Investigating the Performance of Omega Index According to Item Parameters and Ability Levels

Purpose: Several studies can be found in theliterature that investigate the performance of ω undervarious conditions. However no study for the effects of item difficulty, item discrimination, and ability restrictions on the performance of ω could be found. The current study aims to investigate the performance of ω for the conditions given below. Research Methods: b parameter range was restricted in two levels (-2.50 – 0.00, 0.01 – 2.50); a parameterrange, in two levels (0.10 – 0.80 and 0.81 – 1.50). Aftercrossing a and b parameter ranges, four differentitem parameter cells were obtained. 10,000 examinee responses were generated for each itemparameter cell for 20 items. After combining four data sets, an 80-itemdataset was obtained.In order to obtain the effects of source’s and copier’s ability levels to the performance of ω,ability range was divided into four intervals (-3.00 – -1.50, -1.50 – 0.00, 0.00 – 1.50 and 1.50 –3.00). By crossing the ability ranges of source and copier, sixteen different combinations wereobtained. Each of the sixteen ability pairs of source and copier cheating was investigated foritem parameter crossing cells for power study of ω. For Type I error study, no cheating datawere investigated for the same conditions and levels. Findings: Type I error inflations wereobserved for the lower copier ability levels. The results of the power study indicate that whenhigh ability level copier copied answers of the low difficulty level and high discriminativeitems from high ability level source, power of ω was weakened. Implications for Researchand Practice: The study suggests that researchers must pay attention to copiers - source abilitylevel and copied items' difficulty levels while using ω index for detecting answer copying.

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