In the SPRT the null and alternative hypotheses are defined as follows, with □ representing the model parameter : The basic idea is to transform the sequence of observations (which is dependent on the variance) into a sequence of the associated t-statistic (which is independent of the variance). Rushton (1950, 1952) and Hajnal (1961) have further developed the SPRT using the t-statistic. However, the usage of Wald´s SPRT is limited in the case of normally distributed data, because the variance has to be known or specified in the hypothesis. The sequential t-test is based on the Sequential Probability Ratio Test (SPRT) by Abraham Wald (1947), which is a highly efficient sequential hypothesis test. Sequential hypothesis testing is therefore particularly suitable when resources are limited because the required sample size is reduced without compromising predefined error probabilities. Reductions in the sample by 50% and more were found in comparison to analyses with fixed sample sizes (Schnuerch & Erdfelder, 2020 Wald, 1945). The efficiency of sequential designs has already been examined. However, this affects the sample size (N) and the error rates (Schnuerch & Erdfelder, 2020). The data collection will continue as there is not yet enough evidence for either of the two hypotheses.īasically it is not necessary to perform an analysis after each data point - several data points can also be added at once. The data collection is terminated because enough evidence has been collected for the alternative hypothesis (H 1). The data collection is terminated because enough evidence has been collected for the null hypothesis (H 0). With a sequential approach, data is continuously collected and an analysis is performed after each data point, which can lead to three different results (Wald, 1945):
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