Improved tests for homogeneity of variances

Equality of variances is one of the key assumptions of analysis of variances (ANOVA). There are several testing procedures available to validate this assumption, but it is rare to find a test procedure which controls the type I error rate while providing high statistical power. In this article, we introduce a bootstrap test based on the ratio of mean absolute deviances (RMD). We also propose a two-stage testing procedure where we first quantify the skewness of the distributions and then choose an appropriate test for homogeneity of variances. The performances of these test procedures are studied via a simulation study.     

“单子”哲学的数学基础初探

莱布尼茨是个毕达哥拉斯主义者,同时在数学方面又有杰出成就,故而数学对其形而上学影响很大。单子哲学体系三个主要构成部分——单子论、连续律、前定和谐律,都有一定数学基础。通过数学,尤其是莱布尼茨本人的数学成就,能更好地理解单子理论。     

Implementing midwifery continuity of care models in regional Australia: A constructivist grounded theory study

Problem/backgroundStrong international evidence demonstrates significantly improved outcomes for women and their babies when supported by midwifery continuity of care models. Despite this, widespread implementation has not been achieved, especially in regional settings.AimTo develop a theoretical understanding of the factors that facilitate or inhibit the implementation of midwifery continuity models within regional settings.MethodsA Constructivist Grounded Theory approach was used to collect and analyse data from 34 interviews with regional public hospital key informants.ResultsThree concepts of theory emerged: ‘engaging the gatekeepers’, ‘midwives lacking confidence’ and ‘women rallying together’. The concepts of theory and sub-categories generated a substantive theory: A partnership between midwives and women is required to build confidence and enable the promotion of current evidence; this is essential for engaging key hospital stakeholders to invest in the implementation of midwifery continuity of care models.DiscussionThe findings from this research suggest that midwives and women can significantly influence the implementation of midwifery continuity models within their local maternity services, particularly in regional settings. Midwives’ reluctance to transition is based on a lack of confidence and knowledge of what it is really like to work in midwifery continuity models. Similarly, women require education to increase awareness of continuity of care benefits, and a partnership between women and midwives can be a strong political force to overcome many of the barriers.ConclusionImplementation of midwifery continuity of care needs a coordinated ground up approach in which midwives partner with women and promote widespread dissemination of evidence for this model, directed towards consumers, midwives, and hospital management to increase awareness of the benefits.     

邓小平政策观中之“不变”与“变”的思想

邓小平关于“不变”与“变”问题的论述表达了其政策观中一个重要思想 ,本文以系统地评述邓小平这一思想为目的 ,较为详尽地揭示了“不变”与“变”各自的深刻内涵和实质 ,着重分析了坚持现行政策“不变”的意义、作用和保障条件 ,并从哲学的角度论述了“不变”与“变”之间的辩证统一关系 ,以及邓小平这一思想在建设有中国特色社会主义事业中的重要作用     

从贫穷到富裕:中国共产党消除绝对贫困百年辉煌实践

中国共产党的百年奋斗史,就是一部消灭贫困的斗争史。建党100年以来,中国共产党把保障基本人权、促进人的全面发展和实现共同富裕作为反贫困的终极目标,从新民主主义革命时期的“革命凝聚型扶贫”到社会主义革命与建设时期的“恢复生产保障生存救济式扶贫”,从改革开放和社会主义现代化建设新时期的“有计划有组织大规模的区域扶贫综合开发”到党的十八大以来中国特色社会主义新时代的“精准扶贫”“脱贫攻坚”,中国已实现从普遍贫困到基本温饱到全面小康的历史性跨越。建党100年以来,在革命、建设、改革时期都始终坚持中国共产党的领导,不断发挥中国特色社会主义制度优势,着力推动反贫困制度体系创新,走中国特色减贫道路。中国减贫事业取得了伟大的历史性成就,困扰中华民族千百年来的绝对贫困问题得到了历史性解决,积累了丰富的中国经验,改变了世界贫困版图,为全球减贫事业作出卓越贡献。站在新的起点,要不断贯彻“三新”理念,持续巩固拓展脱贫攻坚成果,全面推动党中央重大决策乡村振兴战略落地落实;健全农村低收入人口常态化帮扶机制,加快补短板、强弱项,不断缩小差距、维护公平,使全体人民朝着共同富裕目标扎实迈进。     

美学再思考

审美根本不是自治的,它连接着更大的社会基座。我们需要一种情境性与连续性美学,这是一种描述性的而非规定性的理论,它认识到并拓展了与审美经验的联系,而且呼唤我们作为一个积极的参与者全身心的介入。     

LOCATION OF PARTICULAR POINTS IN NON-PARAMETRIC REGRESSION ANALYSIS

In the random-design non-parametric regression model, the locations of particular values of the regression function or its derivatives are estimated. This paper investigates several stochastic modes of convergence and finds their rate of convergence under regularity assumptions, for a wide class of non-parametric estimators. The approach finds two natural fields of application: estimation of zeros/extrema and non-parametric absolute calibration.     

Optimal correction for continuity in the chi-squared test in 2×2 tables

The most common asymptotic procedure for analyzing a 2 × 2 table (under the conditioning principle) is the ‰ chi-squared test with correction for continuity (c.f.c). According to the way this is applied, up to the present four methods have been obtained: one for one-tailed tests (Yates') and three for two-tailed tests (those of Mantel, Conover and Haber). In this paper two further methods are defined (one for each case), the 6 resulting methods are grouped in families, their individual behaviour studied and the optimal is selected. The conclusions are established on the assumption that the method studied is applied indiscriminately (without being subjected to validity conditions), and taking a basis of 400,000 tables (with the values of sample size n between 20 and 300 and exact P-values between 1% and 10%) and a criterion of evaluation based on the percentage of times in which the approximate P-value differs from the exact (Fisher's exact test) by an excessive amount. The optimal c.f.c. depends on n, on E (the minimum quantity expected) and on the error α to be used, but the rule of selection is not complicated and the new methods proposed are frequently selected. In the paper we also study what occurs when E ≥ 5, as well as whether the chi-squared by factor (n-1).     

A confidence interval for the scale parameter based on sukhtmes two-sample statistic

Sukhatme (1957) introduced a statistic which may be used to test the equality of variances in two independent samples from continuous distributions, centered at zero. It has become evident that this statistic cound be used to construct, analytically, a confidence interval for the scale parameter relating the two random variables(of.Laubscher (1968) and Noether (1967, pp. 66-69 and 1972)). In view of this additional use of the statistic, and since no tables of critical values exist, we provide such a table which makes the application of the statistic a practical proposition. In addition, a normal approximation is suggested for the use outside the range of Table III and the accuracy of this approximation is investigated. The Sukhatme test applied to sample values reduced by t n e i r medians i s studied in a small simulation exercise. It appears that this test when used in conjunction with the critical values of Sukhatme's statistic, is a very conservative one and that it is probably fairly robust with respect to the underlying population distribution.     

The Double Gaussian Approximation for High Frequency Data

Abstract High frequency data have become an important feature of many areas of research. They permit the creation of estimators in highly non‐parametric classes of continuous‐time models. In the context of continuous semi‐martingale models, we here provide a locally parametric ‘double Gaussian’ approximation, to facilitate the analysis of estimators. As in Mykland and Zhang (Econometrica, 77, 2009, p. 1403), the error in the approximation can be offset with a postasymptotic likelihood correction. The current approximation is valid in large neighbourhoods, permitting a sharp analysis of estimators that use local behaviour over asymptotically increasing numbers of observations.