Omnibus tests are statistical tests that are designed to detect any of a broad range of departures from a specific null hypothesis. For example, one might want to test that a random sample came from a population distributed as normal with unspecified mean and variance. A successful genuine omnibus test would lead one to reject this hypothesis if the data came from any other distribution. By contrast, a test of normality that was sensitive specifically to thick-tailed distributions such as Cauchy would not be considered an omnibus test. A genuine omnibus test is consistent for any departure from the null, rejecting a false null hypothesis with probability approaching unity as the sample size increases; however, some statisticians include in the omnibus category certain broad-spectrum tests ...
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