  We completely determine the mod $2$ Seiberg-Witten invariants for any spin
structure on any closed, oriented, smooth $4$-manifold $X$. Our computation
confirms the validity of the simple type conjecture mod $2$ for spin
structures. Our proof also works for families of spin $4$-manifolds and thus
computes the mod $2$ Seiberg-Witten invariants for spin families. The proof of
our main result uses $Pin(2)$-symmetry to define an enhancement of the mod $2$
Seiberg-Witten invariants. We prove a connected sum formula for the enhanced
invariant using localisation in equivariant cohomology. Unlike the usual
Seiberg-Witten invariant, the enhanced invariant does not vanish on taking
connected sums and by exploiting this property, we are able to compute the
enhanced invariant.
