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Old 10-02-2012, 04:42 PM
Location: Waterloo, ON
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So supposedly the US census bureau retabulated the 2000 data according to 2010 census tracts, but my understanding is that this is problematic for comparing weighted density change, mostly due to growth on the fringe and the way census tracts are delineated in fast growing fringe areas.

Basically, imagine you have a subdivision, phase A was built in the 90s with 5000 people on a square mile, and is next to a mostly rural area with 5000 people on 20 square miles (250ppsm). In 2000, these two areas were one census tract, so the weighted density was 476ppsm. Not a very accurate representation, but this is a common problem when calculating weighted density on the suburban fringe. After the 2000 census, this area was divided into two tracts, one for the subdivision and one for the mostly rural area. But in the 00s, another square mile in the rural area was developed at 5000 ppsm for phase B of the subdivision. In 2010, you have.

CT1 = Phase A, 5000 people, 5000 ppsm
CT2 = Phase B+rural, 9750 people, 488 ppsm
Weighted Density: 2017 ppsm

Now the census looks at what the 2000 weighted density was using 2010 tracts

CT1 = Phase A, 5000 people, 5000 ppsm
CT2 = unbuilt Phase B+rural, 5000 people, 250 ppsm
Weighted Density: 2625 ppsm

This is a more accurate depiction of what things were like in 2000, and suggests the weighted density decreased by 23%. Although the depiction of the 2000 density as 2625ppsm is accurate, it is not accurate to say the density went down by 23% when the number of people living in suburban as opposed to rural densities increased. Lets look at what a more accurate depiction of 2010 densities would be.

CT1 = Phase A, 5000 people, 5000 ppsm
CT2 = Phase B, 5000 people, 5000 ppsm
CT3 = rural, 4750 people, 250 ppsm
Weighted Density: 3470 ppsm

It would actually be more accurate to say that the weighted density of this area on the suburban fringe increased by 98%.

However, CT2 likely hasn't been split up into CT2 and CT3 yet, and if it has, we don't really know how exactly how many people live in them since the boundaries would have been changed after the census. Is there a better way to calculate weighted density change?

Well, in 2000, the weighted density was measured as 476 ppsm, and in 2010 as 2625 ppsm, an increase of 451%... ok neither 451% or -23% are very close to 98%, but what if you looked at things on a larger scale, after all, we're interested in the whole urban area, not the suburban fringe. So lets say that there are another 50,000 people living in census tracts identical to CT1 (Phase A), in suburbs built in earlier parts of the 20th century, and even 19th century city neighbourhoods.

i) The 2000 numbers using 2000 Census tracts would be
60,000 people at 4,246 ppsm

ii) The 2010 numbers using 2010 Census tracts would be
64,750 people at 4,320 ppsm

iii) The 2000 numbers using 2010 census tracts (most accurate depiction of reality in 2000) would be
60,000 people at 4,604 ppsm

iv) The 2010 numbers where Phase B and the rural area would be separate tracts (most accurate depiction of reality in 2010) would be
64,750 people at 4,652 ppsm

So the most accurate depiction of reality in terms of weighted density change would be to compare iii) and iv), you get an increase of 1.04%, which makes sense because the proportion of people living at suburban densities (instead of rural) increased a little.

From my understanding, what the US census bureau did was compare ii) with iii), which suggests the weighted density decreased by 6.17%.

The methodology I think should be used is to compare i) and ii). It's not perfect, but you get an increase of 1.76%, a much better representation of reality than a decrease of 6.17%. This is what I did when calculating Canadian UA changes, so it's possible that the increases were slight overestimations of reality. However, the difference between i) vs ii) and iii) vs iv) (reality) gets smaller as urban areas gets bigger. This is because the difference is due to the fact that the percent of the urban area that lives in rural portions of urban-rural tracts is smaller.
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