On the observability of power: are my analogies correct?
Analogy one: the telescope.
“Using a sample to estimate both the population effect and (observed) power, is like taking a picture of the sky and using that to estimate both the average brightness of the stars and the sensitivity of the telescope. This is not possible. Or you use an instrument of known sensitivity and you estimate the population effect, or you calibate the instrument using a known population”
Analogy two: the fuel gauge.
“You cannot look at the fuel gauge and estimate from that both how many liters of fuel you have left and the sensitivity of the gauge. Either you take a calibrated gauge and you estimate how much fuel is in the tank, or you use a known amount of fuel to calibate the gauge”
