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?