Using even and odd coherent states, we define a new state, which is called the spin-type W state. With the spin-type W states, we provide a new scheme for testing fundamental aspects of quantum mechanics and refuting local hidden variable theory without using inequalities. Finally, a scheme for preparing the spin-type W states, and discussion of experimental possibility and the effect of the measurement on physical observables due to a close orthogonality of the two coherent states are given.