Item Response Theory

1Foundations

To measure is to know.

(Source: Lord Kelvin (William Thompson) 1824–1907)

Most observations of behavior are recorded as distinct qualitative events. For example:

a student responds correctly to certain specified questions, responds incorrectly to others, and declines to respond to still others;

on the fifth trial of a learning experiment, the subject recalls six abstract and ten concrete words from a list of thirty;

a reader rates each paragraph of an essay exercise on a scale of rhetorical effectiveness graded from 1 to 7.

a participant in a class discussion group speaks up three times on issue A, once on issue C, but not at all on issues B, D or E;

in response to a social survey, a head of household endorses five out of ten statements concerning a public issue, but disagrees with the others;

an applicant for a secretarial position makes two spelling errors in transcribing 300 words of dictation;

a patient in a primary care clinic reports specific problems with mood, cognition and somatic symptoms of depression during the past two weeks.

These types of data have in common the fact that each respondent is reacting qualitatively to multiple stimuli in a specified set. In the present context, we call all such stimuli items and define item response theory, or “IRT,” as the statistical study of data that arise in this way. That each respondent is responding to more than one item is essential to the definition: if each respondent were presented only one item, an ...