Abstract: Equating is a necessary procedure to the item bank construction and also to the longitudinal test results reporting. Equating based on item response theory (IRT) has gained much attention in recent decades according to its advantages over classical test theory (CTT) based strategy. Many nationwide tests had implemented IRT equating. But there are still many problems in the applications of IRT-based equating. First of all, researchers and practitioners must be aware of the factors that will affect the equating results. Many and many factors will cause errors of various equating methods. The available studies are mainly concerned about the standard errors of equating methods, but rarely about the bias that will occur when we use differently distributed ability sampling to equating parameters under IRT-based item characteristic curve (ICC) equating methods and under anchor-item data collection design. Bias from sampling will lead to misunderstood results. In this paper, sampling error to the IRT-based ICC equating will be addressed.
Under two-parameter logistic item response model, three pair-wise sets of item parameter data were simulated to be equated. Each data set includes 100 items. The distributions of item difficulty parameter are set to be normal distributed. The slope of the equating function were set to be 0.85, 1.00, 1.27 respectively, the intercept were 0.75, 0.60,-0.36 accordingly. Then 930 sets of ability parameter data were simulated to be differently distributed. That is, they had different skewness and kurtosis coefficients. With these simulated item and ability parameters, equating were conducted under item characteristic curve method for each data set.
The results show that equating coefficients are much different with differently distributed ability parameters. The slope coefficients of equating are much stable, while the intercept coefficients are much variable. Also, the relations between intercept coefficients with the ability distribution parameters are systematically proved.
With the results, it indicates that, firstly, the distribution of ability parameter will significantly affects the equating results under item characteristic curve method. Secondly and specifically, the differently distributed ability parameters will significantly and systematically affects the intercept coefficient of equating, but has much less effects on slope coefficient

Key words: item characteristic curve equating, sampling error, ability distribution