Sequentialsampling

Sequentialsampling, often written as sequential sampling, is a statistical framework in which data are evaluated as they are collected and the sampling process may be stopped early based on preplanned criteria. The central idea is to control error rates while potentially reducing the average sample size, avoiding the need to fix the sample size in advance.

A foundational method is the sequential probability ratio test (SPRT) developed by Abraham Wald, which compares two simple hypotheses using likelihood ratio boundaries to decide when to stop and which hypothesis is supported. In practice, more complex designs such as group sequential designs perform a fixed number of interim analyses, using boundaries (for example, Pocock or O’Brien-Fleming) to decide whether to stop or continue while maintaining overall error control.

Bayesian sequential methods offer an alternative approach by updating a posterior distribution with each new observation and defining stopping rules based on posterior probabilities or predictive distributions. Other variants include adaptive or truncated sequential designs, which blend frequentist and Bayesian ideas to balance error control with practical constraints.

Applications of sequentialsampling are widespread and include clinical trials (early stopping for efficacy or futility), quality control, environmental monitoring, and industrial process surveillance. The approach is valued for its potential to reduce resource use and shorten decision times when the accumulating data strongly support a conclusion.

Limitations include the need for careful preplanning to control error rates, increased operational and logistical complexity, and the possibility of biased estimates if interim looks are not properly accounted for in the analysis.