sequentiestatistiek

Sequentiestatistiek, also known as sequential analysis, is a branch of statistical inference where the sample size is not fixed in advance. Instead, observations are taken one by one or in small groups, and after each observation or group, a decision is made as to whether to continue sampling or to stop and draw a conclusion. This allows for the possibility of stopping the experiment or study early if a significant result is reached, or conversely, continuing if the evidence is not yet conclusive.

The primary advantage of sequential analysis is its potential for reducing the sample size required compared to traditional fixed-sample-size methods, leading to savings in time, cost, and resources. This is particularly beneficial in fields such as clinical trials, quality control, and industrial experimentation where early stopping can prevent unnecessary exposure to a potentially ineffective treatment or the production of faulty goods.

The methodology involves defining specific stopping rules. These rules determine when to terminate the sampling process and declare a decision, such as accepting or rejecting a hypothesis. Common sequential procedures include the Sequential Probability Ratio Test (SPRT) developed by Abraham Wald. The SPRT continuously monitors the likelihood ratio of the data under different hypotheses and stops when this ratio exceeds a predetermined upper or lower boundary.

Despite its advantages, sequential analysis also presents challenges. The statistical calculations can be more complex than those for fixed sample sizes, and the analysis of results requires careful consideration of the stopping rule to avoid biased conclusions. The flexibility in sample size means that the distribution of the sample size itself is a random variable that needs to be accounted for in the statistical framework.