multiplehypothesis

Multiple hypothesis testing is a statistical approach used to evaluate multiple competing hypotheses simultaneously, often in scientific research, machine learning, and data analysis. Unlike traditional hypothesis testing, which focuses on a single null hypothesis, multiple hypothesis testing addresses the challenge of analyzing numerous hypotheses—such as in genome-wide association studies, feature selection in predictive models, or quality control in manufacturing. The primary goal is to identify which hypotheses are statistically significant while accounting for the increased likelihood of false positives due to the large number of tests.

A key issue in multiple hypothesis testing is the family-wise error rate (FWER), the probability of making at least one Type I error (rejecting a true null hypothesis) across all tests. Methods to control FWER include the Bonferroni correction, which divides the significance threshold by the number of tests, and the more powerful Holm-Bonferroni or Šidák procedures. Alternative approaches, such as the false discovery rate (FDR), focus on controlling the expected proportion of false positives among the rejected hypotheses, which is useful when many hypotheses are expected to be true.

Multiple hypothesis testing is widely applied in fields like genomics, where thousands of genetic markers may be tested for association with a trait, and in bioinformatics, where gene expression data is analyzed for differential activity. In machine learning, it helps in selecting relevant features by testing their predictive power while minimizing overfitting. The choice of method depends on the research context, the number of hypotheses, and whether strict control of Type I errors or a balance between sensitivity and specificity is prioritized. Proper implementation requires careful consideration of statistical power, effect sizes, and the underlying assumptions of the chosen procedure.