In this paper, we develop Bayes factor based testing procedures for the presence of a correlation or a partial correlation. The proposed Bayesian tests are obtained by restricting the class of the alternative hypotheses to maximize the probability of rejecting the null hypothesis when the Bayes factor is larger than a specified threshold. It turns out that they depend simply on the frequentist t-statistics with the associated critical values and can thus be easily calculated by using a spreadsheet in Excel and in fact by just adding one more step after one has performed the frequentist correlation tests. In addition, they are able to yield an identical decision with the frequentist paradigm, provided that the evidence threshold of the Bayesian tests is determined by the significance level of the frequentist paradigm. We illustrate the performance of the proposed procedures through simulated and real-data examples. 相似文献
As China’s economy is rapidly changing from a planned to a capitalist economy, many families find themselves financially struggling. In some cases, conflicting values and attitudes may contribute to mental health challenges such as depression that would lead to further feelings of helplessness and immobilization. Using a random sample of 1006 low-income households from Pudong District of Shanghai, China, this study aims to examine the relationships between household assets, beliefs about government as the primary way to improve economic circumstances and self-reported depressive symptoms. In addition, this study investigates the mediation effects of beliefs that government is the best change agent for improved life circumstances on the relationship between household assets and depression. We found those who indicated that government was the main means for attaining a better life had significantly higher depression levels whereas higher numbers of household assets were associated with lower depression levels. We also found that viewing government as the most important change agent only partially mediated the relationship between household assets and depression (p?<?.001). Findings from this study support anti-poverty policies and social work related practice initiatives aimed at assisting low income families in China, in particular the need to address psychological as well as economic needs.