This paper proposes test statistics for the comparison of two binomial parameters that come from related samples in the situation just described, that is, in a series of Bernoulli trials that are split into two subsets at the occurrence of the first success in the sequence so that one of the binomial parameters is estimated under negative binomial sampling whereas the other is estimated under binomial sampling.

Consider a fixed number R of replicates of a truncated geometric experiment, each replicate r (1 [less than or equal to] r [less than or equal to] R) consisting of a maximum of T - 1 Bernoulli trials (with success probability [p.