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.     

Assessing Differential Item Functioning in Performance Assessment: Review and Recommendations

How can we best extend DIF research to performance assessment? What are the issues and problems surrounding studies of DIF on complex tasks? What appear to be the best approaches at this time?     

An Analysis of Sex-related Differential Item Functioning in Attitude Assessment

This study analyzes and classifies items that display sex-related Differential Item Functioning (DIF) in attitude assessment. It applies the Educational Testing Services (ETS) procedure that is used for classifying DIF items in testing to classify sex-related DIF items in attitude scales. A total of 982 items that measure attitudes from 23 real data sets were used in the analysis. Results showed that sex DIF is common in attitude scales: more than 27% of items showed DIF related to sex, 15% of the items exhibited moderate to large DIF, and the magnitudes of DIF against males and females were not equal.     

Analysis of Differential Item Functioning in the NAEP History Assessment

The Mantel-Haenszel approach for investigating differential item functioning was applied to U.S. history items that were administered as part o f the National Assessment o f Educational Progress, On some items, blacks, Hispanics, and females performed more poorly than other students, conditional on number-right score. It was hypothesized that this resulted, in part, from the fact that ethnic and gender groups differed in their exposure to the material included in the assessment. Supplementary Mantel-Haenszel analyses were undertaken in which the number o f historical periods studied, as well as score. was used as a conditioning variable. Contrary to expectation, the additional conditioning did not lead to a reduction in the number o f DIF items. Both methodological and substantive explanations for this unexpected result were explored.     

GendermRelated Differential Item Functioning on a Middle-School Mathematics Peformance Assessment

Will performance assessments in mathematics have gender DIF? Do male and female examinees provide similar solution strategies?     

Using Differential Item Functioning Procedures to Explore Sources of Item Difficulty and Group Performance Characteristics

Statistics used to detect differential item functioning can also reflect differential strengths and weaknesses in the performance characteristics of population subgroups. In turn, item features associated with the differential performance patterns are likely to reflect some facet of the item task and hence its difficulty, that might previously have been overlooked. In this study, several item features were identified and coded for a large number of reading comprehension items from the two admissions testing programs. Item features included subject matter content, various properties of item structure, cognitive demand indicators, and semantic content (propositional analysis). Differential item functioning was evaluated for males and females and for White and Black examinees. Results showed a number of significant relationships between item features and indicators of differential item functioning—many of which were consistent across testing programs. Implications of the results for related areas of research are discussed.     

Differential Item Functioning for Minority Examinees on the SAT

The standardization approach to assessing differential item functioning (DIF), including standardized distractor analysis, is described. The results of studies conducted on Asian Americans, Hispanics (Mexican Americans and Puerto Ricans), and Blacks on the Scholastic Aptitude Test (SAT) are described and then synthesized across studies. Where the groups were limited to include only examinees who spoke English as their best language, very few items across forms and ethnic groups exhibited large DIF. Major findings include evidence of differential speededness (where minority examinees did not complete SAT-Verbal sections at the same rate as White students with comparable SAT-Verbal scores) for Blacks and Hispanics and, when the item content is of special interest, advantages for the relevant ethnic group. In addition, homographs tend to disadvantage all three ethnic groups, but the effect of vertical relationships in analogy items are not as consistent. Although these findings are important in understanding DIF, they do not seem to account for all differences. Other variables related to DIF still need to be identified. Furthermore, these findings are seen as tentative until corroborated by studies using controlled data collection designs.     

Differential Item Functioning Analysis for Accommodated Versus Nonaccommodated Students

The No Child Left Behind act resulted in an increased reliance on large-scale standardized tests to assess the progress of individual students as well as schools. In addition, emphasis was placed on including all students in the testing programs as well as those with disabilities. As a result, the role of testing accommodations has become more central in discussions about test fairness and accessibility as well as evidence of validity. This study seeks to examine whether there exists differential item functioning for math and language items between special education examinees receiving accommodations and those not receiving accommodations.     

两种DIF检测方法的模拟研究

本研究通过Monte Carlo模拟,探讨MH和LR两种方法在检测DIF时I型错误率和检出率的情况。实验结果表明两种方法的I型错误均控制在0.05左右(α=0.05),LR方法的I型错误率呈现出更加稳定的状态。一致性DIF时,MH方法的检出率略高于LR方法;而非一致性DIF时,LR方法的检出率大大高于MH方法,MH方法对非一致性DIF不敏感。另外,两种方法一致性DIF的检出率随有DIF题目的比例增加而增加,而非一致性DIF的检出率随比例的增加而有所降低。     

An Analytic Comparison of Effect Sizes for Differential Item Functioning

Three types of effects sizes for DIF are described in this exposition: log of the odds-ratio (differences in log-odds), differences in probability-correct, and proportion of variance accounted for. Using these indices involves conceptualizing the degree of DIF in different ways. This integrative review discusses how these measures are impacted in different ways by item difficulty, item discrimination, and item lower asymptote. For example, for a fixed discrimination, the difference in probabilities decreases as the difference between the item difficulty and the mean ability increases. Under the same conditions, the log of the odds-ratio remains constant if the lower asymptote is zero. A non-zero lower asymptote decreases the absolute value of the probability difference symmetrically for easy and hard items, but it decreases the absolute value of the log-odds difference much more for difficult items. Thus, one cannot set a criterion for defining a large effect size in one metric and find a corresponding criterion in another metric that is equivalent across all items or ability distributions. In choosing an effect size, these differences must be understood and considered.     

Detection of Differential Item Functioning in Multiple Groups

Detection of differential item functioning (DIF) is most often done between two groups of examinees under item response theory. It is sometimes important, however, to determine whether DIF is present in more than two groups. In this article we present a method for detection of DIF in multiple groups. The method is closely related to Lard's chi-square for comparing vectors of item parameters estimated in two groups. An example using real data is provided.     

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.     

Assessment of Differential Item Functioning Under Cognitive Diagnosis Models: The DINA Model Example

The assessment of differential item functioning (DIF) is routinely conducted to ensure test fairness and validity. Although many DIF assessment methods have been developed in the context of classical test theory and item response theory, they are not applicable for cognitive diagnosis models (CDMs), as the underlying latent attributes of CDMs are multidimensional and binary. This study proposes a very general DIF assessment method in the CDM framework which is applicable for various CDMs, more than two groups of examinees, and multiple grouping variables that are categorical, continuous, observed, or latent. The parameters can be estimated with Markov chain Monte Carlo algorithms implemented in the freeware WinBUGS. Simulation results demonstrated a good parameter recovery and advantages in DIF assessment for the new method over the Wald method.     

Detecting Differential Item Functioning Using Logistic Regression Procedures

A logistic regression model for characterizing differential item functioning (DIF) between two groups is presented. A distinction is drawn between uniform and nonuniform DIF in terms of the parameters of the model. A statistic for testing the hypothesis of no DIF is developed. Through simulation studies, it is shown that the logistic regression procedure is more powerful than the Mantel-Haenszel procedure for detecting nonuniform DIF and as powerful in detecting uniform DIF.     

Differential Item Functioning on the SAT-M Braille Edition

This study attempted to pinpoint the causes of differential item difficulty for blind students taking the braille edition of the Scholastic Aptitude Test's Mathematical section (SAT-M). The study method involved reviewing the literature to identify factors that might cause differential item functioning for these examinees, forming item categories based on these factors, identifying categories that functioned differentially, and assessing the functioning o f the items comprising deviant categories to determine if the differential effect was pervasive. Results showed an association between selected item categories and differential functioning, particularly for items that included figures in the stimulus, items for which spatial estimation was helpful in eliminating at least two of the options, and items that presented figures that were small or medium in size. The precise meaning of this association was unclear, however, because some items from the suspected categories functioned normally, factors other than the hypothesized ones might have caused the observed aberrant item behavior, and the differential difficulty might reflect real population differences in relevant content knowledge     

RIM: A Random Item Mixture Model to Detect Differential Item Functioning

In this paper we present a new methodology for detecting differential item functioning (DIF). We introduce a DIF model, called the random item mixture (RIM), that is based on a Rasch model with random item difficulties (besides the common random person abilities). In addition, a mixture model is assumed for the item difficulties such that the items may belong to one of two classes: a DIF or a non-DIF class. The crucial difference between the DIF class and the non-DIF class is that the item difficulties in the DIF class may differ according to the observed person groups while they are equal across the person groups for the items from the non-DIF class. Statistical inference for the RIM is carried out in a Bayesian framework. The performance of the RIM is evaluated using a simulation study in which it is compared with traditional procedures, like the likelihood ratio test, the Mantel-Haenszel procedure and the standardized p -DIF procedure. In this comparison, the RIM performs better than the other methods. Finally, the usefulness of the model is also demonstrated on a real life data set.     

Reasons for Gender-Related Differential Item Functioning in a College Admissions Test

Gender fairness in testing can be impeded by the presence of differential item functioning (DIF), which potentially causes test bias. In this study, the presence and causes of gender-related DIF were investigated with real data from 800 items answered by 250,000 test takers. DIF was examined using the Mantel–Haenszel and logistic regression procedures. Little DIF was found in the quantitative items and a moderate amount was found in the verbal items. Vocabulary items favored women if sampled from traditionally female domains but generally not vice versa if sampled from male domains. The sentence completion item format in the English reading comprehension subtest favored men regardless of content. The findings, if supported in a cross-validation study, can potentially lead to changes in how vocabulary items are sampled and in the use of the sentence completion format in English reading comprehension, thereby increasing gender fairness in the examined test.     

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.     

小学英语测试中的题目功能差异分析研究

本研究采用IRT_△b方法对2015年F省小学英语测试试题进行性别DIF检测,以了解该年度小学英语测试的公平性情况。检测结果表明:共有10道题目存在性别DIF,其中6题有利于男生,4题有利于女生。总体上来看,测试工具对男女生是基本公平的。通过对性别DIF题目产生原因的探讨,为以后的命题提供有益的参考。