KALAMAZOO, Mich.—Four years ago, Kalamazoo College faced a shrinking number of Michigan high-school graduates, declining applications and an endowment getting hammered by the recession.

Then the small, picturesque liberal-arts school decided on a bold step. It started publicizing test results showing what its students had learned in their four years—a surprisingly rare strategy in a higher-education industry that usually prefers to keep such things private.

...