I am studying banks behaviour according to 6 financial rations throughout a 3-years period. I have 32 observations separated into two groups: large (6) and medium-sized banks (26). However, since in my country there are exactly 6 large banks, it does not constitute a sample, but a population, where as there are around 32 medium-sized banks (so my sample is quite large compared to the population).
To compare these two groups each year, I am using the Wilcoxon Signed Rank Test to test:
$$ H_0: \mu_{i,medium} = \mu_{i,large} $$ where $ \mu_{i,large} $ is the mean of financial ration $i$ of the $large$ group, which is a known parameter, which means I should not be comparing two samples. Is the Signed Rank Test adequate here?
However, I figure that since I have data over 3 years, it'd be better to compare these groups throughout the 3-years period as whole (or not?). What technique should I use to do so? Are there any test I should do prior to selecting a test?
Thanks
Bernardo