Etymologically 'analytic' means to provide an analysis of something. A detailed analysis is done by dividing it into smaller parts. The synonym of the term 'analytic' is 'systematic' and 'logical'.
In the given phrase, the term that can be used as a synonym of 'analytic' is 'logical'. All the other three terms do not provide a synonymous meaning to the given word. The methods used in scientific approaches are logical and they provide meaningful and reasonable details about the occurring of the things.
