…+ *s*^{2}* _{B}*)/

The FBI criterion for a match on this one element can be written

Because *E*(*s _{x}*) =

The approximation is very rough because *E*(P{*t < S*}) ≠ P{*t < E*(*S*)}, where *t* stands for the two-sample *t* statistic and *S* stands for But it does show that if δ is very large, this probability is virtually zero (very small false match probability because the probability that the sample means would, by chance, end up very close together is very small). However, if δ is small, the probability is quite close to 1.

The equivalence *t* test proceeds as follows. Assume

where *H*_{0} is the null hypothesis that the true population means differ by at least δ, and the alternative hypothesis is that they are within δ of each other. The two-sample *t* test would reject *H _{0}* in favor of

When v is large *s _{p}* ≈ 0, and therefore the quantity