projective test

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun A psychological test in which a subject's responses to ambiguous or unstructured standard stimuli, such as a series of cartoons, abstract patterns, or incomplete sentences, are analyzed in order to determine underlying personality traits, feelings, or attitudes.

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

• noun any personality test designed to yield information about someone's personality on the basis of their unrestricted response to ambiguous objects or situations