# Statistical significance using PUMS data

I've been having some trouble finding a direct answer to this question, so I thought I'd toss it in here!  I have used PUMS data to calculate rates of poverty for children by race and ethnicity in Illinois.  The results I got are here (margins of error with a 90% confidence level are in parentheses):

White: 13.6% (0.4%)

Black: 38.9% (1.2%)

Asian or Pacific Islander: 10.8% (1.2%)

My question is: To test if these differences are statistically significant, can I still use the Census Bureau's methods that they recommend for the ACS data on data.census.gov?  Typically, I use the Bureau's statistical testing tool Excel spreadsheet and/or this formula:

If  |(Est1 - Est2)/(SE1^2 + SE2^2)| > 1.645, then difference is statistically significant

If that is not the correct way to do it, do you know of any available resources for how to calculate statistical significance for weighted PUMS estimates?  Thank you!

## Top Replies

Parents
• In my original post, perhaps I didn't clarify enough what I am looking to do.  I used replicate weights to calculate the margins of error above.  What I'd like to know is this: to test for statistically significant differences among groups, is it still alright to use the equation in the original post, or is there another recommended method?  If the equation above will not work, I'm thinking a z-test of two proportions would be appropriate.  However, I've never run those kinds of tests with a weighted sample before.

• In my original post, perhaps I didn't clarify enough what I am looking to do.  I used replicate weights to calculate the margins of error above.  What I'd like to know is this: to test for statistically significant differences among groups, is it still alright to use the equation in the original post, or is there another recommended method?  If the equation above will not work, I'm thinking a z-test of two proportions would be appropriate.  However, I've never run those kinds of tests with a weighted sample before.

Children
• Hi Bill -- just to make sure everyone is on the same page, I think it's important to distinguish between two things:

1. The margins of error (MOEs) for the *proportions* of kids in poverty
2. The MOEs for the *difference in proportions* between two groups, which depend on #1. As you described above, you compare the difference in proportions to this MOE to test for a statistically significant difference.

Calculating #1 using replicate weights, as you did, is the most important thing; everything below assumes that's the case. From there, there are two basic paths to calculating #2.:

• 2A: You can use the formula you described above -- (MOE1^2 + MOE2^2) ^ 0.5. That is, square the two margins of error, add those squares together, and take the square root of that sum.
• You mentioned that you've never run that test with a weighted sample, but as long as you've used the weights to calculate the proportions and the MOEs for the *proportions* (#1), you've got everything you need. You can treat it like any estimate contained in the summary files, since they both come from the ACS microdata. (But this is only a conceptual similarity; the PUMS contains only a portion of the records in the confidential ACS microdata and undergoes additional disclosure avoidance procedures.)
• 2B: You can calculate it directly in stats programs at the same time that you calculate #1 using the replicate weights. That will account for the covariance of the two estimates (as I understand it; I could be wrong).

It sounds like you're asking whether #2A will be good enough, and I think it is. I did a brief look at child poverty rates by race in the Twin Cities metro, and #2B yields MOEs for the *difference in proportions* that are within 2-3% of the MOEs you would derive using #2A. This might matter for marginally significant differences between groups, but I'd guess that in most cases your conclusions about statistically significant differences wouldn't depend on how you calculate the MOEs for the *difference in proportions*.

Again, though, I'd defer to those with more statistical expertise than I have.

I hope this helps, but please respond if anything is unclear.