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The sequential analysis of series often requires nonparametric procedures, where the most powerful ones frequently use rank transformations. Reranking the data sequence after each new observation can become too intensive computationally. This led to the idea of sequential ranks, where only the most recent observation is ranked. However, difficulties finding, or approximating, the null distribution of the statistics may have contributed to the lack of popularity of these methods. In this article, we propose transforming the sequential ranks into sequential normal scores that are independent and asymptotically standard normal random variables. Thus, original methods based on the normality assumption may be used. A novel approach permits the inclusion of a priori information in the form of quantiles. It is developed as a strategy to increase the sensitivity of the scoring statistic. The result is a powerful convenient method to analyze non normal data sequences. Also, four variations of sequential normal scores are presented using examples from the literature. Researchers and practitioners might find this approach useful to develop nonparametric procedures to address new problems extending the use of parametric procedures when distributional assumptions are not met. These methods are especially useful with large data streams where efficient computational methods are required. [ABSTRACT FROM PUBLISHER]

Sequential ranks are defined as ranks of such observations, which have been observed so far in a sequential design. This article studies hypotheses tests based on sequential ranks for different situations. The locally most powerful sequential rank test is derived for the hypothesis of randomness against a general alternative, including the two-sample difference in location or regression in location as special cases for the alternative hypothesis. Further, the locally most powerful sequential rank tests are derived for the one-sample problem and for independence of two samples in an analogous spirit as the classical results of Hájek and Šidák (1967) for (classical) ranks. The locally most powerful tests are derived for a fixed sample size and the results bring arguments in favor of existing tests. In addition, we propose a sequential testing procedure based on these statistics of the locally most powerful tests. Principles of such sequential testing are explained on the two-sample Wilcoxon test based on sequential ranks. [ABSTRACT FROM PUBLISHER]