Statistical power

Power called (English for force, power, energy), also test strength or selectivity, describes in the statistics, the significance of a statistical test.

The strength test indicates the probability that a significance test for the benefit of a specific alternative hypothesis H1 ( for example, " There is a difference " ) decides if this is correct. The objectionable hypothesis is H0, the null hypothesis is called. High Power Test speaks against, low power test for the null hypothesis H0.

The strength test is 1 - β, where β denotes the probability of committing a type 2 error.

Decision table

Choice of β -defect levels

For efficacy studies of medical treatments suggests Cohen (1969: 56) for a β 4 times as high as before for the significance level α. If α = 5 %, the β - error level should be therefore 20%. Located in an investigation, the β - error probability ( probability of a type 2 error ) under the 20% limit, the strength test (1- β ) is therefore greater than 80 %.

It should here be noted that the β - error for a given, fixed significance level α in general can not be controlled directly. In many asymptotic or non-parametric tests of the β - error is unpredictable or there exist only simulation studies. In some tests, such as the t-test, the β - error can be controlled if the statistical analysis is preceded by a sample size planning.

Determinants of statistical power

The test strength (1- β ) is larger:

• With increasing difference of ( that means a big difference between two sub-populations is overlooked rarer than a little difference)
• With decreasing characteristic scattering
• ( is not set otherwise) with increasing level of significance
• With increasing sample size, because the standard error is less then:
• With one-sided tests in comparison to two-sided tests: For the two-sided test, you need a larger by about 25 % sample size to achieve the same power as for the one-sided test.