The SPRT Sign Chart for Process Dispersion

A nonparametric sequential probability ratio test control chart to monitor the process dispersion based on the sequential sign statistic is proposed. The statistical performance of this chart is evaluated by comparing it with that of the charts for dispersion based on sign statistic in the existing literature. It is found that the proposed chart outperforms all these charts uniformly in detecting a shift of any size over a wide range. An implementation of the chart is illustrated through an example.

Efficiency in Sequential Testing: Comparing the Sequential Probability Ratio Test and the Sequential Bayes Factor Test

In a sequential hypothesis test, the analyst checks at multiple steps during data collectionwhether sufficient evidence has accrued to make a decision about the tested hypotheses.As soon as sufficient information has been obtained, data collection is terminated. Here,we compare two sequential hypothesis testing procedures that have recently been proposedfor use in psychological research: the Sequential Probability Ratio Test (SPRT; Schnuerch& Erdfelder, 2020) and the Sequential Bayes Factor Test (SBFT; Schönbrodt et al., 2017).We show that although the two methods have been presented as distinct methodologies inthe past, they share many similarities and can even be regarded as two instances of thesame overarching hypothesis testing framework. We demonstrate that the two methods usethe same mechanisms for evidence monitoring and error control, and that differences inefficiency between the methods depend on the exact specification of the statistical modelsinvolved. Given the close relationship between the SPRT and SBFT, we argue that thechoice of the sequential testing method should be regarded as a continuous choice withina unified framework rather than a dichotomous choice between two methods. We presentseveral considerations researchers can make to navigate the design decisions in the SPRTand SBFT.