对异方差的分析及补救措施

经典假设要求误差项的观测值是从具有相同方差的分布中抽取的（同方差性）,如果一个正确设定的方程的误差项违背了经典假设,就会出现异方差;如果方程存在严重的异方差,就需要对方程进行补救。     

测量误差二次多项式回归模型随机误差方差的相合估计

在实际应用中,测量误差二次多项式回归模型随机误差方差σc^2的值经常是不能确定的,这给模型进一步处理带来麻烦,我们从收集的样本（Xt,Yt）,t=1,2,…,n,定义一个函数来估计一的值,进而得到一的相合估计值。     

Examining the Precision of Cut Scores Within a Generalizability Theory Framework: A Closer Look at the Item Effect

An Angoff standard setting study generally yields judgments on a number of items by a number of judges (who may or may not be nested in panels). Variability associated with judges (and possibly panels) contributes error to the resulting cut score. The variability associated with items plays a more complicated role. To the extent that the mean item judgments directly reflect empirical item difficulties, the variability in Angoff judgments over items would not add error to the cut score, but to the extent that the mean item judgments do not correspond to the empirical item difficulties, variability in mean judgments over items would add error to the cut score. In this article, we present two generalizability-theory–based analyses of the proportion of the item variance that contributes to error in the cut score. For one approach, variance components are estimated on the probability (or proportion-correct) scale of the Angoff judgments, and for the other, the judgments are transferred to the theta scale of an item response theory model before estimating the variance components. The two analyses yield somewhat different results but both indicate that it is not appropriate to simply ignore the item variance component in estimating the error variance.     

Relationships of Measurement Error and Prediction Error in Observed‐Score Regression

The focus of this paper is assessing the impact of measurement errors on the prediction error of an observed‐score regression. Measures are presented and described for decomposing the linear regression's prediction error variance into parts attributable to the true score variance and the error variances of the dependent variable and the predictor variable(s). These measures are demonstrated for regression situations reflecting a range of true score correlations and reliabilities and using one and two predictors. Simulation results also are presented which show that the measures of prediction error variance and its parts are generally well estimated for the considered ranges of true score correlations and reliabilities and for homoscedastic and heteroscedastic data. The final discussion considers how the decomposition might be useful for addressing additional questions about regression functions’ prediction error variances.     

权回归模型下几种估计性能的比较

在给定的权回归模型下,讨论了最小二乘估计、最优加权最小二乘估计和线性无偏最小方差估计的性能比较,得出了在随机误差方差矩阵可逆条件下,可算出最优加权最小二乘估计与线性无偏最小方差估计误差方差阵的差表达式,并在一定条件下,两者趋于一致。     

The importance of shared environment in mother-infant attachment security: a behavioral genetic study

In a sample of 157 monozygotic and dizygotic twins, genetic and environmental influences on infant attachment and temperament were quantified. Only unique environmental or error components could explain the variance in disorganized versus organized attachment as assessed in the Ainsworth Strange Situation Procedure. For secure versus nonsecure attachment, 52% of the variance in attachment security was explained by shared environment, and 48% of the variance was explained by unique environmental factors and measurement error. The role of genetic factors in attachment disorganization and attachment security was negligible. Genetic factors explained 77% of the variance in temperamental reactivity, and unique environmental factors and measurement error explained 23%. Differences in temperamental reactivity were not associated with attachment concordance.     

一种基于科学计算器的方差分析计算方法

利用科学计算器直接计算出总标准差和总方差以及处理标准差和处理方差,然后用方差乘以自由度得到二者的平方和,再根据平方和公式计算出误差的平方和及方差。该方法在计算程序上比传统方法更简便,可用于统计计算和教学。     

城镇化对居民生活能源消费的影响分析

居民生活能源消费与城镇化进程密切相关,利用1983-2012年数据对二者进行实证分析,发现二者存在长期均衡稳定的关系,同时二者表现为双向格兰杰原因,且城镇化对居民生活能源消费的影响更大。误差修正模型的结果不仅表明城镇化对居民生活能源消费具有影响,也表明了居民生活能源消费同样受其自身的影响。方差分解的结果证实城镇化发展对居民生活能源消费具有长期正向影响的作用,以此提出推进城镇化建设政策建议。     

Longitudinal confirmatory factor analysis: Common,time‐specific,item‐specific,and residual‐error components of variance

Following Cronbach (1970) and others, it is useful to decompose test score variation into common factor, time‐specific, item‐specific, and residual components. In the traditional approach to factor analysis, only two sources of variance can be estimated: common factor variance and a uniqueness term that confounds specific sources of variation and residual error. When the same items are measured on different occasions, however, it is possible to separate specific variance and residual error. Two approaches, the first‐order approach described by Raffalovich and Bohrnstedt (1987) and a second‐order approach based on Jöreskog and Sörbom (1989; Jöreskog, 1974) are considered initially. The two approaches, although based on different rationales, both suffer a similar weakness in that two of the four sources of variance are confounded. In the Raffalovich and Bohrnstedt approach, time‐specific variance is confounded with common factor variance that generalizes across items and time. In the second‐order approach based on Jöreskog and Sörbom, time‐specific variance is confounded with residual error. Here we demonstrate that by combining features from both approaches we can eliminate these weaknesses and estimate all four of Cronbach's sources of variance, and that this combined approach is easily generalized to a wide variety of applications.     

Detecting Individual Differences in Change: Methods and Comparisons

This study examined and compared various statistical methods for detecting individual differences in change. Considering 3 issues including test forms (specific vs. generalized), estimation procedures (constrained vs. unconstrained), and nonnormality, we evaluated 4 variance tests including the specific Wald variance test, the generalized Wald variance test, the specific likelihood ratio (LR) variance test, and the generalized LR variance test under both constrained and unconstrained estimation for both normal and nonnormal data. For the constrained estimation procedure, both the mixture distribution approach and the alpha correction approach were evaluated for their performance in dealing with the boundary problem. To deal with the nonnormality issue, we used the sandwich standard error (SE) estimator for the Wald tests and the Satorra–Bentler scaling correction for the LR tests. Simulation results revealed that testing a variance parameter and the associated covariances (generalized) had higher power than testing the variance solely (specific), unless the true covariances were zero. In addition, the variance tests under constrained estimation outperformed those under unconstrained estimation in terms of higher empirical power and better control of Type I error rates. Among all the studied tests, for both normal and nonnormal data, the robust generalized LR and Wald variance tests with the constrained estimation procedure were generally more powerful and had better Type I error rates for testing variance components than the other tests. Results from the comparisons between specific and generalized variance tests and between constrained and unconstrained estimation were discussed.     

USING ANALYSIS OF VARIANCE WITH A DICHOTOMOUS DEPENDENT VARIABLE: AN EMPIRICAL STUDY1

A study was conducted to determine if analysis of variance techniques are appropriate when the dependent variable has a dichotomous (zero-one) distribution. Several 1-, 2-, and 3-way analysis of variance configurations were investigated with regard to both the size of the Type I error and the Power. The findings show the analysis of variance to be an appropriate statistical technique for analyzing dichotomous data in fixed effects models where cell frequencies are equal under the following conditions: (a) the proportion of responses in the smaller response category is equal to or greater than .2 and there are at least 20 degrees of freedom for error, or (b) the proportion of responses in the smaller response category is less than .2 and there are at least 40 degrees of freedom for error.     

Stepping Up Test Score Conditional Variances

In Woodruff (1990), I derived estimates for the conditional standard error of measurement in prediction (CSEMP), the conditional standard error of estimation (CSEE), and the conditional standard error of prediction (CSEP). My original estimates assume that the conditional residual error score variances and the conditional residual true score variances, obtained from the regression of an observed score onto a parallel observed score, obey the same step-up rules as do the marginal error score variance and the marginal true score variance. The present article derives alternative estimates for the various test score conditional variances that do not depend on these assumptions.     

The Conventional Wisdom About Group Mean Scores

Not infrequently, investigators assume that reliability for groups is greater than reliability for persons, and/or that error variance for groups is less than error variance for persons. Using generalizability theory, it is shown that this conventional wisdom is not necessarily true. Examples are provided from the course evaluation literature and the performance testing literature     

Estimation of Measurement Error Variance at Specific Score Levels

An improved method is derived for estimating conditional measurement error variances, that is, error variances specific to individual examinees or specific to each point on the raw score scale of the test. The method involves partitioning the test into short parallel parts, computing for each examinee the unbiased estimate of the variance of part-test scores, and multiplying this variance by a constant dictated by classical test theory. Empirical data are used to corroborate the principal theoretical deductions.     

Variability of Estimated Variance Components and Related Statistics in a Performance Assessment

Generalizability theory provides a conceptual and statistical framework for estimating variance components and measurement precision. The theory has been widely used in evaluating technical qualities of performance assessments. However, estimates of variance components, measurement error variances, and generalizability coefficients are likely to vary from one sample to another. This study empirically investigates sampling variability of estimated variance components using data collected in several years for a listening and writing performance assessment. This study also evaluates stability of estimated measurement precision from year to year. The results indicated that the estimated variance components varied from one study to another, especially when sample sizes were small. The estimated measurement error variances and generalizability coefficients also changed from one year to another. Measurement precision projected by a generalizability study may not be fully realized in an actual decision study. The study points out the importance of examining variability of estimated variance components and related statistics in performance assessments.     

Clustering-based selective neural network ensemble

INTRODUCTION Neural network ensemble is becoming a hot spot in machine learning and data mining recently. Many researchers have shown that simply combining the output of many neural networks can generate more accurate predictions than that of any of the individual networks. Most previous work either focused on how to combine the output of multiple trained networks or how to directly design a good set of neural networks. Theoretical and empirical work showed that a good ensemble is one wh…     

单因素方差分析中有关统计量的计算

通过列表计算或利用计算器完成单因素试验的方差分析中有关统计量的计算比较麻烦,针对这个问题,根据单因素方差分析的理论,结合列表计算的方法,用Basic语言编写了计算组间平均平方和,误差平均平方和,完成单因素方差分析的程序.利用该程序,计算的工作可以由计算机完成.     

圆度测量中偏置误差的软补偿

This paper analyses three causes of offset error in roundness measurement and presents corresponding compensation methods.The causes of offset error include excursion error resulting from the deflection of the sensor's line of measurement from the rotational center in measurement (datum center), eccentricity error resulting from the variance between the workpiece's geometrical center and the rotational center, and tilt error resulting from the tilt between the workpiece's geometrical axes and the rotational centerline.     

Prior knowledge, attitude, and strategy use in an introduction to statistics course

The present study used both quantitative and qualitative methods to investigate the learning and motivational strategies used by students in a beginning-level statistics course. The research questions that guided the investigation are: (1) Do motivational variables account for unique variance in the academic performance of statistics students? (2) Do deeper-level processing strategies account for unique variance in the academic performance of statistics students? (3) Do successful students report using different motivation and learning strategies than unsuccessful students in a beginning-level statistics course?     

THE ISSUE OF ITEM AND TEST VARIANCE FOR CRITERION-REFERENCED TESTS1

It has been argued that item variance and test variance are not necessary characteristics for criterion-referenced tests, although they are necessary for normreferenced tests. This position is in error because it considers sample statistics as the criteria for evaluating items and tests. Within a particular sample, an item or test may have no variance, but in the population of observations for which the test was designed, calibrated, and evaluated, both items and tests must have variance.