I am a licensed/credentialed/practicing political scientist, a longstanding member of the American Political Science Association. My publications fall under the "qualitative" rather than "quantitative" label because I have not found much use for statistical analysis in what interests me, though I recognize its value for some other inquiries. The basic problem -- besides my own lack of sophisticated quantitative methods -- is that the N is so small for the number of presidents and for the number of major foreign policy crises or decisions. My approach has been case studies, a lot of them, looking for patterns rather than "laws."
This is background for understanding my recent disappointment in a well-hyped book, Who Governs? Presidents, Public Opinion, and Manipulation by James Druckman and Lawrence Jacobs. The ever-valuable Monkey Cage blog, now on the Washington Post, called it to my attention with effusive praise. I even bought it sight unseen -- not my usual practice.
Then I read it and was greatly disappointed. The authors develop an elegant methodology of coding presidential statements and then relating them to time-lagged opinion polls to show how presidents use and try to manipulate public opinion. They also brag, repeatedly, about using "archival records" from recent presidencies. They claim that their statistics show interesting effects -- but nowhere do they have even a single instance linking opinion to a particular presidential action and then to a subsequent poll.
Fortunately, they mention earlier works that do answer my questions and give concrete examples. Let me list these more informative works: The Provisional Pulpit by Brandon Rottinghaus, which has several case studies of both foreign and domestic policy issues and then lists the various circumstances that most often lead to successful presidential influence; The Evolution of Presidential Polling by Robert M. Eisinger; and Polling to Govern by Diane Heith, who documents the numbers of White House officials involved in polling but acknowledges the key causation problem: "However, no pollster, staffer, or president ever publicly acknowledges any influence for public opinion on presidential decision making."
In any event, I think there is more evidence for likely influence in particular cases than the elaborate quantitative analyses provide. Maybe I'm a latent historian.