Standard Deviation (SD) [from the sample] = sqrt (p*q) ::: example: sqrt (0.09) = 0.3
Variance [of the mean] = (p*q) / n ::: example: 0.09/100 = 0.0009
Standard Error (SE) [of the mean] = sqrt (p*q) / sqrt n ::: example: sqrt (0.9 * 0.1) / sqrt (100) = 0.03
Standard Error (of the mean) is often applied in probabilitistic analysis, where one is interested in estimating the "uncertainty" in the model parameters and model variables.
Consider the standard error for the Beta weight for a predictor variable in a regression model.
With randomized trial analysis, one is more likely to focus on the "standard deviation" and "variance" to describe the sample data.
-- Briggs A et al. Decision Modelling for Health Economic Evaluation. Oxford University Press, 2006.
-- Lewandowski A. Statistical Tables -- www.alewand.de/stattabneu/stattab.htm.