An Empirical Comparison of DDF Detection Methods for Understanding the Causes of DIF in Multiple-Choice Items

This study compared and illustrated four differential distractor functioning (DDF) detection methods for analyzing multiple-choice items. The log-linear approach, two item response theory-model-based approaches with likelihood ratio tests, and the odds ratio approach were compared to examine the congruence among the four DDF detection methods. Data from a college-level mathematics placement test were analyzed to understand the causes of differential functioning. Results indicated some agreement among the four detection methods. To facilitate practical interpretation of the DDF results, several possible effect size measures were also obtained and compared.     

题组DIF检验方法在HSK（高等）阅读理解中的应用

本研究引入能够处理题组效应的项目功能差异检验方法,为篇章阅读测验提供更科学的DIF检验法。研究采用GMH法、P—SIBTEST法和P—LR法对中国汉语水平考试（HSK）（高等）阅读理解试题进行了DIF检验。结果表明,这三种方法的检验结果具有较高的一致性,该部分试题在性别与国别变量上不存在显著的DIF效应。本研究还将传统的DIF检验方法与变通的题组DIF检验方法进行了比较,结果表明后者具有明显的优越性。     

Using Log-Linear Smoothing to Improve Small-Sample DIF Estimation

This study examined the extent to which log-linear smoothing could improve the accuracy of differential item functioning (DIF) estimates in small samples of examinees. Examinee responses from a certification test were analyzed using White examinees in the reference group and African American examinees in the focal group. Using a simulation approach, separate DIF estimates for seven small-sample-size conditions were obtained using unsmoothed (U) and smoothed (S) score distributions. These small sample U and S DIF estimates were compared to a criterion (i.e., DIF estimates obtained using the unsmoothed total data) to assess their degree of variability (random error) and accuracy (bias). Results indicate that for most studied items smoothing the raw score distributions reduced random error and bias of the DIF estimates, especially in the small-sample-size conditions. Implications of these results for operational testing programs are discussed.     

An Empirical Bayes Approach to Mantel-Haenszel DIF Analysis

We developed an empirical Bayes (EB) enhancement to Mantel-Haenszel (MH) DIF analysis in which we assume that the MH statistics are normally distributed and that the prior distribution of underlying DIF parameters is also normal. We use the posterior distribution of DIF parameters to make inferences about the item's true DIF status and the posterior predictive distribution to predict the item's future observed status. DIF status is expressed in terms of the probabilities associated with each of the five DIF levels defined by the ETS classification system: C–, B–, A, B+, and C+. The EB methods yield more stable DIF estimates than do conventional methods, especially in small samples, which is advantageous in computer-adaptive testing. The EB approach may also convey information about DIF stability in a more useful way by representing the state of knowledge about an item's DIF status as probabilistic.     

An NCME Instructional Module on Using Differential Step Functioning to Refine the Analysis of DIF in Polytomous Items

Traditional methods for examining differential item functioning (DIF) in polytomously scored test items yield a single item‐level index of DIF and thus provide no information concerning which score levels are implicated in the DIF effect. To address this limitation of DIF methodology, the framework of differential step functioning (DSF) has recently been proposed, whereby measurement invariance is examined within each step underlying the polytomous response variable. The examination of DSF can provide valuable information concerning the nature of the DIF effect (i.e., is the DIF an item‐level effect or an effect isolated to specific score levels), the location of the DIF effect (i.e., precisely which score levels are manifesting the DIF effect), and the potential causes of a DIF effect (i.e., what properties of the item stem or task are potentially biasing). This article presents a didactic overview of the DSF framework and provides specific guidance and recommendations on how DSF can be used to enhance the examination of DIF in polytomous items. An example with real testing data is presented to illustrate the comprehensive information provided by a DSF analysis.     

Using Analogy to Help Young Children Understand

Analogies offer conceptual models for supporting the development of understanding. Contrary to some expectations, there is growing evidence that young children can reason analogically. Much of this evidence comes from experiments intended to test psychological theories. This study aimed to gauge the practical potential of analogy in topics often considered by teachers difficult for young children to understand. Aspects of young children's understanding of current electricity were compared in two conditions, namely with and without an analogy (87 and 89 children, respectively; 6‐7 years of age). The results indicated that the analogy was of practical value in teaching for understanding. It is suggested that their bases be carefully prepared prior to teaching the target topic and that what is to be understood is modelled directly and is explicitly related to its equivalent in the topic. Further investigations to determine conditions for the effective use of analogies when teaching young children, who benefits particularly and in what ways seem warranted.     

An NCME Instructional Module on Latent DIF Analysis Using Mixture Item Response Models

The purpose of this ITEMS module is to provide an introduction to differential item functioning (DIF) analysis using mixture item response models. The mixture item response models for DIF analysis involve comparing item profiles across latent groups, instead of manifest groups. First, an overview of DIF analysis based on latent groups, called latent DIF analysis, is provided and its applications in the literature are surveyed. Then, the methodological issues pertaining to latent DIF analysis are described, including mixture item response models, parameter estimation, and latent DIF detection methods. Finally, recommended steps for latent DIF analysis are illustrated using empirical data.     

A SIBTEST Approach to Testing DIF Hypotheses Using Experimentally Designed Test Items

This paper considers a modification of the DIF procedure SIBTEST for investigating the causes of differential item functioning (DIF). One way in which factors believed to be responsible for DIF can be investigated is by systematically manipulating them across multiple versions of an item using a randomized DIF study (Schmitt, Holland, & Dorans, 1993). In this paper: it is shown that the additivity of the index used for testing DIF in SIBTEST motivates a new extension of the method for statistically testing the effects of DIF factors. Because an important consideration is whether or not a studied DIF factor is consistent in its effects across items, a methodology for testing item x factor interactions is also presented. Using data from the mathematical sections of the Scholastic Assessment Test (SAT), the effects of two potential DIF factors—item format (multiple-choice versus open-ended) and problem type (abstract versus concrete)—are investigated for gender Results suggest a small but statistically significant and consistent effect of item format (favoring males for multiple-choice items) across items, and a larger but less consistent effect due to problem type.     

Using a Taxonomy of Differential Step Functioning to Improve the Interpretation of DIF in Polytomous Items: An Illustration

The assessment of differential item functioning (DIF) in polytomous items addresses between-group differences in measurement properties at the item level, but typically does not inform which score levels may be involved in the DIF effect. The framework of differential step functioning (DSF) addresses this issue by examining between-group differences in the measurement properties at each step underlying the polytomous response variable. The pattern of the DSF effects across the steps of the polytomous response variable can assume several different forms, and the different forms can have different implications for the sensitivity of DIF detection and the final interpretation of the causes of the DIF effect. In this article we propose a taxonomy of DSF forms, establish guidelines for using the form of DSF to help target and guide item content review and item revision, and provide procedural rules for using the frameworks of DSF and DIF in tandem to yield a comprehensive assessment of between-group measurement equivalence in polytomous items.     

Thinking Like a Scientist: Using Vee-Maps to Understand Process and Concepts in Science

It is considered important for students to participate in scientific practices to develop a deeper understanding of scientific ideas. Supporting students, however, in knowing and understanding the natural world in connection with generating and evaluating scientific evidence and explanations is not easy. In addition, writing in science can help students to understand such connections as they communicate what they know and how they know it. Although tools such as vee-maps can scaffold students?? efforts to design investigations, we know less about how these tools support students in connecting scientific ideas with the evidence they are generating, how these connections develop over time, or how writing can be used to encourage such connections. In this study, we explored students?? developing ability to reason scientifically by examining the relationship between students?? understanding of scientific phenomena and their understanding of how to generate and evaluate evidence for their ideas in writing. Three high school classes completed three investigations. One class used vee-mapping each time, one used vee-mapping once, and one did not use vee-mapping. Students?? maps and written reports were rated for understanding of relevant science procedural and conceptual ideas. Comparisons between groups and over time indicate a positive relationship between improved procedural and conceptual understanding. Findings also indicate that improved procedural understanding preceded improved conceptual understanding, and thus, multiple experiences were needed for students to connect evidence and explanation for science phenomena.     

Using Excel to Simulate Pendulum Motion and Maybe Understand Calculus a Little Better

As part of a first-year college Introductory Physics course, I have students construct an Excel^®: spreadsheet based on the differential equation for pendulum motion (we take a pendulum having a light bar rather than a string, so it can go ‘over the top’). In extensive discussions with the students, I find that forcing them to make the spreadsheet themselves, entering velocities as position differences divided by time, etc., leads to a firmer grasp of basic calculus concepts. And, the instant graphical response of the finished product gives a sense of accomplishment as well as a lot of fun while building intuition about pendulum motion.     

Using Dimensionality-Based DIF Analyses to Identify and Interpret Constructs That Elicit Group Differences

In this paper I describe and illustrate the Roussos-Stout (1996) multidimensionality-based DIF analysis paradigm, with emphasis on its implication for the selection of a matching and studied subtest for DIF analyses. Standard DIF practice encourages an exploratory search for matching subtest items based on purely statistical criteria, such as a failure to display DIF. By contrast, the multidimensional DIF paradigm emphasizes a substantively-informed selection of items for both the matching and studied subtest based on the dimensions suspected of underlying the test data. Using two examples, I demonstrate that these two approaches lead to different interpretations about the occurrence of DIF in a test. It is argued that selecting a matching and studied subtest, as identified using the DIF analysis paradigm, can lead to a more informed understanding of why DIF occurs.     

Using Excel to Simulate Pendulum Motion and Maybe Understand Calculus a Little Better

As part of a first-year college Introductory Physics course, I have students construct an Excel^®: spreadsheet based on the differential equation for pendulum motion (we take a pendulum having a light bar rather than a string, so it can go over the top). In extensive discussions with the students, I find that forcing them to make the spreadsheet themselves, entering velocities as position differences divided by time, etc., leads to a firmer grasp of basic calculus concepts. And, the instant graphical response of the finished product gives a sense of accomplishment as well as a lot of fun while building intuition about pendulum motion.     

Using Weighted Sum Scores to Close the Gap Between DIF Practice and Theory

We make a distinction between the operational practice of using an observed score to assess differential item functioning (DIF) and the concept of departure from measurement invariance (DMI) that conditions on a latent variable. DMI and DIF indices of effect sizes, based on the Mantel-Haenszel test of common odds ratio, converge under restricted conditions if a simple sum score is used as the matching or conditioning variable in a DIF analysis. Based on theoretical results, we demonstrate analytically that matching on a weighted sum score can significantly reduce the difference between DIF and DMI measures over what can be achieved with a simple sum score. We also examine the utility of binning methods that could facilitate potential operational use of DIF with weighted sum scores. A real data application was included to show this feasibility.     

职务犯罪的特征

当前我国职务犯罪主要有以下几个特点:第一、权力的依附性与特殊的隐秘性;第二、向新的领域扩展和出现新的犯罪形式;第三、发案率高、涉及金额之巨,呈愈演愈烈之态势;第四、职务犯罪窝案、串案呈大幅度上扬,高官逐渐增多;第五、作案后携巨款外逃越来越多。     

应如何正确理解"多值解析函数"

本文针对多值函数因其多值性而引起的复杂性,抓住关键,突出重点,归纳出学习多值解析函数应注意的几个问题,从而突破“多值解析函数”这一教学难点。