# Standard Deviation and Standard Errors

I used ATUS replicate weights to calculate the standard errors for the Activity-level weighted means (as per procedure outlined in the ATUS User’s Guide section 7.5). Now, I would like to run a series of t-tests using these summary measures between different activities. However, most functions (I am using R) require standard deviation as input. The common conversion formula for the sample mean SE to SD is SE = SD/sqrt(n), where n is the sample size. Does this conversion to standard deviation apply to the estimates of weighted mean and the standard error generated using ATUS methodology? If not, what should I do to get standard deviations from standard errors generated using ATUS replicate weights?

Thank you.

I don’t know the answer to your question, and I’m not very familiar with the R survey commands, but I suspect that there are specialized survey commands that can be used to perform t-tests with replicate weights, without going through the intermediate step of calculating the standard deviation.

There’s a useful article about a similar issue here. It is based on using Stata, but explains a lot of the statistical issues clearly.

This is beyond the purview of IPUMS User Support, but I would advise reaching out to the ATUS staff at BLS with this question. They can be reached through this form. You may also want to ask at stats.stackexchange.com.

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For completeness sake, I am sharing the answer to my question, having contacted BLS support. To compute t-statistics without using standard deviations, here’s the modified answer from the support staff:

Estimating (for example) (Mean time||feeling in Activity A) – (Mean time||feeling in Activity B) across the replicate weights and applying the formula from the Users Guide will still work. (The t statistic being ((estimated Mean time||feeling in Activity A) – (estimated Mean time||feeling in Activity B)) / (replicate weight standard error for (mean time||feeling A – B))

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