Is FA wrong?

[cyanide12345678]

---

Members don't see this ad.

Okay so Power is 1 - Beta. And FA describes that as "the probability of rejecting the null hypothesis when it is false".

That statement is really messing up with my understanding of power and beta. Below is how I think of power and beta.

Beta = probability of Falsely accepting the null hypothesis (so saying there is no difference when there is a difference)

Power = 1 - Beta = Probability of not making a beta error. So by definition you correctly accept null hypothesis (so saying there is a difference when there really is a difference). Which makes sense because you use power when you want to show that the effect of a given drug is NOT inferior/different from the standard of care (for example, showing that abciximab has same efficacy as warfarin).

And this is what I understand from the FA definition of power (probablility of rejecting the null hypothesis when it is false).

Probability of rejecting null hypothesis when it is false = 1 - probability of rejecting null hypothesis when it is true ( aka alpha). So essentially my point is that they're explaining power as 1 - alpha rather than 1 - beta.

So am i wrong here? Or did first aid just explain power as 1 - alpha in words rather than 1 - beta.

 

[jokerman55]

FA isn't wrong here. I tried reading what you are stating many times and I think there is something in the wording your using that is confusing. This is how I think of it.

alpha error = you find a significant difference when there isn't any. alpha error = p value (i.e prob that the difference is due to chance alone)

beta error = you don't find a significant difference when in reality there is. This is what pharma companies want to avoid. Hey if my drug actually works, then I want my billion dollar trial to be able to show it. So pharm companies want to minimize this beta error, so they came up with the term power = 1-beta. If you maximize the power, then you minimize beta error. (power of 0.8 means beta = 0.2 ;; power of 0.9 means beta = 0.1.) For clinical trials the power is typically set at 0.8 but now days there is a push to make it 0.9 to further decrease risk of wasting your money.

 

[Psai]

Power: probability of rejecting null hypothesis when it is false

null hypothesis - there is no difference between your measured population and the real population

false null hypothesis - there is a difference (in real life)

rejecting null hypothesis - there is a difference (you see a measured difference)

Power: probability of you seeing a difference when there actually is a difference

basically, high power is a good thing

 

[thehundredthone]

Okay so Power is 1 - Beta. And FA describes that as "the probability of rejecting the null hypothesis when it is false".

That statement is really messing up with my understanding of power and beta. Below is how I think of power and beta.

Beta = probability of Falsely accepting the null hypothesis (so saying there is no difference when there is a difference)

Power = 1 - Beta = Probability of not making a beta error. So by definition you correctly accept null hypothesis

Your negation is incorrect. The probability of not (falsely) accepting the null hypothesis when it is false is the probability of rejecting the null hypothesis when it is false. The sum probability in this case is your action when the null hypothesis is false, not being right or wrong.

(so saying there is a difference when there really is a difference).

You mean saying there's no difference when there really is no difference.

Probability of rejecting null hypothesis when it is false = 1 - probability of rejecting null hypothesis when it is true.

Same mistake here. In probability, the truth or the basis is always the constant, not the inferences drawn on it.

Here's what it should read like:
Probability of rejecting null hypothesis when it is false = 1 - probability of accepting the null hypothesis when it is false
Power = 1 - beta