Calculating standard deviation

[vesuccio]

I have what is hopefully a very simple question. Using the Closed Population (Closed captures) Capture-Recapture Model in program MARK, I have estimated the number of crayfish in a population using a 3.8 year mark-recapture data set. While the results include the Standard Error (SE) and 95% Confidence Interval for N-hat, I am need the Standard Deviation (SD). To estimate the SD from the SE I need the number of observations using to estimate N-hat (e.g. "N"). Should I use the number of parameters in the model (e.g. all the c's and p's and N-hat) or the number of individuals in the data set (e.g. M t+1) for "N"? Or another value?

Thanks in advance for your time and help.

[jlaake]

This question arises more often than it should and something similar may already be on this forum. When you were taught your intro stats course you were undoubtedly taught about means and it was explained that the standard error of a mean was the standard deviation of the data divided by the square root of the sample size. The key here is that the standard deviation of the data is a measure of the spread (variability) of data around a mean and a standard error is a measure of precision of a parameter (eg a mean) and the relationship between them holds for a mean. What you want for a parameter is the standard error and you could also call it the "standard deviation" of the parameter (not the data). In some stats books you'll see the standard error for a mean also called the standard deviation of the mean to differentiate it from the standard deviation of the data. If you compute a bootstrap standard error for a parameter, it is the standard deviation of the individual bootstrap values. Thus the standard error is what you want; although the motivation for your question was unclear from your posting.

[vesuccio]

Thank you for the explanation.