Suppose I measure the height of the students in my class: I make a lot of measurements for each student, since each one is rather imprecise, and so I end up with the data: student : measured height, where each student appears many times.
Now I split the class into two groups: say, those, born in Winter/Spring and Summer/Autumn, and I am interested in comparing the means.
The question is how to weight my measurements for, say, Winter/Spring group: should I find the sample mean for each student, and treat the all students with equal weights? - then I somehow loose info that for some students with more measurements my sample mean is much more precise?
Or should I pool all the measurements for the group and consider each as a data point? - then it can happen, that there are a lot of measurements, but of very few students, and I get a false confidence in my estimate (say, with t-test for 2 groups).
Any thoughts? Is there a standard way to go?