[R-sig-ME] statistical basis for using mixed model in a situation

[Juliet Hannah]

All,

Consider a simple two-group design in which one wants to test if the
means of these two groups are different. Assume a simple
t-test (un-paired) is sufficient. Let's say there are 10 samples in
Group A and 10 in group B.

Now, let's say each sample was measured in triplicate so that Group A
has 30 arising from 10 measured in triplicate.

Here is my question:

We could average the triplicates and proceed with the t-test.

But I have also observed people fitting a mixed model with a random
intercept for the triplicates.

What is the statistical basis for selecting one approach over the other?

Off the top of my head, this seems a little different from examples
such as students nested within classes and so on, but
I am unable to properly characterize it statistically.

Thanks,

Juliet