This code simulates test parameters and test results in some common situations. The simulation is based on Item Response Theory (IRT) model and typical parameters' values. If the exam is used for selection of candidates (i.e., for university admission or jobs), we always have some very capable candidates who failed the test because of the test imperfection as well as those less capable who succeeded because of the same imperfection and their successful guessing. Short multiple-choice tests are quite bad solution for such a selection. Exam administrators want to decrease ratio of these false negative and false positive cases. The scatter plot and confusion matrix show how many of them we have at this simulated test.
R Shiny simulation is available online on Shiny Apps portal at https://srdjan-verbic.shinyapps.io/Exam_simulation/.