Simultaneous Confidence Intervals for the Population Cell Means,for Two-by-Two Factorial Data,that Utilize Uncertain Prior Information

Consider a two-by-two factorial experiment with more than one replicate. Suppose that we have uncertain prior information that the two-factor interaction is zero. We describe new simultaneous frequentist confidence intervals for the four population cell means, with simultaneous confidence coefficient 1 ? α, that utilize this prior information in the following sense. These simultaneous confidence intervals define a cube with expected volume that (a) is relatively small when the two-factor interaction is zero and (b) has maximum value that is not too large. Also, these intervals coincide with the standard simultaneous confidence intervals obtained by Tukey’s method, with simultaneous confidence coefficient 1 ? α, when the data strongly contradict the prior information that the two-factor interaction is zero. We illustrate the application of these new simultaneous confidence intervals to a real data set.     

‘I'm not a family therapist. OK?’ Working Constructively with Families in Aged Psychiatry

This paper reports on the first phase of a larger study aimed at investigating factors hindering family work and exploring ways to improve the amount and quality of family contact within a community aged mental health service in Melbourne, Australia. During the first phase of the project, 28 mental health professionals were interviewed about their views and experiences. Interviews were transcribed, coded, and analysed in terms of repeating themes. The range of attitudes, beliefs and feelings about family work is summarised in this paper. Polarities emerged around questions of whether or not to engage family members, and if so, what function family work fulfils. The interviews also provided useful information on clinicians' beliefs about what would increase the possibility of family work. The paper concludes with a discussion about how to recognize and value family work in this area and target sustainable interventions during the second phase of the study.     

Optimal inventory cycle counting

The heart of inventory transactions management involves obtaining an accurate count of on-hand inventories employing different procedures. Among such procedures cycle counting is said to provide better inventory record accuracy for financial control and production planning. However, these procedures use rather arbitrary basis for classifying items and for setting the count frequency within each strata. This paper develops a simple optimization model of inventory cycle counting based on traditional stratified sampling theory. Such a model allows the inventory manager to make statistically supported statements regarding inventory record accuracy so as to meet financial control requirements with a minimum of cycle counting effort. A numerical example is included to illustrate the model.     

THE COVERAGE PROBABILITY OF CONFIDENCE INTERVALS IN 2r FACTORIAL EXPERIMENTS AFTER PRELIMINARY HYPOTHESIS TESTING

We consider a 2^r factorial experiment with at least two replicates. Our aim is to find a confidence interval for θ, a specified linear combination of the regression parameters (for the model written as a regression, with factor levels coded as ?1 and 1). We suppose that preliminary hypothesis tests are carried out sequentially, beginning with the rth‐order interaction. After these preliminary hypothesis tests, a confidence interval for θ with nominal coverage 1 ?α is constructed under the assumption that the selected model had been given to us a priori. We describe a new efficient Monte Carlo method, which employs conditioning for variance reduction, for estimating the minimum coverage probability of the resulting confidence interval. The application of this method is demonstrated in the context of a 2³ factorial experiment with two replicates and a particular contrast θ of interest. The preliminary hypothesis tests consist of the following two‐step procedure. We first test the null hypothesis that the third‐order interaction is zero against the alternative hypothesis that it is non‐zero. If this null hypothesis is accepted, we assume that this interaction is zero and proceed to the second step; otherwise, we stop. In the second step, for each of the second‐order interactions we test the null hypothesis that the interaction is zero against the alternative hypothesis that it is non‐zero. If this null hypothesis is accepted, we assume that this interaction is zero. The resulting confidence interval, with nominal coverage probability 0.95, has a minimum coverage probability that is, to a good approximation, 0.464. This shows that this confidence interval is completely inadequate.     

Optimum invariant tests on discriminant coefficients or means of multinormal population with additional information

Some optimum invariant tests are derived for certain hypotheses on discriminant coefficients or means when some extra observations are available on some components of a random vector X, which is distributed as N(μ,Σ), where μ and Σ are unknown.     

Improved estimation of variance components in balanced hierarchical mixed models

The problem of simultaneous estimation of variance components is considered for a balanced hierarchical mixed model under a sum of squared error loss. A new class of estimators is suggested which dominate the usual sensible estimators. These estimators shrink towards the geometric mean of the component mean squares that appear in the ANOVA table. Numerical results are tabled to exhibit the improvement in risk under a simple model.