BACKGROUND AND AIMS It has been proposed that more use should be made of Bayes factors in hypothesis testing in addiction research. Bayes factors are the ratios of the likelihood of a specified hypothesis (e.g. an intervention effect within a given range) to another hypothesis (e.g. no effect). They are particularly important for differentiating lack of strong evidence for an effect and evidenc...

1. Decide on a claim and an alternative claim. (Null hypothesis must have an “equal” in it. Alternative hypothesis usually has the claim that will cause you to “spend money” or “change something” if you decide that it is true.) 2. Choose a test statistic to summarize the data, whose sampling distribution if the null hypothesis is true can be determined, and which depends on the parameter of int...

We study a variant of quantum hypothesis testing wherein an additional ‘inconclusive’ measurement outcome is added, allowing one to abstain from attempting discriminate the hypotheses. The error probabilities are then conditioned on successful attempt, with inconclusive trials disregarded. completely characterise this task in both single-shot and asymptotic regimes, providing exact formulas for...

Process capability indices are considered as an important concept in statistical quality control. They have been widely used in the manufacturing industry to provide numerical measures on process performance. Moreover, some incapability indices have been introduced to account the process performance. In this paper, we focus on the one proposed by Chen ~cite{Che:Stat}. In today's modern world, a...