#### Statistical Glossary

**Relative Efficiency (of tests):**

The relative efficiency of two tests is a measure of the relative power of two tests. Suppose tests 1 and 2 are tests for the same null-hypothesis and at the same significance level "alpha" (probability of type I error). The relative efficiency of test 2 with respect to test 1 is the ratio N_{1} / N_{2}, where N_{2} is the sample size of test 2 required to achieve the same power for a given alternative as is achieved by test 1 using a sample of size M N_1 .

This measure usually depends on the significance level "alpha", the alternative hypothesis, and the sample size N_{1} of test 1.

Note: the relative efficiency of tests should not be confused with the relative efficiency of estimators.