February 22, 2009

Lies, damned lies, and statistics

So as everyone knows, I’m a big geek, and I got upset about this article in the NY Times this morning.

This is a great example of not enough statistics to really tell the story. The article presents a graph which shows Japanese per-capita household income stayed relatively constant from about 1995 to 2005 (or even dropped a bit). Sounds horrible, right?

Here’s the problem: there are a lot of ways to get a mean (or average), so it’s not always a very useful number without some other figures to back it up.

If we have 10 Japanese people – Akira and his nine friends, we can get an average of $10,000 income in several ways:

A-Everyone makes exactly $10k.
B-Akira makes $91k, each friend makes $1k
C-Akira makes $1k, each friend makes $11k
etc, etc.

In other words, the average doesn’t tell us much about whether or not *most* Japanese people are better off today than they were 10 years ago – it could be that really rich people are less rich, but everyone else is better off, or it could be that most people are really doing worse.

So if we want to know what actually happend to the typical Japanese household, we’d generally be better off looking at the median – which is the income level at which exactly half of our subjects fall above and half below the number in question. In combination with the mean (average), it will tell a much more useful story. Yet for some reason this basic information never makes it into this kind of reporting – even in a prestigious paper like the Times.

As an aside, some of the “problems” they report are hilarious:
-People re-using bath water to do laundry. Oh horrors!
-Whiskey sales down 80% – Noooo!
-Fewer people wanting to buy cars. Um, how is this bad again? Sounds like a big win for public transportation and bicycles to me…
-And best of all – the family that _watches a non-flatscreen TV_. That’s pretty much like living in a cave and eating gruel with bugs in it, or so you might think based on the breathless description in the Times.