tl;dr: Data is not the plural of anecdote. Both are valid. They are not mutually exclusive. Synthesizing them for a given situation is the act of modeling.

Two of my posts may help, and one Quora answer may help.

The first concerns the structure of narrative thinking. Narratives are models built up from anecdotal data.

http://www.ribbonfarm.com/2010/0...

The second has to do with modeling. When you try to go beyond the dichotomy of statistical modeling versus first-principles modeling, you get into some tricky territory.

http://www.ribbonfarm.com/2011/0...

Finally, the Quora answer:

Venkatesh Rao's answer to Why are spreadsheet champions considered to be expert data analysts while computer science majors take a back seat?

There is a chasm that you have to jump between just exploring empirical data and making sense of it via models. This answer is mainly about how that transition can happen.

Favorite relevant quote: "I don't trust experimental data until it has been verified with a good model." I forget who that is from.