Error in the design of an experiment Suppose that we have a population with a subpopulation that exhibits a certain characteristic. We are interested in the performance of a group of people from the population on a group test. The question is do groups of people composed of individuals entirely from the subpopulation perform better than groups of people from the population. In order to apply statistical techniques to make this determination I propose the following. First randomly select a large number of groups from the population and measure each groups performance statistics. Next randomly select the same number of groups from the subpopulation and measure each groups performance statistics. Compare the statistics(primarily moments of the empirical distributions) from the two categories to draw conclusions about performance. My question is what if any are the flaws with this experiment and how to fix them?
For example let's say we have 10,000 people in our population and we want to see how well a group of 10 people performs(in terms of time to completion) on a scavenger hunt. We want to know if groups of people composed of high IQ individuals do better. We start by taking a random sample of 1000 groups of 10 from the population and measure their performance on a scavenger hunt. Next we consider people from the group of 10,000 that have an IQ over 140. We take a sample of 1000 groups of 10 from this subpopulation and measure their performance on a scavenger hunt. We compare statistics associated to the two groups to determine if indeed groups of high IQ individuals perform better.
 A: First let us say tha there are two populations of people - IQ>140 and IQ<=140 (pop A and B). 
The procedure you propose is correct. Only two discussion points:
1) there is no need for the same number of groups sampled from population A and B. Your experiment is not paired - in the sense that there is no correspondence between a group selected from pop A and another selected from pop B. You will be performing a non-paired statistical test to compare the set of groups.
2) The only issue that requires some further thinking is whether the same person X can be part of two different groups (either from pop A or B). That is, when you sample 10 people from population A do you have to be sure that these people have not been part of any other group tested? I dont think so. The claim being tested is that groups with members only from population A perform differently than groups with member only from population B. So to perform some statistics you need a set of groups (all of them different). But it is the group  that is different among themselves. If person X belong to group A1 and A2, the groups can still be different - provided that at least one person in A1 is not in A2! So I think there is no problem if the same person gets selected to two different groups. 
