What is the power of a study—what is the power calculation?

Often say it is the number of people in a study. Power is the probably to correctly reject the null hypothesis. Said differently power is the probability we will correctly get a small pvalue

But a power calculation is slightly more than that it is the number of people required to adequetyly statistically calculate the number of people that would be necessary to reject your null hypothesis of no difference when there actually is a difference.

Lets say we have a blood pressure drug and we want to see if it works

Well if you only enroll a small number of people you might not be able to tell a difference between those in the active and those in the control arm

Remember depending on baseline bp you might only see a 4-5mmg hg improvement in your blood pressure and in almost every trial I have ever seen even those individuals that get the placebo have a 1-2mm hg improvement in their bp so with large confidence intervals that are likely to overlap with just a small number of people being tested you wont find a statistical difference between the two drugs. You will end up accepting the null hypothesis since you will see overlap, this is sad because maybe there is real difference but you didn’t enroll enough people to find that difference.

But lets say you want to enroll 5 million people in your trial

This is great, you will have much smaller confidence intervals and you will be able to see there is a difference and properly reject the null hypothesis and be able to get an answer but you might waist years or decades trying to enroll that many people. This is timely and expensive.