I have some experimental data from two groups, where each group contains data from $n$ subjects. The data are in the form of a time series for each subject, but are not all the same length. To be clear: there are $n$ time series of variable length in each of my 2 groups. I would like to test for statistical differences between the two groups (call them $a$ and $b$). Generally, the question I'd like to ask is of the form: are the means/medians/variance/IQR/some other descriptive statistic of the data in group $a$ the same as those in group $b$? More specifically, are the variances for each time series in group $b$ larger than those in group $a$?
This seems like a straightforward enough question to answer. My confusion lies because I am dealing with time series data. Do I compute the mean/variance of each time series first, then run an a hypothesis test on these descriptive data? And what is the best way to select a hypothesis test? It seems that there are a number which could address my question, such as Mann-Whitney U, Tukey's range test, the t test, and so on. If I introduce a third group, $c$, is ANOVA more appropriate to test for similarities between the groups? Another thing I have to bear in mind is small sample sizes: I have read about bootstrapping but I'm unsure if ($i$) that is applicable in my situation and ($ii$) how I would go about applying it.
I appreciate that these are probably common issues, but I'm just looking for some pointers and any underlying assumptions I should bear in mind.