padj

Padj, short for adjusted p-value, is a p-value that has been modified to account for the problem of multiple hypothesis testing. It is widely used in high-throughput analyses such as transcriptomics, where thousands of tests are performed simultaneously. Many statistical software packages, including DESeq2, EdgeR, and limma, report padj values alongside raw p-values.

The most common method to compute padj is the Benjamini-Hochberg procedure, which controls the false discovery rate (FDR). Other methods exist, such as Bonferroni adjustment (family-wise error rate control) or Storey’s q-values. The resulting padj can be interpreted as the smallest FDR at which a test would be deemed significant.

A smaller padj indicates stronger evidence against the null after correcting for multiple testing. A common threshold is padj < 0.05, indicating an estimated 5% FDR for the set of significant results. However, padj is not the probability that a given null hypothesis is true; it is a statement about the expected proportion of false discoveries among declared significant results.

Padj depends on the number of tests and their dependency structure. Some dependencies can affect the FDR control. Reporting padj alongside effect sizes and confidence intervals provides a fuller picture. Researchers should choose a correction method appropriate to their study design and interpret padj values in context.

In differential expression analysis, padj is used to identify genes whose observed changes are unlikely to be due to chance after multiple testing correction. In other domains, padj can be used similarly for genome-wide association studies, proteomics, or metabolomics where many hypotheses are tested concurrently.