The concept of an inferiority index was introduced in Li & Chi (2011). Under normal distributions, there is a function linking the index to the variance ratio and the scaled relative difference measure. The inverse function will map a given index and variance ratio to a margin which can then be used to define a NI hypothesis. A test statistic is derived which is asymptotically normal. This talk will present research results under Bernoulli distributions. It is shown that for each binary effect measure, one can derive the link function between the inferiority index, the control rate and the effect measure. Through these link functions, equivalent NI hypotheses may be defined for the binary effect measures. Corresponding test statistics are derived and their relative performance can then be meaningfully compared. Applications to anti-bacterial drug trials will be illustrated.