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Numerical Approximations of Power

There are two ways to determine the power of a statistical test, analytical and numerical (that is, experimentally) and quite often, the numerical method is a more practical approach. To determine the power of a test given a sample size $ n$, you need only to follow these steps:
  1. Generate $ n$ simulated data points (see Section 3.8 for details on how this can be accomplished).
  2. Apply your test to the data.
  3. Determine if your test correctly rejected the null hypothesis.
  4. Return to Step 1 and repeat many, many times.
  5. The power of your test is:

    $\displaystyle \textrm{Power} = \frac{\textrm{\char93  of times H}_0 \textrm{ was correctly
rejected}}{\textrm{Total \char93  of tests}}

Frank Starmer 2004-05-19