# How to compare means of two sets when one set is a subset of another and the sample sizes are not

I have two samples containing citation counts for some publications. Of those samples one is a subset of the another. That is, subset contains some exact citation counts appearing on the other sample. e.g.

Sample1 Sample2 (Subgroup)
50      50
24      24
12      -
5       5
4       4
43      43
2       -
2       -
1       -
1       -


So I want to decide if the numbers from the subset are good enough to represent group1? On this matter:

1. I have intended to apply student t-test but i could not be sure how to apply it. The reason is that the samples are dependent so I could not apply unpaired t-test requiring both samples must come from independent populations. On the other hand, paired t-test also does not look suitable since sample sizes must be equal.
2. In case of an outlier should I remove it? To me it is not logical since it is not normally an outlier but a publication cited quite a lot so it belongs to the same sample. How to deal with such cases? If I do not remove it, it causes the variance to be too big affecting statistical tests...Is it a good idea to replace it with median instead of mean since citation distributions generally tend to be highly skewed?

Giving the information and my trials how could I manage this issue?

• Please don't call these kind of objects sets in the future. Sets contain no element more than once by definition. The set defined by the array you call 'set1' would for instance be {1,2,4,5,12,24,43,50} – Jeremias K Jan 21 '16 at 10:19
• I'm not sure I know what "good enough to represent" means. What sort of "loss" would you suffer if you used set2 in place of set1? – mef Jan 21 '16 at 12:00
• @mef I simply wanted to compare two groups' means whether they differ significantly. If they do not differ significantly I will conclude that my subset is a good representative of the original set. – mlee_jordan Jan 21 '16 at 13:20