padjust

Padjust is a general term used to describe procedures that adjust p-values when multiple statistical tests are performed. The aim is to reduce the likelihood of false positives by accounting for the increased chance of observing significant results purely by chance. Adjusted p-values are typically interpreted against the same significance level as the original p-values, but with a corrected threshold that reflects the number of tests and their dependencies.

Common methods for padjust include both family-wise error rate (FWER) controls and false discovery rate (FDR) controls. FWER methods, such as the Bonferroni correction and Holm’s step-down procedure, aim to limit the probability of making one or more type I errors among all tests. Other FWER methods include Hochberg’s step-up procedure and Hommel’s method, which can offer more power under certain conditions. FDR methods aim to control the expected proportion of false discoveries among the rejected hypotheses; the Benjamini-Hochberg (BH) procedure is the most widely used, with the Benjamini-Yekutieli (BY) adjustment providing a more conservative option under arbitrary dependence among tests.

Implementation and usage vary by software. In the R programming environment, the p.adjust function performs p-value adjustments using methods such as "holm", "hochberg", "hommel", "bonferroni", "BH", and "BY". In Python, similar functionality is provided by libraries like statsmodels, under functions that implement multiple testing corrections. When applying padjust, researchers consider the dependence structure of tests and the desired balance between discovery rate and type I error risk.

Applications of padjust are common in genomics, proteomics, neuroimaging, and other fields involving large-scale hypothesis testing. Proper reporting typically includes both raw and adjusted p-values to convey the impact of multiple testing correction.