![]() 20 or less), andĬohen´s d (either as the expected effect size or as the lower limit for a substantial effect). The □ error probability (usually 0.05 or less), In summary, three specifications are required to calculate a sequential t-test: The A and B boundaries are calculated with the previously defined error rates □ (Type I error) and □ (Type II error) as follows: The focus in the work of Armitage was on the Sequential (Paired) Analysis. Wald (1945) defined the following rules for the SPRT: Condition The sequential probability ratio test (SPRT) is the term that is used. To account for the fact that the algebraic sign is unknown in a two-sided test, the t-value is squared (Rushton, 1952).Īfter the calculation of the test statistic, the decision will be either to continue sampling or to terminate the sampling and accept one of the hypotheses. More specifically, it is the ratio of the likelihood of the alternative hypothesis to the likelihood of the null hypothesis at the m-th step of the sampling process (LR m). ![]() The test statistic of the SPRT is based on a likelihood ratio, which is a measure of the relative evidence in the data for the given hypotheses. 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. In cases where the endpoint of interest takes longer to observe, counterparts to the paired t-test that can accommodate right censoring are desirable. Sequential hypothesis testing is therefore particularly suitable when resources are limited because the required sample size is reduced without compromising predefined error probabilities. When paired designs are based on time-to-event endpoints that are available very quickly, tests such as Wilcoxon’s signed-rank test or a standard paired t-test may be employed in an analysis. 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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