Posterior Probabilities With Different Prior Probabilities and Their Effect on the Attribute Mastery Probabilities
One of the features of cognitive diagnosis is that we have to deal with a large number of knowledge states. The number of knowledge states goes up often from a few hundreds to several thousands for a large-scale assessment. This phenomenon is quite natural because when we think about individual differences, our common sense tells us everybody is different. We often come from different cultures, different school systems with a wide variety of curricula, and different families with several levels of educational and socioeconomic backgrounds. Most of all, each student has his or her unique experience and learning style. It is natural to assume that a larger number of knowledge state exists when thousands of students take a test, especially a large-scale assessment.