A statistical test that makes certain assumptions about the population distribution underlying the sample, most common among them being the assumption of normality. When these assumptions are met, parametric tests are the most powerful for a given sample size; but if one or more of the assumptions are violated, then non parametric tests provide a robust alternative with as high or higher power.
Most conventional tests are parametric in nature. Among these:
Chi-Square test of one variance
F-test of two variances