In psychological assessment, Ferguson designed a sequential mastery test using the SPRT methodology as early as 1969. In some disciplines of psychology, the SPRT has already enjoyed great popularity for many years. We provide guidance for navigating these design decisions based on individual preferences and simulation-based design analyses. Our simulations indicate that when deciding on a sequential design within a unified sequential testing framework, researchers need to balance the needs of test efficiency, robustness against model misspecification, and appropriate uncertainty quantification. We demonstrate that the two methods use the same mechanisms for evidence monitoring and error control, and that differences in efficiency between the methods depend on the exact specification of the statistical models involved, as well as on the population truth. We show that although the two methods have different philosophical roots, they share many similarities and can even be mathematically regarded as two instances of an overarching hypothesis testing framework. Here, we compare two sequential hypothesis testing procedures that have recently been proposed for use in psychological research: Sequential Probability Ratio Test (SPRT Psychological Methods, 25(2), 206–226, 2020) and the Sequential Bayes Factor Test (SBFT Psychological Methods, 22(2), 322–339, 2017). As soon as sufficient information has been obtained, data collection is terminated. This process is experimental and the keywords may be updated as the learning algorithm improves.In a sequential hypothesis test, the analyst checks at multiple steps during data collection whether sufficient evidence has accrued to make a decision about the tested hypotheses. These keywords were added by machine and not by the authors. Lorden’s 2-SPRT is a more recent development that has some exciting possibilities for tests of hypotheses concerning population density and is discussed in the latter parts of this chapter. Wald’s sequential probability ratio test was the earliest sequential test and is described first. This permits most computations to be completed in advance of sampling and to be stored in handheld calculators, laptop computers, or printed on cards or sheets. The sequential hypothesis testing we consider requires some prior knowledge of the population distribution. Generally, the accumulated total of the observations relative to the number of observations taken determines when sampling is stopped. The observations are taken at random over the sampling area. As in sequential estimation, sequential hypothesis testing requires taking observations sequentially until some stopping criterion is satisfied. This approach is appropriate when we are interested in determining whether the population density is above or below a stated threshold. The focus of this chapter is sequential hypothesis testing. Several sequential estimation procedures are discussed in Chapter 4. Sequential estimation is used when the purpose of sampling is to obtain precise parameter estimates. Sequential sampling may be used (1) to obtain precise estimate(s) of the parameters), or (2) to test hypotheses concerning the parameters. Sequential sampling is a fast efficient tool for many sampling problems.
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