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

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SUMMARY

The probability of making at least one type I error in RNA-seq data analysis is calculated using the formula P=1-(1-a)^m, where 'm' represents the number of tests conducted and 'a' is the probability of a type I error. The discussion clarifies that 'm0' refers to the number of true null hypotheses among all tests, which should not be rejected. Understanding this distinction is crucial for accurate statistical analysis in RNA-seq studies. The conversation emphasizes the importance of correctly interpreting the variables in the context of hypothesis testing.

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Hamsi
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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
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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
 
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Hamsi said:
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?
 
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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.
 
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.
 
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That makes sense. Thank you very much!
 

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