False Discovery Rate (FDR)

What is a False Discovery Rate? False Discovery Rate Explained

The False Discovery Rate (FDR) is a statistical concept and method used in multiple testing problems, particularly in hypothesis testing when conducting multiple comparisons simultaneously. It addresses the issue of controlling the proportion of false discoveries among all the rejected null hypotheses.

In statistical hypothesis testing, researchers often perform multiple tests simultaneously, such as testing the effects of multiple variables or comparing multiple groups. The more tests conducted, the higher the likelihood of encountering false positives (Type I errors), which are findings mistakenly considered significant when they are not.

The FDR provides a way to control the expected proportion of false discoveries among all the rejections of null hypotheses. It is defined as the expected ratio of false positives (rejected null hypotheses that are actually true) to the total number of rejections.

The FDR is typically controlled at a pre-specified level, denoted as α. Commonly used methods to control the FDR include the Benjamini-Hochberg procedure and the Benjamini-Yekutieli procedure.

The Benjamini-Hochberg procedure is one of the most widely used methods for controlling the FDR. It ranks the p-values obtained from the multiple tests and compares them to a critical value derived based on the desired FDR level. It progressively adjusts the critical value for each p-value, starting from the most significant test and moving towards less significant ones.

By controlling the FDR, researchers can control the overall rate of false discoveries while still allowing for some flexibility in identifying potentially significant findings. This is particularly important in large-scale studies or when performing exploratory analyses involving numerous hypotheses.

It’s worth noting that controlling the FDR does not guarantee that all significant findings are true positives. It only ensures that, on average, a certain proportion of the rejections are expected to be false discoveries. Therefore, follow-up validations and replication studies are crucial to confirm the significance and reliability of the identified results.

The FDR has become a popular method in various scientific fields, including genomics, neuroscience, and social sciences, where researchers often encounter multiple testing problems and need to balance the control of false discoveries with the discovery of meaningful findings.