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。     

Creating Realistic Data Sets with Specified Properties via Simulation

We explain how to simulate both univariate and bivariate raw data sets having specified values for common summary statistics. The first example illustrates how to ‘construct’ a data set having prescribed values for the mean and the standard deviation – for a one‐sample t test with a specified outcome. The second shows how to create a bivariate data set with a specified correlation coefficient.     

Student and Teacher Outcomes of The Superkids Quasi-Experimental Study

In this article, we report kindergarten student and teacher outcomes from a quasi-experimental evaluation of The Superkids, a systematic, phonics-based, comprehensive K-2 reading program. We recruited 23 kindergarten teachers to implement The Superkids program from a diverse, yet predominantly ethnic minority, group of classrooms from across the United States. We then employed a precise computerized matching methodology to derive a statistically equivalent comparison group of 20 control teachers who implemented their standard “business as usual” core literacy program. Multilevel analyses of classroom-level effects of The Superkids revealed achievement advantages of more than 1/10 of a standard deviation, d = 0.11, to 1/4 of a standard deviation, d = 0.25, for the treatment group on the 5 subtests from the Stanford Achievement Test, 10th edition (SAT-10). Four measures of teachers’ self-reported satisfaction with the core reading program used in their classrooms also revealed statistically significant advantages for Superkids of nearly three-quarters of a standard deviation, d = 0.72, to nearly 1½ standard deviation units, d = 1.49.     

标准偏差估算公式的推证

针对标准偏差估算公式中对偏差的平方取平均值时为什么除于n-1而不除于n(n为测量次数)的问题,根据测量误差理论,给出了严密的推理证明。     

Introducing the mean absolute deviation ‘effect’ size

This paper revisits the use of effect sizes in the analysis of experimental and similar results, and reminds readers of the relative advantages of the mean absolute deviation as a measure of variation, as opposed to the more complex standard deviation. The mean absolute deviation is easier to use and understand, and more tolerant of extreme values. The paper then proposes the use of an easy to comprehend effect size based on the mean difference between treatment groups, divided by the mean absolute deviation of all scores. Using a simulation based on 1656 randomised controlled trials each with 100 cases, and a before and after design, the paper shows that the substantive findings from any such trial would be the same whether raw-score differences, a traditional effect size like Cohen's d, or the mean absolute deviation effect size is used. The same would be true for any comparison, whether for a trial or a simpler cross-sectional design. It seems that there is a clear choice over which effect size to use. The main advantage in using raw scores as an outcome measure is that they are easy to comprehend. However, they might be misleading and so perhaps require more judgement to interpret than traditional ‘effect’ sizes. Among the advantages of using the mean absolute deviation effect size are its relative simplicity, everyday meaning, and the lack of distortion of extreme scores caused by the squaring involved in computing the standard deviation. Given that working with absolute values is no longer the barrier to computation that it apparently was before the advent of digital calculators, there is a clear place for the mean absolute deviation effect size (termed ‘A’).     

Use of Standard Deviations as Predictors in Models Using Large-Scale International Data Sets

Measures of variability are successfully used in predictive modeling in research areas outside of education. This study examined how standard deviations can be used to address research questions not easily addressed using traditional measures such as group means based on index variables. Student survey data were obtained from the Organisation for Economic Co-operation and Development to examine standard deviation predictors in multilevel models. These predictors and interactions explained additional variation in the dependent variable beyond the control variables. Models using biased and unbiased standard deviations were compared. Meaningful differences were found between the models. Findings supported how standard deviation predictors may increase explanatory power and accuracy of models commonly used in educational research.     

Child and informant influences on behavioral ratings of preschool children

This study investigated relationships among teacher, parent, and observer behavioral ratings of 3‐ and 4‐year‐old children using intra‐class correlations and analysis of variance. Comparisons within and across children from middle‐income (MI; N = 166; mean age = 54.25 months, standard deviation [SD] = 8.74) and low‐income (LI; N = 199; mean age = 51.21 months, SD = 7.22) backgrounds revealed significant agreement between the raters but also considerable differences in both ranking and absolute scores between raters. Teachers and parents consistently rated children from LI classrooms as having more behavioral problems and fewer prosocial behaviors. Results are conceptualized with respect to how differential expectations, comparison groups, and types of interaction with children can affect the evaluation of child behavior. Results point to the need for multiple sources of evaluation when assessing children for behavioral difficulties, particularly children from lower income backgrounds. © 2010 Wiley Periodicals, Inc.     

蛋白质修正卡方分布函数

利用统计分析和数据挖掘的知识,给出了蛋白质残基原子与其他原子的接触距离和接触数的定义,并根据蛋白质的种类的不同,计算了接触距离的数学期望和标准差,得到血红蛋白、激素和肌蛋白残基的概率分布,构造出类蛋白质ASP残基接触数的修正卡方分布函数.     

A Lower Bound for the Most Deviant Z Score

This article demonstrates that the lower bound for the most deviant Z score and the upper bound for the sample standard deviation are attained simultaneously.     

Effects of nonnormal data on parameter estimates and fit indices for a model with latent and manifest variables: An empirical study

Research in covariance structure analysis suggests that nonnormal data will invalidate chi‐square tests and produce erroneous standard errors. However, much remains unknown about the extent to and the conditions under which highly skewed and kurtotic data can affect the parameter estimates, standard errors, and fit indices. Using actual kurtotic and skewed data and varying sample sizes and estimation methods, we found that (a) normal theory maximum likelihood (ML) and generalized least squares estimators were fairly consistent and almost identical, (b) standard errors tended to underestimate the true variation of the estimators, but the problem was not very serious for large samples (n = 1,000) and conservative (99%) confidence intervals, and (c) the adjusted chi‐square tests seemed to yield acceptable results with appropriate sample sizes.     

What Divisor for the Sample Variance?

Simulation is used to show why the divisor in the sample variance is n, - 1. Choice of the divisor for the sample standard deviation is also discussed.     

回归分析方法在经济管理工作中的一个应用

本文通过对运输车队每天油耗数据的收集整理，采用回归分析方法 ，得出运输车队平均油耗与均方差之间存在显著的线性关系，从而可考虑通过缩小一个车队油耗的均方差来降低平均油耗，达到节约用油提高经济效益的目的。     

An empirical investigation of two variance estimation procedures for use with criterion-referenced tests

This study investigated two procedures for estimating the population standard deviation of nonnormed tests. Two normed tests, both whose population standard deviation was known, were administered to 272 students in grades 3–6. One of the normed tests was treated as a criterion-referenced test; the two variance estimation procedures were applied to the scores from this test. Substantial differences were found between both estimated statistics and the actual standard deviation. The first estimation procedure estimated the standard deviation systematically higher, whereas the second procedure's estimation was systematically lower. These results are discussed in terms of using such procedures for program evaluation.     

Does group composition affect learning by invention?

Schwartz and Martin (Cogn Instr 22:129?C184, 2004) as well as Kapur (Instr Sci, this issue, 2012) have found that students can be better prepared to learn about mathematical formulas when they try to invent them in small groups before receiving the canonical formula from a lesson. The purpose of the present research was to investigate how the effectiveness of invention activities may be mediated by composition of the small groups in terms of their mathematical skills. In two studies, small groups of undergraduates engaged in an ??inventing standard deviation?? task. Results suggested that groups may need at least one member with high math ability to take advantage of ??learning by invention??. Groups consisting of both high and low math ability members generated a broader range of solution attempts during the invention task, and this seemed to be related to better uptake of the standard deviation formula from a later lesson.     

TEST LENGTH AND THE STANDARD ERROR OF MEASUREMENT

Lord (1959) has shown that the standard error of measurement of a test is, for all practical purposes, directly proportional to the square root of the number of items on the test. More specifically, Lord found empirically that the standard error of a test was equal to .     if the reliability of the test was computed by the Kuder-Richardson (KR) 20 formula. If the KR-21 formula was used, the standard error was equal to .     . The present paper sets out to show how these relationships may be derived from the defining formulas of reliability and standard error of measurement, if certain simple assumptions about values of test statistics are made.     

A Meta‐Analysis of the Relationship Between Experiential Learning and Learning Outcomes

Experiential learning activities have been used for over 40 years with the hope that they increase students learning. However, a definitive study that showed their overall effectiveness has not been produced. The purpose of this study is to address this gap in the literature. This meta‐analysis examined a 43‐year span and identified 13,626 journal articles, dissertations, thesis articles, and conference proceedings written about experiential learning and found only 89 of these studies contained empirical data with both a treatment and control group. Meta‐analysis of these studies show that students experienced superior learning outcomes when experiential pedagogies were employed. Further, learning outcomes were almost a half standard deviation higher (d = .43) in classes employing experiential learning pedagogies versus traditional learning environments. This review definitively, and quantitatively, shows the importance of experiential learning activities. We use these results to discuss future research areas that need to be addressed based on our analysis of potential moderators and provide recommendations on how to best employ experiential learning pedagogies.     

How Vocabulary Interventions Affect Young Children at Risk: A Meta-Analytic Review

Abstract

This meta-analytic review examines how word-learning interventions affect young children, at risk for reading difficulties, on vocabulary outcomes. We quantitatively reviewed 51 studies with 138 effect sizes (N = 7,403) to assess the association between vocabulary training and word learning. Using a random-effects model, we found a mean effect size of nearly 1 standard deviation indicating a strong training effect overall. Moderator analyses indicated that children from low-socioeconomic-status (SES) families experienced significantly lower word-learning gains than those from middle- and upper-SES families who had one or more risk factor (e.g., English Language Learner, language delays). This was true regardless of the total number of risk factors present. However, risk factors in addition to poverty did compound this SES disadvantage. Further, multivariate meta-regression analyses indicated that the sole risk factor associated with lower effect sizes was poverty controlling for all other risk factors. Subgroup moderator analyses indicated a number of instructional and pedagogical factors associated with greater effect sizes. Taken together, these results highlight the importance of creating interventions powerful enough to accelerate children's vocabulary development if we are to narrow the reading achievement gap.     

聚甘氨酸修饰电极方波伏安法测定人体尿酸

利用方波伏安法研究了尿酸在聚甘氨酸修饰玻碳电极上的电化学氧化行为.结果表明:在0.01 mol/L磷酸盐缓冲液(pH=7)中,尿酸在+0.31 mv左右产生一个氧化峰,峰电流与尿酸在1.0×10-6—1.0×10-5mol/L浓度范围呈较好的线性关系,相关系数为0.9945.该方法可用于直接测定人体尿酸,回收率为95.5%-104.1%,相对标准偏差为1.4%.     

What Is the Long‐Run Impact of Learning Mathematics During Preschool?

The current study estimated the causal links between preschool mathematics learning and late elementary school mathematics achievement using variation in treatment assignment to an early mathematics intervention as an instrument for preschool mathematics change. Estimates indicate (n = 410) that a standard deviation of intervention‐produced change at age 4 is associated with a 0.24‐SD gain in achievement in late elementary school. This impact is approximately half the size of the association produced by correlational models relating later achievement to preschool math change, and is approximately 35% smaller than the effect reported by highly controlled ordinary least squares (OLS) regression models (Claessens et al., 2009; Watts et al., 2014 ) using national data sets. Implications for developmental theory and practice are discussed.     

From Ancient Greece to Modern Education: Universality and Lack of Generalization of the Socratic Dialogue

Two thousand four hundred years ago Socrates gave a remarkable lesson of geometry, perhaps the first detailed record of a pedagogical method in vivo in history [ Plato. (2008) . Apología de Sócrates. Menón. Crátilo. Madrid: Alianza Editorial]. Socrates asked Meno's slave 50 questions requiring simple additions or multiplications. At the end of the lesson the student discovered by himself how to duplicate a square using the diagonal of the given one as the side of the new square. We studied empirically the reproducibility of this dialogue in educated adults and adolescents of the 21st century. Our results show a remarkable agreement between Socratic and empiric dialogues. Even in questions in which Meno's slave made a mistake, within an unbounded number of possible erred responses, the vast majority of participants produced the same error as Meno's slave. Our results show that the Socratic dialogue is built on a strong intuition of human knowledge and reasoning which persists more than 24 centuries after its conception, providing one of the most striking demonstrations of universality across time and cultures. At the same time, they also emphasize its educational failure. After following every single question including Socrates' “diagonal argument,” almost 50% of the participants failed to learn the simplest generalization when asked to double the area of a square of different size.