### What is item difficulty?

The item difficulty parameter can be used to compare the difficulty of different questions (items) and identify items that may be too easy or too difficult for a specific test taker. A question with a high difficulty parameter means that most people are expected to get the question wrong, while a question with a low difficulty parameter is expected to be answered correctly by most people. Understanding the difficulty of items can help to select questions for each individual test taker that are challenging but not impossible to answer.
In the Item Response Theory (IRT) models used by BRGHT, item difficulty refers to the IQ level required to have a 50% chance of correctly answering the question. The item difficulty can be seen in the Item Characteristic Curve (ICC) of a question. The ICC is a graphical representation of the relationship between item difficulty and the probability of a correct response for different levels of ability.
The second of the two ICC graphs below, belongs to the most difficult question of the two. This can be determined by looking at the position of the curve. The first ICC is located on the left side of the figure, indicating that the question is relatively easy (low item difficulty) because someone with a low IQ already has a high chance of giving the correct answer. The second ICC is shifted to the right, indicating that the item difficulty is high, because a high IQ is needed to have a reasonable chance at giving the correct answer.
Below are examples of ICCâ€™s of an easy question and a difficult question.
In the first ICC, someone with an IQ of 90 has a 50% chance of giving the correct answer, and the average IQ is 100, so the question is answered correctly by more than half of the people.
For the question that belongs to this ICC, someone with an IQ of 118 has a 50% chance of giving the correct answer, and the average IQ is 100, so this question is answered correctly by less than half of the people. Someone with an IQ of 90 only has around 20% chance of getting the right answer to this question. The question that belongs to this ICC is much more difficult than the question that belongs to the other ICC.