# Chapter 3 Information

The term information in a Rasch model context, refers to where the item or test is most useful for distinguishing between respondents. The item information is simply the probability of a correct response to the item times the probability of an incorrect response. The item information can be calculated for each ability ($$D$$-score), in which case the maximum information is provided at the difficulty score of the item. The item information by age shows at which ages the item provides information to measure the $$D$$-score. The formulas to calculate item information are explained in paragraph 6.4 of Booklet I.

One of the assumptions behind the Rasch model is the assumption of local independence. This assumption holds that the probability to pass an item is independent given the ability score. And because of this assumptions, the sum of item information for all items in a test, gives the test information.

In the current chapter we will show how we can use the item information and test information for test construction in order to create an informative and efficient instrument. This is illustrated in several examples in the following paragraphs:

• Item information by ability (3.1)
• Item information by age (3.2)
• Test information by ability (3.3)
• Test information by age (3.4)