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Sequential probability ratio test
About: Sequential probability ratio test is a research topic. Over the lifetime, 1248 publications have been published within this topic receiving 22355 citations.
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TL;DR: In this article, the problem of testing which of two normally distributed treatments has the largest mean, when the tested populations incorporate a covariate, was considered and an optimal allocation that minimizes, in a continuous time setting, the expected sampling costs was derived.
Abstract: We consider the problem of testing which of two normally distributed treatments has the largest mean, when the tested populations incorporate a covariate. From the class of procedures using the invariant sequential probability ratio test we derive an optimal allocation that minimizes, in a continuous time setting, the expected sampling costs. Simulations show that this procedure reduces the number of observations from the costlier treatment and categories while maintaining an overall sample size closer to the “pairwise” procedure. A randomized trial example is given.
8 citations
Journal Article•
TL;DR: In this paper, the authors examined whether the unidimensional sequential probability ratio test (SPRT) can be pro- ductively combined with multidimensional adaptive testing (MAT) and concluded that MAT will result in a higher percentage of correct classifications than UCAT when more than two dimensions are measured.
Abstract: It is examined whether the unidimensional Sequential Probability Ratio Test (SPRT) can be pro- ductively combined with multidimensional adaptive testing (MAT). With a simulation study, it is investigated whether this combination results in more accurate simultaneous classifications on two or three dimensions compared to several instances of unidimensional adaptive testing (UCAT) in combination with SPRT. The number of cut scores, and the correlation between the dimensions measured were varied. The average test length was mainly influenced by the number of cut scores (one, four) and the adaptive algorithm (MAT, UCAT). With MAT, a lower average test length was achieved in comparison to the UCAT. It is concluded that MAT will result in a higher percentage of correct classifications than UCAT when more than two dimensions are measured.Key words: classification, computerized adaptive testing, item response theory, multidimensional adaptive testing, sequential probability ratio test(ProQuest: ... denotes formulae omitted.)Multidimensional adaptive testing (MAT) is a special approach to the assessment of two or more latent abilities in which the selection of the test items presented to the examinee is based on the responses given by the examinee to previously administered items (e.g., Frey & Seitz, 2009). The main advantage of MAT is its capacity to substantially increase measurement efficiency compared to sequential testing or unidimensional computerized adaptive testing (UCAT). Most of the studies on MAT are focusing its application for assessing individual abilities located on continuous scales. Currently, only very little is known about the capabilities of MAT regarding the classification of test takers to one of several ability categories (e.g., pass vs. fail). To fill in this gap, the present paper focuses on the combination of MAT with the sequential probability ratio test (SPRT; e.g., Kings- bury & Weiss, 1983; Reckase, 1983). The SPRT is a classification method that already has been used successfully in combination with UCAT (e.g., Eggen, 1999; Eggen & Straetmans, 2000; Spray & Reckase, 1996; Thompson, 2007b).Regarding MAT, Spray, Abdel-fattah, Huang, and Lau (1997) made an attempt to modi- fy the SPRT in order to use it with MAT based on items with within-item multidimen- sionality. Items with within-item multidimensionality are allowed to measure more than one dimension simultaneously (Wang, Wilson, & Adams, 1997). Dealing with within- item multidimensionality, the multidimensional item response theory (IRT) model used with MAT is a compensatory model (e.g., Reckase, 2009). With such an IRT-model, the linear combination of the abilities measured leads to a curvilinear function. Therefore, the test statistic of the SPRT, which is a likelihood ratio test, cannot be updated by two unique values required by the SPRT. For details, see Spray et al. (1997). Considering multidimensional pass-fail tests, Spray and colleagues did not find a satisfactory solution for implementing a multidimensional SPRT into such a MAT.Nevertheless, from a practical point of view, tests entailing items measuring exactly one dimension each (between-item multidimensionality) are much more common than tests based on an item pool with within-item multidimensionality. Hence, the present paper focusses on the combination of MAT and SPRT for items with between-item multidi- mensionality. Note that when the MAT approach of Segall (1996) is used for items with between-item multidimensionality, information from items which measure one dimen- sion is used as information about the person's score on other dimensions. This is done by incorporating assumption about the multivariate ability distribution in terms of correla- tions between the measured dimensions. Several studies showed that using this infor- mation results in substantial increase in measurement efficiency compared to using sev- eral unidimensional adaptive tests (e. …
8 citations
12 May 2008
TL;DR: This work considers the problem of distributed detection in a large wireless sensor network and proposes an adaptive data fusion scheme, group-ordered sequential probability ratio test (GO-SPRT), which achieves significant savings in the cost of data fusion.
Abstract: We consider the problem of distributed detection in a large wireless sensor network. An adaptive data fusion scheme, group-ordered sequential probability ratio test (GO-SPRT), is proposed. This scheme groups sensors according to the informativeness of their data. Fusion center collects sensor data sequentially, starting from the most informative data and terminates the process when the target performance is reached. To analyze the average sample number, we establish the asymptotic equivalence between GO-SPRT, a multinomial experiment, and a normal experiment. Closed-form approximates are obtained. Our analysis and simulations show that, compared with fixed sample size test and traditional sequential probability ratio test (SPRT), the proposed scheme achieves significant savings in the cost of data fusion.
8 citations
8 citations
TL;DR: In this article, the robustness of the sequential probability ratio test on the mean of the negative binomial distribution to misspecification of the dispersion parameter, k, is investigated.
Abstract: The usual sequential probability ratio test on the mean of the negative binomial distribution assumes that the dispersion parameter, k, is known. This paper addresses the robustness of this test to misspecification of k. The operating characteristic surface is examined as a function of both the mean and k. By examining this function over a range of values of k, one can assess the robustness of the test with regard to improper specification of k. Both analytic and simulation results are presented. The analytic approach taken is generalized to other multiparameter distributions. This problem is motivated by the sampling of insect pests to determine whether their density exceeds an economic threshold.
8 citations