Asian American is a broad term
I work for a non profit in Chicago that serves the Korean American community. I need detailed information on Korean Americans in different counties. If I use Asian Americans my data is incorrect. It is frustrating, but I know that it is the fault of the setup of these surveys. They do not consider all topics when being detailed on ethnicity...thank you for the data on this site, data.census.gov....well, 2010-2015 data is pretty old and it does not help to identify needs of this community.
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You may be able to use table B02015 Asian Alone by Selected Groups -- this doesn't get people who are multiracial (although it would include any Asian/Latino respondents since Latino identity is treated separately from race)
Here's that table for all counties in Illinois: https://censusreporter.org/data/table/?table=B02015&geo_ids=050|04000US17&primary_geo_id=04000US17 Note very high MOEs for some cases, which is common when a small population is divided into so many subgroups.
Korean is not included in the Ancestry tables, which I think is acknowledged here
https://www.census.gov/topics/population/ancestry/about/faq.html#par_textimage_2
"In most of our ancestry tables we do not show groups that are shown elsewhere in the race and Hispanic tables"hope this helps