Alternative Methods for Item Parameter Estimation: From CTT to IRT

It is desirable for an educational assessment to be constructed of items that can differentiate different performance levels of test takers, and thus it is important to estimate accurately the item discrimination parameters in either classical test theory or item response theory. It is particularly challenging to do so when the sample sizes are small. The current study reexamined the relationship between the biserial correlation coefficient and the discrimination parameter to investigate whether the biserial correlation coefficient estimator could be modified and whether biserial-based estimators could be used as alternate estimates of the item discrimination indices. Results show that the modified and alternative approaches work slightly better under certain circumstances (e.g., for small sample sizes or shorter tests), assuming normality of the latent ability distribution. Applications of these alternative estimators are presented in item scaling and weighted differential item functioning analyses. Recommendations and limitations are discussed for practical use of these proposed methods.