Parallel Tests & Equating: Theory, Principles, and Practice by: I.G.A. Lokita P. & Rina Sari

Parallel Tests & Equating: Theory, Principles, and Practice

by: I.G.A. Lokita P. & Rina Sari

Equating is the strongest form of linking between the scores on two tests. Equating may be viewed as a form of scale aligning in which very strong requirements are placed on the tests being linked. The goal of equating is to produce a linkage between scores on two test forms such that the scores from each test form can be used as if they had come from the same test. Strong requirements must be put on the blueprints for the two tests and on the method used for linking scores in order to establish an effective equating. Among other things, the two tests must measure the same construct at almost the same level of difficulty and with the same degree of reliability.

What Constitutes an Equating?

The goal of equating is what distinguishes it from other forms of linking. The goal of

score equating is to allow the scores from both tests to be used interchangeably. Experience has shown that the scores and tests that produce the scores must satisfy very strong requirements to achieve this demanding goal of interchangeability. In an ideal world, test forms would be assembled to be strictly parallel so that they would have identical psychometric properties. Equating would then be unnecessary. In reality, it is virtually impossible to construct multiple forms of a test that are strictly parallel, and equating is necessary to fine-tune the test construction process.

Five requirements are widely viewed as necessary for a linking to be an equating (Holland & Dorans, 2006). Those requirements are:

1. The Equal Construct Requirement: The two tests should both be measures of the same construct (latent trait, skill, ability).

2. The Equal Reliability Requirement: The two tests should have the same level of reliability.

3. The Symmetry Requirement: The equating transformation for mapping the scores of Y

to those of X should be the inverse of the equating transformation for mapping the scores of X to those of Y.

4. The Equity Requirement: It should be a matter of indifference to an examinee as to which of two tests the examinee actually takes.

5. The Population Invariance Requirement: The equating function used to link the scores of X and Y should be the same regardless of the choice of (sub) population from which it is derived.

With respect to best practices, Requirements 1 and 2 mean that the tests need to be built

to the same specifications, while Requirement 3 precludes regression methods from being a formof test equating. Lord (1980) argued that Requirement 4 implies both Requirements 1 and 2.

Requirement 4 is, however, hard to evaluate empirically and its use is primarily theoretical

(Hanson, 1991; Lord, 1980). As noted by Holland and Dorans (2006), Requirement 5, which is easy to assess in practice, also can be used to explain why Requirements 1 and 2 are needed. If two tests measure different things or are not equally reliable, then the standard linking methods will not produce results that are invariant across certain subpopulations of examinees. Dorans and Holland (2000) used Requirement 5, rather than Requirement 4, to develop quantitative measures of equatability that indicate the degree to which equating functions depend on the subpopulations used to estimate them. For example, a conversion table relating scores on a mathematics test to scores on a verbal test developed on data for men would be very different from one developed from data on women, since, women tend to do less well than men on 6 mathematics tests.

Reference

Dorans, N.J., Moses, T.P & Eignor, D.R. 2010. Principles and Practices of Test Score

          Equating. Princeton: ETS.