On another site the issue has come up that questions may not be upvoted but answers are. I would like to get some statistical support for this. Are there already existing apps that can do this kind of analysis?
This is not something you could obtain from the API. The API basically exposes some of the features of the site (e.g. search, writing posts, voting itself) in a programmatic way. For analysis like this, you'll need SEDE, the Stack Exchange Data Explorer and support for that is on Meta Stack Exchange; there's even a chatroom dedicated to SEDE.