A Five-Decision Testing Procedure to Infer the Value of a Unidimensional Parameter

ABSTRACT

A statistical test can be seen as a procedure to produce a decision based on observed data, where some decisions consist of rejecting a hypothesis (yielding a significant result) and some do not, and where one controls the probability to make a wrong rejection at some prespecified significance level. Whereas traditional hypothesis testing involves only two possible decisions (to reject or not a null hypothesis), Kaiser’s directional two-sided test as well as the more recently introduced testing procedure of Jones and Tukey, each equivalent to running two one-sided tests, involve three possible decisions to infer the value of a unidimensional parameter. The latter procedure assumes that a point null hypothesis is impossible (e.g., that two treatments cannot have exactly the same effect), allowing a gain of statistical power. There are, however, situations where a point hypothesis is indeed plausible, for example, when considering hypotheses derived from Einstein’s theories. In this article, we introduce a five-decision rule testing procedure, equivalent to running a traditional two-sided test in addition to two one-sided tests, which combines the advantages of the testing procedures of Kaiser (no assumption on a point hypothesis being impossible) and Jones and Tukey (higher power), allowing for a nonnegligible (typically 20%) reduction of the sample size needed to reach a given statistical power to get a significant result, compared to the traditional approach.     

空气雾化钻井试验架研制剖析

解决空气雾化钻井井眼净化问题,试验架是关键装置、基础设备和必要手段。对空气雾化钻井试验架的研制过程进行了深入剖析,介绍了在试验架研制中应遵循的一些基本原则,试验架基本结构,试验架主要参数,试验结果可靠性分析,试验研究进行情况,以及研制过程中的经验教训等内容,体现了空气雾化钻井试验架研制工作的特点与特色。     

Optimal financing and dividend policy with Markovian switching regimes

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Testing equality of variances for several normal populations

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A new confidence interval in errors-in-variables model with known error variance

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