Unfortunately, parametric methods such as the t-test or ordinary least squares (OLS), make very strong assumptions about the distribution of the data. To some extent, they still work if the distributional assumptions are relaxed, but it really depends to which extent these assumptions are violated.
Nonparametric methods do not work with the usual parametrized distributions and are instead designed to work with any distribution. This gives them a distinct flexibility, and we are no longer required to check any distributional assumption on the data. If the data follows the same distribution that its parametric counterpart requires, they usually perform almost as well.
