Abstract:

This is a post-hoc simulation study which investigates the effect of different item difficulty distributions, sample sizes, and test lengths on measurement precision while estimating the examinee parameters in right and left-skewed distributions. First of all, the examinee parameters were obtained from 20-item real test results for the right-skewed and left-skewed sample groups of 500, 1000, 2500, 5000, and 10000. In the second phase of the study, four different tests were formed according to the b parameter values: normal, uniform, left skewed and right skewed distributions. A total of 80 conditions were formed within the scope of this research by selecting 20-item and 30-item condition as the test length variable. In determining the measurement precision, the RMSE and AAD values were calculated. The results were evaluated in terms of the item difficulty distributions, sample sizes, and test lengths. As a result, in right-skewed examinee distribution, the highest measurement precision was obtained at the normal b distribution and the lowest measurement precision was obtained at the right skewed b distribution. A higher measurement precision was obtained in the 30-item test, however, it was observed that the change in the sample size didn’t affect the measurement precision significantly in right-skewed examinee distribution. In the left skewed distribution, the highest measurement precision was obtained at the normal b distribution and the lowest measurement precision was obtained at the left-skewed b distribution. Also it was observed that the change in the sample size and test length didn’t affect the measurement precision significantly in the left-skewed distribution.

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