New monte carlo results on the robustness of the anova f,w and f statistics

Because the usual F test for equal means is not robust to unequal variances, Brown and Forsythe (1974a) suggest replacing F with the statistics F or W which are based on the Satterthwaite and Welch adjusted degrees of freedom procedures. This paper reports practical situations where both F and W give * unsatisfactory results. In particular, both F and W may not provide adequate control over Type I errors. Moreover, for equal variances, but unequal sample sizes, W should be avoided in favor of F (or F ), but for equal sample sizes, and possibly unequal variances, W was the only satisfactory statistic. New results on power are included as well. The paper also considers the effect of using F or W only after a significant test for equal variances has been obtained, and new results on the robustness of the F test are described. It is found that even for equal sample sizes as large as 50 per treatment group, there are practical situations where the F test does not provide adequately control over the probability of a Type I error.     

OPTIMAL DESIGN FOR EARLY‐GENERATION PLANT‐BREEDING TRIALS WITH UNREPLICATED OR PARTIALLY REPLICATED TEST LINES

Some subtle difficulties in optimal design are highlighted by the example of unreplicated field trials laid out on plots with spatial errors defined by uniformity trials. There is a dual problem of the arrangement of control plots and maximizing the number of test‐line entries. A simulation study is conducted by randomizing the allocation of genotypes to the plots of four uniformity trials in accordance with the rules defining a number of competing designs. Results are summarized in terms of the ‘SE ratio’, which reflects the improvement in precision of a given design relative to a completely random design on the same plots. The definition of the SE ratio overcomes problems induced by differential shrinkage and consequent precision of test and control lines. A general result applying to all designs shows a curvilinear improvement in SE ratio with increasing error degrees of freedom of the design. The actual arrangement of check plots is of less importance than their increasing number, which contributes to increasing error degrees of freedom. Overall measures, including expected genetic gain, are used to illustrate the choice of a balance between the total number of test‐line entries and the error degrees of freedom.     

Secondary design considerations for minimum bias estimation

Several authors have suggested the method of minimum bias estimation for estimating response surfaces. The minimum bias estimation procedure achieves minimum average squared bias of the fitted model without depending on the values of the unknown parameters of the true surface. The only requirement is that the design satisfies a simple estimability condition. Subject to providing minimum average squared bias, the minimum bias estimator also provides minimum average variance of ?(x) where ?(x) is the estimate of the response at the point x.

To support the estimation of the parameters in the fitted model, very little has been suggested in the way of experimental designs except to say that a full rank matrix X of independent variables should be used. This paper presents a closer look at the estimability conditions that are required for minimum bias estimation, and from the form of the matrix X, a formula is derived which measures the amount of design flexibility available. The design flexibility is termed “the degrees of freedom” of the X matrix and it is shown how the degrees of freedom can be used to decide if other design optimality criteria might be considered along with minimum bias estimation. Several examples are provided.     

The Role of Religion and Spirituality in Clinical Social Work

Abstract

Social work has a history of treating the whole person in his/her environment, however, the effort to be scientific in our approach to clinical practice often has obscured our examination of the religious and spiritual beliefs and practices of our clients and in our own lives. Consequently, there has been very little guidance to date on how curriculum can help integrate the professional identities of MSW/MDiv students. An elective practice course, “The Role of Religion and Spirituality in Clinical Social Work” in our accredited graduate social work program provides a transitional space for this integration to occur through a guiding framework of psychodynamic, systems, and postmodern theories.     

A structured overview of 50 years of small-world research

This paper offers a structured overview of 50 years of small-world research. Initially formulated by Pool and Kochen in the mid-1950s, the small-world concept can be divided into six research foci, based on three dimensions (structural, process-related, psychological), and two process-related themes (diffusion, search). Building on this analytical distinction, the article provides a historical summary of the different phases of research on the small-world problem, and summarizes the empirical and theoretical progress on different facets of the small-world phenomenon. The paper concludes with a brief assessment of accomplishments and open questions, suggesting some possible future research areas.     

The chi-square controversy: what if Pearson had R?

One of the most famous controversies in the history of Statistics regards the number of the degrees of freedom of a chi-square test. In 1900, Pearson introduced the chi-square test for goodness of fit without recognizing that the degrees of freedom depend on the number of estimated parameters under the null hypothesis. Yule tried an ‘experimental’ approach to check the results by a short series of ‘experiments’. Nowadays, an open-source language such as R gives the opportunity to empirically check the adequateness of Pearson's arguments. Pearson paid crucial attention to the relative error, which he stated ‘will, as a rule, be small’. However, this point is fallacious, as is made evident by the simulations carried out with R. The simulations concentrate on 2×2 tables where the fallacy of the argument is most evident. Moreover, this is one of the most employed cases in the research field.     

A class of statistics based on the information concept

The methodic use of Shannon's entropy as a basic concept, complementing probability, leads to a new class of statistics which provides, inter alia, a measure of mutual dissimilarity y between several frequency distributions. Application to contin-gency tables with any number of dimensions yields a dimension-less, standardised contingency coefficient which depends on the direction of inference and will combine multiplicatively with the number of observed events. This class of statistics further in-cludes a continuous modification W of the number of degrees of freedom in a table, and a measure Q of its overall information content. Numerical illustrations and comparisons with former re-sults are worked out. Direct applications include the optimal partition of a quasicontinuum into cells by maximizing Q, the ordering of unordered tables by minimising local values of y, and a tentative absolute weighting of inductive inference based on the minimal necessary shift, required by an hypothesis, between the actually observed data and a set of assumed future events.     

Efficient computation of the noncentral x2 distribution

In this article we compare and contrast finite algorithms for computing the noncentral x² distribution function for odd or even degrees of freedom with the algorithms proposed recently by Ashour & Abdel-Samad (1990). We also obtain an alternative error bound for Ruben's (1974a) algorithm for even degrees of freedom and analyze the rate of convergence of two common infinite series representations for computing the cdf     

The bias of the mle of box's degrees of freedom correction factor for correlation in anova

Approximate expressions for the mean and variance of the MLE of Box's 2-way ANOVA degrees of freedom factor are given for the case when the usual F test for column effects is appropriate even though there is correlation across columns. A simulation study is performed showing the approximations are good for a variety of numbers of rows and columns. The results confirm that the estimated degrees of freedom factor is badly biased when no factor at all should be used.     

制动蹄块加工的分析与计算

本文着重介绍了摩托车制动蹄块外圆加工的正确计算模型和加工方法,使加工出的蹄块在制动状态和轮毂完全贴合,制动效果达到并超过国标(GB5382—85)规定的要求.