population-weighted density

[Linus Van Pelt]

I don't recall this being noted here in the 2010 census discussion. The Census Bureau has adopted an interesting new measure of population density called population-weighted density which is designed to remedy some shortcomings of traditional unweighted density. (They are still also publishing traditional density figures). The basic issue is that the traditional unweighted density measure is highly sensitive to choices of where to draw the boundaries of an area, and an intuitively overall dense area can be heavily penalized by the inclusion of a large low-density fringe. This is particularly an issue given the census bureau's definition of a metro area based on commuting patterns rather than urban form, and it produces odd results like the New York and Los Angeles areas being similar in density. The population-weighted density of an area is instead the average density of each resident's census tract. This captures the conditions in which most people are actually living; an urban area where most people are living in dense local conditions will have high weighted density even if a small number of people are commuting into the city from a quasi-rural area.

More formally D=∑(Pidi)/∑Pi, where D is population-weighted density and Pi and di are the population and unweighted density of the ith census tract respectively.

The 10 MSA's with the highest weighted density in the 2010 census are as follows. To my mind at least, this list better captures what is meant intuitively by a dense urban area. For example LA really is, contrary to stereotype, one of the densest metros, but still New York is far and away the densest area in the country.

1. New York-Northern New Jersey-Long Island - 31,251.4
2. San Francisco-Oakland-Fremont - 12,144.9
3. Los Angeles-Long Beach-Santa Ana - 12,113.9
4. Honolulu - 11,548.2
5. Chicago-Joliet-Napierville - 8,613.4
6. San Jose-Sunnyvale-Santa Clara - 8,417.7
7. Boston-Cambridge-Quincy - 7,980.1
8. Philadelphia-Camden-Wilmington - 7,773.2
9. Miami-Fort Lauderdale-Pompano Beach - 7,395.3
10. San Diego-Carlsbad-San Marcos - 6,920.5

[Linus Van Pelt]

And here is the census bureau's map of all metro areas by population-weighted density:

[traininthedistance]

Strikes me as a better way to rank metros by density, or at least as a way to rank the density of urban cores, but the actual numbers they spit out are not quite realistic.  

31 thousand people per square mile is, like, Brooklyn levels of density- in other words, obviously quite a bit more dense than the median NYC-area resident experiences.  Yes, there is plenty of city, but even here the majority of metro area residents live in the suburbs.

[traininthedistance]

And, also, I am not surprised at all to see Los Angeles remain high on the list.  The LA metro has some of the densest suburbs in the nation, and (due to hard geographic constraints like mountains and water) a general lack of large-lot exurbs, and that counts for a lot.

[Linus Van Pelt]

Strikes me as a better way to rank metros by density, or at least as a way to rank the density of urban cores, but the actual numbers they spit out are not quite realistic.  

31 thousand people per square mile is, like, Brooklyn levels of density- in other words, obviously quite a bit more dense than the median NYC-area resident experiences.  Yes, there is plenty of city, but even here the majority of metro area residents live in the suburbs.

Because it's a census-tract-based measure you have to be careful about comparing the numbers to overall density numbers which give equal weight to uninhabited areas. Brooklyn's overall density of about 36 thousand per mile includes Prospect Park, Green-Wood Cemetery, various uninhabited areas in the Jamaica Bay parks and the industrial harbour, etc. But there are actually relatively few residential census tracts in Brooklyn that are that low in density; the average Brooklyn resident lives in a much denser tract. So the NY number is not saying that the average resident of the area lives in conditions like Brooklyn. 31 thousand per mile at the residential tract level is more typical of certain areas of Queens or the north Bronx.

[muon2]

It's impressive to see what weighting does to the overall US 2010 pop density. It goes from 81 to over 5000. It shows the large fraction of the population that lives in cities and suburbs.

[traininthedistance]

Strikes me as a better way to rank metros by density, or at least as a way to rank the density of urban cores, but the actual numbers they spit out are not quite realistic.  

31 thousand people per square mile is, like, Brooklyn levels of density- in other words, obviously quite a bit more dense than the median NYC-area resident experiences.  Yes, there is plenty of city, but even here the majority of metro area residents live in the suburbs.

Because it's a census-tract-based measure you have to be careful about comparing the numbers to overall density numbers which give equal weight to uninhabited areas. Brooklyn's overall density of about 36 thousand per mile includes Prospect Park, Green-Wood Cemetery, various uninhabited areas in the Jamaica Bay parks and the industrial harbour, etc. But there are actually relatively few residential census tracts in Brooklyn that are that low in density; the average Brooklyn resident lives in a much denser tract. So the NY number is not saying that the average resident of the area lives in conditions like Brooklyn. 31 thousand per mile at the residential tract level is more typical of certain areas of Queens or the north Bronx.

Mm, good point.  I'd be surprised if even Queens levels of density accurately capture the experience of the median metro-area resident: I mean, there are almost 20 million metro area residents, and only 8.3 million New Yorkers.  So the median metro area resident has to be outside of the city limits.  Now, granted, there are some very dense areas outside of the city- but really not that many- the stretch of Hudson County from Jersey City up to tiny, jam-packed Guttenberg is the only really large and really consistently dense-enough part.  For example, take a look at the urban areas of Essex County- for instance Irvington, which doesn't really have any open space to speak of that could skew the numbers, and is quite obviously one of the most "urban" areas outside of the city, but still clocks in at under 20K people per square mile.

And, of course, there are hundreds of thousands of NYC residents who live in areas less dense than that, as well.  Virtually all of Staten Island, for instance.  Yes, the median tract in the NYC metro should obviously be the densest median tract in the country.  But I'd be shocked if it broke 20K people per square mile.

[Linus Van Pelt]

Strikes me as a better way to rank metros by density, or at least as a way to rank the density of urban cores, but the actual numbers they spit out are not quite realistic.  

31 thousand people per square mile is, like, Brooklyn levels of density- in other words, obviously quite a bit more dense than the median NYC-area resident experiences.  Yes, there is plenty of city, but even here the majority of metro area residents live in the suburbs.

Because it's a census-tract-based measure you have to be careful about comparing the numbers to overall density numbers which give equal weight to uninhabited areas. Brooklyn's overall density of about 36 thousand per mile includes Prospect Park, Green-Wood Cemetery, various uninhabited areas in the Jamaica Bay parks and the industrial harbour, etc. But there are actually relatively few residential census tracts in Brooklyn that are that low in density; the average Brooklyn resident lives in a much denser tract. So the NY number is not saying that the average resident of the area lives in conditions like Brooklyn. 31 thousand per mile at the residential tract level is more typical of certain areas of Queens or the north Bronx.

Mm, good point.  I'd be surprised if even Queens levels of density accurately capture the experience of the median metro-area resident: I mean, there are almost 20 million metro area residents, and only 8.3 million New Yorkers.  So the median metro area resident has to be outside of the city limits.  Now, granted, there are some very dense areas outside of the city- but really not that many- the stretch of Hudson County from Jersey City up to tiny, jam-packed Guttenberg is the only really large and really consistently dense-enough part.  For example, take a look at the urban areas of Essex County- for instance Irvington, which doesn't really have any open space to speak of that could skew the numbers, and is quite obviously one of the most "urban" areas outside of the city, but still clocks in at under 20K people per square mile.

And, of course, there are hundreds of thousands of NYC residents who live in areas less dense than that, as well.  Virtually all of Staten Island, for instance.  Yes, the median tract in the NYC metro should obviously be the densest median tract in the country.  But I'd be shocked if it broke 20K people per square mile.

Yes, it is a mean, not a median. As far as I know the corresponding statistic with the median has not been published, but I would definitely think the mean would be higher than the median here. Much of Manhattan for example is way more than double the metro area average.

[muon2]

Strikes me as a better way to rank metros by density, or at least as a way to rank the density of urban cores, but the actual numbers they spit out are not quite realistic.  

31 thousand people per square mile is, like, Brooklyn levels of density- in other words, obviously quite a bit more dense than the median NYC-area resident experiences.  Yes, there is plenty of city, but even here the majority of metro area residents live in the suburbs.

Because it's a census-tract-based measure you have to be careful about comparing the numbers to overall density numbers which give equal weight to uninhabited areas. Brooklyn's overall density of about 36 thousand per mile includes Prospect Park, Green-Wood Cemetery, various uninhabited areas in the Jamaica Bay parks and the industrial harbour, etc. But there are actually relatively few residential census tracts in Brooklyn that are that low in density; the average Brooklyn resident lives in a much denser tract. So the NY number is not saying that the average resident of the area lives in conditions like Brooklyn. 31 thousand per mile at the residential tract level is more typical of certain areas of Queens or the north Bronx.

Mm, good point.  I'd be surprised if even Queens levels of density accurately capture the experience of the median metro-area resident: I mean, there are almost 20 million metro area residents, and only 8.3 million New Yorkers.  So the median metro area resident has to be outside of the city limits.  Now, granted, there are some very dense areas outside of the city- but really not that many- the stretch of Hudson County from Jersey City up to tiny, jam-packed Guttenberg is the only really large and really consistently dense-enough part.  For example, take a look at the urban areas of Essex County- for instance Irvington, which doesn't really have any open space to speak of that could skew the numbers, and is quite obviously one of the most "urban" areas outside of the city, but still clocks in at under 20K people per square mile.

And, of course, there are hundreds of thousands of NYC residents who live in areas less dense than that, as well.  Virtually all of Staten Island, for instance.  Yes, the median tract in the NYC metro should obviously be the densest median tract in the country.  But I'd be shocked if it broke 20K people per square mile.

Yes, it is a mean, not a median. As far as I know the corresponding statistic with the median has not been published, but I would definitely think the mean would be higher than the median here. Much of Manhattan for example is way more than double the metro area average.

I think that would probably be true of the US density as well.

[Хahar 🤔]

And, also, I am not surprised at all to see Los Angeles remain high on the list.  The LA metro has some of the densest suburbs in the nation, and (due to hard geographic constraints like mountains and water) a general lack of large-lot exurbs, and that counts for a lot.

In general, California suburbs are much denser than those on the East Coast.