I am working on a project to create demographic data for a series of custom planning areas that do not match Census boundaries. In order to do this we are allocating ACS 5-year data across block group boundaries using point-level housing units as weights. Our testing showed that the method compares well to commercial products that provide demographic estimates for custom geographies.
Doing this for count data is straightforward, but we would also like to use median household income. Is that possible using simple proportional weighting? Is there a better way?
Hi, Mara -- taking a weighted average of block group medians can give you misleading results, because the median depends on the income distributions of the different block groups. If the block group pieces…
Hi, Mara -- taking a weighted average of block group medians can give you misleading results, because the median depends on the income distributions of the different block groups. If the block group pieces you're combining have roughly symmetrical distributions of income and contribute roughly the same number of households to each custom planning area, then taking the weighted average will be fine. But those conditions aren't likely to be satisfied. So the best way to do this would probably be to apportion the household income distributions themselves (table B19001), just like you're doing for other count data. Once you've got the estimated distribution for the custom planning area, you can estimate its median, as described here (pp. 3-5).
One caution: the formula given there assumes a symmetrical distribution within the category containing the median. That assumption is probably not satisfied in many areas. If accuracy is very important, you could use other information about the income distribution (tables B19025, B19080, B19081, B19082) to refine those calculations. And if you wanted to refine the weighting itself, and you have sub-block group information on rents or home values, you could also see whether one portion of the block group is likely to be disproportionately higher-income or lower-income. I just wanted to mention this in case you need very refined estimates of median incomes; I'm not suggesting you should go to all this trouble for an uncertain payoff. (Speaking for myself, it would take a lot to get me to pursue this!)
Regardless, though, estimating the median based on the income distribution you derive by apportioning block group counts will be better in most cases than taking a weighted average of block group medians. Good luck!
Matt Schroeder Thank you for your detailed answer. I will look at using the income levels instead.