## Item-response theory :

Item response theory (IRT) is a mathematical and statistical model that is used to measure individuals’ abilities, attitudes, or other psychological characteristics. IRT is commonly used in educational and psychological assessments, such as standardized tests, to evaluate how well an individual has mastered a particular concept or skill.

One of the key advantages of IRT is that it allows for the development of more precise and accurate measurement scales. Traditional test development methods often involve the use of psychometric techniques, such as classical test theory (CTT), to create and evaluate test items. However, CTT has several limitations, such as its inability to account for individual differences in test-taking ability and its reliance on arbitrary cut-off scores to determine an individual’s proficiency.

IRT overcomes these limitations by modeling the relationship between individuals’ abilities and their responses to test items. This allows for the creation of more precise and accurate measurement scales, as well as the ability to estimate an individual’s ability level based on their responses to a given set of test items.

One of the most commonly used IRT models is the one-parameter logistic model (1PL), which is used to measure an individual’s proficiency on a binary response item (i.e., a question that can only be answered with a “yes” or “no”). The 1PL model assumes that an individual’s probability of answering a binary item correctly is a function of their proficiency level and the difficulty of the item.

For example, consider a multiple-choice test that includes a question with four possible answer choices. The 1PL model would estimate the probability that an individual with a certain proficiency level would choose the correct answer, given the difficulty of the question and the other answer choices.

Another commonly used IRT model is the two-parameter logistic model (2PL), which is used to measure an individual’s proficiency on a multiple-choice item. The 2PL model assumes that an individual’s probability of answering a multiple-choice item correctly is a function of their proficiency level, the difficulty of the item, and the desirability of the answer choices.

For example, consider a multiple-choice test that includes a question with four possible answer choices. The 2PL model would estimate the probability that an individual with a certain proficiency level would choose the correct answer, given the difficulty of the question and the desirability of the other answer choices. The 2PL model allows for the creation of more precise and accurate measurement scales, as it takes into account the impact of the answer choices on an individual’s response.

Overall, IRT is a powerful and flexible approach to test development and evaluation that allows for the creation of more precise and accurate measurement scales. It is commonly used in educational and psychological assessments, such as standardized tests, to evaluate individuals’ abilities, attitudes, or other psychological characteristics. IRT is particularly useful in situations where traditional test development methods, such as classical test theory, may not be as effective.