. If you want to reply to the whole list, use your mailer's 'Reply-to-All' button to send your message automatically to [log in to unmask] *******************************************************