| Summary: | 博士 === 國立交通大學 === 統計學研究所 === 95 === The significance test is a method for measuring statistical evidence against null hypothesis H0 by computing p-value. The classical significance test chooses a test statistic T = t(X) and determines the extreme set representing the sample set with values t(x) greater than or equal to t(x0), where x0 is the observed sample. It may be difficult to choose a suitable test statistic for the test, or there is no generally accepted optimal theory to support the existed significance tests. Now, we propose a new significance test, called the highest density significance (HDS) test, setting extreme set including those sample points with probabilities less than or equal to it of x0. It applies the concept that the smaller probability of an observation X = x0 reveals stronger evidence of departure from H0. This test virtually classifies the sample space of random sample X into extreme set and the non-extreme set through a concept of probability ratio. We also show that this test shares an optimal property for that it has smallest volume among the class of non-extreme sets of significance tests with the same p-value. Further, we extend HDS test to set up a control chart which can monitor all the parameters simultaneously and the probability of type I error is precisely attained. Unlike the classical control charts that track statistics such as sample mean or sample range R, it is tracking the density value of the sample point to classify if it is in control.
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