I am trying to calculate some statistical properties pertaining to mobility of cargo inside cells for my research, but due to my poor statistical skills I am in need of a little guidance. I think the short version of my question is how to calculate the standard error of the mean with samples that are weighted differently.

In more detail...

I am studying the speed distribution of particles moving inside of cells. It turns out that a useful way to study the speed distribution for my experiments is to plot the survival function (1-CD or cumulative distribution).

Now I want to estimate the error in the survival functions. In order to do this, I simply repeated the experiment several times (5-10). For each experiment I calculated a survival function. From there I calculate a weighted mean SF, where the weights are proportional to the number of samples in each SF. (One experiment might have 100 particles, while another might have 500, so I figured I should give them different weights.)

I found on Wikipedia an equation for calculating the weighted variance (URL below). From the weighted variance I now want to calculate the standard error of the mean so that I can compare one batch of control experiments to another batch of experiments where a 'motion-killing drug' has been applied to the cells. This way I can determine whether differences between the two batches of experiments are meaningful.

For equally weighted samples I know the equation is simply SEM = SD/(N^0.5). Any ideas how (or if) this equation should be modified when the samples are weighted?

Thanks!

J

http://en.wikipedia.org/wiki/Weighted_mean