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.