Fisher information is the amount of information data provide about a parameter. For item information, this is the amount of information the response to an item provides about a person parameter. For test information, this is the amount of information all of the items encountered by a person provide about a person parameter.
All dichotomous items have the same Rasch-derive item information. For a response of probability p, the item information is the binomial variance of the probability, p(1-p). This function is:
For polytomous items, the information function depends on the rating scale structure. The better targeted the item is on the person the more Fisher information the item provides about the person parameter. This motivates some item selection techniques for computer-adaptive testing. An algorithm for the Fisher item information function for polytomous items is given at www.rasch.org/rmt/rmt191a.htm.
The test information function is the sum of the item information functions. The standard error of a measure is the inverse square-root of the test information at the location of the maximum-likelihood parameter estimate (or higher). Here is the test information function for the Knox Cube Test in Example 1.
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Test (sample) reliability is a summary of the interaction between the sample distribution and the test information function.
