Thursday, February 23, 2006

Bias? (And some interesting thoughts on assumptions about income disparities)

According to the New York Times and The Associated Press: Average U.S. Family Income declines. The headline is somewhat revealing, seeing as what the story actually says:

The average income of American families, after adjusting for inflation, declined by 2.3 percent in 2004 compared to 2001 while their net worth rose but at a slower pace. The Federal Reserve reported Thursday that the drop in inflation-adjusted incomes left the average family income at $70,700 in 2004. The median, or point where half the families earned more and half less, did rise slightly in 2004 after adjusting for inflation to $43,200, up 1.6 percent from the 2001 level.

Yes, most people think of the mean when they use the word average. But one wonders if the mean were slightly higher while the median was slightly lower if the story would be reported the same.

The most interesting aspect of this story? For all the talk that the rich are getting richer and the poor are getting poorer, these numbers don't really show that to be true (and it doesn't take a statistician to figure this out). A 2.3% decline in the mean corresponding with a 1.6% increase in the median could very well mean that the numbers of those with relatively high incomes have declined, while those in the middle (and maybe at the bottom) have improved a slight bit. The median of course, is not effected by extreme outlying values- in this case, those with incredibly high incomes who might throw off the mean. The fact that the median has increased while the mean has declined seems to be a good indication that those at the top of the economic ladder have fallen off a bit, whereas those in the middle and on the bottom have stayed the same or gotten better. (I suppose it is possible that those on the very bottom have gotten poorer. However, it seems illogical to assume that the poor have seen their wages fall, while those in the lower and middle income brackets have seen their incomes rise.) I'm no statistician, but these assumptions seem logical. So much for the rich getting richer while the poor get poorer.


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