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Acceptance regions for the modified Duncan's test.  

Acceptance regions for the modified Duncan's test.  

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Summary Notes for a course on Statistics for Search Marketing presented in 2007

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... It is important to underline that the two-stage test accepts one of nine hypotheses, so it is possible to arrive at a decision about the modification of the means or probabilities. It is also worth remarking that the computation is simple because the critical values needed in the two stages of the procedure are reported in Pollastri (2008) and in Pollastri and Riva (2012). This paper is organised as follows. ...
... Stage 1: for a fixed probability of type I errorα, using the estimate of ρ, the critical values h(α, |ρ|) and k(α, |ρ|) can be calculated through the tables provided in Pollastri and Riva (2012). Then: ...
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The subject of this paperis a two-stage hypothesis test, which may have interesting applications in several situations related to the opinion research field. Such test is based on the components of a Bivariate Correlated Normal random variable. In particular, it is based on the exact distribution of their minimum and maximum modulus. This test was proposed for the first time by Duncan in Miller (1981), and was recently improved by Pollastri (2008). In the latter paper a variant of such test is described, since two samples in two different times or situations are considered. Two kinds of applications are provided to show the wide range of usage.