The performance of tests when observations have different variances

It is common to test if there is an effect due to a treatment. The commonly used tests have the assumption that the observations differ in location, and that their variances are the same over the groups. Different variances can arise if the observations being analyzed are means of different numbers of observations on individuals or slopes of growth curves with missing data. This study is concerned with cases in which the unequal variances are known, or known to a constant of proportionality. It examines the performance of the ttest, the Mann–Whitney–Wilcoxon Rank Sum test, the Median test, and the Van der Waerden test under these conditions. The t-test based on the weighted means is the likelihood ratio test under normality and has the usual optimality properties. The other tests are compared to it. One may align and scale the observations by subtracting the mean and dividing by the standard deviation of each point. This leads to other, analogous test statistics based on these adjusted observations. These statistics are also compared. Finally, the regression scores tests are compared to the other procedures.     

A note on millers's empirical weights for heteroscedastic linear regression

For heteroscedastic simple linear regression when the variances are proportional to a power of the mean of the response variable, Miller (1986) recommends the following procedure: do a weighted least squares regression with the weights (empirical weights) estimated by the inverse of the appropriate power of the response variable. The practical appeal of this approach is its simplicity.

In this article some of the consequences of this simple procedure are considered. Specifically, the effect of this procedure on the bias of the point estimators of the regression coefficients and on the coverage probabilities of their corresponding confidence intervals is examined. It is found that the performance of the process of employing empirical weights in a weighted least squares regression depends on : (1) the particular regression parameter (slope or intercept) of interest, (2) the appropriate power of the mean of the response variable involved, and (3) the amount of variation in the data about the true regression line.     

A Variance Estimator for Systematic Sampling from a Deliberately Ordered Population

ABSTRACT

The systematic sampling (SYS) design (Madow and Madow, 1944 Madow , L. H. , Madow , W. G. ( 1944 ). On the theory of systematic sampling . Ann. Math. Statist. 15 : 1 – 24 .[Crossref] , [Google Scholar]) is widely used by statistical offices due to its simplicity and efficiency (e.g., Iachan, 1982 Iachan , R. ( 1982 ). Systematic sampling a critical review . Int. Statist. Rev. 50 : 293 – 303 .[Crossref], [Web of Science ®] , [Google Scholar]). But it suffers from a serious defect, namely, that it is impossible to unbiasedly estimate the sampling variance (Iachan, 1982 Iachan , R. ( 1982 ). Systematic sampling a critical review . Int. Statist. Rev. 50 : 293 – 303 .[Crossref], [Web of Science ®] , [Google Scholar]) and usual variance estimators (Yates and Grundy, 1953 Yates , F. , Grundy , P. M. ( 1953 ). Selection without replacement from within strata with probability proportional to size . J. Roy. Statist. Soc. Series B 1 : 253 – 261 . [Google Scholar]) are inadequate and can overestimate the variance significantly (Särndal et al., 1992 Särndal , C. E. , Swenson , B. , Wretman , J. H. ( 1992 ). Model Assisted Survey Sampling . New York : Springer-Verlag , Ch. 3 .[Crossref] , [Google Scholar]). We propose a novel variance estimator which is less biased and that can be implemented with any given population order. We will justify this estimator theoretically and with a Monte Carlo simulation study.     

城镇家庭住房困难影响因素研究——基于广东省调查数据的发现

利用2010年广东家庭追踪调查城镇部分数据,研究转型期城镇家庭住房困难状况,结果发现：城镇家庭收入与住房困难成“倒U”关系,其他因素如家庭规模、户籍分割及高房价背景均与住房困难存在明显关系,但住户特征与住房困难的关系较弱。显然,理解转型期城市住房困难现象不能仅从市场的收入逻辑进行解释,住房市场嵌入在各种制度因素之中,旧的分配制度与新的市场因素均会左右城镇家庭的住房状况,住房困难是家庭特征、市场环境及国家力量共同作用的结果。     

从认知社会语言学的世界英语变体研究看中国英语研究

认知社会语言学从文化认知和社会语言系统的浮现性、动态性和开放性提出认知和语言是复合适应系统,并通过世界英语变体在特定社会文化语境下的语义变异及其背后的的文化认知理据论证了英语变体对特定文化认知的适应性和创新性。世界英语变体的认知社会语言学视角和方法对推进和深化我国目前的中国英语研究具有重要的启示,对中国英语研究、世界英语变体研究乃至英语全球化的认识都有重要的意义。     

Simultaneous Confidence Intervals for Monotone Contrasts of Normal Means

The one-way ANOVA model is considered. The variances are assumed to be either equal but unknown or unequal and unknown. Two-stage procedures for generating simultaneous confidence intervals (SCI) for the class of monotone contrasts of the means are presented. The intervals are of fixed length and independent of the unknown variances.     

基于世界英语框架下的大学英语教学

世界英语、国际英语的出现与发展,给英语教学带来了新的任务与课题。在英语全球化的冲击下,人们该如何定义\"标准英语\"?传统意义上的\"标准英语\"是否还是现阶段英语教学的唯一标准?通过介绍英语全球化与本土化背景下的英语发展与现状,分析了世界英语理论给我国大学英语教学的启示:标准英语虽然是基本的英语教学标准,但现阶段的大学英语教学必须让教师和学生树立起世界英语与英语全球化的意识,从而培养学生更广泛地使用英语进行语言文化交流的能力。     

Global Englishes, Rip Slyme, and performativity

In this article I suggest that while recent sociolinguistic work focusing on crossing, styling the Other or language boundaries is raising significant questions concerning how we relate language, identity and popular culture, these insights have largely passed by the sociolinguistics of world Englishes. This latter work is still caught between arguments about homogeneity and heterogeneity, between arguments based on liberal accommodationism, linguistic imperialism or linguistic hybridity that do not allow for sufficiently complex understandings of what is currently happening with global Englishes. Focusing particularly on rap music, I suggest that we need, at the very least, a critical understanding of globalization, a focus on popular cultural flows, and a way of taking up performance and performativity in relationship to identity and culture.