Item-Fit Analysis in Educational Assessment: Effects of Test Length, Sample Size, and Missing Data under the Partial Credit Model

This study is situated within Educational Studies, particularly the field of educational measurement and assessment. It investigates the accuracy of traditional and modified item-fit indices used to evaluate the quality of test items in educational and psychological assessments based on polytomous item response theory models. Specifically, the study compares the performance of the traditional S-χ² index and the modified Mimpute-χ² index under varying conditions of test length, sample size, and missing data. A simulation design was employed using three levels of test length: 20, 40, and 60 items; three levels of sample size: 250, 500, and 1,000 examinees; and three levels of missing data: 1%, 10%, and 20%. Two sets of simulated polytomous response data were generated using WinGen software. The first dataset was generated according to the Partial Credit Model to evaluate the Type I error rates of the two indices, whereas the second dataset was generated according to the Graded Response Model to estimate statistical power in detecting item misfit. The results showed statistically significant differences between the two indices across most experimental conditions. The modified Mimpute-χ² index outperformed the traditional S-χ² index by producing lower Type I error rates while maintaining higher statistical power. The findings also indicated that test length, sample size, and missing data percentage influenced the performance of both indices. While the traditional S-χ² index performed adequately when the missing data rate was low, particularly at 1%, its accuracy declined as the proportion of missing data increased. In contrast, the modified Mimpute-χ² index demonstrated more stable and consistent performance across missing data conditions. These findings contribute to Educational Studies by supporting more accurate test-item evaluation and strengthening the validity and reliability of educational assessment practices. The study recommends using modified item-fit procedures when analyzing polytomous test data with incomplete responses in educational testing contexts.