Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more. 
See also: Types of Error, KolmogorovSmirnov OneSample Test  
Power of a Test
The power of a statistical test is defined as the probability of correctly rejecting a false null hypothesis. Power is therefore defined as: 1  β, where β is the Type II error probability. A test with a low power is of little worth, although the level of significance α may be high (the results are inconclusive since the null hypothesis is true only with a low probability). Note that for a given setup of an experiment, the power of a test and
the level of significance are related to each other: decreasing the level
of significance α (which is favorable, since
the probability of making an error when rejecting the null hypothesis is
lowered) also decreases the power of a test (which is bad, since the probability
of making a type II error increases). Thus, without changing the experiment,
we have to make a compromise between a low level of significance and the
high power of the test.


Last Update: 20121008