This test is an advancement over Tajima's D,[2] which is used to differentiate neutrally evolving sequences from those evolving non-randomly (through directional selection or balancing selection, demographic expansion or contraction or genetic hitchhiking).
Fay and Wu's H is frequently used to identify sequences which have experienced selective sweeps in their evolutionary history.
Due to the outgroup species, you can now tell what the ancestral state of the allele was before the two lineages split.
If, for example, the ancestral allele was different, you can now say that there was a selective sweep in that region (could be due to linkage too).
A significantly positive Fay and Wu's H indicates a deficit of moderate- and high-frequency derived single nucleotide polymorphisms (SNPs) relative to equilibrium expectations, whereas a significant negative Fay and Wu's H indicates an excess of high-frequency derived SNPs.