Four Correlation Coefficients with a Third Blocking Variable: Their Efficacy,Relative Efficiency,and Test Statistics

Abstract

The efficacy and the asymptotic relative efficiency (ARE) of a weighted sum of Kendall's taus, a weighted sum of Spearman's rhos, a weighted sum of Pearson's r's, and a weighted sum of z-transformation of the Fisher–Yates correlation coefficients, in the presence of a blocking variable, are discussed. The method of selecting the weighting constants that maximize the efficacy of these four correlation coefficients is proposed. The estimate, test statistics and confidence interval of the four correlation coefficients with weights are also developed. To compare the small-sample properties of the four tests, a simulation study is performed. The theoretical and simulated results all prefer the weighted sum of the Pearson correlation coefficients with the optimal weights, as well as the weighted sum of z-transformation of the Fisher–Yates correlation coefficients with the optimal weights.     

Planning for the 1950 Censuses of Population and Agriculture

The change from the z of “Student's” 1908 paper to the t of present day statistical theory and practice is traced and documented. It is shown that the change was brought about by the extension of “Student's” approach, by R.A. Fisher, to a broader class of problems, in response to a direct appeal from “Student” for a solution to one of these problems.     

Large Differences between Partial Correlation Coefficients

A plot of each ranking of N objects in N-dimensional space is shown to provide geometric interpretations of Kendall's tau and Spearman's rho and also of the relationship of rho to a sum of inversion weights. The computation of rho from a sum of inversion weights is shown to allow sequential calculation of rho.     

Determining the effects of intraclass correlation on factorial experiments

This paper considers the effects of the presence of eqmi-correlation between observations in a k-way factorial experiment, A technique to provide unbiased F-tests is also constructed.     

A stochastic version of the malthusian trap model: Consequences for the empirical relationship between economic growth and population growth in LDC's

A stochastic version of the Malthusian trap model relating the growth rate of income per capita to the population growth rate of a given country is described. This model is applied to the a priori evaluation of the cross‐sectional correlation between these two growth rates under two additional assumptions: i) the relations in the model at national levels include country‐specific and time‐invariant random components, and ii) these growth rates are measured with a certain degree of temporal aggregation. It is shown that these two assumptions can explain near‐zero correlations between the two growth rates even if there exist a strongly negative effect of population growth on economic growth. However it is not clear whether these assumptions fully explain such insignificant correlations. Indeed, the implementation of the model is complicated by the structural shifts which are likely to occur in the equations over the course of the demographic transition.     

阅读理解测试的变量研究

本文通过对实验素材和结果的定量分析 ,探讨了可读性、题材、测试题型 (自变量 )与测试结果 (因变量 )之间的相关关系。证明了 :1.不同的题材具有不同的区分能力 ;2 .不同的题型是造成分数差异的主要因素。指出 :在被试的能力范围内 ,可读性对测试结果的影响 ,并不如国外 36项研究所表明的那么明显。含多种题材和题型的阅读理解测试 ,更能有效地反映被试在阅读理解过程中各个层次的能力。     

体育产业关联效应的实证分析--以六省、市(区)为例

体育产业化发展已成为当今体育发展的一个必然趋势.我国体育产业伴随着经济的持续增长以及居民消费水平的提高和消费结构的变化,已进入快速发展的阶段,这是产业演进规律的必然结果.体育作为一个产业正在成为我国新的经济增长点.通过对体育产业关联效应的分析,对于促进体育产业及其相关产业的快速、健康发展,推动经济增长具有重要的理论和现实意义.     

Data depth and correlation

Summary: We describe depth–based graphical displays that show the interdependence of multivariate distributions. The plots involve one–dimensional curves or bivariate scatterplots, so they are easier to interpret than correlation matrices. The correlation curve, modelled on the scale curve of Liu et al. (1999), compares the volume of the observed central regions with the volume under independence. The correlation DD–plot is the scatterplot of depth values under a reference distribution against depth values under independence. The area of the plot gives a measure of distance from independence. Correlation curve and DD-plot require an independence model as a baseline: Besides classical parametric specifications, a nonparametric estimator, derived from the randomization principle, is used. Combining data depth and the notion of quadrant dependence, quadrant correlation trajectories are obtained which allow simultaneous representation of subsets of variables. The properties of the plots for the multivariate normal distribution are investigated. Some real data examples are illustrated. *This work was completed with the support of Ca Foscari University.     

Small area estimation for longitudinal surveys

Over the last few years many studies have been carried out in Italy to identify reliable small area labour force indicators. Considering the rotated sample design of the Italian Labour Force Survey, the aim of this work is to derive a small area estimator which borrows strength from individual temporal correlation, as well as from related areas. Two small area estimators are derived as extensions of an estimation strategies proposed by Fuller (1990) for partial overlap samples. A simulation study is carried out to evaluate the gain in efficiency provided by our solutions. Results obtained for different levels of autocorrelation between repeated measurements on the same outcome and different population settings show that these estimators are always more reliable than the traditional composite one, and in some circumstances they are extremely advantageous.The present paper is financially supported by Murst-Cofin (2001) Lutilizzo di informazioni di tipo amministrativo nella stima per piccole aree e per sottoinsiemi della popolazione (National Coordinator Prof. Carlo Filippucci).     

论儒道思想对王羲之书法美学思想及书法的影响

中国文化的核心是"儒道"互补.儒家推崇"中和"之美,道家向往"自然"之趣.王羲之的书法美学思想是儒道并蓄,因而使他的书法艺术兼具中和、自然之美.