  Locality and realism are two main assumptions in deriving Bell's
inequalities. Though the experimentally demonstrated violations of Bell's
inequalities rule out local realism, it is, however, not clear what role each
of the two assumptions solely plays in the observed violations. Here we show
that two testable inequalities for the statistical predictions of two-qubit
systems can be derived by assuming either locality or realism. It turns out
that quantum mechanics respects a nonlocal classical realism, and it is
locality that is incompatible with experimental observations and quantum
mechanics.
