  In a general metric theory of gravitation in four dimensions, six
polarizations of a gravitational wave are allowed: two scalar and two vector
modes, in addition to two tensor modes in general relativity. Such additional
polarization modes appear due to additional degrees of freedom in modified
gravity theories. Also graviton mass, which could be different in each
polarization, is another characteristic of modification of gravity. Thus,
testing the existence of additional polarization modes and graviton mass can be
a model-independent test of gravity theories. Here we extend the previous
framework of correlation analysis of a gravitational-wave background to the
massive case and show that a ground-based detector network can probe for
massive stochastic gravitational waves with its mass around ~10^{-14} eV. We
also show that more than three detectors can cleanly separate the mixture of
polarization modes in detector outputs and determine the graviton mass.
