Standard Error of Measurement

The standard error of measurement (SEM) is the standard deviation of errors of measurement that are associated with test scores from a particular group of examinees. When used to calculate confidence bands around obtained test scores, it can be helpful in expressing the unreliability of individual test scores in an understandable way. Score bands can also be used to interpret intraindividual and interindividual score differences. Interpreters should be wary of over-interpretation when using approximations for correctly calculated score bands. It is recommended that SEMs at various score levels be used in calculating score bands rather than a single SEM value.     

Conditional Standard Errors of Measurement for Scale Scores

Standard errors of measurement of scale scores by score level (conditional standard errors of measurement) can be valuable to users of test results. In addition, the Standards for Educational and Psychological Testing (AERA, APA, & NCME, 1985) recommends that conditional standard errors be reported by test developers. Although a variety of procedures are available for estimating conditional standard errors of measurement for raw scores, few procedures exist for estimating conditional standard errors of measurement for scale scores from a single test administration. In this article, a procedure is described for estimating the reliability and conditional standard errors of measurement of scale scores. This method is illustrated using a strong true score model. Practical applications of this methodology are given. These applications include a procedure for constructing score scales that equalize standard errors of measurement along the score scale. Also included are examples of the effects of various nonlinear raw-to-scale score transformations on scale score reliability and conditional standard errors of measurement. These illustrations examine the effects on scale score reliability and conditional standard errors of measurement of (a) the different types of raw-to-scale score transformations (e.g., normalizing scores), (b) the number of scale score points used, and (c) the transformation used to equate alternate forms of a test. All the illustrations use data from the ACT Assessment testing program.     

Stabilizing Conditional Standard Errors of Measurement in Scale Score Transformations

The focus of this article is on scale score transformations that can be used to stabilize conditional standard errors of measurement (CSEMs). Three transformations for stabilizing the estimated CSEMs are reviewed, including the traditional arcsine transformation, a recently developed general variance stabilization transformation, and a new method proposed in this article involving cubic transformations. Two examples are provided and the three scale score transformations are compared in terms of how well they stabilize CSEMs estimated from compound binomial and item response theory (IRT) models. Advantages of the cubic transformation are demonstrated with respect to CSEM stabilization and other scaling criteria (e.g., scale score distributions that are more symmetric).     

Conditional Standard Errors of Measurement for Scale Scores Using IRT

An IRT method for estimating conditional standard errors of measurement of scale scores is presented, where scale scores are nonlinear transformations of number-correct scores. The standard errors account for measurement error that is introduced due to rounding scale scores to integers. Procedures for estimating the average conditional standard error of measurement for scale scores and reliability of scale scores are also described. An illustration of the use of the methodology is presented, and the results from the IRT method are compared to the results from a previously developed method that is based on strong true-score theory.     

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.     

Estimators of Conditional Scale-Score Standard Errors of Measurement: A Simulation Study

This paper describes four procedures previously developed for estimating conditional standard errors of measurement for scale scores: the IRT procedure (Kolen, Zeng, & Hanson. 1996), the binomial procedure (Brennan & Lee, 1999), the compound binomial procedure (Brennan & Lee, 1999), and the Feldt-Qualls procedure (1998). These four procedures are based on different underlying assumptions. The IRT procedure is based on the unidimensional IRT model assumptions. The binomial and compound binomial procedures employ, as the distribution of errors, the binomial model and compound binomial model, respectively. By contrast, the Feldt-Qualls procedure does not depend on a particular psychometric model, and it simply translates any estimated conditional raw-score SEM to a conditional scale-score SEM. These procedures are compared in a simulation study, which involves two-dimensional data sets. The presence of two category dimensions reflects a violation of the IRT unidimensionality assumption. The relative accuracy of these procedures for estimating conditional scale-score standard errors of measurement is evaluated under various circumstances. The effects of three different types of transformations of raw scores are investigated including developmental standard scores, grade equivalents, and percentile ranks. All the procedures discussed appear viable. A general recommendation is made that test users select a procedure based on various factors such as the type of scale score of concern, characteristics of the test, assumptions involved in the estimation procedure, and feasibility and practicability of the estimation procedure.     

On the Virtues and Vices of the Standard Error of Measurement

Although it has been known for over a half-century that the standard error of measurement is in many respects superior to the reliability coefficient for purposes of evaluating the fallibility of a psychological test, current textbooks and journal literature in tests and measurements still devote far more attention to test reliability than to the standard error. The present paper provides a list of ten salient features of the standard error, contrasting it to the reliability coefficient, and concludes that the standard error of measurement should be regarded as a primary characteristic of a mental test.     

A Comparison of Score Level Estimates of the Standard Error of Measurement

Numerous methods have been proposed and investigated for estimating · the standard error of measurement (SEM) at specific score levels. Consensus on the preferred method has not been obtained, in part because there is no standard criterion. The criterion procedure in previous investigations has been a single test occasion procedure. This study compares six estimation techniques. Two criteria were calculated by using test results obtained from a test-retest or parallel forms design. The relationship between estimated score level standard errors and the score scale was similar for the six procedures. These relationships were also congruent to findings from previous investigations. Similarity between estimates and criteria varied over methods and criteria. For test-retest conditions, the estimation techniques are interchangeable. The user's selection could be based on personal preference. However, for parallel forms conditions, the procedures resulted in estimates that were meaningfully different. The preferred estimation technique would be Feldt's method (cited in Gupta, 1965; Feldt, 1984).     

条件期望在最优预测中的应用

文中研究了条件期望性质及与Radon-Nikodym定理的关系,并举例分析了它在最优预测中的应用.     

A Comparison of Methods of Estimating Conditional Standard Errors of Measurement for Testlet-Based Test Scores Using Simulation Techniques

The primary purpose of this study was to investigate the appropriateness and implication of incorporating a testlet definition into the estimation of procedures of the conditional standard error of measurement (SEM) for tests composed of testlets. Another purpose was to investigate the bias in estimates of the conditional SEM when using item-based methods instead of testlet-based methods. Several item-based and testlet-based estimation methods were proposed and compared. In general, item-based estimation methods underestimated the conditional SEM for tests composed for testlets, and the magnitude of this negative bias increased as the degree of conditional dependence among items within testlets increased. However, an item-based method using a generalizability theory model provided good estimates of the conditional SEM under mild violation of the assumptions for measurement modeling. Under moderate or somewhat severe violation, testlet-based methods with item response models provided good estimates.     

数控加工物理仿真误差测量与精度预测模型构建研究

数控加工物理仿真主要研究切削加工中切削力、切削热、机床运动误差、加工系统颤振以及负载变化对零件精度影响的预测问题,目前已成为虚拟制造研究的热点之一.主要针对虚拟数控加工误差测量及精度预测模型构建的基础理论与典型方法进行系统的阐述,从而为工程技术人员开展精度预测系统研发提供参考.     

标准误差在航海数学中的应用

针对在航海数学观测平差过程中,因标准误差公式过多且符号比较相近,导致学生使用公式时经常混淆的难点,通过对标准误差公式在特点、含义、应用等方面的具体描述,强化学生对标准误差概念的理解与认识,从而正确运用。     

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.     

利用条件期望解决最优预测问题举例

条件期望在预测问题中有重要作用.本文利用“均方误差最小”解决一类最优预测问题,举例分析条件期望在预测实际问题中的应用.     

电阻测量中减小系统误差的措施

伏安法测电阻是实验室测量电阻的常用方法。但是,在测量过程中所选择的测量电路不同,所选择的仪器、仪表不同,测量的结果和误差大小也不尽相同。为此,在这里讨论如何减小实验测量误差,以便提高实验的精确程度,对提高学生实验能力有着极为重要的意义。     

Defining Score Scales in Relation to Measurement Error

Scale scores for educational tests can be made more interpretable by incorporating score precision information at the time the score scale is established. Methods for incorporating this information are examined that are applicable to testing situations with number-correct scoring. Both linear and nonlinear methods are described. These methods can be used to construct score scales that discourage the overinterpretation of small differences in scores. The application of the nonlinear methods also results in scale scores that have nearly equal error variability along the score scale and that possess the property that adding a specified number of points to and subtracting the same number of points from any examinee's scale score produces an approximate two-sided confidence interval with a specified coverage. These nonlinear methods use an arcsine transformation to stabilize measurement error variance for transformed scores. The methods are compared through the use of illustrative examples. The effect of rounding on measurement error variability is also considered and illustrated using stanines     

交换测量法误差理论的研究

对交换测量法的函数关系f=√xy所带来的间接测量误差进行理论研究,给出完全消除该间接测量误差的原理机制的形式表述,并通过实验加以验证。     

普通话水平测试测评误差探究

普通话水平测试具有"语音标准的模糊性、成绩评定的主观性、测评方式的个别性"特点,这不可避免地导致测评误差.因此为缩小测评误差,提高测试质量,我们必须深层次地分析导致误差的原因,探讨缩小误差的有效途径.     

普通话水平测试测评误差探究

普通话水平测试具有“语音标准的模糊性、成绩评定的主观性、测评方式的个别性”特点，这不可避免地导致测评误差。因此为缩小测评误差，提高测试质量，我们必须深层次地分析导致误差的原因，探讨缩小误差的有效途径。