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DIF Analysis Galina Larina of March, 2012 University of Ostrava

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DIF analysis Definitions Item impact – “significant group difference on an item, e.g., when one group has a higher proportion of examinees answering an item correctly than another group ” – Due to the true group differences in proficiency or due to item bias Differential Item Functioning (DIF) – “It occurs when test-takers having identical levels on the latent trait that the test was designed to measure but belonging to different groups, have different probabilities of endorsing (or answering correctly) a particular item” – Examinees in different groups are matched on the proficiency If an item is found to be poor-fitting in the whole data set or within any group of test-takers, it should be remove from subsequent DIF analysis

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DIF analysis Effectless of fit statistics WinstepsConquest InfitOutfitInfitOutfit Mean1.00 Maximum Minimum Item Infit and outfit mean square errors for simulated 50-item test in which item 25 has DIF

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DIF analysis Types of DIF Uniform DIFNon-uniform DIF Non-uniform mixed DIF

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DIF analysis Statistical methods for evaluating DIF CTT methods – Conditional p-value difference – Delta plot – Standardization Chi-square methods – Mantel-Haenszel – etc. IRT methods

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DIF analysis Mantel-Haenszel method Base group Focal group

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DIF analysis Mantel-Haenszel method Average factor by which the likelihood that a base group member gets the item correct exceeds the corresponding likelihood for comparable focal group members For statistically significant DIF on an item, Prob. < 0.05

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DIF analysis Mantel-Haenszel method MH procedure is an extension of the chi-square test of independence Advantages: – Easy to compute – Modest sample size requirements – Effect size ETS DIF classification rules – ‘Large DIF’ absolute value of MH D-DIF greater than or equal to 1.5, chi-square test sig. at 0.05 level/ Category C – ‘Moderate DIF’ at least 1.0 (and less) than 1.5) and the chi- square test sig. at 0.05 level/ Category B

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DIF analysis Rasch approaches Separate calibration t-test first proposed by Wright and Stone Where d i1 is the difficulty of item I in calibration 1, d i2 is the difficulty of item i in calibration 2 based on groups 2, s 2 i1 is the standard error of estimate for d i1, and s 2 i2 is the standard error of estimate for d i2 Winsteps applies the above formula in DIF analysis

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DIF analysis IRT approaches The between fit approach is based on a single calibration that contains at least two subpopulations of interest. where J is a number of subpopulations, N is a number of person in each populations, x ni is the score for person n responding to item i, and p ni is the probability of person n responding correctly to item i given the overall estimates for the ability of the person and the difficulty of the item

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DIF analysis Winsteps DIF label start in person label column 20 DIF label start in person label with a width 1 Column 20 with width 1

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DIF analysis Winsteps Press OK Press Entry Number

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DIF analysis Winsteps Pairwise comparison This should be at least 0.5 logits for DIF to be noticeable For statistically significant DIF on an item, Prob. < 0.05 For statistically significant DIF on an item, t > |2|

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DIF analysis Winsteps Item 1

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DIF analysis Winsteps Item 1

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DIF analysis Winsteps. Plots Press OK

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DIF analysis Winsteps. Plots. Item 1

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