Equating

Test equating traditionally refers to the statistical process of determining comparable scores on different forms of an exam. It can be accomplished using either classical test theory or item response theory.

In item response theory, equating is the process of placing scores from two or more parallel test forms onto a common score scale. The result is that scores from two different test forms can be compared directly, or treated as though they came from the same test form. When the tests are not parallel, the general process is called linking. It is the process of equating the units and origins of two scales on which the abilities of students have been estimated from results on different tests. The process is analogous to equating degrees Fahrenheit with degrees Celsius by converting measurements from one scale to the other. The determination of comparable scores is a by-product of equating that results from equating the scales obtained from test results.

Suppose that Dick and Jane both take a test to become licensed in a certain profession. Because the high stakes (you get to practice the profession if you pass the test) may create a temptation to cheat, the organization that oversees the test creates two forms. If we know that Dick scored 60% on form A and Jane score 70% on form B, do we know for sure which one has a better grasp of the material? What if form A is composed of very difficult items, while form B is relatively easy? Equating analyses are performed to address this very issue, so that scores are as fair as possible.

In item response theory, person locations are estimated on a scale; i.e. locations are estimated in relation to a unit and origin. It is common in educational assessment to employ tests in order to assess different groups of students with the intention of establishing a common scale by equating the origins, and sometimes units, of the scales obtained from response data from the different tests. The process is referred to as equating or test equating.

In item response theory, two different kinds of equating are horizontal and vertical equating. Vertical equating refers to the process of equating tests administered to groups of students with different abilities, such as students in different grades (years of schooling). Horizontal equating refers the equating of tests administered to groups with similar abilities; for example, two tests administered to students in the same grade in two consecutive calendar years. Different tests are used to avoid practice effects.

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