# What does it mean for a statistical test to have a power of 0.8?

The power is a continuous function of the parameter. If a statistical test has a power of 0.8, does that mean the power function is 0.8 at all parameters except the null hypothesis? Or does it mean the power function is almost everywhere 0.8 or at most 0.8?

• Power to do what? – Michael M Jan 23 at 20:15
• Detect a difference that’s real – Numbers Jan 23 at 20:15
• What kind of difference that is real? – Alexis Jan 23 at 21:32
• The conventional* 80% is taken at a specific alternative -- e.g. for a location test, at a given difference in population mean (specified effect size). At smaller effect sizes power is smaller, at larger effect sizes, power is larger. $\qquad$ * well, conventional in some application areas. – Glen_b -Reinstate Monica Jan 23 at 23:38