RNA-seq data analaysis: probability of making at least one type I error

[Hamsi]

Homework Statement

I need to derive a mathematical expression for the probability of making at least one type I error. In this expressrion i need to use the number of true null hypothesis m0.

Also the number of genes is p and the number of tests is m.

Relevant Equations

-

In general the probability of getteing at least one type I error is P=1-(1-a)^m. With m being the number of tests and a the probabiliy of getting a type I error. But i do not know how to get an expression with m0

 

[haruspex]

i need to use the number of true null hypothesis .

Please explain what that means. Can you post the whole question as given to you?

 

[Hamsi]

Thank you for looking at my question! This is the entire problem set. I got stuck on question D. The previous questions (a-c) are not neceassy for question D, Ithink. I would appreciate anything the can get me a step further.

 

[haruspex]

Ok, I think I understand. They are defining m₀ as the number of tests, out of all the tests conducted, for which the null hypothesis is true; i.e. these are the ones that ought not be rejected. Calling it the "number of true null hypothesis " is just poor English.
The m in the formula you quote is the same thing. It is not the total number of tests.
If you wanted a formula based on the total number of tests you would need to plug in a value for the proportion of tests in which the null hypothesis is correct.
E.g. if the null hypothesis were false in every case then the probability of a type I error in the batch would be zero.

 

[Hamsi]

That makes sense. Thank you very much!