# False Discovery Rate

Posted October 27, 2023 by Rohith and Anusha ‐ 2 min read

Statistics is a powerful tool that helps us make sense of data and draw meaningful conclusions from it. In the world of statistics, controlling the rate of false discoveries is crucial to ensure the reliability of research findings. One of the key concepts in this regard is the False Discovery Rate (FDR). In this blog post, we will explore what FDR is, why it is important, and how it is calculated.

## Understanding False Discovery Rate (FDR) #

• In statistics, a false discovery occurs when a null hypothesis is rejected when it is actually true.

• The False Discovery Rate (FDR) is the proportion of these false discoveries among all the discoveries made.

• In simpler terms, it represents the rate of Type I errors in multiple hypothesis testing.

• Multiple hypothesis testing arises when researchers test several hypotheses simultaneously, increasing the chance of finding false positives.

## Controlling False Discoveries #

• Controlling false discoveries is essential in various fields such as genomics, finance, and drug discovery.

• FDR control methods help researchers manage the trade-off between identifying true positives and minimizing the number of false positives.

• One commonly used method to control FDR is the `Benjamini-Hochberg` procedure.

• This method adjusts the p-values obtained from multiple tests, ensuring that the FDR is kept at a desired level (often denoted as q).

## Calculating FDR: Benjamini-Hochberg Procedure #

### Sort the p-values #

• Arrange the p-values from multiple tests in ascending order.

### Calculate critical value #

• Determine the critical value using the formula:

Critical Value= `(i/N)×q`, where `i` is the rank of the p-value, and `N` is the total number of tests.

### Compare with p-values #

• Compare each p-value with its corresponding critical value.

• If the p-value is less than or equal to the critical value, reject the null hypothesis.

### Stop the procedure #

• Continue comparing p-values until you find the first p-value that is greater than its critical value.

• Reject all null hypotheses corresponding to p-values before this point.

## Importance of FDR in Scientific Research #

### Reduces Type I errors #

• By controlling FDR, researchers minimize the risk of incorrectly rejecting null hypotheses, leading to more reliable results.

### Facilitates Reproducibility #

• Findings with controlled FDR are more likely to be replicated in future studies, enhancing the credibility of scientific research.

### Optimizes Resources #

• Avoiding unnecessary follow-up experiments or investments in false leads saves time and resources.

## Conclusion #

• Understanding and controlling the False Discovery Rate is fundamental in modern statistics.

• Researchers and data scientists must be aware of the challenges posed by multiple hypothesis testing and employ methods like the `Benjamini-Hochberg` procedure to ensure the validity of their findings.

• By doing so, the scientific community can continue to make robust and meaningful contributions to knowledge and innovation.