浅谈等级相关系数与斯皮尔曼等级相关系数

针对目前很多专著中将等级相关系数和斯皮尔曼等级相关系数混为一谈的情况,指出两者存在区别,并从数学上严格加以证明,提出了两种计算公式相等的唯一性条件,最后指出两者之间的关系。     

等级相关系数与点双列相关系数计算公式的导出

证明了等级相关系数与点双列相关系数的计算公式可以由积差相关系数的计算公式导出。     

The Effects of the Number of Scale Points and Non-Normality on the Generalizability Coefficient: A Monte Carlo Study

Increasingly, assessment practitioners use generalizability coefficients to estimate the reliability of scores from performance tasks. Little research, however, examines the relation between the estimation of generalizability coefficients and the number of rubric scale points and score distributions. The purpose of the present research is to inform assessment practitioners of (a) the optimum number of scale points necessary to achieve the best estimates of generalizability coefficients and (b) the possible biases of generalizability coefficients when the distribution of scores is non-normal. Results from this study indicate that the number of scale points substantially affects the generalizability estimates. Generalizability estimates increase as scale points increase, with little bias after scales reach 12 points. Score distributions had little effect on generalizability estimates.     

用相关系数衡量单摆法测重力加速度实验的准确性

在用单摆测重力加速度的实验中,为了能够快速得到实验结果的准确性,文章提出了应用origin软件给出测量过程中随机误差的表达方法,用相关系数来表示单摆法测重力加速度实验中的随机误差大小.该方法简单方便,并且能够直观地反映出实验数据的可靠性.     

相关系数含义的理解

1885年,高尔顿第一次提出了回归(regression)的概念。10年后,皮尔逊提出了著名的皮尔逊相关系数r,直到今天,这一相关系数也在被广泛地应用。100多年来,r发展成了一个更宽泛、更多样化、更概念化的统计量。本文展示了9个公式,每个公式是分别从几何、代数和三角的角度计算r的方法。r的解释,是关于平均数的公式,关于方差的公式,两个平均数的比率,两个方差的比率,直线的斜率,角的余弦和椭圆的切线。     

两类关于k-对称点的解析函数子族的一些系数不等式

介绍了两类关于k-对称点的新的解析函数子族Mp^（k） （a） 和 Np^（K） （a）获得了一些属于它们及其具有正系数的子族的函数的系数不等式．     

Tables for Finding the Partial Coefficient of Correlation

Within a conceptual framework of factors influencing time use, this study examined how career teachers would allocate extra work time, if available. The survey sample of 893 teachers had received teaching certificates from the University of Michigan from 1946 through 1976. Multiple group discriminant analysis was used to determine if groups of teachers preferring different time allocations could be distinguished by personal, environmental, and role factors. Four distinct groups of teachers preferring instructional tasks, student counseling, parent counseling, or committee activities, respectively, were identifiable in a modestly successful prediction model. Teachers selected professional time uses congruent with their perceived skills and attitudes toward professional success. Implication for practice, particularly regarding work assignments and incentive systems, are presented.     

Shorter Method for Computing the Coefficient of Correlation

ABSTRACT

Handwriting is used throughout the school day and is important to demonstrate knowledge. This research evaluated how handwriting instructional practices and intrinsic and extrinsic factors in actual classroom settings impacted learning handwriting over the course of the school year. Findings indicated that extrinsic factors (educational instructional practices, spatial constraints) and intrinsic factors (task cognitive complexity) influenced handwriting performance, but not always in the same way for writing product and process measures. In addition, stronger relationships were found between writing process measures and handwriting fluency than legibility. Even though handwriting improved over the school year, some instructional practices resulted in a widening performance gap as the school year progressed. The impact of these findings for implementing and differentiating handwriting instruction and guiding future research is discussed.     

随机变量的Kendall相关系数的推广

多维随机变量之间常常存在着复杂的相依关系,而度量相依关系指标大多只刻画二维随机变量之间相依程度。借助Copula工具及利用Kendall相关系数是和谐概率的线性变化的特点,将二维Kendall相关系数推广到n维,并在此基础上探讨其性质以及不同维度的Kendall相关系数之间的关系。     

渐开线少齿差齿轮副承载能力系数

渐开线少齿差齿轮副,由于是内啮合,齿轮副的齿对之间的间隙很小,在受力后轮齿变形而使得同时有多对齿啮合。本文用简明的几何推导,弹性力学的方法,推导出了轮齿受载弹性变形后同时啮合的确切齿对和承受载荷最大的齿对的载荷与总载荷的比例系数——承载能力系数。利用承载能力系数可算出更符合实际的各齿对分别承受的载荷。经样机的设计、制造和试验结果表明,本文提出的计算方法和公式是正确的,可以有效地提高齿轮副的承载能力。     

探究符合某些条件的等腰三角形顶点个数的方法

探求符合某些条件的等腰三角形顶点个数问题是数学竞赛中备受青睐的一个重要测试点,因为解决此类问题涉及三角形与圆的知识的综合运用以及分类思想、对称思想的渗透,具有知识性、思想性的考查与训练价值.解决此类问题的方法,主要是线段垂直平分线与辅助圆的灵活运用以及分类讨论时做到不重不漏.下面以举例形式作分析说明.     

A Pragmatic Approach to Spearman's Rank Correlation Coefficient

A full understanding of correlation requires an appreciation of bivariate distributions, but increasingly rank correlation coefficients are Being used as a measure of agreement with pupils for whom such appreciation is not possible. How can we justify the formula used?     

Discriminating Quantity: New Points for Teaching Children with Down Syndrome About Number?

ABSTRACT

The focus of much mathematics teaching has been on the acquisition of counting, an area where children with Down syndrome can experience particular difficulties. Research with typically developing children has highlighted how early awareness of quantity provides a strong platform for the acquisition of later mathematical skills and programmes of early intervention have been introduced. Many of these studies are embedded in the work and traditions of developmental and cognitive psychology and can be difficult to access. Consequently, this is an area that has been largely ignored in the curricula of children with Down syndrome. This paper seeks to make this literature more available. It systematically reviews previous research with children with Down Syndrome on these early foundations. It considers seemingly contradictory findings in the light of differences in tasks, their presentation and instructions, and the responses required, in order to draw conclusions and reflect on the implications for teaching and learning. Some of these propositions are in contrast to existing practices and call for further research to test their effectiveness.     

关于偏相关系数的计算公式的一点注记

首先对偏相关系数的常用的定义与计算方法作了归纳,然后从多元正态分布理论中的条件分布的结论出发,推导得出通过相关系数阵或协方差阵求逆的方法来计算偏相关系数的公式,从而对利用相关系数阵求逆方法计算偏相关系数的公式给出了合理的解释。