Variance of mean of means

I apologize for a simple question, but I haven't been able to find an answer. Let's say I'm measuring something with multiple replicates, and each replicate is subsampled - a typical nested design like shown here: http://www.nature.com/nmeth/journal/v11/n10/images_article/nmeth.3137-F2.jpg. The group mean is the mean of the means of each replicate, but what is the overall variance (i.e., variance of the group mean)? The variance of the means of each replicate would seem to underestimate the overall variance since each mean isn't a data point but has its own statistical distribution. On the other hand, pooling the subsamples to find the variance would be pseudoreplication... thoughts? I feel like I am missing something very obvious here.

• It sounds like you're creating a sampling distribution, in which case the variance would be the standard error (squared), but I feel like I'm missing something about your intent or design – HEITZ Jun 26 '17 at 23:43
• When you create a sampling distribution of means, you can calculate the variance of those means. But is there any way to calculate the actual variance - not the variance of means, but the true (estimated) variance of the parameter? Does that make sense? – housetyrell Jun 28 '17 at 14:13