Much experimental work and some mathematical analyses have been conducted in comparing triangle and duo-trio tests in sensory difference testing. In this paper we assume the existence or conception of subjective responses on a response scale and relate these to corresponding probabilities of correct choices in triangle and duo-trio tests and to expected difference from control in the difference-from-control test. The two probabilities mentioned are expressed in terms of the power function of analysis of variance but required special evaluations in this problem. A table showing comparisons of the several tests is presented and includes some comparisons suggested by other authors. With the associations among tests developed, it is now possible to make realistic efficiency comparisons among them. Examples of power efficiency comparisons are given and it is found that the asymptotic relative efficiency of the triangle test to the duo-trio test is 112%.