We propose an experimental scheme to investigate incomplete erasure of which-way information encoded in atomic hyperfine states.Due to the incomplete erasure of the which-way information, it is shown that the interference pattes of the atomic wave packets initially confined in a spin-dependent optical lattice are destroyed to a certain extent, which provides a new straight way to test further the validity of the theoretical model developed in our recent work.The remarkable merit of the proposal is that it is simple and can be implemented easily.