Reliability/ Error of Cross-Tabs for a Categorical Variable

USA
1

I’m using ACS-IPUMS to create cross-tabs of various housing and demographic characteristics for the nine-county Bay Area. I’m wondering if you can point me to documentation on how to calculate the reliability of these estimates. Here’s an example of one cross-tab I’m interested in reporting-- housing structure type and built year.

This is the frequency weighted cross-tab:

                               After              Before 
                                   Recession     Recession (2000-2006)

Single-family, detach 165,116 530,215
Missing Middle 112,968 262,295
Multifamily (20+ unit 187,093 263,660
Other 11,547 39,069
Total 476,724 1,095,239

Based on this cross-tab, I would like to report that 35% of housing stock developed after the recession was single-family vs. 48% of housing stock developed in the years immediately preceding. How can I be sure there are enough cases in a given cell to provide a reliable estimate? What checks are appropriate?

Here is the un-weighted cross-tab:
After Before
Recession Recession
Single-family, detach 1,611 5,191
Missing Middle 976 2,251
Multifamily (20+ unit 1,595 2,193
Other 119 399
Total 4,301 10,034

2

In general, there is no bright line rule about how many observations are sufficient to provide reliable estimates, instead more is always better. That being said, you have about a thousand or more unweighted observations in each of the categories, so these estimates should be relatively reliable. The best way to go about testing this is to calculate a measure of the margin of error around your point estimates. There are a number of ways to do this and it will depend on the specific statistical software you prefer to use. I’d suggest looking into the help documentation of the statistical software to learn how to include a measure of the margin of error associated with these estimates.