A Comparison of Item Sampling Plans in the Application of Multiple Matrix Sampling

This study used a Monte Carlo approach to investigate the effect of item sampling by item stratification on parameter estimation when applying multiple matrix sampling to achievement data. From the results of this study it was concluded that the item sampling method and sampling plan which is a practical compromise in terms of precision and sample size is one based on item stratification by item discrimination and a sampling plan with a moderate number of subtests. This sampling condition provides reasonable precision of the mean and variance estimates but requires only a moderately sized sample.     

The Use of Multiple Matrix Sampling for Survey Research

Multiple matrix sampling procedures can be employed to improve survey research when the results of matrix sampling are equivalent to those obtained by the traditional census testing approach. This study examined the use of multiple matrix sampling as a strategy for the collection of data and compared rates of response when subgroups of items were administered as opposed to an entire instrument. In addition, the study investigated whether responses were equivalent in the two sampling procedures and whether bias was present. The results indicate that multiple matrix sampling is a viable and reasonable procedure to use when a mail survey questionnaire consists of a large number of pages and/or items.     

关于可逆矩阵定义的注记

本文就矩阵可逆性的定义进行讨论，给出矩阵可逆的另一定义形式，并利用这一定义，证明了逆矩阵的存在性和唯一性．说明新定义与传统定义是一致的，不过新的定义在使用上要简单一些。     

关于“矩阵的直积”一文的注记

本文指出文[1]的定义及性质均是矩阵论中已有定义及已知性质,并进一步探讨了矩阵的直积的一些新的性质。     

"三角的"Cartan矩阵的Coxeter矩阵为周期矩阵的充要条件

对一类阿廷环上"三角的"Cartan矩阵的Coxeter矩阵的周期性进行了研究,给出了其为周期矩阵的1个充要条件,并由此给出了文[2]中的猜想的1种特殊情形的证明.     

高等代数教学中关于“矩阵对角化”的一点注记

矩阵对角化是高等代数中的基本内容,也是学习近世代数等后继课程所必须掌握的重要知识点之一.结合在高等代数教学过程中的体会,介绍了矩阵对角化的基本结论、矩阵对角化在矩阵计算等方面的应用和一类矩阵的对角化.对于不能对角化的矩阵,给出了化为“上三角矩阵”的条件.     

标准形在矩阵秩证明题教学中的应用

如何处理好习题课是当前形势下线性代数教学中值得关注的一个方面。矩阵的秩是线性代数的一个重要概念。与矩阵的秩相关的证明题是非常难的,掌握它们的证明能很好地培养学生数学思维能力。本文将重点介绍在习题课教学中,矩阵标准形的概念在矩阵秩的相关证明题中的应用。通过推导矩阵秩的分解定理来引导学生对基础知识的应用,加深概念的理解。     

对HSK部分等级的验证性研究

中国汉语水平考试(HSK)的作用之一是界定留学生进入中国大学入系学习时所应具备的汉语能力。根据有关规定,HSK三级和六级分别是进入中国大学理工西医类和文史中医类入系学习的最低标准。本文采用安哥夫、边缘组及对照组三种方法对此标准进行了验证性研究。     

分层抽样下多项选择敏感问题随机抽样调查方法及应用

目的是为多项选择敏感性问题提供科学的、精度更高的随机抽样调查方法及其统计量的计算公式,设计出多项选择敏感问题分层抽样下的随机抽样调查模型,并推导出在此模型下总体比例的估计量及其估计方差的计算公式,计算出敏感属性比例95％的置信区间。并在湖南城市学院本科学生考试作弊情况的实例调查中取得了信誉度较高的应用效果。     

关于预处理在全局优化中的应用的一个注记

本文通过对几何规划，广义线性规划，半定规则等数学规划问题的探讨，阐明了把一个复杂的全局优化算法应用于所全局优化问题求解之前，为了改进和尽可能简化问题，作一些基本的预处理（比如固定某个变量，紧界，变换变量等）是必要的，在一些简单情况下，通过一个变换可使一个表面上看似非凸的问题化为一个凸规划，甚至是线性规划。     

A Comparison of Angoff and Bookmark Standard Setting Methods

This article presents a comparison of simplified variations on two prevalent methods, Angoff and Bookmark, for setting cut scores on educational assessments. The comparison is presented through an application with a Grade 7 Mathematics Assessment in a midwestem school district. Training and operational methods and procedures for each method are described in detail along with comparative results for the application. An alternative item ordering strategy for the Bookmark method that may increase its usability is also introduced. Although the Angoff method is more widely used, the Bookmark method has some promising features, specifically in educational settings. Teachers are able to focus on the expected performance of the "barely proficient" student without the additional challenge of estimating absolute item dificulty.     

A Short Note on the Relationship Between Pass Rate and Multiple Attempts

For a certification, licensure, or placement exam, allowing examinees to take multiple attempts at the test could effectively change the pass rate. Change in the pass rate can occur without any change in the underlying latent trait, and can be an artifact of multiple attempts and imperfect reliability of the test. By deriving formulae to compute the pass rate under two definitions, this article provides tools for testing practitioners to compute and evaluate the change in the expected pass rate when a certain (maximum) number of attempts are allowed without any change in the latent trait. This article also includes a simulation study that considers change in ability and differential motivation of examinees to retake the test. Results indicate that the general trend shown by the analytical results is maintained—that is, the marginal expected pass rate increases with more attempts when the testing volume is defined as the total number of test takers, and decreases with more attempts when the testing volume is defined as the total number of test attempts.     

Field Note: Standard Web Application for Information Exchange on Agroforestry in India

Abstract

Purpose

To explain how training and education events (TEEs) can be designed to increase the likelihood of achieving behavioural objectives.     

The Effect of Various Factors on Standard Setting

This paper reports two studies of standard setting using Angoff's method. Results of the first study suggest that specialization within broad content areas does not affect an expert's estimates of the performance of the borderline group. This is reassuring because the knowledge base of many professions is so large that no individual can be considered an expert in all aspects of it. Results of the second study support the recommendation that performance data be provided during the standard-setting process. They are frequently used by experts, but will not have an impact on the standard unless the distribution of item difficulties is skewed markedly. It also increases the correspondence between p-values and estimates of borderline group performance, thereby reducing errors in pass/fail decisions. Overall, the results support recommendations often made in standard-setting literature, but they need to be replicated with other groups of experts     

实对称矩阵正交相似变换标准形的应用

通过实例探讨了实对称矩阵的正交相似变换标准形在矩阵问题中的应用。     

A Conceptual Framework for a Psychometric Theory for Standard Setting with Examples of Its Use for Evaluating the Functioning of Two Standard Setting Methods

A conceptual framework is proposed for a psychometric theory of standard setting. The framework suggests that participants in a standard setting process (panelists) develop an internal, intended standard as a result of training and the participant's background. The goal of a standard setting process is to convert panelists' intended standards to points on a test's score scale. Psychometrics is involved in this process because the points on the score scale are estimated from ratings provided by participants. The conceptual framework is used to derive three criteria for evaluating standard setting processes. The use of these criteria is demonstrated by applying them to variations of bookmark and modified Angoff standard setting methods.     

Note on Sources of Sampling Variability in Science Performance Assessments

In 1993, we reported in Journal of Educational Measurement that task-sampling variability was the Achilles' heel of science performance assessment. To reduce measurement error, tasks needed to be stratified before sampling, sampled in large number, or possibly both. However, Cronbach, Linn, Brennan, & Haertel (1997) pointed out that a task-sampling interpretation of a large person x task variance component might be incorrect. Task and occasion sampling are confounded because tasks are typically given on only a single occasion. The person x task source of measurement error is then confounded with the pt x occasion source. If pto variability accounts for a substantial part of the commonly observed pt interaction, stratifying tasks into homogenous subsets—a cost-effective way of addressing task sampling variability—might not increase accuracy. Stratification would not address the pro source of error. Another conclusion reported in JEM was that only direct observation (DO) and notebook (NB) methods of collecting performance assessment data were exchangeable; computer simulation, short-answer, and multiple-choice methods were not. However, if Cronbach et al. were right, our exchangeability conclusion might be incorrect. After re-examining and re-analyzing data, we found support for Conbach et al. We concluded that large task-sampling variability was due to both the person x task interaction and person x task x occasion interaction. Moreover, we found that direct observation, notebook and computer simulation methods were equally exchangeable, but their exchangeability was limited by the volatility of student performances across tasks and occasions.