In a context-free preference situation, we conduct a laboratory experiment in which we test higher order ambiguity attitudes (order 2, order 3, and order 4) using a simple model with two states of nature (good and bad). We compare ambiguity attitudes when the random variable capturing ambiguity is introduced on the probability associated with the good state of nature versus the bad state of nature. In addition, in the case of order 3, we compare ambiguity attitudes when the random variable capturing ambiguity is presented as two harms (as usual in decision theory) versus one harm and one favor. We first establish the theoretical prediction of a general consistency of ambiguity attitudes. Ceteris paribus, these attitudes should remain invariant with respect to (i) the state of nature to which ambiguity is associated, and to (ii) the type of the change (harm or favor) in the probability to which ambiguity is associated. Our empirical results systematically contradict this formal prediction pointing to the behavioral importance of ambiguity framing.