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

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In this study Type I Error and the power rates of ω and GBT (generalized binomial test) indices were investigated for several nominal alpha levels and for 40 and 80-item test lengths with 10,000-examinee sample size under several test level restrictions. As a result, Type I error rates of both indices were found to be below the acceptable nominal alpha levels.  The power study showed that average test difficulty was very effective for power (true detection) rates of indices. Clear patterns were observed for the increase of test difficulty in favor of both ω and GBT power rate. Contrary to expectations; average test discrimination was not as effective as average test difficulty. The results of the interaction effects of item discrimination and difficulty showed that for the cases whose b parameters were lower than 0 with weak discrimination, indices had weak power for both ω and GBT. In addition, for the cases whose b parameter levels were below zero with high discrimination indices, the power performance of both answer-copying indices were very weak. Results for test length showed that with the increase of test length the power rate of both ω and GBT tended to increase. Also, ω performed slightly better than GBT or very close to GBT for 80-item test length however, ω performed better than GBT in terms of power rate for the cases with 40-item test length

In this study Type I Error and the power rates of omega (ω) and GBT (generalized binomial test) indices were investigated for several nominal alpha levels and for 40 and 80-item test lengths with 10,000-examinee sample size under several test level restrictions. As a result, Type I error rates of both indices were found to be below the acceptable nominal alpha levels. The power study showed that average test difficulty was very effective for power (true detection) rates of indices. Clear patterns were observed for the increase of test difficulty in favor of both ω and GBT power rate. Contrary to expectations; average test discrimination was not as effective as average test difficulty. The results of the interaction effects of item discrimination and difficulty showed that for the cases whose b parameters were lower than 0 with weak discrimination, indices had weak power for both ω and GBT. In addition, for the cases whose b parameter levels were below zero with high discrimination indices, the power performance of both answer-copying indices were very weak. Results for test length showed that with the increase of test length the power rate of both ω and GBT tended to increase. Also, ω performed slightly better than GBT or very close to GBT for 80-item test length however, ω performed better than GBT in terms of power rate for the cases with 40-item test length.