According to my Oxford English-French dictionary, "analytical" is used in the field of philosophy, "analytic" in the field of psychology, i.e. "psychoanalytic". The Oxford Concise is more nuanced still: "analytical" is used in the philological field (though "analytic" is not excuded) with "analytic" being used in logic.
In other similar adjectival forms, "-ic" seems to be more common in British English, and "-ical" in American English".
I think that analyrical sounds like the tendency of being fond of the act of analysing. (She is analytical)
Analytic sounds like things having been analyzed well having been or used for analysis. (This is an analytic data)
Did I understand correctly?