Power of a statistical test

This is essentially the ability to show a difference if one exists (i.e. to reject the null hypothesis). It is defined as 1 - the type 2 error.

• what level of power should be used:
  • the power of a study defines the ability of a study to demonstrate an association or causal relationship between two variables, given that an association exists
    • for example, 80% power in a clinical trial means that the study has a 80% chance of ending up with a p value of less than 5% in a statistical test (i.e. a statistically significant treatment effect) if there really was an important difference (e.g. 10% versus 5% mortality) between treatments
    • if a study has a low power then the study results will be questionable (the study might have been too small to detect any differences)
    • 80% is often considered an acceptable level of power for a study

Notes:

• power can be calculated before (a priori) or after (post hoc) data is collected
  • priori power calculation is conducted prior to the research study, and is typically used to determine an appropriate sample size to achieve adequate power
  • post-hoc power calculation is conducted after a study has been completed, and uses the obtained sample size and effect size to determine what the power was in the study, assuming the effect size in the sample is equal to the effect size in the population