padjusted

Padjusted, often abbreviated as padj, refers to a p-value that has been corrected for multiple hypothesis testing. When many statistical tests are performed simultaneously, the chance of obtaining false positives increases. The adjusted p-value represents the smallest significance threshold at which a given hypothesis would be considered significant under a chosen adjustment method and error-rate control.

Common adjustment methods include Bonferroni, Holm, Hochberg, and family-wise error rate oriented procedures, as well as false discovery rate methods such as Benjamini-Hochberg and Benjamini-Yekutieli. Each method trades off different error rates and makes different assumptions about test independence. Software tools typically provide a function to compute padj from a vector of raw p-values and a specified method; for example, the p.adjust function in R returns adjusted p-values according to the selected approach.

Interpreting padjusted values depends on the method used. A result with padj below a chosen significance level (commonly 0.05) is considered significant under the corresponding error-rate control. However, padj does not convey the probability that the null hypothesis is true; rather, it reflects the evidence against the null after accounting for multiple comparisons. Padjusted values are widely used in high-throughput settings such as genomics, transcriptomics, and other large-scale screening tasks where thousands of hypotheses are tested simultaneously.

Limitations include the fact that different adjustment methods control different error metrics and rely on assumptions about test independence. Dependencies among tests or atypical distributions can affect the performance of padjusted values, so interpretation should consider the chosen method and study design.