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I was looking at the sig.level=Significance level (Type I error probability) from https://www.rdocumentation.org/packages/pwr/versions/1.3-0/topics/pwr.t.test

Can someone please explain me is Significance level (𝛼) equal to P value or FDR or what is relation between ?

I know that FDR depends on the p-value threshold and also on the truth and that False discovery rate (FDR) is the expected proportion of Type I errors.

if Type 1 Error Rate = "Probability of rejecting the null if it's true" = p-value threshold

and

Type 1 Error Rate = False Discovery Rate IF the null hypothesis is true and probability of making Type I error is 𝛼.

Also if my 𝛼 is 0.05 which means that that I want the probability that a null finding will be called significant to be less than 5%. In other words, I want the probability of a type I error, or a false positive, to be less than 5%.

How then do I explain 𝛼 in relation to p value or FDR?

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  • $\begingroup$ It is $\alpha$. $\endgroup$
    – Dave
    Aug 3, 2020 at 16:49
  • $\begingroup$ Thanks Dave, I edited it $\endgroup$
    – anamaria
    Aug 3, 2020 at 16:51
  • $\begingroup$ So is your question about the relationship between $\alpha$, false discovery rate, and p-value? $\endgroup$
    – Dave
    Aug 3, 2020 at 16:57
  • $\begingroup$ Yes, indeed that is my question $\endgroup$
    – anamaria
    Aug 3, 2020 at 17:08

1 Answer 1

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The false discovery rate (FDR) is the expected proportion of type I errors, which is where you incorrectly reject the null hypothesis.

α is the p-value you choose to use. You have defined it as 0.05, which is a common choice. At this p-value, there's a 5% chance of a Type 1 error.

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