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[Baars01]

I have googled this extensively to little avail.

I have two biological sample sets consisiting of technical reps which I each average yielding an uncertain mean with standard deviation (remember, this value is biological, not technical). These sample sets signficantly differ (t-test). I can take the mean of these by averaging the two means, but how do I get the standard deviation of this mean.
I do this for a number of sample set "pairs" and the variance is mostly similar (they pass Levene's test). I normally would use the square root (i.e. zD = sqr(zX^2 + zY^2)) but I'm worried about applying this to sample set pairs which differ significantly and to those that have unequal variance.

What would be the best solution for this?

Thanks