If there is a flawed methodology in surveys, it is in this Pew global survey. It is supposed to show the improvement of US image around the world. So Pew decided to take Lebanon--which has 1% of the Arab population and less than 1% of world Muslim population--as the only country surveyed in the entire Middle East. (And Lebanon always polled differently than Arab countries for many reasons that we can't get into here, but certainly related to the Hariri assassination and its aftermath). And notice how Turkey and Pakistan polled, for example. They, and not Lebanon, are the indicators of Arab/Muslim population than Lebanon.