Item Characteristic Curve

Item Characteristic Curve is a concept used in designing questions mostly for psychometric or educational testing. It enables testing non observable abilities such as arithmetic ability, reading ability or comprehension or personality of a person. These are also referred to as latent traits and are quite difficult to measure. However, by defining a range of abilities of a human being, we can plot a graph for the probability of a person with a given ability score to answer the item (or question) correctly. Intuitively, a person of lower ability will exhibit lower probability of cracking a particular question and a person with higher ability will be closer to probability = 1 for answering the question correctly. Thus for each of the options in a question in such a questionnaire, we can plot a item characteristic curve. This is why this theory is also referred to as the Probabilistic Test Theory. This is a method for demonstrating reliability and validity of measurement.

Reference - Basics of Item Response Theory by Frank B Baker; A visual guide to item Response Theory by Ivailo Partchev; Item Response Theory by Nick Shryane