Posts filed under “Mathematics”

Estimated Relative Standard Errors in Housing Data

Regarding yesterday’s New Home Starts, an emailer writes: 

You used to discuss the Commerce Dept.’s standard statistical error regularly. In light of that surprising Housing Start number, could you please update that?

Sure thing. I love this sort of data sifting exercise. (I used to do this all the time, but I could actually hear readers falling asleep through my screen).

Let’s go to the Census Department release.

HOUSING STARTS
Privately-owned housing starts in April were at a seasonally adjusted annual rate of 1,032,000. This is 8.2 percent (±14.5%)* above the revised March estimate of 954,000, but is 30.6 percent (±6.7%) below the revised April 2007 rate of 1,487,000.

As is so often the case, the devil is in the details:

As far as the April Hosuing Starts go, a monthly change (seasonally adjusted annual rate) was 8.2%, versus an
estimated relative standard error of ±14.5%.  Hence, the monthly change is not statistically significant; that is, it is uncertain whether there was an increase or decrease in Housing Starts from March to April.

As to the 30.6% year over year drop — that is ±6.7% — and therefore is statistically significant.

[UPDATE: Flenerman in comments asks the same question]

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And I thought I was the only one who cared about such mathematical trivialities . . .

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Sources:
NEW RESIDENTIAL CONSTRUCTION IN APRIL 2008
Manufacturing and Construction Division
U.S. Census Bureau, MAY 16, 2008 AT 8:30 A.M. EDT

http://www.census.gov/const/newresconst.pdf

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