Comparison of Item Difficulty Estimates in a Basic Statistics Test using ltm and CTT Software Packages in R

Two free computer software packages “ltm” and “CTT” in the R software environment were tested to demonstrate its usefulness in an item test analysis. The calibration of the item difficulty parameters given the binary responses of two hundred five examinees for the fifteen items multiple choice test were analyzed using the Classical Test Theory (CTT) and Item Response Theory (IRT) methodologies. The software latent trait model “ltm” employed the IRT framework while the software classical test theory functions “CTT” operated under CTT. The IRT Rasch model was used to model the responses of the examinees. The conditional maximum likelihood estimation method was used to estimate the item difficulty parameters for all the items. On the other hand, all the item difficulty indices using the “CTT” software were also calculated. Both the statistical analyses of this study were done in the R software. Results showed that among the fifteen items, the estimates of their item difficulty parameters differed mostly on their values between the two methods. In an IRT framework, items showed extreme difficulty or easy cases as compared to CTT. However, when the estimated values were categorized into intervals and labelled according to its verbal difficulty description, both methodologies showed some similarities in their item difficulties.

@article{Pimentel2020,
  title     = {Comparison of Item Difficulty Estimates in a Basic Statistics Test using ltm and CTT Software Packages in R},
  journal   = {International Journal of Advanced Computer Science and Applications},
  volume    = {11},
  number    = {3},
  year      = {2020},
  publisher = {The Science and Information Organization},
  author    = {Jonald L. Pimentel and Marah Luriely A. Villaruz},
  doi       = {10.14569/IJACSA.2020.0110346},
  url       = {https://doi.org/10.14569/IJACSA.2020.0110346}
}