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

Purpose: Several studies can be found in the literature that investigate the performance of ω under various 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 parameter range, in two levels (0.10 – 0.80 and 0.81 – 1.50). After crossing a and b parameter ranges, four different item parameter cells were obtained. 10,000 examinee responses were generated for each item parameter 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 were obtained. Each of the sixteen ability pairs of source and copier cheating was investigated for item parameter crossing cells for power study of ω. For Type I error study, no cheating data were investigated for the same conditions and levels. Findings: Type I error inflations were observed for the lower copier ability levels. The results of the power study indicate that when high ability level copier copied answers of the low difficulty level and high discriminative items from high ability level source, power of ω was weakened. Implications for Research and Practice: The study suggests that researchers must pay attention to copiers - source ability level and copied items' difficulty levels while using ω index for detecting answer copying