When we think of the power curve associated with some statistical test, we usually envisage a curve that looks something like (half or all of) an inverted Normal density. That is, the curve rises smoothly and monotonically from a height equal to the significance level of the test (say 1% or 5%), until eventually it reaches its maximum height of 100%.
The latter value reflects the fact that power is a probability.
But is this picture that invariably comes to mind - and that we see reproduced in all elementary econometrics and statistics texts - really the full story?
Actually - no!