The Accuracy of Estimating the Item Difficulty Parameter of the One-Parameter Logistic Model Using the Pairwise Method in Light of Changes in Sample Size and Test Length

This study aimed to investigate the accuracy of estimating the item difficulty parameter of the one-parameter logistic model using the pairwise method in light of changes in sample size and test length. To achieve the study's objective, data on binary responses were generated for five different sample sizes (50, 100, 250, 500, and 1000 examinees) and four different test lengths (20, 30, 40, and 70 items) using the Simra function from the pairwise package in the R programming language. The ability and difficulty parameters were determined to be normally distributed between -3 and 3, with a mean of 0 and a standard deviation of 1. To answer the study's questions, the researchers utilized the R program to estimate the difficulty parameter using the pairwise method and to estimate the ability using the weighted likelihood estimation method. The results revealed statistically significant differences (α = 0.05) in the standard errors of the estimates of the difficulty parameter due to sample size, particularly for the sample size of 1000 examinees. Additionally, there were statistically significant differences (α = 0.05) in the standard errors of the estimates of the ability parameter due to sample size, test length, and their interaction. The study recommended conducting further research to compare the likelihood method, the Bayesian method, and the pairwise method in terms of the accuracy of estimating item parameters.