Application of Equipercentile Techniques to Test Scale Construction: Scaling and Equating of the ACT ASSET Placement Test Battery

ACT Research Report Series89-3Application of Equipercentile Techniques to Test Scale Construction: Scaling and Equating of the ACT ASSET Placement Test BatteryRonald T. Cope For additional copies write: ACT Research Report Series P.O. Box 168 Iowa City, Iowa 52243©1989 by The American College Testing Program. All rights reserved. APPLICATION OF EQUIPERCENTILE TECHNIQUES TO TEST SCALE CONSTRUCTION: SCALING AND EQUATING OF THE ACT ASSETPLACEMENT TEST BATTERYRonald T. Cope L ABSTRACTSix tests of the ASSET placement test program were scaled by adapting an equipercentile technique usually restricted to equating different forms of a single test. The purpose of applying this technique was to transform raw scores into scale scores having for all tests approximately the same percent of examinees of a representative weighted sample of ASSET user institutions scoring at or below given scale scores. Scale scores with such normative interpretations were intended to aid test users in changing from the use of the original Forms A to the new Forms B and C of the Basic Skills tests and Forms B of the Advanced Mathematics tests. Obtained percents of examinees at or below given scale scores showed close agreement across the six scaled testsof the ASSET battery. Scalescore meansand standarddeviations were nearlyequal across tests, with means about 40.5and standarddeviations about 6.2.Subsequent equating of basicski 11s FormsC to Forms Ballowed conversion ofraw scores on Forms C to seale scores. \ APPLICATION OF EQUIPERCENTILE TECHNIQUES TO TEST SCALE CONSTRUCTION: SCALING AND EQUATING OF THE ACT ASSETPLACEMENT TEST BATTERYIntroductionRaw Scores Versus Scale Scores and Equating Equating different forms of a test and converting raw scores to scale scores have been increasingly common practices in educational testing.Equating and scaling now enjoy widespread use because they convey advantages over using only raw or number-right scores for reporting test results. If only one form of a test exists, reporting resuLts in terms of raw scores may suffice. But after additional forms have been created, use of only raw scores creates problems of difficult interpretation and misinterpretation.First, consider the advantages of equating. Creating multiple forms of a test with equal difficulty throughout the range of raw scores remains an extremely difficult, if not impossible, task. Without adjustment for these differences of difficulty, a student who happens to receive a hard form of a test is unfairly disadvantaged. Equating is a statistical procedure that adjusts for these inevitable differences. Equating allows scores from different forms of a test to be used interchangeably. One way to report the results of equating Forms A and B of a test would be to construct tables that convert Form B raw scores to Form A raw scores. Then both converted Form B raw scores and Form A raw scores could be treated as Form A raw scores.Placing all scores on the Form A raw score scale would allow direct comparison of groups taking the forms.Converting raw scores to scaLe scores further enhances interpretation. With scaling, raw scores, which have no intrinsic normative meaning, can be transformed into a scale having easy-to-remember reference poincs with convenient normative interpretations. ScaLe scores avoid problems such as 2having to explain to a student who took an easy form y of a test why points were subtracted from his or her raw score to convert them to raw scores of hard form x. Scale scores convey meaning abstracted from the particulars of individual forms' raw scores.Test Equating; Equivalent Groups Design,Equipercentile Method Procedures for equating different forms of a test consist of (1) a design for collecting data, and (2) a method of using the data to produce tables or formulas or charts giving raw-to-raw or raw-to-scale score conversions. (See Petersen, Kolen, and Hoover, 1989, and Angoff, 1984, for general discussions of test equating). The equivalent-groups design uses the test administration procedure known as spiraling: If, for example, two forms A and B are to beequated, they are packaged in the order ABABAB . . . so that the first examinee receives Form A; the second, Form B; the third, Form A; and so on. Within the limits of random sampling error, the groups taking the forms are equivalent. Consequently, statistical differences of scores obtained this way can be attributed to form differences.One widely-used method for using the obtained data to complete the equating process associates raw scores of the same percentile rank. This equipercentile method is illustrated in Figure 1. Because of sampling error, the lines of the graph will be bumpy. To le