ABSTRACT
The assumptions which must be satisfied in order to ensure that the sign test for equivalence be an exactly valid procedure exhibiting some basic optimality property are as weak as in the case of its traditional one-and two-sided analogue. This means that the data have to be given by n mutually independent pairs (X1, Y1), . . . , (Xn, Yn) of random variables following all the same bivariate distribution which may be of arbitrary form. In particular, the distribution of the (Xi, Yi) is allowed to be discrete. Within each such random pair, the first and second component gives the result of applying the two treatments, say A and B, under comparison to the respective observational unit. Except for treatment, the observations Xi and Yi are taken under completely homogeneous conditions so that each intraindividual difference Di ≡ Xi − Yi can be interpreted as an observed treatment effect. For definiteness, we assume further that large values of the X ’s and Y ’s are favorable, which implies that A has been more efficient than B in the ith individual if and only if the value taken on by Di turns out to be positive.
