A Test of Independence in Two-Way Contingency Tables Based on Maximal Correlation

Maximal correlation has several desirable properties as a measure of dependence, including the fact that it vanishes if and only if the variables are independent. Except for a few special cases, it is hard to evaluate maximal correlation explicitly. We focus on two-dimensional contingency tables and discuss a procedure for estimating maximal correlation, which we use for constructing a test of independence. We compare the maximal correlation test with other tests of independence by Monte Carlo simulations. When the underlying continuous variables are dependent but uncorrelated, we point out some cases for which the new test is more powerful.     

Predictive control of posterior robustness for sample size choice in a Bernoulli model

In this article we consider the sample size determination problem in the context of robust Bayesian parameter estimation of the Bernoulli model. Following a robust approach, we consider classes of conjugate Beta prior distributions for the unknown parameter. We assume that inference is robust if posterior quantities of interest (such as point estimates and limits of credible intervals) do not change too much as the prior varies in the selected classes of priors. For the sample size problem, we consider criteria based on predictive distributions of lower bound, upper bound and range of the posterior quantity of interest. The sample size is selected so that, before observing the data, one is confident to observe a small value for the posterior range and, depending on design goals, a large (small) value of the lower (upper) bound of the quantity of interest. We also discuss relationships with and comparison to non robust and non informative Bayesian methods.     

A BAYESIAN METHOD FOR THE CHOICE OF THE SAMPLE SIZE IN EQUIVALENCE TRIALS

In this paper we consider a Bayesian predictive approach to sample size determination in equivalence trials. Equivalence experiments are conducted to show that the unknown difference between two parameters is small. For instance, in clinical practice this kind of experiment aims to determine whether the effects of two medical interventions are therapeutically similar. We declare an experiment successful if an interval estimate of the effects‐difference is included in a set of values of the parameter of interest indicating a negligible difference between treatment effects (equivalence interval). We derive two alternative criteria for the selection of the optimal sample size, one based on the predictive expectation of the interval limits and the other based on the predictive probability that these limits fall in the equivalence interval. Moreover, for both criteria we derive a robust version with respect to the choice of the prior distribution. Numerical results are provided and an application is illustrated when the normal model with conjugate prior distributions is assumed.     

On the predictive performance of a non-optimal action in hypothesis testing

Statistical Methods & Applications - In Bayesian decision theory, the performance of an action is measured by its posterior expected loss. In some cases it may be convenient/necessary to use a...     

Job Satisfaction: A Study of Sydney Adults

About one quarter of the 20,434 men and about one fifth of the 17,211 women who had a Medicheck screening expressed dissatisfaction with their job. Single men and single women were the least satisfied. The most positive aspects of work for men and women were that the job was interesting and that there was independence and freedom. Boredom, as well as not using one's potential, discriminated clearly between those satisfied with their job and those not, for both men and women. Job dissatisfaction was closely associated with other psychosocial problems and in particular with life dissatisfaction.     

The Contribution of Practice Skills in a Care Management Process for Family Caregivers

Practice skills are believed to improve practice, yet, little is known about the extent to which skills affect outcomes. This exploratory study examined the extent to which 3 practice skills specific to a care management context for family caregivers, including communication skills, supportive skills, and linking skills, were associated with fidelity of a care management process. Twenty-one care managers who used a single process to serve 113 family caregivers were included in the study. Bivariate correlation analysis revealed the 3 practice skills are positively associated with process fidelity. Implications for social work practice, education, and research are discussed.     

Robust Bayesian sample size determination for avoiding the range of equivalence in clinical trials

This article considers sample size determination methods based on Bayesian credible intervals for θ$\theta$, an unknown real-valued parameter of interest. We consider clinical trials and assume that θ$\theta$ represents the difference in the effects of a new and a standard therapy. In this context, it is typical to identify an interval of parameter values that imply equivalence of the two treatments (range of equivalence). Then, an experiment designed to show superiority of the new treatment is successful if it yields evidence that θ$\theta$ is sufficiently large, i.e. if an interval estimate of θ$\theta$ lies entirely above the superior limit of the range of equivalence. Following a robust Bayesian approach, we model uncertainty on prior specification with a class Γ$\Gamma$ of distributions for θ$\theta$ and we assume that the data yield robust evidence   if, as the prior varies in Γ$\Gamma$, the lower bound of the credible set inferior limit is sufficiently large. Sample size criteria in the article consist in selecting the minimal number of observations such that the experiment is likely to yield robust evidence. These criteria are based on summaries of the predictive distributions of lower bounds of the random inferior limits of credible intervals. The method is developed for the conjugate normal model and applied to a trial for surgery of gastric cancer.