Test Equating, Scaling, and Linking by Michael J. Kolen & Robert L. Brennan

Author:Michael J. Kolen & Robert L. Brennan
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

Process

Administration

Forms

Construct score scale

1

A

Equate using spiraling

2

B

C

Equate using spiraling

3

D

E

Equate using spiraling

4

E

F

G

Equate using spiraling

5

G

H

I

The process of double linking has much to recommend it. It provides a built-in stability check on the equating process. Two conversions that differ more than would be expected by chance might suggest problems with statistical assumptions, quality control (e.g., scores incorrectly computed), administration (e.g., spiraling was not properly performed), or security (e.g., a security breach led to many examinees’ having access to one of the old forms). If such problems are suspected, then one of the links could be eliminated without destroying the ability to equate in the testing program. (Note, however, that if a security breach led to many examinees having had access to one of the old forms, then the scores of the examinees who took that old form might not be valid.) In addition, the use of double linking can provide for greater equating stability than the use of a single link, especially when the two old forms are chosen from different administrations, as was done in Administrations 4 and 5 in Table 8.4.

The average of two links also can be shown to contain less random equating error than the use of a single link. Consider the following situation. In one equating, Form C is equated directly to Form A; and in a second equating, Form C is equated first to Form B and then to Form A. For simplicity, assume that the error variance in equating is the same for any single equating. The equating of Form C to Form A contains the same amount of equating error variance as the equating of Form B to Form A. Refer to the error variance at a particular score point on Form C as var. Also assume that all equatings are independent.

In this case, the equating error in equating Form C to Form A equals var. Equating error variance in equating Form C to Form A through Form B equals 2var. The average of the equivalents of the two equatings equals the sum of the equivalents divided by 2. In this case, equating error variance for the average can be shown to equal

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