Applying the Mantel-Haenszel Procedure to Complex Samples of Items

This Monte Carlo study examined the effect of complex sampling of items on the measurement of differential item functioning (DIF) using the Mantel-Haenszel procedure. Data were generated using a 3-parameter logistic item response theory model according to the balanced incomplete block (BIB) design used in the National Assessment of Educational Progress (NAEP). The length of each block of items and the number of DIF items in the matching variable were varied, as was the difficulty, discrimination, and presence of DIF in the studied item. Block, booklet, pooled booklet, and extra-information analyses were compared to a complete data analysis using the transformed log-odds on the delta scale. The pooled booklet approach is recommended for use when items are selected for examinees according to a BIB design. This study has implications for DIF analyses of other complex samples of items, such as computer administered testing or another complex assessment design.     

Variance Estimation for Differential Test Functioning Based on Mantel-Haenszel Statistics

This article concerns the simultaneous assessment of DIF for a collection of test items. Rather than an average or sum in which positive and negative DIF may cancel, we propose an index that measures the variance of DIF on a test as an indicator of the degree to which different items show DIF in different directions. It is computed from standard Mantel-Haenszel statistics (the logodds ratio and its variance error) and may be conceptually classified as a variance component or variance effect size. Evaluated by simulation under three item response models (IPL, 2PL, and 3PL), the index is shown to be an accurate estimate of the DTF generating parameter in the case of the 1PL and 2PL models with groups of equal ability. For groups of unequal ability, the index is accurate under the I PL but not the 2PL condition; however, a weighted version of the index provides improved estimates. For the 3PL condition, the DTF generating parameter is underestimated. This latter result is due in part to a mismatch in the scales of the log-odds ratio and IRT difficulty.     

Item Difficulty of Four Verbal Item Types and an Index of Differential Item Functioning for Black and White Examinees

In this study, the authors explored the importance of item difficulty (equated delta) as a predictor of differential item functioning (DIF) of Black versus matched White examinees for four verbal item types (analogies, antonyms, sentence completions, reading comprehension) using 13 GRE-disclosed forms (988 verbal items) and 11 SAT-disclosed forms (935 verbal items). The average correlation across test forms for each item type (and often the correlation for each individual test form as well) revealed a significant relationship between item difficulty and DIF value for both GRE and SAT. The most important finding indicates that for hard items, Black examinees perform differentially better than matched ability White examinees for each of the four item types and for both the GRE and SAT tests! The results further suggest that the amount of verbal context is an important determinant of the magnitude of the relationship between item difficulty and differential performance of Black versus matched White examinees. Several hypotheses accounting for this result were explored.     

高校英语专业四级考试阅读理解能力研究

基于Grabe＆Stoller（2005）的阅读能力层次理论以及《高校英语专业四级考试大纲（2004）》对于基础阶段英语专业学生英语阅读能力的考查要求,从能力分类、能力层次评价以及题目难度和区分度与能力层次关系的角度,研究2010年TEM4阅读理解试题中体现的阅读理解能力。结果表明,教师对题目的能力分类和能力层次评价存在明显分歧,但题目难度和区分度与题目能力层次存在正相关。     

Linguistic Complexity,Schematic Representations,and Differential Item Functioning for English Language Learners in Math Tests

This article examines nonmathematical linguistic complexity as a source of differential item functioning (DIF) in math word problems for English language learners (ELLs). Specifically, this study investigates the relationship between item measures of linguistic complexity, nonlinguistic forms of representation and DIF measures based on item response theory difficulty parameters in a state fourth-grade math test. This study revealed that the greater the item nonmathematical lexical and syntactic complexity, the greater are the differences in difficulty parameter estimates favoring non-ELLs over ELLs. However, the impact of linguistic complexity on DIF is attenuated when items provide nonlinguistic schematic representations that help ELLs make meaning of the text, suggesting that their inclusion could help mitigate the negative effect of increased linguistic complexity in math word problems.     

Identifying the Causes of DIF in Translated Verbal Items

Translated tests are being used increasingly for assessing the knowledge and skills of individuals who speak different languages. There is little research exploring why translated items sometimes function differently across languages. If the sources of differential item functioning (DIF) across languages could be predicted, it could have important implications on test development, scoring and equating. This study focuses on two questions: “Is DIF related to item type?”, “What are the causes of DIF?” The data were taken from the Israeli Psychometric Entrance Test in Hebrew (source) and Russian (translated). The results indicated that 34% of the items functioned differentially across languages. The analogy items were the most problematic with 65% showing DIF, mostly in favor of the Russian-speaking examinees. The sentence completion items were also a problem (45% D1F). The main reasons for DIF were changes in word difficulty, changes in item format, differences in cultural relevance, and changes in content.     

Assessing risk of commercial sexual exploitation among children involved in the child welfare system

The objective of this study was to assess item characteristics indicative of the severity of risk for commercial sexual exploitation among a high-risk population of child welfare system involved youth to inform the construction of a screening tool. Existing studies have discerned factors that differentiate Commercial Sexual Exploitation of Children (CSEC) victims from sexual abuse victims, yet no research has been conducted to discriminate which items in a high risk population of youth are most predictive of CSEC. Using the National Survey of Child and Adolescent Well-Being (NSCAW) cohorts I and II, we examined responses from 1063 males and 1355 females ages 11 and older, over three interview periods.A 2-parameter logistic Item Response Theory (2 PL IRT) model was employed in order to examine item performance as potential indicators for the severity of risk for CSEC. Differential Item Functioning (DIF) analysis was conducted in order to examine potential differences in item responses based on gender. Modeling strategies to assess item difficulty and discrimination were outlined and Item Characteristic Curves for the final retained items were presented. Evidence for uniform DIF were present within items that asked about runaway, any drug use, suicidality, and experiencing severe violence. Results from this study can inform the construction of a screening instrument to assess the severity of risk for experiencing CSEC.     

The Relationship of Content Characteristics of GRE Analytical Reasoning Items to Their Difficulties and Discriminations

In actual test development practice, the number o f test items that must be developed and pretested is typically greater, and sometimes much greater, than the number that is eventually judged suitable for use in operational test forms. This has proven to be especially true for one item type–analytical reasoning-that currently forms the bulk of the analytical ability measure of the GRE General Test. This study involved coding the content characteristics of some 1,400 GRE analytical reasoning items. These characteristics were correlated with indices of item difficulty and discrimination. Several item characteristics were predictive of the difficulty of analytical reasoning items. Generally, these same variables also predicted item discrimination, but to a lesser degree. The results suggest several content characteristics that could be considered in extending the current specifications for analytical reasoning items. The use of these item features may also contribute to greater efficiency in developing such items. Finally, the influence of these various characteristics also provides a better understanding of the construct validity of the analytical reasoning item type.     

Identifying Sources of Differential Item and Bundle Functioning on Translated Achievement Tests: A Confirmatory Analysis

Increasingly, tests are being translated and adapted into different languages. Differential item functioning (DIF) analyses are often used to identify non-equivalent items across language groups. However, few studies have focused on understanding why some translated items produce DIF. The purpose of the current study is to identify sources of differential item and bundle functioning on translated achievement tests using substantive and statistical analyses. A substantive analysis of existing DIF items was conducted by an 11-member committee of testing specialists. In their review, four sources of translation DIF were identified. Two certified translators used these four sources to categorize a new set of DIF items from Grade 6 and 9 Mathematics and Social Studies Achievement Tests. Each item was associated with a specific source of translation DIF and each item was anticipated to favor a specific group of examinees. Then, a statistical analysis was conducted on the items in each category using SIBTEST. The translators sorted the mathematics DIF items into three sources, and they correctly predicted the group that would be favored for seven of the eight items or bundles of items across two grade levels. The translators sorted the social studies DIF items into four sources, and they correctly predicted the group that would be favored for eight of the 13 items or bundles of items across two grade levels. The majority of items in mathematics and social studies were associated with differences in the words, expressions, or sentence structure of items that are not inherent to the language and/or culture. By combining substantive and statistical DIF analyses, researchers can study the sources of DIF and create a body of confirmed DIF hypotheses that may be used to develop guidelines and test construction principles for reducing DIF on translated tests.     

Possible Determinants of Differential Item Functioning: Familiarity, Interest, and Emotional Reaction

This study evaluated the connection between gender differences in examinees' familiarity, interest, and negative emotional reactions to items on the Advanced Placement Psychology Examination and the items' gender differential item functioning (DIF). Gender DIF and gender differences in interest varied appreciably with the content of the items. Gender differences in the three variables were substantially related to the items' gender DIF (e.g., R = .50). Much of the gender DIF on this test may be attributable to gender differences in these variables.     

ASSESSING STRENGTHS AND WEAKNESSES OF TEACHER KNOWLEDGE IN ASIA, EASTERN EUROPE, AND WESTERN COUNTRIES: DIFFERENTIAL ITEM FUNCTIONING IN TEDS-M

The “Teacher Education and Development Study in Mathematics” assessed the knowledge of primary and lower-secondary teachers at the end of their training. The large-scale assessment represented the common denominator of what constitutes mathematics content knowledge and mathematics pedagogical content knowledge in the 16 participating countries. The country means provided information on the overall teacher performance in these 2 areas. By detecting and explaining differential item functioning (DIF), this paper goes beyond the country means and investigates item-by-item strengths and weaknesses of future teachers. We hypothesized that due to differences in the cultural context, teachers from different countries responded differently to subgroups of test items with certain item characteristics. Content domains, cognitive demands (including item difficulty), and item format represented, in fact, such characteristics: They significantly explained variance in DIF. Country pairs showed similar patterns in the relationship of DIF to the item characteristics. Future teachers from Taiwan and Singapore were particularly strong on mathematics content and constructed-response items. Future teachers from Russia and Poland were particularly strong on items requiring non-standard mathematical operations. The USA and Norway did particularly well on mathematics pedagogical content and data items. Thus, conditional on the countries’ mean performance, the knowledge profiles of the future teachers matched the respective national debates. This result points to the influences of the cultural context on mathematics teacher knowledge.     

Using multidimensional Rasch analysis to validate the Chinese version of the Motivated Strategies for Learning Questionnaire (MSLQ-CV)

This article used the multidimensional random coefficients multinomial logit model to examine the construct validity and detect the substantial differential item functioning (DIF) of the Chinese version of motivated strategies for learning questionnaire (MSLQ-CV). A total of 1,354 Hong Kong junior high school students were administered the MSLQ-CV. Partial credit model was suggested to have a better goodness of fit than that of the rating scale model. Five items with substantial gender or grade DIF were removed from the questionnaire, and the correlations between the subscales indicated that factors of cognitive strategy use and self-regulation had a very high correlation which resulted in a possible combination of the two factors. The test reliability analysis showed that the subscale of test anxiety had a lower reliability compared with the other factors. Finally, the item difficulty and step parameters for the modified 39-item questionnaire were displayed. The order of the step difficulty estimates for some items implied that some grouping of categories might be required in the case of overlapping. Based on these findings, the directions for future research were discussed.     

Item Function Characteristics and Dimensionality for Alternative Response Formats in Mathematics

The purpose of this study was to investigate the technical properties of stem-equivalent mathematics items differing only with respect to response format. Using socio- economic factors to define the strata, a proportional stratified random sample of 1,366 Connecticut sixth-grade students were administered one of three forms. Classical item analysis, dimensionality assessment, item response theory goodness-of-fit, and an item bias analysis were conducted. Analysis of variance and confirmatory factor analysis were used to examine the functioning of the items presented in the three different formats. It was found that, after equating forms, the constructed-response formats were somewhat more difficult than the multiple-choice format. However, there was no significant difference across formats with respect to item discrimination. A differential item functioning (DIF) analysis was conducted using both the Mantel-Haenszel procedure and the comparison of the item characteristic curves. The DIF analysis indicated that the presence of bias was not greatly affected by item format; that is, items biased in one format tended to be biased in a similar manner when presented in a different format, and unbiased items tended to remain so regardless of format.     

Differential Item Functioning in Biodata: Opportunity Access as an Explanation of Gender- and Race-Related DIF

Investigations of differential item functioning (DIF) have been conducted mostly on ability tests and have found little evidence of easily interpretable differences across various demographic subgroups. In this study, we examined the degree to which DIF in biographical data items referencing academically relevant background, experiences, and interests was related to differences in judgments about access to these experiences by members of different gender and race subgroups. DIF in the location parameter was significantly related (r = –.51, p < .01) to gender differences in perceived accessibility to experience. No significant relationships with accessibility were observed for DIF in the slope parameter across gender groups or for the slope and location parameters associated with DIF across Black and White groups. Practical implications for use of biodata and theoretical implications for DIF research are discussed.     

The effect of images on item statistics in multiple choice anatomy examinations

Although multiple choice examinations are often used to test anatomical knowledge, these often forgo the use of images in favor of text‐based questions and answers. Because anatomy is reliant on visual resources, examinations using images should be used when appropriate. This study was a retrospective analysis of examination items that were text based compared to the same questions when a reference image was included with the question stem. Item difficulty and discrimination were analyzed for 15 multiple choice items given across two different examinations in two sections of an undergraduate anatomy course. Results showed that there were some differences item difficulty but these were not consistent to either text items or items with reference images. Differences in difficulty were mainly attributable to one group of students performing better overall on the examinations. There were no significant differences for item discrimination for any of the analyzed items. This implies that reference images do not significantly alter the item statistics, however this does not indicate if these images were helpful to the students when answering the questions. Care should be taken by question writers to analyze item statistics when making changes to multiple choice questions, including ones that are included for the perceived benefit of the students. Anat Sci Educ 10: 68–78. © 2016 American Association of Anatomists.     

Effect of the Medium of Item Presentation on Examinee Performance and Item Characteristics

Studies that have investigated differences in examinee performance on items administered in paper-and-pencil form or on a computer screen have produced equivocal results. Certain item administration procedures were hypothesized to be among the most important variables causing differences in item performance and ultimately in test scores obtained from these different administration media. A study where these item administration procedures were made as identical as possible for each presentation medium is described. In addition, a methodology is presented for studying the difficulty and discrimination of items under each presentation medium as a post hoc procedure.     

Detection of Gender-Related Differential Item Functioning in a Mathematics Performance Assessment

This study used three different differential item functioning (DIF) detection proce- dures to examine the extent to which items in a mathematics performance assessment functioned differently for matched gender groups. In addition to examining the appropriateness of individual items in terms of DIF with respect to gender, an attempt was made to identify factors (e.g., content, cognitive processes, differences in ability distributions, etc.) that may be related to DIF. The QUASAR (Quantitative Under- standing: Amplifying Student Achievement and Reasoning) Cognitive Assessment Instrument (QCAI) is designed to measure students' mathematical thinking and reasoning skills and consists of open-ended items that require students to show their solution processes and provide explanations for their answers. In this study, 33 polytomously scored items, which were distributed within four test forms, were evaluated with respect to gender-related DIF. The data source was sixth- and seventh- grade student responses to each of the four test forms administrated in the spring of 1992 at all six school sites participatingin the QUASARproject. The sample consisted of 1,782 students with approximately equal numbers of female and male students. The results indicated that DIF may not be serious for 3 1 of the 33 items (94%) in the QCAI. For the two items that were detected as functioning differently for male and female students, several plausible factors for DIF were discussed. The results from the secondary analyses, which removed the mutual influence of the two items, indicated that DIF in one item, PPPl, which favored female students rather than their matched male students, was of particular concern. These secondary analyses suggest that the detection of DIF in the other item in the original analysis may have been due to the influence of Item PPPl because they were both in the same test form.     

A Mixture Model Analysis of Differential Item Functioning

Once a differential item functioning (DIF) item has been identified, little is known about the examinees for whom the item functions differentially. This is because DIF focuses on manifest group characteristics that are associated with it, but do not explain why examinees respond differentially to items. We first analyze item response patterns for gender DIF and then illustrate, through the use of a mixture item response theory (IRT) model, how the manifest characteristic associated with DIF often has a very weak relationship with the latent groups actually being advantaged or disadvantaged by the item(s). Next, we propose an alternative approach to DIF assessment that first uses an exploratory mixture model analysis to define the primary dimension(s) that contribute to DIF, and secondly studies examinee characteristics associated with those dimensions in order to understand the cause(s) of DIF. Comparison of academic characteristics of these examinees across classes reveals some clear differences in manifest characteristics between groups.     

DIF Detection Using Multiple‐Group Categorical CFA With Minimum Free Baseline Approach

The aim of this study is to assess the efficiency of using the multiple‐group categorical confirmatory factor analysis (MCCFA) and the robust chi‐square difference test in differential item functioning (DIF) detection for polytomous items under the minimum free baseline strategy. While testing for DIF items, despite the strong assumption that all but the examined item are set to be DIF‐free, MCCFA with such a constrained baseline approach is commonly used in the literature. The present study relaxes this strong assumption and adopts the minimum free baseline approach where, aside from those parameters constrained for identification purpose, parameters of all but the examined item are allowed to differ among groups. Based on the simulation results, the robust chi‐square difference test statistic with the mean and variance adjustment is shown to be efficient in detecting DIF for polytomous items in terms of the empirical power and Type I error rates. To sum up, MCCFA under the minimum free baseline strategy is useful for DIF detection for polytomous items.     

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.