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Vertical Scaling

In educational measurement, evaluation of students’ growth in knowledge, skills, or aptitude over time has important implications to educators and policy makers. One common method of measuring growth is through the use of vertical scales. Vertical scaling is a special form of linking, which aims at adjusting score differences on tests that differ in content and/or difficulty. Successful linking enables educators and researchers to make statements such as “a score of 155 on Test X corresponds to a score of 365 on Test Y,” where the content specifications in Tests X and Y need not be exactly the same. Vertical scaling is intended to establish the concordance relationship between scores on tests measuring educational achievement or aptitude at different academic grades. Proper vertical scaling enables educators and researchers to answer questions such as “given a raw score of 20, what are the corresponding scale scores in Grade 3 and 4, respectively?” Furthermore, the vertically scaled scores in different grades are directly comparable with each other. However, different from “equating,” which conducts linking on test forms with very similar content and statistical specifications, there often exist systematic differences in both content and difficulty between test forms in vertical scaling, so vertically scaled scores on different forms cannot be regarded as interchangeable. This entry reviews the applications, advantages, implementations, and limitations of vertical scaling in educational measurement.

Applications and Advantages in Educational Measurement

Some well-known practices of vertical scaling in educational achievement batteries include its applications on the Iowa Tests of Basic Skills, the California Test of Basic Skills, and the California Achievement Tests. As vertical scaling creates a common scale for students’ scores over grades, one can compare students’ achievement from one grade to another so as to evaluate students’ growth pattern over time. In addition to evaluating students’ performance, vertically scaled scores are used as the input in some value added models to evaluate a teacher’s contribution to students’ achievement. Another advantage of vertical scaling is that it also places item statistics from different grades onto the same scale, which may lead to more efficient use of the field-test items. For instance, some field-test items initially constructed for Grade 4 may be found more appropriate for Grade 3, so instead of being discarded from the item pool, those items can be used to construct the test forms for Grade 3.

Implementations

Data Collection Design

To create vertical scales, three data collection designs are often used to adjust test form differences: a common-items design, scaling test design, and equivalent-groups design. Figures 1 and 2 show the basic setups for each of the three designs. Each design has some variations. As shown in Figure 1, a common-items design administers a common block of items between every two adjacent grade levels. Under this design, students’ responses to the common items serve as an anchor to estimate their ability differences and further to put their scores on the entire test onto a same scale. Linking is conducted between every two adjacent grades. For example, fourth graders’ performance is linked to the third graders’ through block b, the fifth graders’ is linked to the fourth graders’ through block c, and so on. The choice of common items plays a critical role in the linking result as well as the growth measurement. With this design, growth is measured grade by grade over the content areas represented by each common item block. For example, the growth from Grades 3 to 4 is measured on the content areas covered by block b but not on the unique content areas covered by block c.

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