You can use multilevel modeling (AKA mixed modeling), which is useful for analyzing nested data (i.e., observations within individuals). Not only can this technique be applied to unbalanced data, in which some individuals may have more observations than others, it uses all available data. That is, it does not drop individuals with missing observations--only the missing observations are not included. Moreover, it uses maximum likelihood, meaning that it provides reliable estimates for data missing at random.

You can use multilevel modeling (AKA mixed modeling), which is useful for analyzing nested data (i.e., observations within individuals). Not only can this technique be applied to unbalanced data, in which some individuals may have more observations than others, it uses all available data. That is, it does not drop individuals with missing observations--only the missing observations are not included. Moreover, it uses maximum likelihood, meaning that it provides reliable estimates for data missing at random.

You can still possibly compare the means (and distributions) between the two groups by using t-tests, which don't require the same number of observations in each group. It depends on your research question and what exactly you are comparing, and on the nature of your data.

Dear Jerry, thank You for Your answer. Sure, a lot depends on my data. Imagine, I have got 2 groups of jumping children:)

Child 1 performs 3 jumps on 1, 1.2 and 0.8 m.

Child 2 performs 5 jumps on 0.6, 0.8, 0.8, 0.9 and 1 m.

and so on.

I think that hypothetically each child has his unique distribution of lengths of the jump. So, I don't understand how I can use t-test not for mean values but for observations.

Mixed models are the way to go. Check out my paper (in Russian) cogjournal.org/2/1/pdf/ChetverikovRJCS2015.pdf

I also like Bodo Winter's tutorials:

www.bodowinter.com/tutorial/bw_LME_tutorial2.pdf