Shortcut to assessing "competitiveness" of various competitive full tuition or better scholarships?

@MotherOfDragons is correct, no schools in the Ivy League offer merit. Some selective schools do offer a very limited number of merit scholarships, but they are very very competitive. Those schools include Duke, Vanderbilt, UNC, Notre Dame, UVA and WashU. I’m sure there are some I am missing.