Using Subpopulation Invariance to Assess Test Score Equity

Score equity assessment (SEA) is introduced, and placed within a fair assessment context that includes differential prediction or fair selection and differential item functioning. The notion of subpopulation invariance of linking functions is central to the assessment of score equity, just as it has been for differential item functioning and differential prediction. Advanced Placement (AP) data are used for illustrative purposes. The use of multiple-choice and constructed response items in AP provides an opportunity to observe a case where subpopulation invariance of linking functions does not hold (U.S. History), and a case in which it does hold (Calculus AB). The lack of invariance for U.S. History might be attributed to several sources. The role of SEA in assessing the fairness of test assembly processes is discussed.     

Gender‐Based Differential Prediction by Curriculum Samples for College Admissions

A longstanding concern about admissions to higher education is the underprediction of female academic performance by admission test scores. One explanation for these findings is selection system bias, that is, not all relevant KSAOs that are related to academic performance and gender are included in the prediction model. One solution to this problem is to include these omitted KSAOs in the prediction model, many of these KSAOs are 'noncognitive' and “hard‐to‐measure” skills in a high‐stakes context. An alternative approach to capture relevant KSAOs is using representative performance samples. We examined differential prediction of first year‐ and third year academic performance by gender based on a curriculum‐sampling test that was designed as a small‐scale simulation of later college performance. In addition, we examined differential prediction using both frequentist and Bayesian analyses. Our results showed no differential prediction or small female underprediction when using the curriculum‐sampling tests to predict first year GPA, and no differential prediction for predicting third year GPA. In addition, our results suggest that more comprehensive curriculum samples may show less differential prediction. We conclude that curriculum sampling may offer a practically feasible method that yields minimal differential prediction by gender in high‐stakes operational selection settings.     

Differential Prediction in the Use of the SAT and High School Grades in Predicting College Performance: Joint Effects of Race and Language

The literature on differential prediction of college performance of racial/ethnic minority students for standardized tests and high school grades indicates the use of these predictors often results in overprediction of minority student performance. However, these studies typically involve native English‐speaking students. In contrast, a smaller literature on language proficiency suggests academic performance of those with more limited English language proficiency may be underpredicted by standardized tests. These two literatures have not been well integrated, despite the fact that a number of racial/ethnic minority groups within the United States contain recent immigrant populations or heritage language speakers. This study investigates the joint role of race/ethnicity and language proficiency in Hispanic, Asian, and White ethnic groups across three educational admissions systems (SAT, HSGPA, and their composite) in predicting freshman grades. Our results indicate that language may differentially affect academic outcomes for different racial/ethnic subgroups. The SAT loses predictive power for Asian and White students who speak another best language, whereas it does not for Hispanic students who speak another best language. The differential prediction of college grades of linguistic minorities within racial/ethnic minority subgroups appears to be driven by the verbally loaded subtests of standardized tests but is largely unrelated to quantitative tests.     

纯电动客车荷电状态低故障预测

针对纯电动客车荷电状态(SOC)低故障预测问题,在分析其开始充电SOC序列的周期性波动规律及变化趋势的基础上,构建差分自回归滑动平均模型(ARIMA)进行车辆SOC的短期预测,最后比较预测结果与故障阈值以判断是否发生故障。以某车企的纯电动客车为例进行实证分析,研究结果表明:差分自回归滑动平均模型的故障预测真阳率为96.4%,误诊率为10.3%,说明方法具有良好的预测可行性。     

USING DEMOGRAPHIC SUBGROUP AND DUMMY VARIABLE EQUATIONS TO PREDICT COLLEGE FRESHMAN GRADE AVERAGE

The purpose of this study was to determine whether adjustments for the differential prediction observed among sex, racial/ethnic, or age subgroups in one freshman class at a college could be used to improve prediction accuracy for these subgroups in future freshman classes. For older students, dummy variable and separate subgroup prediction equations were found, on cross-validation, to be more accurate than the total group equations. For sex subgroups, dummy variable and separate subgroup equations were only moderately effective in improving prediction accuracy. For racial/ethnic subgroups, they were more often than not less accurate, on cross-validation, than total group equations. Among all three kinds of demographic subgroupings, shifts over time in colleges' mean grade averages were found to be a more important source of prediction bias than differential prediction.     

基于不确定阻滞增长模型的奥运会撑杆跳高最佳成绩感知拟合预测

针对前25届奥运会撑竿撑杆跳高的最佳成绩存在迭代数据统计缺陷,设计了一种基于不确定阻滞增长模型的奥运会撑杆跳高最佳成绩感知拟合预测模型.基于此,在中国北京奥运会撑杆跳高感知拟合预测的结果显示,运用不确定阻滞增长模型在撑杆跳高最佳成绩感知拟合预测比常微分方程模型统计撑杆跳高项目感知结构分析的优越性.     

Race-Based Differential Prediction in Air Force Technical Training Programs

Bayesian Johnson-Neyman methodology was used to investigate differential prediction by race in United States Air Force technical training programs. Meaningful Johnson-Neyman regions of differences were found in eight of nine comparisons. In all nine training courses the regressions for blacks were flatter than for whites and the race-differentiated regression lines intersected within the range of predictor test scores. In six cases the cut-score for course qualification was within the Johnson-Neyman region, and in every case the bias was negative for blacks. It is noted that if the cut score had been set substantially higher the bias would have been positive for blacks in all cases. This analysis may explain why earlier studies that averaged bias across the predictor distribution yielded mixed results. It is hypothesized that the consistent results obtained here are a consequence of the lower predictability found in the black subpopulation.     

改进的灰色模型在基础沉降预测中的应用

一般的灰色残差修正GM(1,1)模型只是单纯利用差分来代替微分,而且用原始沉降数据第一点的值作为时间响应函数的初始值,导致了一定的误差。提出一种多项式逼近法改进后的残差修正GM(1,1)模型,该模型利用多项式在离散观测点上的导数代替常用的差分,同时添加一个初值参数C_0做出调整。实验验证,改进模型具有较好的准确性和工程应用价值。     

数学建模的几种基本预测方法的探讨

针对学生在建立预测模型时不能准确判别使用合适的预测模型,归纳了几种使用较多的预测方法:微分方程模型、时间序列方法、灰色预测和BP神经网络。对每种预测模型做了简单的介绍分析和适当地对某些模型进行了改进,总结了相应的优缺点以及各自适用的预测范围。     

PROGRAMS OF STUDY AS A BASIS FOR SELECTION, PLACEMENT AND GUIDANCE OF COLLEGE STUDENTS

Studies of collegiate success and attrition are generally conducted at the all-college level. The definition of academic programs that are homogeneous in the abilities and interests of their students and the grading standards of their faculties may lead to more accurate prediction of success and more effective control of attrition.
Homogeneous curricular groups were defined via Ward's hierarchical grouping analysis applied to curricular means on high school percentile rank, four ACT subscores, first semester GPA, and 16 Kuder scores. Programs so defined differed on scientific-verbal and competitive level dimensions. Prediction of grades was more accurate within programs than colleges. Drop and transfer rates were correlated with discriminant scores.
The programs are discussed as promising units within which differential selection and placement strategies might reduce attrition.     

江苏省用电量的灰色预测模型

本文应用灰色预测法对江苏省用电量进行预测。通过对2004———2009年江苏省用电量原始数据进行生成处理来寻找系统的规律,生成有较强规律性的数据序列,然后建立相应的微分方程模型,从而预测用电量的未来发展趋势,并通过残差修正模型使得模型的精确程度有所提高。     

Detecting bias in selection for higher education: three different methods

This study examined selection bias in Israeli university admissions with respect to test language and gender, using three approaches for the detection of such bias: Cleary’s model of differential prediction, boundary conditions for differential prediction and difference between d’s (the Constant Ratio Model). The university admissions process in Israel, like those in many countries, is based on a combination of school-related achievement and a general scholastic aptitude test. The selection process was found to be biased in favour of Arabic speakers and not biased with respect to gender. The three approaches for detecting selection bias were similar in the pattern of the results they produced, but differed, as expected, in the magnitude of the bias they detected. The discussion focuses on the results both with respect to the specific groups studied (first research question) and with respect to the three approaches for detecting selection bias (second research question).     

HIDDEN OPPORTUNITIES IN THE PREDICTION OF COLLEGE GRADES FOR DIFFERENT SUBGROUPS

The purpose of this paper was to examine the problems and opportunities of academic prediction for different ethnic groups. Several recent studies of academic prediction for blacks and whites were reviewed in regard to: 1) the situation in which the data were obtained; 2) the prediction technique employed, and 3) the data distribution likely to give rise to the obtained prediction indices. It was suggested that a total-group regression equation which "benefits" a minority group by overpredicting mean grade may actually be very disadvantageous if accompanied by a large error of estimate. The damage can be produced by precluding selection of the most qualified minority group members and thus lowering the groups' performance. Differential process theory was proposed as a potential source of explanations for differential prediction. It was proposed that alternative strategic approaches to scholastic tasks might alter the covariance of predictor tests with grades. Finally, it was suggested that, under certain circumstances, the patterns of standardized regression weights in the prediction of grades, might suggest group difference in problem-solving strategies.     

基于神经网络的体外预应力筋极限应力的预测

鉴于影响体外预应力筋极限应力的因素较多,采用BP和RBF两种人工神经网络模拟方法进行体外预应力筋极限应力进行预测。通过和试验数据比较分析,预测结果与试验结果的相对误差均在10%以内,满足工程需要,因此,采用神经网络预测体外预应力筋极限应力是可行的。     

一阶线性偏微分方程求解的教学方法新探

通过常微分方程与偏微分方程之间的关系我们寻找到一种特殊的规范变换,通过此变换将复杂的偏微分方程的求解转化为可积分的偏微分方程(含参数的常微分方程)的求解.     

基于Logistic回归模型的人口预测分析

Logistic函数在人口、资源、环境和生态诸多系统的预测中是一个非常重要的模型．然而,Logistic模型中参数的确定又是一件较困难的事情．本文基于数值微分和最小二乘曲线拟合对Logistic回归模型进行参数估计,据此计算了我国1980年到2005年总人口数的误差,并预测了2015年我国的人口总数。     

Why Do Achievement Measures Underpredict Female Academic Performance?

In the context of college admissions, the current study examined whether differential prediction of first‐year grade point average (FYGPA) by gender could be explained by an omitted variable problem—namely, academic discipline, or the amount of effort a student puts into schoolwork and the degree to which a student sees him/herself as hardworking and conscientious. Based on nearly 10,000 college students, the current study found that differences in intercepts by gender were reduced by 45% with the inclusion of academic discipline in a model that already included high school grade point average (HSGPA) and ACT Composite score. Moreover, academic discipline resulted in an additional 4% of variance accounted for in FYGPA. Gender differences in slopes were not statistically significant (p > .001) regardless if academic discipline was included in the model. The findings highlight the utility of taking a more holistic approach when making college admission decisions. Namely, the inclusion of noncognitive measures has benefits that are twofold: increased predictive validity and reduced differential prediction.     

Ongoing issues in test fairness

In the attempt to identify or prevent unfair tests, both quantitative analyses and logical evaluation are often used. For the most part, fairness evaluation is a pragmatic attempt at determining whether procedural or substantive due process has been accorded to either a group of test takers or an individual. In both the individual and comparative approaches to test fairness, counterfactual reasoning is useful to clarify a potential charge of unfairness: Is it plausible to believe that with an alternative assessment (test or item) or under different test conditions an individual or groups of individuals may have fared better? Beyond comparative questions, fairness can also be framed by moral and ethical choices. A number of ongoing issues are evaluated with respect to these topics including accommodations, differential item functioning (DIF), differential prediction and selection, employment testing, test validation, and classroom assessment.     

Predicting College Performance of American Indians: A Large‐Sample Examination of the SAT

Extensive research has examined the validity and fairness of standardized tests in academic admissions. However, due to their underrepresentation in higher education, American Indians have gained much less attention in this research. In the present study, we examined for American Indian students (1) group differences on SAT scores, (2) the predictive and incremental validity of SAT over high school grades, (3) the effect of socioeconomic status on SAT validity, (4) differential prediction in the use of SAT scores, and (5) potential omitted variables that could explain differential prediction for American Indian students. Results provided evidence of predictive and incremental validity of SAT scores, and the validity of SAT scores was largely independent of socioeconomic status. Overprediction was found when using SAT scores to predict college performance and it was reduced when including high school grades as an additional predictor. This study provides substantial evidence of the validity and fairness of SAT scores for American Indians.     

Assessing Differential Prediction of College Grades by Race/Ethnicity with a Multilevel Model

Previous research notes the importance of understanding racial/ethnic differential prediction of college grades across multiple institutions. Institutional variation in selection indices is especially important given some states' laws governing public institutions' admissions decisions. This paper employed multilevel moderated multiple regression to study the variation of selection indices across 30 institutions and the accuracy of selection indices in predicting college grades for students of different racial/ethnic backgrounds. Several benefits of multilevel models for cross-institutional differential prediction studies were described and include: controlling for institutional differences in range restriction, providing reliability estimates of least squares estimates, and adjusting criterion scores for differences in coursework difficulty. The findings from this study provide evidence of institutional variation in selection indices, which challenges current laws aimed at standardizing them. Specifically, there was evidence that the predictor slope coefficients varied across institutions, in addition to the estimates that measured intercept differences for African and Asian American students. Across universities, the results mirrored previous findings: high school grade point average (GPA) differentially predicted grades for African Americans, SAT verbal scores differentially predict grades for Asian Americans, and SAT math scores were better predictors of Asian Americans' grades.