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

• Hamsi
In summary, the probability of getting at least one type I error is defined as P=1-(1-a)^m, where m is the number of tests and a is the probability of getting a type I error. However, in question D, m0 is used to represent the number of tests for which the null hypothesis is true. This is equivalent to the m in the formula, but it is not the total number of tests. To find a formula based on the total number of tests, you would need to incorporate the proportion of tests in which the null hypothesis is true.
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
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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

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?

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.

Hamsi
That makes sense. Thank you very much!

## 1. What is the purpose of analyzing RNA-seq data and calculating the probability of making type I errors?

The purpose of analyzing RNA-seq data is to identify and quantify gene expression levels in a particular biological sample. Calculating the probability of making type I errors allows researchers to determine the likelihood of falsely identifying a gene as differentially expressed when it is not, potentially leading to incorrect conclusions.

## 2. What are type I errors in the context of RNA-seq data analysis?

In the context of RNA-seq data analysis, type I errors refer to the incorrect identification of a gene as differentially expressed when it is actually not. This can occur due to random chance or technical issues in the experimental design or analysis process.

## 3. How is the probability of making type I errors calculated in RNA-seq data analysis?

The probability of making type I errors in RNA-seq data analysis is typically calculated using statistical tests, such as the t-test or ANOVA, which take into account factors such as sample size, variability, and significance levels. These tests generate a p-value, which represents the probability of observing the data if there is no true difference in gene expression between groups.

## 4. What is an acceptable level of type I error in RNA-seq data analysis?

There is no universally accepted level of type I error in RNA-seq data analysis, as it may vary depending on the research question and the amount of data available. However, a commonly used threshold is a p-value of less than 0.05, which indicates a 5% chance of falsely identifying a gene as differentially expressed.

## 5. How can researchers minimize the risk of making type I errors in RNA-seq data analysis?

To minimize the risk of making type I errors in RNA-seq data analysis, researchers can carefully design their experiments and select appropriate statistical methods. It is also important to validate any significant findings through replication studies or alternative methods, and to consider the biological relevance of the identified genes in the context of the research question.

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