Which test to use to compare means of groups with overlapping data? I have 7 groups of data. I want to test if there is a significant difference between these groups of data.
However, some of this data is overlapping. ie. some data in Group 1 might be in group 3. Some data in group 6 might also be in group 7 for example. The groups are therefore not perfectly matched.
Secondly, because of this reason, the number of entries in each group are different. For example, group 1 has 54 entries, whereas group 4 has 94 entries.
Is there a particular test I can use to test if there is a significant difference between the groups?
I hope I have made this clear. Many thanks for your help. 
 A: I am not sure the following test and procedure are the best for overlapping data, but let us come back to it in the end. 
The first thing to do is to chose a test to compare the mean of two groups, and a natural choice would be the Students's t test. A more adequate approach to your specific problem might be the Hotelling's T-square distribution, but I do not know much about it so I'll leave it to those more acquainted with it than me.
If you choose to perform several t-tests (one for each pair of samples), or any kind of test that deliver a p-value, you will have to correct for the fact that you are doing multiple testing. What you'll have to correct is the level at which you will reject the null hypothesis, and how to correct for it is explained in this answer.
At this point is important to note that if you choose to walk down this path then you are formally correcting for multiple independent tests. Your tests are not independent, because the data overlap, so if you choose m as the number of tests you are being too conservative. It would be preferable to estimate the number of independent tests from your data m' and correct only for it (but it might not be obvious at all). 
